2016 – 2017
Third Grade
MATHEMATICS
Curriculum Map
Volusia County Schools
Mathematics Florida Standards
Table of Contents
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
X.
1
Critical Areas for Mathematics in Grade 3…………….……………….…..2
Mathematics Florida Standards: Grade 3 Overview.…………………..…3
Standards for Mathematical Practice ………………………………..……..4
Common Addition and Subtraction Situations.……………………..…….5
Common Multiplication and Division Situations………………………….6
Common Strategies ……………………………………………………………7
5E Learning Cycle: An Instructional Model……………………………....11
Instructional Math Block………………………………………………….…..12
Units
A. Unit 1……………..……………………………………………………….….13
B. Unit 2……………..…………………………………………………………..18
C. Unit 3……………………………………………………………………….. .33
D. Unit 4………………………………………………………………………....48
Appendices
Appendix A: Formative Assessment Strategies ………………...……..57
Appendix B: Intervention/Remediation Guide……………………..……67
Glossary of Terms for the Mathematics Curriculum Map…………......68
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Critical Areas for Mathematics in Grade 3
In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and
division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1);
(3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing
two-dimensional shapes.
(1) Students develop understanding of the meanings of multiplication and division of whole numbers through activities and problems
involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an
unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or
the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly
sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By
comparing a variety of solution strategies, students learn the relationship between multiplication and division.
(2) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of
unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the
size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3
of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3
equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent
numbers equal to and less than. They solve problems that involve comparing fractions by using visual fraction models and strategies
based on noticing equal numerators or denominators.
(3) Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number
of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard
unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical
columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using
multiplication to determine the area of a rectangle.
(4) Students describe, analyze, and compare properties of two-dimensional shapes (i.e., quadrilaterals). They compare and classify
shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry
by expressing the area of part of a shape as a unit fraction of the whole.
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Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Grade 3 Overview
Domain: Operations and Algebraic Thinking
Cluster 1: Represent and solve problems involving multiplication and division.
Cluster 2: Understand properties of multiplication and the relationship between multiplication and division.
Cluster 3: Multiply and divide within 100.
Cluster 4: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Domain: Number and Operations in Base Ten
Cluster 1: Use place value understanding and properties of operations to perform multi-digit arithmetic.
Domain: Geometry
Cluster 1: Reason with shapes and their attributes.
Domain: Number and Operations—Fractions
Cluster 1: Develop understanding of fractions as numbers.
Domain: Measurement and Data
Cluster 1: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
Cluster 2: Represent and interpret data.
Cluster 3: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Cluster 4: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between
linear and area measures.
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Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Standards for Mathematical Practice
Students will:
1. Make sense of problems and persevere in solving them. (SMP.1)
Mathematically proficient students in Grade 3 know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a
problem and look for ways to solve it. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does
this make sense?” They listen to the strategies of others and will try different approaches. Students in Grade 3 will often use another method to check their answers.
2. Reason abstractly and quantitatively. (SMP.2)
Mathematically proficient students in Grade 3 recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem
at hand, considering both the appropriate units involved and the meaning of quantities. This involves two processes- decontexualizing and contextualizing. In Grade 3, students represent situations
by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 8 bags of cookies with the same amount of cookies in each bag. If there are 48 cookies how many cookies
are in each bag?” Grade 3 students are expected to translate that situation into the equation: 8 × __ = 48 or 48 / 8 = __ and then solve the task. Students also contextualize situations during the
problem solving process. For example, while solving the task above, students can refer to the context of the task to determine that they were given the number of bags, and the total number of
cookies, but they need to find the number of cookies in each bag.
3. Construct viable arguments and critique the reasoning of others. (SMP.3)
Mathematically proficient students in Grade 3 may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they
participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. For example,
when comparing the fractions 1/3 and 1/5, students may generate their own representation of both fractions and then critique each others’ reasoning in class, as they connect their arguments to the
representations that they created.
4. Model with mathematics. (SMP.4)
Mathematically proficient students in Grade 3 experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects,
acting out, making a chart, list, or graph, creating equations, etc. Students should have ample opportunities to connect the different representations and explain the connections. Grade 3 students
should evaluate their results in the context of the situation and reflect on whether the results make sense.
5. Use appropriate tools strategically. (SMP.5)
Mathematically proficient students in Grade 3 consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance,
they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the
possible rectangles.
6. Attend to precision. (SMP.6)
Mathematically proficient students in Grade 3 develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning.
They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square
units.
7. Look for and make use of structure. (SMP.7)
Mathematically proficient students in Grade 3 look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and
distributive properties).
8. Look for and express regularity in repeated reasoning. (SMP.8)
Mathematically proficient students in Grade 3 notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for
using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x
8 to arrive at 40 + 16 which equals 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?”
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Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Common Addition and Subtraction Situations
Result Unknown
Add to
Take from
Put
Together/
Take Apart2
Compare 3
Change Unknown
Start Unknown
Two bunnies sat on the grass. Three more
bunnies hopped there. How many bunnies
are on the grass now?
Two bunnies were sitting on the grass. Some
more bunnies hopped there. Then there
were five bunnies. How many bunnies
hopped over to the first two?
Some bunnies were sitting on the grass.
Three more bunnies hopped there. Then
there were five bunnies. How many bunnies
were on the grass before?
2+3=?
Five apples were on the table. I ate two
apples. How many apples are on the table
now?
2+?=5
Five apples were on the table. I ate some
apples. Then there were three apples. How
many apples did I eat?
?+3=5
Some apples were on the table. I ate two
apples. Then there were three apples. How
many apples were on the table before?
5–2=?
5-?=3
?–2=3
Total Unknown
Addend Unknown
Both Addends Unknown1
Five apples are on the table. Three are red
and the rest are green. How many apples are
green?
Grandma has five flowers. How many can
she put in her red vase and how many in her
blue vase?
3 + ? = 5, 5 – 3 = ?
5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 + 4 + 1
5 = 2 + 3, 5 = 3 + 2
Three red apples and two green apples are
on the table. How many apples are on the
table?
3+2=?
Difference Unknown
Bigger Unknown
Smaller Unknown
(“How many more?” version):
(Version with “more”):
(Version with “more”):
Lucy has two apples. Julie has five apples.
How many more apples does Julie have than
Lucy?
Julie has 3 more apples than Lucy. Lucy has
two apples. How many apples does Julie
have?
Julie has three more apples than Lucy. Julie
has five apples. How many apples does Lucy
have?
(“How many fewer?” version):
(Version with “fewer”):
(Version with “fewer”):
Lucy has two apples. Julie has five apples.
How may fewer apples does Lucy have than
Julie?
Lucy has three fewer apples than Julie. Lucy
has two apples. How many apples does Julie
have?
Lucy has three fewer apples than Julie. Julie
has five apples. How many apples does Lucy
have?
2 + ? = 5, 5 – 2 = ?
2 + 3 = ?, 3 + 2 = ?
5 – 3 = ?, ? + 3 = 5
1
These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand that the
= sign does not always mean makes or results in, but always does mean is the same number as.
2
Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers less than
or equal to 10.
3
For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The other
versions are more difficult.
5
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Common Multiplication and Division Situations4
Unknown Product
Equal Groups
Arrays5, Area6
Compare
General
Group Size Unknown
(“How many in each group?” Division)
Number of Groups Unknown
(“How many groups?” Division)
3×6=?
There are 3 bags with 6 plums in
each bag. How many plums are
there in all?
3 × ? = 18 and 18 ÷ 3 = ?
If 18 plums are shared equally into 3
bags, then how many plums will be in
each bag?
? × 6 = 18 and 18 ÷ 6 = ?
If 18 plums are to be packed 6 to a
bag, then how many bags are
needed?
Measurement example. You
need 3 lengths of string, each 6
inches long. How much string will
you need altogether?
Measurement example. You have 18
inches of string, which you will cut into
3 equal pieces. How long will each
piece of string be?
There are 3 rows of apples with 6
apples in each row. How many
apples are there?
If 18 apples are arranged into 3 equal
rows, how many apples will be in each
row?
Measurement example. You have
18 inches of string, which you will
cut into pieces that are 6 inches
long. How many pieces of string
will you have?
If 18 apples are arranged into
equal rows of 6 apples, how many
rows will there be?
Area example. What is the area
of a 3 cm by 6 cm rectangle?
Area example. A rectangle has area
18 square centimeters. If one side is 3
cm long, how long is a side next to it?
A blue hat costs $6. A red hat
cost 3 times as much as the blue
hat. How much does the red hat
cost?
A red hat costs $18 and that is 3 times
as much as a blue hat costs. How
much does the blue hat cost?
Measurement example. A rubber
band is 6 cm long. How long will
the rubber band be when it is
stretched to be 3 times as long?
Measurement example. A rubber band
is stretched to be 18 cm long and that
is 3 times as longs as it was at first.
How long was the rubber band at first?
a×b=?
a × ? = p and p ÷ a = ?
Area example. A rectangle has
area 18 square centimeters. If one
side is 6 cm long, how long is a
side next to it?
A red hat costs $18 and a blue hat
costs $6. How many times as
much does the red hat cost as the
blue hat?
Measurement example. A rubber
band was 6 cm long at first. Now it
is stretched to be 18 cm long.
How many times as long is the
rubber band now as it was at first?
? × b = p and p ÷ b = ?
4The
first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples.
language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3
rows and 6 columns. How m any apples are in there? Both forms are valuable.
6Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement
situations.
5The
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Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Addition Strategies
Name
Clarification
Counting All
 student counts every number
 students are not yet able to add on from either addend, they must mentally build every
number
Counting On
 transitional strategy
 student starts with 1 number and counts on from this point
Student Work Sample
8+9
1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17
8+9
8…9,10,11,12,13,14,15,16,17
 student recalls sums for many doubles
8+9
 student uses fluency with ten to add quickly
8 + (8 + 1)
(8 + 8) + 1
16 + 1= 17
8+9
Doubles/Near Doubles
(7 +1) + 9
7 + (1 + 9)
7 + 10 = 17
23 + 48
Making Tens
Making Friendly Numbers/
Landmark Numbers
Compensation
Breaking Each Number into its
Place Value
Adding Up in Chunks
 friendly numbers are numbers that are easy to use in mental computation
 student adjusts one or all addends by adding or subtracting to make friendly numbers
 student then adjusts the answer to compensate
23 + (48 + 2)
23 + 50= 73
73 – 2 = 71
8+6
 student manipulates the numbers to make them easier to add
 student removes a specific amount from one addend and gives that exact amount to the
other addend
8-1=7 6+1=7
7+7=14
24 + 38
 strategy used as soon as students understand place value
 student breaks each addend into its place value (expanded notation) and like place value
amounts are combined
 student works left to right to maintain the magnitude of the numbers
(20 + 4) + (30 + 8)
20 + 30 = 50
4 + 8 = 12
 follows place value strategy
 student keeps one addend whole and adds the second addend in easy-to-use chunks
 more efficient than place value strategy because student is only breaking apart one addend
50 + 12 = 62
45 + 28
45 + (20 + 8)
45 + 20 = 65
65 + 8 = 73
Children do not have to be taught a particular strategy. Strategies for computation come naturally to young children. With opportunity and encouragement, children invent
strategies for themselves.
7
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Subtraction Strategies
Name
Adding Up
Counting Back/Removal
Clarification
 student adds up from the number being subtracted (subtrahend) to the whole
(minuend)
 the larger the jumps, the more efficient the strategy
 student uses knowledge of basic facts, doubles, making ten, and counting on
 strategy used by students who primarily view subtraction as taking away
 student starts with the whole and removes the subtrahend in parts
 student needs the ability to decompose numbers in easy-to-remove parts
 student breaks each number into its place value (expanded notation)
 student groups like place values and subtracts
Place Value
Keeping a Constant
Difference
Adjusting to Create an
Easier Number
 student understands that adding or subtracting the same amount from both
numbers maintains the distance between the numbers
 student manipulates the numbers to create friendlier numbers
 strategy requires students to adjust only one of the numbers in a subtraction
problem
 student chooses a number to adjust, subtracts, then adjusts the final answer to
compensate
 students must understand part/whole relationships to reason through this strategy
Student Work Sample
14 – 7
7… 8,9,10,11,12,13,14 (+1 each jump)
7 + 3= 10
10 + 4= 14
3 + 4= 7
65 – 32
65 – (10 + 10 + 10 + 2)
65, 55, 45, 35, 33
65 – (30 + 2)
65 – 30 = 35
35 – 2 = 33
999 – 345
(900 + 90 + 9) – (300 + 40 + 5)
900 – 300 = 600
90 – 40 = 50
9–5=4
600 + 50 + 4 = 654
123 – 59
123 + 1 = 124
59 + 1 = 60
124 – 60 = 64
123 – 59
59 + 1 = 60
123 – 60 = 63
I added 1 to make an easier number.
63 + 1 = 64
I have to add 1 to my final answer
because I took away 1 too many.
Children do not have to be taught a particular strategy. Strategies for computation come naturally to young children. With opportunity and encouragement, children invent strategies for themselves.
8
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Multiplication Strategies
Name
Clarification
 beginning strategy for students who are just learning multiplication
 connection to an array model provides an essential visual model
 students who are comfortable multiplying by multiples of 10
Friendly Numbers/
Landmark Numbers
Breaking Factors into Smaller
Factors
Doubling & Halving
15+15+15+15+15+15 = 90
2 × 15 = 30
2 × 15 = 30
2 × 15 = 30
30 + 30 + 30 = 90
Repeated Addition/Skip
Counting
Partial Products
Student Work Sample
6 × 15
 strategy based on the distributive property and is the precursor for our
standard U.S. algorithm
 student must understand that the factors in a multiplication problem can
be broken into addends
 student can then use friendlier numbers to solve more difficult problems
 strategy relies on students’ understanding of breaking factors into
smaller factors
 associative property
 used by students who have an understanding of the concept of arrays
with different dimensions but the same area
 student can double and halve numbers with ease
 student doubles one factor and halves the other factor
9 × 15
Add 1 group of 15
10 × 15 = 150
We must now take off 1 group of 15.
150 – 15 = 135
12 × 15
12 × (10 + 5)
12 × 10 = 120
12 × 5 = 60
120 + 60 =180
12 × 25
(3 × 4) × 25
3 × (4 × 25)
(4 × 25) + (4 × 25) + (4 × 25) = 300
8 × 25
8÷2 = 4
25 × 2 = 50
4 × 50 = 200
Children do not have to be taught a particular strategy. Building a conceptual understanding before procedural knowledge helps students navigate and explore different
approaches to computation. Children’s invented algorithms for multiplication and division generally build on their procedures for adding and subtracting multi-digit numbers.
9
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Division Strategies
Name
Repeated Subtraction/Sharing
Multiplying Up
Clarification
 early strategy students use when they are developing multiplicative
reasoning
 repeated subtraction is one of the least efficient division strategies
 presents opportunities to make connections to multiplication
 strategy is a natural progression from repeated subtraction
 student uses strength in multiplication to multiply up to reach the dividend
 students relying on smaller factors and multiples will benefit from discussions
related to choosing more efficient factors
 maintains place value
 allows students to work their way toward the quotient by using friendly
numbers such as ten, five, and two
 as the student chooses larger numbers, the strategy becomes more efficient
Partial Quotients
Proportional Reasoning
 students who have a strong understanding of factors, multiples, and
fractional reasoning
 students’ experiences with doubling and halving to solve multiplication
problems can launch an investigation leading to the idea that you can divide
the dividend and the divisor by the same number to create a friendlier
problem
Student Work Sample
30 ÷ 5
30 – 5 = 25
25 – 5 = 20
20 = 5 = 15
15 – 5 = 10
10 – 5 = 5
5–5=0
I took out 6 groups of 5
30 ÷ 5 = 6
384 ÷ 16
10 × 16 = 160
10 × 16 = 160
2 × 16 = 32
2 × 16 = 32
384 – 160 = 224
224 – 160 = 64
64 – 32 = 32
32 – 32 = 0
10 + 10 + 2 + 2 = 24
384 ÷ 16
16 384
-160
224
-160
64
-32
32
-32
0
384 ÷ 16
×10
×10
24
×2
×2
384 ÷ 16
÷2 ÷2
192 ÷ 8
÷2 ÷2
96 ÷ 4
÷2 ÷2
48 ÷ 2 = 24
384 ÷ 16 = 24
Children do not have to be taught a particular strategy. Building a conceptual understanding before procedural knowledge helps students navigate and explore different approaches to computation. Children’s
invented algorithms for multiplication and division generally build on their procedures for adding and subtracting multi-digit numbers.
10
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
5E Learning Cycle: An Instructional Model
ENGAGEMENT
EXPLORATION
EXPLANATION
ELABORATION
EVALUATION
The engagement phase of the model
is intended to capture students’
interest and focus their thinking
on the concept, process, or skill
that is to be learned.
The exploration phase of the model is
intended to provide students with a
common set of experiences from
which to make sense of the concept,
process or skill that is to be learned.
The explanation phase of the model is
intended to grow students’
understanding of the concept,
process, or skill and its associated
academic language.
The elaboration phase of the model is
intended to construct a deeper
understanding of the concept,
process, or skill through the
exploration of related ideas.
The evaluation phase of the model is
intended to be used during all phases
of the learning cycle driving the
decision-making process and
informing next steps.
During this engagement phase,
the teacher is on center stage.
During the exploration phase,
the students come to center stage.
During the elaboration phase,
the teacher and students
share center stage.
What does the teacher do?
provide new information that
extends what has been learned
provide related ideas to explore
pose opportunities (examples and
non-examples) to apply the
concept in unique situations
remind students of alternate ways
to solve problems
encourage students to persevere
in solving problems
During the evaluation phase,
the teacher and students
share center stage.
What does the teacher do?
observe students during all
phases of the learning cycle
assess students’ knowledge and
skills
look for evidence that students
are challenging their own thinking
present opportunities for students
to assess their learning
ask open-ended questions:
o What do you think?
o What evidence do you have?
o How would you explain it?
What does the student do?
participate actively in all phases
of the learning cycle
demonstrate an understanding of
the concept
solve problems
evaluate own progress
answer open-ended questions
with precision
ask questions
Evaluation of Exploration
The role of evaluation during the
exploration phase is to gather an
understanding of how students are
progressing towards making sense of
a problem and finding a solution.
During the explanation phase,
the teacher and students
share center stage.
What does the teacher do?
 ask for justification/clarification of
newly acquired understanding
 use a variety of instructional
strategies
 use common student experiences
to:
o develop academic language
o explain the concept
 use a variety of instructional
strategies to grow understanding
 use a variety of assessment
strategies to gage understanding
What does the student do?
 record procedures taken towards
the solution to the problem
 explain the solution to a problem
 communicate understanding of a
concept orally and in writing
 critique the solution of others
 comprehend academic language
and explanations of the concept
provided by the teacher
 assess own understanding
through the practice of selfreflection
Evaluation of Explanation
The role of evaluation during the
explanation phase is to determine the
students’ degree of fluency (accuracy
and efficiency) when solving
problems.
Strategies and procedures used by
students during this phase are
highlighted during explicit instruction in
the next phase.
Conceptual understanding, skill
refinement, and vocabulary acquisition
during this phase are enhanced
through new explorations.
Application of new knowledge in
unique problem solving situations
during this phase constructs a deeper
and broader understanding.
The concept, process, or skill is
formally explained in the next phase
of the learning cycle.
The concept, process, or skill is
elaborated in the next phase
of the learning cycle.
The concept, process, or skill has
been and will be evaluated as part of
all phases of the learning cycle.
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What does the teacher do?
create interest/curiosity
raise questions
elicit responses that uncover
student thinking/prior knowledge
(preview/process)
remind students of previously
taught concepts that will play a
role in new learning
familiarize students with the unit
What does the student do?
show interest in the topic
reflect and respond to questions
ask self-reflection questions:
o What do I already know?
o What do I want to know?
o How will I know I have learned
the concept, process, or skill?
make connections to past learning
experiences
Evaluation of Engagement
The role of evaluation during the
engagement phase is to gain access
to students’ thinking during the
pre-assessment event/activity.
Conceptions and misconceptions
currently held by students are
uncovered during this phase.
These outcomes determine the
concept, process, or skill to be
explored in the next phase
of the learning cycle.
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What does the teacher do?
provide necessary materials/tools
pose a hands-on/minds-on
problem for students to explore
provide time for students to
“puzzle” through the problem
encourage students to work
together
observe students while working
ask probing questions to redirect
student thinking as needed
What does the student do?
manipulate materials/tools to
explore a problem
work with peers to make sense of
the problem
articulate understanding of the
problem to peers
discuss procedures for finding a
solution to the problem
listen to the viewpoint of others
Volusia County Schools
Mathematics Department
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
What does the student do?
generate interest in new learning
explore related concepts
apply thinking from previous
learning and experiences
interact with peers to broaden
one’s thinking
explain using information and
experiences accumulated so far











Evaluation of Elaboration
The role of evaluation during the
elaboration phase is to determine the
degree of learning that occurs
following a differentiated approach to
meeting the needs of all learners.
Grade 3 Math Curriculum Map
May 2016
Elementary Instructional Math Block
Time
Components
Description
5
minutes
Opening:
Hook/Warm-up
(engage/explore)
Teachers will engage students to create interest for the whole group mini
lesson or to review previous learning targets by posing a hands-on mindson problem for students to explore.
15
minutes
Whole Group:
Mini Lesson & Guided
Practice
(explore/explain/evaluate)
During this time, the learning target will be introduced through explicit
instruction by the teacher or through exploration/discovery by the
students. Teachers model their thinking and teach or reinforce vocabulary
in context. Teacher leads students to participate in guided practice of the
new learning target.
Students will explore using manipulatives and having conversations about
their new learning. Students and teachers explain and justify what they
are doing. Teachers are using probing questions to redirect student
thinking during guided practice. Teachers provide explicit instruction to
scaffold the learning if the majority of the students are struggling.
Formative techniques are used to evaluate which students will need
interventions and which students will need enrichment.
35-45
minutes
Small Group:
Guided Practice &
Collaborative/
Independent Practice
(explain/evaluate/
explore/ elaborate)
The teacher will work with identified, homogeneous groups to provide
intervention or enrichment. The students will explain their thinking
through the use of a variety of instructional strategies. The teacher will
evaluate student understanding and address misconceptions that still
exist.
Students will work in groups using cooperative structures or engaging in
mathematical tasks. These activities are related to the mini lesson,
previously taught learning targets, or upcoming standards. Students will
continue to explore the learning targets by communicating with peers.
All students will elaborate to construct a deeper understanding while
engaging in collaborative and independent practices. Students will
evaluate their own understanding through the practice of self-reflection.
5
minutes
Closure:
Summarize
(explain/evaluate)
The teacher will revisit the learning target and any student discoveries.
Students will explain and evaluate their understanding of the learning
target through a variety of techniques. The teacher will evaluate
students’ depth of understanding to drive future instruction.
Formative techniques occur throughout each piece of the framework.
12
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum MapGra
May 2016
Standards for Mathematical Practice
Students will:
(to be embedded throughout instruction as appropriate)
Make sense of
problems and
persevere in solving
them.
Reason abstractly
and quantitatively.
Construct viable
arguments and
critique the
reasoning of others.
Model with
mathematics.
Use appropriate
tools strategically.
Attend to precision.
Look for and make
use of structure.
Look for and
express regularity
in repeated
reasoning.
SMP.1
SMP.2
SMP.3
SMP.4
SMP.5
SMP.6
SMP.7
SMP.8
MAFS Domains: Operations and Algebraic Thinking
Number and Operations in Base Ten
Learning Targets
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For
example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Pacing: Weeks 1 - 6
August 15 – September 23
Standards
MAFS.3.OA.4.9
Students will:

identify and describe addition patterns that occur in number charts and addition tables.
HINT: This standard will be further developed in unit 2 with patterns of multiplication.
HINT: Students need ample opportunities to observe and identify important numerical patterns related to operations.
E.g.,
o
o
o


Any sum of two even numbers is even.
Any sum of two odd numbers is even.
Any sum of an even number and an odd number is odd.
explain simple addition patterns using properties of operations (i.e. When one changes the order of the addends they will still get
the same sum, 6 + 4 = 10 and 4 + 6 = 10).
explain complex addition patterns, including patterns that are not explicit, using properties of operations.
Vocabulary
addends
addition table
column
decrease
diagonal
equation
even
increase
number chart
odd
operation
pattern
row
sum
HINT: It is important to create opportunities for students to use strategies to observe addition patterns.
120 Chart
Moving from left to right within a row, the ones place increases by one.
Moving from top to bottom within a column, the tens place increases by one.
Moving from top to bottom/left to right diagonally, the ones and tens place both increase by one.
Moving from top to bottom/right to left diagonally, the ones place decreases by one while the tens place increases by one.
Addition Table
Moving from left to right within a row, the numbers increase by one.
Moving from top to bottom within a column, the numbers increase by one.
Moving from top to bottom diagonally, the numbers skip count by 2.
The sum of two even numbers is always even.
The sum of two odd numbers is always even.
The sum of one odd and one even number is always odd.
The sums of doubles fall on a diagonal.
13
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Use place value understanding to round whole numbers to the nearest 10 or 100.
MAFS.3.NBT.1.1
Students will:
HINT: Prior to implementing rules for rounding, students need to have opportunities to investigate place value. A strong
understanding of place value is essential when rounding numbers.


identify the digit of a number to 999 that corresponds with a given place value.
(This is a 2nd grade learning target.)
identify possible answers (i.e. Step 1 below) and halfway points (i.e. Step 2 below) when rounding.
decrease
digit
estimate
halfway point
increase
place value
reasonable
rounding
E.g., Round 138 to the nearest 10.



round whole numbers to the nearest 10 through the use of a number line, hundred chart, place value chart, etc.
round whole numbers to the nearest 100 through the use of a number line, hundred chart, place value chart, etc.
determine possible starting numbers when given a rounded number.
E.g.,


understand that the purpose of rounding is to make mental math easier and to check the reasonableness of an answer.
explain the results of rounding.
14
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship
between addition and subtraction.
MAFS.3.NBT.1.2
Students will:





recall basic addition and subtraction facts.
(This is a 2nd grade learning target.)
understand the inverse relationship between addition and subtraction.
add and subtract fluently within 1,000 using a variety of strategies.
explain and justify the strategy used to solve a problem.
determine an error in an addition or subtraction problem and show the correct answer.
HINT: Fluency is knowing how a number can be composed and decomposed and using that information to be flexible (use a
variety of strategies) and efficient (use a reasonable number of steps and time).
compose
decompose
decrease
difference
digit
equal to
equation
equivalent
fewer
increase
inverse
place value
strategy
sum
HINT: Refer to page 7-8 in the Third Grade Mathematics Curriculum Map for clarification of Addition and Subtraction Strategies.
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.
Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
MAFS.3.OA.4.8
Students will:
HINT: Second grade teaches two-step word problems using addition and subtraction within 100.

add and/or subtract two-step word problems within 1000 using a variety of strategies.
E.g., Jerry earned 231 points at school last week. This week he earned 79 points. If he uses 60 points to earn free time on a
computer, how many points will he have left?




choose the correct operation to perform the first computation, and choose the correct operation to perform the second
computation in order to solve two-step word problems.
represent problems using equations with an unknown quantity represented by letters or symbols (variable).
create a two-step word problem from an equation with a variable.
use estimation strategies (including rounding) to determine the reasonableness of answers.
addends
addition
decompose
decrease
difference
equation
estimation
increase
operation
rounding
strategy
subtraction
sum
symbol
variable
HINT: Refer to page 7-8 in the Third Grade Mathematics Curriculum Map for clarification of Addition and Subtraction Strategies.
15
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 1 Suggested Instructional Resources
MAFS
AIMS
Lakeshore
Teacher Guide,
p. 8
OA.4.9
(+)
Daily Math Practice
Journal,
pp. 10, 14, 16
MFAS
Adding Odd Numbers
Adding Odds and Evens
NBT.1.1
How Did You Solve It?
Card 20
All Aboard for
Rounding
Teacher Guide,
pp. 8-9
Mystery Number Rounding
Problem
Number Line
Round Up
Reproducibles,
pp. 3, 7
Rounding to the Nearest
Hundred
Numbers in
the Round
Daily Math Practice
Journal, pp. 22, 24, 26,
28, 29
The Smallest and Largest
Numbers Possible
How Did You Solve It?
Cards 21-23
www.k5mathteachingresources.com
OA.9
Odd and Even Sums
www.cpalms.org
Tricky Rice Math Pattern
The Power of Patterns
Discovery Can:
Algebraic Thinking
Cards 1-4, 21-25
Magnetic Place Value
Blocks
Internet
enVision
www.IXL.com/signin/volusia
C.2, D.2, H.4, L.4
https://learnzillion.com/
Video: Identify addition and
subtraction patterns using a
100s chart
Author: Jeanette Simpson
hcpss.instructure.com/cours
es/97
OA.9 Lessons
OA.9 Formatives
www.k5mathteachingresources.com
NBT.1
http://achievethecore.org
www.cpalms.org
Rockin’ Round the Number Line
1
Rockin’ Round the Number Line
2
Rounding for the Decades
https://learnzillion.com/
Unit: 3
Lesson: 1 – Understand
rounding to the nearest 10
Lesson: 2 – Understand
rounding to the nearest 100
Lesson: 3 – determining
which values will round to a
specific number
hcpss.instructure.com/cours
es/97
NBT.1 Lessons
NBT.1 Formatives
www.IXL.com/signin/volusia
B.1, B.2, B.4, B.5, B.7, B.8,
P.1
2-3 POD
http://achievethecore.org
Pick A Problem Cards
26-30, 37, 40
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
16
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 1 Suggested Instructional Resources
MAFS
AIMS
Lakeshore
MFAS
Teacher Guide,
p. 9
Adding and Subtracting
Using Properties
String Bead
Subtraction
Reproducibles,
p. 3
Addition Within 1000
Daily Math Practice
Journal,
pp. 22, 24, 26, 28, 29
Subtraction Within 1000
NBT.1.2
Base Place:
The Pluses
How Did You Solve It?
Cards 24-27
Pick A Problem Cards
31-36, 38
Wanda’s Method
Internet
www.k5mathteachingresources.com
NBT.2
3 Digit Addition Split
www.cpalms.org
Decoding Decomposing
(Adding two 4 digit numbers)
hcpss.instructure.com/cours
es/97
NBT.2 Lessons
NBT.2 Formatives
enVision
www.IXL.com/signin/volusia
C.1, C.3, C.4, C.8 – Addition
D.1, D.3, D.4, D.6– Subtraction
2-3 SE;
RMC
https://learnzillion.com/
Unit: 3
Lesson: 6 – Use place value
strategies to add or subtract
Lesson: 10 – comparing
strategies of addition and
subtraction to look for efficiency
http://achievethecore.org
Discovery Can:
Operations Cards 3-5, 810
OA.4.8
(+, -)
Picturing a
Solution
Problem Solving
Strategy Puzzles (blue)
Teacher Guide,
p. 7
How Did You Solve It?
Card 17
www.k5mathteachingresources.com
OA.8
Two Step Word Problems – Set
1
Pick A Problem Cards
7,9
www.cpalms.org
Chess Wish List
hcpss.instructure.com/cours
es/97
OA.8 Lessons
OA.8 Formatives
www.IXL.com/signin/volusia
M.9, O.5 – One-step
M.11 – Multi-step
https://learnzillion.com/
Lesson: Interpreting a two-step
word problem
Created by: Steve Lebel
2-4 SE;
RMC; POD
3-8 SE;
A&R; RMC
2-8A
3-1A
3-4A
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
17
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Standards for Mathematical Practice
Students will:
(to be embedded throughout instruction as appropriate)
Make sense of
problems and
persevere in solving
them.
Reason abstractly
and quantitatively.
Construct viable
arguments and
critique the
reasoning of others.
Model with
mathematics.
Use appropriate
tools strategically.
Attend to precision.
Look for and make
use of structure.
Look for and
express regularity
in repeated
reasoning.
SMP.1
SMP.2
SMP.3
SMP.4
SMP.5
SMP.6
SMP.7
SMP.8
MAFS Domains: Operations and Algebraic Thinking
Number and Operations in Base Ten
Learning Targets
Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a
context in which a total number of objects can be expressed as 5 x 7.
Pacing: Weeks 7 - 19
September 26 – December 20
Standards
MAFS.3.OA.1.1
Students will:




identify the symbol for multiplication (×) and its meaning (i.e., “groups of”, “rows of”, and “times as many, big, long, etc.”).
identify parts of multiplication equations (e.g., factors and product).
interpret a situation requiring multiplication using pictures, objects, words, numbers, and equations.
describe a context that could be represented with basic multiplication.
E.g., Jim purchased 5 packages of muffins. Each package contained 3 muffins. How many muffins did Jim purchase?
5 groups of 3, 5 x 3 = 15.
Describe another situation where there would be 5 groups of 3 or 5 x 3.
Vocabulary
each
equal groups
equation
expression
factors
groups of
multiplication facts
multiply (×)
pattern
product
rows of
HINT: Refer to page 6 in the Third Grade Mathematics Curriculum Map for clarification of Common Multiplication Situations.
It is expected that students will become proficient in finding the unknown number in all positions.
18
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by
using drawings and equations with a symbol for the unknown number to represent the problem.
MAFS.3.OA.1.3
array
column
Students will:
combinations
compare
 use the following situations to solve real-world and mathematical problems related to multiplication within 100.
each
o equal groups (repeated addition): Stan has 4 bags of cookies with 5 in each bag. How many cookies does he have?
equal groups
o array model: Mrs. Smith arranges the desks in her classroom. She has 4 rows with 3 desks in each row. How many
equation
desks are in her classroom?
expression
factor
groups of
measurement
multiply (×)
number of groups
unknown
pattern
per (hour, mile, etc.)
price
product
o compare: Sam has 4 baseball cards. Elise has 4 times as many. How many does Elise have?
rate
repeated addition
HINT: Word problem contexts may include but are not limited to:
rows of
o measurement: A piece of ribbon is 2 inches long. How long is another piece of ribbon that is 4 times as long?
o combination: How many different combinations of one flavor of ice cream and one topping can be made from 3 different size of group unknown
skip count
flavors and 3 different toppings?
strategy
o price: The Sweet Shop bakery sells pies for $4 each. How much do 2 pies cost?
variable
o rate: Bradley rides his bike 5 miles each day for 5 days. How many miles does he ride in all?

represent multiplication word problems using drawings, and equations with unknown numbers (i.e., variables) in all positions.
HINT: In the early stages of representing an unknown with a variable, students should be discouraged from using x as a
variable in multiplication situations as it could easily be confused with the multiplication symbol.


describe a context that could be represented as the product of two whole numbers (e.g., 4 x 5 is a way to show the total
number of pencils in 4 cans with 5 pencils in each).
solve two-step word problems involving multiplication.
HINT: Refer to page 6 in the Third Grade Mathematics Curriculum Map for clarification of Common Multiplication and Division
Situations. It is expected that students will become proficient with all situations.
19
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Apply properties of operations as strategies to multiply and divide. E.g., If 6 x 4 = 24 is known, then
4 x 6 = 24 is also known. (Commutative Property of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then
15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 – 30. (Associate Property of multiplication.) Knowing that 8 x 5 = 40, and 8 x 2 = 16, one can find 8 x 7 as
8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive Property).
MAFS.3.OA.2.5
Students will:
HINT: Properties of operations are used to make problems easier to solve.
The distributive property is the precursor for the standard algorithm for multiplication which is taught in Fifth grade.
represent expressions using various objects, pictures, words, and symbols in order to develop understanding of properties of
multiplication.
apply properties of operations as strategies to multiply.
o Commutative Property of multiplication: E.g., 3 × 2 is the same value as 2 × 3
o Identity Property of multiplication: E.g., 5 × 1 = 5 and 1 × 3 = 3
o Zero Product Property: E.g., 2 × 0 = 0 and 0 × 4 = 0
o Associative Property: E.g., 2 × 3 × 3 = 2 x (3 x 3)
o Distributive Property : helps find products a student does not know using products they do know


equation
equivalent
expression
factor
inverse operation
parentheses
product
strategy
symbol
E.g., How can the distributive property be applied to determine the product of 9 × 6?
Student 1
9×6
9 × 5 = 45
9×1=9
(9 × 5) + (9 × 1) =
45 +
9 = 54

Student 2
9×6
9 × 3 = 27
9 × 3 = 27
(9 × 3) + (9 × 3) =
27 + 27 = 54
Student 3
9×6
5 × 6 = 30
4 × 6 = 24
(5 × 6) + (4 × 6) =
30 + 24 = 54
determine the error in the steps of a distributive property strategy.
HINT: Students are NOT expected to identify the properties by name.
Refer to page 9 in the Third Grade Mathematics Curriculum Map for clarification of Multiplication Strategies.
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For
example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MAFS.3.OA.4.9
Students will:



explain multiplication patterns using properties of operations.
identify and describe multiplication patterns that occur in multiplication tables.
explain simple and complex multiplication patterns, including patterns that are not explicit, using properties of operations.
E.g.,
Each row is a listing of the first 12 multiples of the numbers found in the first column on the chart.
Each column is a listing of the first 12 multiples of the numbers found in the first row on the chart.
All even numbers can be divided by 2.
A skip counting pattern occurs in each row and column.
Changing the order of the factors does not change the product (Commutative Property).
The product of two even numbers is always even.
The product of two odd numbers is always odd.
The product of one even and one odd number is always even.
The product of doubles falls on a diagonal.
20
Volusia County Schools
Mathematics Department
column
diagonal
even
factors
multiples
multiplication table
odd
pattern
product
row
Grade 3 Math Curriculum Map
May 2016
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of
operations.
MAFS.3.NBT.1.3
Students will:


use base ten blocks, diagrams, or hundreds charts to multiply one-digit numbers by multiples of 10.
apply understanding of multiplication and the meaning of the multiples of 10.
E.g., 4 x 50 is 4 groups of 5 tens or 20 tens. Twenty tens equals 200.


factor
multiples
multiply
pattern
place value
product
strategy
recognize patterns in multiplying by multiples of 10.
multiply one-digit numbers by multiples of 10 using strategies based on place value and properties of operation, in
mathematical and real world contexts.
E.g., 9 x 80 = 9 x (8 x 10) , or (9 x 8) x 10

solve for a missing factor using strategies based on place value and properties of operations.
E.g., 5 × n = 150, n × 5 = 150, 150 = n × 5, 150 = 5 × n
HINT: This standard expects that students go beyond tricks that hinder understanding such as “just adding zeroes” and explain
and reason about their products.
E.g., “When you multiply a number by 10, you increase the value 10 times, changing the value by one place.”
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.
Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
MAFS.3.OA.4.8
Students will:

add, subtract, and/or multiply two-step problem situations using a variety of strategies.
(This standard will be further developed later in this unit to include division.)
E.g., Jonathan saves $5 a week. His goal is to save $65 by the time his family goes to Disney.
After six weeks, how much money does Jonathan still need to save?


add
equations
estimate
multiply
operation
subtract
symbol
variable
choose the correct operation to perform the first computation, and choose the correct operation to perform the second
computation in order to solve two-step word problems.
represent problems using equations with an unknown quantity represented by letters or symbols (variable).
E.g., Mike runs 2 miles a day. His goal is to run 25 miles. After 5 days, how many miles does Mike have left to run in
order to meet his goal? 5 × 2 = m 25 – m = ?


use mental computation and estimation strategies (including rounding) to determine the reasonableness of answers.
create a two-step word problem from an equation with a variable.
HINT: Adding and subtracting numbers should include numbers within 1,000, and multiplying numbers should include singledigit factors and products less than 100.
21
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40,
one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
MAFS.3.OA.3.7
Students will:
HINT: By the end of Grade 3, students are to know from memory multiplication facts with factors 0 – 10.
It is important to create opportunities for students to practice this standard on an ongoing basis to demonstrate mastery
by the end of the year.



basic facts
factor
factor pairs
multiply
product
strategy
demonstrate fluency with multiplication facts through 10.
(This standard will be further developed later in this unit to include division.)
multiply any two numbers with a product within 100 with ease by choosing and using strategies that will get to the answer
quickly.
determine factor pairs of a product with fluency.
HINT: Fluency is knowing how a number can be composed and decomposed and using that information to be flexible (use a
variety of strategies) and efficient (use a reasonable number of steps and time).
MAFS.3.OA.1.2
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned
equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context
in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Students will:




identify the symbol for division (÷) and its meaning (e.g., “divided into”, “partitioned into, and separated into”).
explain division as a set of objects partitioned into an equal number of shares.
identify parts of division equations (i.e., dividend, divisor, and quotient).
interpret quotients in division.
E.g., 50 ÷ 10 = 5; can be 5 groups with 10 items in each group or 10 groups with 5 items in each group.

dividend
division
divisor
equation
expression
groups
partition
quotient
represent
shares
represent a context that could be described as the quotient of two whole numbers (e.g., 8 ÷ 2 is a way to show the equal
sharing of 8 cookies between 2 boys).
HINT: Start representing division expressions with concrete manipulatives (objects).
22
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by
using drawings and equations with a symbol for the unknown number to represent a problem.
MAFS.3.OA.1.3
array
column
Students will:
comparison
dividend
 use the following situations to solve real-world and mathematical problems involving division with divisors and quotients within
division
100.
divisor
equal parts
o equal groups: Hector has 12 hammers. He puts 4 in each compartment in his tool box. How many compartments
equation
does it take to hold all of his hammers?
expression
groups
measurement
o arrays: A marching band has 28 members. The director puts the members into equal rows of 7. How many rows does partition
price
it take to contain all of the band members?
quotient
rate
repeated subtraction
represent
row
symbol
variable
o comparison: Wanda read 10 pages of her book. Felecia read 2 pages of her book. How many times as many pages
did Wanda read than Felecia?
HINT: Word problem contexts may include but are not limited to:
o measurement: Kylie is making bracelets from a string that measures 30 inches. Each bracelet requires 6 inches of
string. How many bracelets can she make?
o partitive (partitioning): Robbie has 35 bugs and 7 jars. He will put all of the bugs in jars. If he partitions the bugs
equally, how many bugs will be in each jar?
o price: A new video game costs $30 which is 5 times as much as a used video game. How much does a used video
game cost?
o rate: Frank rode a roller coaster several times in a row without getting off. He spent a total of 15 minutes on the roller
coaster. If each ride took 5 minutes, how many times did he ride the roller coaster?

represent problems using equations with a symbol (variable) to represent unknown quantities.
E.g., 15 ÷ n = 3, 3 = 15 ÷ n

solve two-step situational word problems involving division.
HINT: Refer to page 6 in the Third Grade Mathematics Curriculum Map for clarification of Common Multiplication and Division
Situations.
Refer to page 10 in the Third Grade Mathematics Curriculum Map for clarification of Division Strategies.
23
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Apply properties of operations as strategies to multiply and divide. E.g., If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative Property
of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 =30. (Associate Property of multiplication.)
Knowing that 8 x 5 = 40, and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive Property).
MAFS.3.OA.2.5
Students will:

represent expressions using various objects, pictures, words, and symbols in order to develop understanding of properties of
division.
HINT: Refer to page 6 in the Third Grade Mathematics Curriculum Map for clarification of Common Multiplication and Division
Situations.

apply properties of operations as strategies to divide.
o Divisive Identity Property of division – any number divided by one will stay the same (E.g., 26 ÷ 1 = 26).
o Zero Property of division – The zero property of division has two rules:
dividend
divisor
equation
equivalent
expression
group size
inverse operation
number of groups
quotient
value
Rule1- If you divide zero by any number the answer will be zero. You have nothing to divide (E.g., 0 ÷ 12 = 0).
Rule2- If any number is divided by zero, then the problem cannot be solved. You cannot divide by nothing. (E.g., 12 ÷ 0)

explain how the properties of operations can apply to division and use those properties to make it easier to find the quotient.
HINT: Students are not expected to identify the properties by name.
Refer to page 10 in the Third Grade Mathematics Curriculum Map for clarification of Division Strategies.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown
number that makes the equation true in each of the equations 8 x ? = 48,
5 = __ ÷ 3, 6 x 6 = ?.
MAFS.3.OA.1.4
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
MAFS.3.OA.2.6
Students will:



identify the inverse operation of a multiplication or division equation (e.g., the inverse operation of 7 x 3 = 21 is 7 = 21 ÷ 3).
determine the unknown number (variable) in multiplication and division problems.
use variables (blank spaces, geometric shapes or letters) to demonstrate inverse operations for multiplication and division.
E.g., 4 x _ = 36 and 36 ÷ _ = 4;


÷ 9 = 7 and 9 x 7 =
; m = 48 ÷ 6 and 48 = m x 6
understand division as an unknown factor-problem.
create a multiplication problem with an unknown factor when given a division problem (e.g., given 32÷8, create 8 x
= 32).
basic facts
dividend
divisor
equations
equivalent
expressions
factor
group size unknown
inverse operation
number of groups
unknown
product
quotient
variable
HINT: Refer to page 6 in the Third Grade Mathematics Curriculum Map for clarification of Common Multiplication and Division
Situations. It is expected that students will become proficient with all situations involving an unknown number in all
positions.
24
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.
Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
MAFS.3.OA.4.8
Students will:




use the four operations to solve two-step problem situations fluently using a variety of strategies.
choose the correct operation to perform the first computation, and choose the correct operation to perform the second
computation in order to solve two-step word problems.
represent problems using equations with an unknown quantity represented by letters or symbols (variable).
write equations to represent a two-step word problem.
add
divide
equation
estimate
multiply
operation
subtract
symbol
variable
E.g. Mike runs 2 miles a day. His goal is to run 25 miles. After 5 days, how many miles does Mike have left to run in order to
meet his goal? 5 × 2 = m 25 – m = ?


create a two-step word problem from an equation with a variable.
use mental computation and estimation strategies (including rounding) to determine the reasonableness of answers to one- and
two-step problems.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40,
one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
MAFS.3.OA.3.7
Students will:
HINT: By the end of Grade 3, students are to know from memory multiplication facts with factors 0 – 10. It is important to create
opportunities for students to practice this standard on an ongoing basis to demonstrate mastery by the end of the year.


understand the inverse relationship between multiplication and division.
divide whole numbers within 100 fluently (i.e., accurately, efficiently, and flexibly).
basic facts
dividend
division
divisor
factor
inverse operation
multiply
product
quotient
strategy
HINT: Fluency is knowing how a number can be composed and decomposed and using that information to be flexible (use a
variety of strategies) and efficient (use a reasonable number of steps and time).
Refer to pages 9 & 10 in the Third Grade Mathematics Curriculum Map for clarification of Multiplication and Division
Strategies.
25
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
MAFS
AIMS
Lakeshore
Accounting
for Butterflies
Teacher Guide,
p. 4
Figuring
Fingers and
Tallying Toes
Daily Math Practice
Journal,
pp. 2, 4, 6, 8, 18, 20
OA.1.1
Problem Solving
Strategy Puzzles
(purple)
Discovery Can:
Algebraic Thinking
Cards 6-20
Discovery Can:
Operations Cards 6, 1122
How Did You Solve It?
Cards 1-3
Teacher Guide,
pp. 3-4
OA.1.3
(×)
Daily Math Practice
Journal,
pp. 3, 5, 7, 9, 11, 13, 17,
19
26
MFAS
Interpreting Multiplication
Multiplication on a Number
Line
What Does 21 Mean?
Writing Multiplication Word
Problems
Internet
www.k5mathteachingresources.com
OA.1
www.IXL.com/signin/volusia
E.1, E.2, E.3, E.4, E.5, E.6,
E.7, N.9
www.cpalms.org
Cheezy Arrays
Hip, Hip, Array!
Circle and Stars
Array to Multiply
https://learnzillion.com/
Unit: 1
Lesson: 1 – The Carrot Patch;
Use equal groups to
understand multiplication
Lesson: 2 – Practice
representing multiplication in
different ways
hcpss.instructure.com/cours
es/97
OA.1 Lessons
OA.1 Formatives
Finding an Unknown
Product
enVision
www.k5mathteachingresources.com
OA.3
Building Arrays
Number Story Arrays – Set 1
Number Story Arrays – Set 2
Multiplication Word Problems
http://achievethecore.org
www.IXL.com/signin/volusia
E.3, H.5, H.6, H.7, H.13, L,5,
L,6
https://learnzillion.com/
Unit: 1
Lesson: 6 – Understand how
to use drawings and equations
to solve multiplication and
division problems
5-1 SE
5-2 SE
5-3 SE
5-4 SE
5-5 SE
www.cpalms.org
Problem Solving
Strategy Puzzles
Chip Chip Array
(purple)
hcpss.instructure.com/cours
http://achievethecore.org
Discovery Can:
es/97
Algebraic Thinking
Cards 6-20
OA.3 Lessons
Discovery Can:
OA.3 Formatives
Operations Cards 6, 1122
How Did You Solve It?
Cards 3, 6-7
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
AIMS
OA.2.5
(×)
MAFS
Put it on the
Table
OA.4.9
Pattern
Detective
Lakeshore
MFAS
Teacher Guide,
p. 5
Break Apart Put Together
Reproducibles,
p. 3
Using the Associative
Property of Multiplication
How Did You Solve It?
Cards 10-14
Pick A Problem Cards 7,
9, 10, 14, 23, 24, 25
Decomposing into Equal
Addends
Daily Math Practice
Journal,
pp. 2, 19, 21
How Did You Solve It?
Cards 10-12
Meeting the Reading Goal
Multiplication of Even
Numbers
Patterns Within the
Multiplication table
Internet
www.k5mathteachingresources.com
OA.5
Decompose a Factor – Version
1
www.cpalms.org
Amazing Arrays
Efficient Multiplication
Hungry Zero
hcpss.instructure.com/cours
es/97
OA.5 Lessons
OA.5 Formatives
www.k5mathteachingresources.com
OA.9
Patterns in the Multiplication
Table
www.cpalms.org
Patterns Within the
Multiplication Table
enVision
www.IXL.com/signin/volusia
N.6, N.7, N.8, N.10
https://learnzillion.com/
Unit: 12
Lesson: 6 – Use the
properties of multiplication to
solve problems
Unit: 9
Lesson: 2 – Practice
switching factor order
6-3 SE
7-1 SE
7-2 SE
7-3 SE
7-4 SE
7-5 SE
7-6 SE
7-7 SE
7-1A
http://achievethecore.org
www.IXL.com/signin/volusia
C.2, D.2, H.4, L.4
6-1 SE
6-2 SE
https://learnzillion.com/
Unit: 8
Lesson: 4 - Find patterns and
describe them using properties
of operations
hcpss.instructure.com/cours
http://achievethecore.org
es/97
OA.9 Lessons
OA.9 Formatives
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
27
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
AIMS
NBT.1.3
MAFS
Crazy Clues
Lakeshore
MFAS
Teacher Guide,
pp. 10-11
Explaining Multiplication
Using Multiples of Ten
Reproducibles,
p. 3
How Are These Two
Problems Related?
Daily Math Practice
Journal, pp. 22, 23, 24,
25, 26, 27
Multiplying by Multiples of
Ten
How Did You Solve It?
Cards 28-32
Magnetic Place Value
Blocks
Teacher Guide,
p. 7
Packages of 50
Books at the Book Fair
Party Beverages
OA.4.8
(+, -, ×)
Daily Math Practice
Journal, pp. 3, 7, 9, 11,
13, 17, 19, 21
How Did You Solve It?
Card 18
Pick A Problem Cards
10,12,14,20,21
Internet
www.k5mathteachingresources.com
NBT.3
Multiply by Multiples of 10
www.cpalms.org
Fishing for Multiples of 10
Tens, Tens, and More Tens
Ten Ten We all Win
hcpss.instructure.com/cours
es/97
NBT.3 Lessons
NBT.3 Formatives
www.k5mathteachingresources.com
OA.8
www.cpalms.org
Getting the Hang of Two Step
Word Problems
hcpss.instructure.com/cours
es/97
OA.8 Lessons
OA.8 Formatives
enVision
www.IXL.com/signin/volusia
F.11, H.1
6-4 SE
https://learnzillion.com/
Unit: 8
Lesson: 1 – Use place value
to multiply with multiples of 10
Lesson: 2 – Fluently multiply
one-digit numbers by multiples
of 10
http://achievethecore.org
www.IXL.com/signin/volusia
M.9, O.5 – one-step
M.11 – multi-step
6-5 SE
7-8 SE
https://learnzillion.com/
Unit: 1
Lesson: 7 – use multiplication
and division to solve word
problems
Unit: 12
Lesson: 4 – Use the
properties of multiplication to
make multiplication easier
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
28
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
MAFS
AIMS
Salute to
Facts
Lakeshore
Daily Math Practice
Journal,
pp. 8, 12, 14, 18
MFAS
Fluency with Basic
Multiplication Facts
Fluency with Mulitplication
OA.3.7
(×)
Discovery Can:
Operations Cards 1, 6,
11-22
Camp Fair
Shares
Teacher Guide,
p. 3
Boxing Bags
and Matches
Reproducibles,
p. 3
OA.1.2
Daily Math Practice
Journal, pp. 3, 5, 7, 9, 15
Interpreting Division
Using a Number Line to
Solve a Division Problem
What Does the Six Mean?
Internet
enVision
www.k5mathteachingresources.com
OA.7
Multiply and Divide within 100 –
I Have Who Has (several
options)
www.cpalms.org
Amazing Arrays
www.IXL.com/signin/volusia
F.1, F.2, F.3, F.4, F.5, F.6, F.7,
F.8, F.9, G.1, G.2, G.3, G.5,
G.6, G.7, G.9, G.10, G.11,
G.13, G.14, G.20
hcpss.instructure.com/cours
es/97
OA.7 Lessons
OA.7 Formatives
www.k5mathteachingresources.com
OA.2
Sharing or Grouping
http://achievethecore.org
www.cpalms.org
Pet Store Partitive Division
https://learnzillion.com/
www.IXL.com/signin/volusia
I.1, I.2, I.4, L.6
https://learnzillion.com/
Unit: 1
Lesson: 3 – Understand how
to represent division in more
than one way
Lesson: 4 – Practice
representing division in
different ways
Writing a Problem With a
hcpss.instructure.com/cours
Discovery Can:
Quotient
es/97
Operations Cards
2, 7, 21-25
OA.2 Lessons
Discovery Can:
OA.2 Formatives
Algebraic Thinking
http://achievethecore.org
Cards 17-20
How Did You Solve It?
Cards 1-3
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
29
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
OA.1.3
(÷)
MAFS
AIMS
Lakeshore
MFAS
Teacher Guide,
pp. 3-4
Finding the Number of
Groups
Daily Math Practice
Journal,
p. 5
Finding the Group Size the
Group Size
Discovery Can:
Algebraic Thinking
Cards 6-20
Discovery Can:
Operations Cards 6, 1122
How Did You Solve It?
Cards 8-9
Internet
enVision
www.k5mathteachingresources.com
OA.3
www.IXL.com/signin/volusia
E.3, H.5, H.6, H.7, H.13, L.5,
L.6
www.cpalms.org
Division by matching equations
to the real world examples
Two interpretations of division
https://learnzillion.com/
Unit: 15
Lesson: 6 – Use the most
efficient strategy to solve a
multiplication or division word
problem
Unit: 7
Lesson 3 – Choose efficient
strategies to solve division
problems
hcpss.instructure.com/cours
es/97
OA.3 Lessons
OA.3 Formatives
8-1 SE
8-2 SE
9-7 SE
http://achievethecore.org
Teacher Guide, p. 5
OA.2.5
(÷)
Reproducibles, p. 3
How Did You Solve It?
Cards 10-14
Does It Work For Division
www.k5mathteachingresources.com
OA.5
www.cpalms.org
Break Apart and Put Together
Simplifying Multiplication with
the Distributive Property
www.IXL.com/signin/volusia
N.6, N.7, N.8, N.10
9-5 SE
https://learnzillion.com/
http://achievethecore.org
hcpss.instructure.com/cours
es/97
OA.5 Lessons
OA.5 Formatives
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
30
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
MAFS
AIMS
Lakeshore
Daily Math Practice
Journal, pp. 2, 4, 6, 10,
16, 20
Discovery Can:
Algebraic Thinking
Cards 6-10
MFAS
Find the Unknown Number
Missing Number In Division
Equations
Missing Numbers in
Multiplication Equations
OA.1.4
Multiplication and Division
Equations
Internet
www.k5mathteachingresources.com
OA.4
Missing Numbers: Division
www.cpalms.org
Tasty Algebra
Discovering the Mystery Factor
Through Arrays
hcpss.instructure.com/cours
es/97
OA.4 Lessons
OA.4 Formatives
enVision
www.IXL.com/signin/volusia
G.4, G.8, G.12, G.17, K.10
9-6 SE
8-3B
https://learnzillion.com/
Unit: 15
Lesson: 4 – Understanding
the relationship between
multiplication and division to
multiply and divide within 100
Lesson: 5 – Solve division
problems using the
relationship between
multiplication and division
Unit: 7
Lesson: 7 – Find unknown in
multiplication and division
using inverse operations
http://achievethecore.org
Teacher Guide,
p. 6
OA.2.6
Reproducibles,
p. 5
Daily Math Practice
Journal,
pp. 8, 10, 13
Alien Math
Changing Division
Equations into Multiplication
Equations
www.k5mathteachingresources.com
OA.6
www.cpalms.org
Grandma Wants to Know
Three Is Not a Crowd!
hcpss.instructure.com/cours
es/97
OA.6 Lessons
OA.6 Formatives
www.IXL.com/signin/volusia
G.17, H.7, I.3, I.5, N.10
https://learnzillion.com/
Unit: 15
Lesson: 7 – Represent
unknown quantities in
equations using letters
Lesson: 8 - Solving two-step
word problems using a
variable representing an
unknown quantity
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
31
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
MAFS
AIMS
Zoo Books
Lakeshore
Teacher Guide,
p. 7
OA.3.7
(÷)
OA.4.8
(+, -, ×, ÷)
Reproducibles,
p. 6
Daily Math Practice
Journal, pp. 3, 7, 9, 11,
12, 13, 15, 17, 19, 21
Discovery Can:
Operations Cards 16-20
How Did You Solve It?
Card 17, 18
Pick A Problem Cards 7,
8,9,10,12,14,20,21,84
Daily Math Practice
Journal,
pp. 8, 12, 14, 18
Discovery Can:
Operations Cards 2, 7,
23-25
Pick A Problem Cards
15, 17, 18
MFAS
Bake Sale
Zoo Field Trip
Internet
www.k5mathteachingresources.com
OA.8
Two-Step Word Problems set 2
Books at the Book Fair
Party Beverages
www.cpalms.org
Getting the Hang of Two Step
Word Problems
hcpss.instructure.com/cours
es/97
OA.8 Lessons
OA.8 Formatives
enVision
www.IXL.com/signin/volusia
M.9, O.5 – one-step
M.11 – multi-step
9-4 SE
https://learnzillion.com/
Unit: 15
Lesson: 3 – Choose the most
efficient strategy to solve a
word problem
Lesson: 10 – Solving two-step
word problems using more
than 1 variable
http://achievethecore.org
Fluency With Division
www.k5mathteachingresources.com
OA.7
Multiply and Divide within 100 –
I Have Who Has
hcpss.instructure.com/cours
es/97
OA.7 Lessons
OA.7 Formatives
www.IXL.com/signin/volusia
J.1, J.2, J.3, J.4, J.5, J.6, J.7,
J.8, J.9, K.1, K.2, K.3, K.4,
K.5, K.6, K.7, K.8, K.9, K.10,
K.11, K.12, M.3, M.4, N.6,
N.10
8-3 SE
9-1 SE
9-2 SE
9-3 SE
9-5 SE
9-6 SE
https://learnzillion.com/
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
32
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Standards for Mathematical Practice
Students will:
(to be embedded throughout instruction as appropriate)
Make sense of
problems and
persevere in solving
them.
Reason abstractly
and quantitatively.
Construct viable
arguments and
critique the
reasoning of others.
Model with
mathematics.
Use appropriate
tools strategically.
Attend to precision.
Look for and make
use of structure.
Look for and
express regularity
in repeated
reasoning.
SMP.1
SMP.2
SMP.3
SMP.4
SMP.5
SMP.6
SMP.7
SMP.8
MAFS Domains: Geometry
Number and Operations – Fractions
Measurement and Data
Learning Targets
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4
parts with equal area, and describe the area of each part as ¼ of the area of the shape.
Pacing: Weeks 20 - 29
January 4 – March 6
Standards
MAFS.3.G.1.2
Students will:

partition shapes into 2, 3, 4, 6, or 8 parts with equal-sized areas.
HINT: Shapes may include: quadrilateral, equilateral triangle, isosceles triangle, regular hexagon, regular octagon, and circle.



explain that the denominator represents the number of equal-sized parts, that make up the whole.
explain that the numerator represents the count of the number of equal-sized parts.
describe the area of each part as a unit fraction of the whole.
E.g., This figure was partitioned/divided into four equal parts. Each part is 1/4 of the total area of the figure. 1/4 is the unit
fraction of the whole (e.g., 4/4).
Vocabulary
denominator
equal parts
fraction
fractional parts
model
numerator
one-eighth
one-half
one-fourth
one-sixth
one-third
partition
separate
unit fraction
whole
1 1 1 1
4 4 4 4
33
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Understand a fraction1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity
formed by a parts of size 1/b.
MAFS.3.NF.1.1
Students will:

identify one of the equal parts of a partitioned shape as a unit fraction represented as 1/b.
HINT: Shapes may include: quadrilateral, equilateral triangle, isosceles triangle, regular hexagon, regular octagon, and circle.
1
Students should represent fractions numerically with a horizontal fraction bar (e.g., ).
2

determine the number of equal parts that make a whole from a given model.
E.g.,
The unit fraction is 1/2.
There are 2 equal parts.
1/2 means that there is
1 one-half.
2 equal parts make 1 whole.
The unit fraction is 1/4.
There are 4 equal parts.
2/4 means that there are
2 one-fourths.
4 equal parts make 1 whole.
The unit fraction is 1/6.
There are 6 equal parts.
3/6 means that there are
3 one-sixths.
6 equal parts make 1 whole.
1
1
1
1
4
3
3
3
3
3
compare
denominator
equal parts
equivalent fractions
fraction
fractional parts
model
numerator
one-eighth
one-half
one-fourth
one-sixth
one-third
partition
separate
unit fraction
whole
HINT: Fraction may be greater than 1 (e.g., + + + = ).

demonstrate and explain how breaking a shape into more equal-sized parts creates smaller equal-sized parts.
E.g., 1 of 3 parts is larger than 1 of 8 parts of the same whole.
HINT: Set models (parts of a group) are not explored in third grade.
34
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts.
Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b
and that its endpoint locates the number a/b on the number line.
MAFS.3.NF.1.2
Students will:

partition the intervals between whole numbers on a number line (i.e., linear model) into equal-sized segments of 2, 3, 4,
6, and 8.
HINT: This is the first time students are exposed to the numbers that are between whole numbers on a number line.



denominator
eighths
equal parts
fourths
fraction
fractional parts
halves
linear model (number
line)
model
numerator
partition
separate
sixths
thirds
unit fraction
whole
identify one of the equal parts as a unit fraction represented as 1/b.
recognize that a fractional part is labeled based on how far it is from zero, a/b.
determine the number of equal parts that make one whole from a given number line.
E.g.,
4/4 makes the whole
2 and 3 unit fractions from “0”
unit fraction


read, write, and identify a fraction (i.e., denominators 2, 3, 4, 6, 8) from a given number line.
represent fractions greater than 1 with like and unlike denominators, on a number line.
E.g., Locate
7
4
on the number line.
HINT: On FSA items only whole number marks may be labeled on number lines.
35
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, (e.g., 1/2= 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a
visual fraction model.
c. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. E.g., Express 3 in the form 3 = 3/1;
recognize that 6/1 = 6, locate 4/4 and 1 at the same point of a number line diagram.
MAFS.3.NF.1.3
denominator
eighths
equal parts
equivalent fractions
fourths
Students will:
fraction
fractional parts
 identify and represent equivalent fractions using visual models and linear models.
halves
linear model (number
HINT: Expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.
line)
model
 locate equivalent fractions on a number line.
numerator
 explain fractional equivalence (i.e., same amount of the whole or same point on a number line).
partition
HINT: At this grade level, students only explore equivalent fractions using models, rather than using algorithms or procedures. separate
sixths
thirds
E.g.,
unit fraction
Using the number line and fraction strips to see fraction
whole
equivalence.
1
2
0


1
4
2
4
2
2
3
4
4
4
=1
=1
1
6
1
6
1
6
1
2
use models to show and explain whole numbers as fractions.
express numerically whole numbers as a fraction with denominators 2, 3, 4, 6, 8.
E.g.,
5/1 = 5
7 = 7/1
8/2 = 4
3 = 12/4
1 = 6/6
HINT: On FSA items only whole number marks may be labeled on number lines.
36
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are
valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
MAFS.3.NF.1.3
Students will:


recognize that comparisons are valid only when the two fractions refer to the same whole.
compare two fractions with the same denominator with and without visual models (e.g., number lines, fraction strips, fraction
circles, color tiles, pattern blocks, drawings).
HINT: Student should be able to reason without visual models about the size of pieces (e.g., 3/8 of a pizza is less than 7/8 of
the same pizza).

compare two fractions with the same numerator with and without visual models.
HINT: Students should be able to reason without visual models about the size of pieces (e.g., 2/6 of a candy bar is more than
2/8 of the same candy bar).



use symbols (i.e., <, >, =) to compare fractions.
explain and justify the reasonableness of answers using a visual fraction model.
generate a fraction that falls between two given fractions with the same numerator or denominator.
compare
denominator
eighths
equal parts
equivalent fractions =
fourths
fraction
fractional parts
greater than >
halves
less than <
model
numerator
partition
separate
sixths
thirds
unit fraction
whole
HINT: Expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot,
where the horizontal scale is marked off in appropriate units-whole number, halves, or quarters.
MAFS.3.MD.2.4
Students will:



use a ruler to measure lengths of objects in whole, half, and quarter inches.
record measurement data in an appropriate data collection table.
make a line plot with the horizontal scale marked off in whole number, half, or quarter units to display the data that is collected.
E.g.,
Holly’s Pencils
x
x
x
x
data
half inch
inch
increments
label
length
line plot
quarter inch
scale
title
unit
HINT: Line Plots are only used to record linear measurement data.
37
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and
“how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph
might represent 5 pets.
MAFS.3.MD.2.3
Students will:

identify different parts of a picture graph (e.g., title, scale, key, categories, category label, and data) and a bar graph (e.g.,
title, scale, scale label, categories, category label, x-axis, y-axis, and data).
read and interpret scaled picture and bar graphs in order to solve one- and two-step “how many more” and “how many less”
problems.
identify the correct display of a given set of data.
pose a question to be answered through a survey or experiment.
collect data through a survey or experiment.
determine the appropriate increments for a scaled bar graph and appropriate key for a scaled picture graph.
construct scaled bar graphs and scaled picture graphs with several categories, that appropriately display data collected from
observations, surveys and experiments.






E.g.,
Scaled Picture Graph


category
category label
data
experiment
horizontal
increments
key
label
least
line plot
most
represent
results
scale
scaled bar graph
scaled picture graph
survey
symbols
title
unit
vertical
x-axis
y-axis
Scaled Bar Graph
complete a picture graph or bar graph by using addition and/or subtraction to find missing data values.
analyze and draw conclusions about data (including identification of missing data) displayed in the form of bar graphs and
picture graphs.
HINT: Addition and subtraction, of whole numbers may be used when analyzing data.
38
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an
unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
MAFS.3.MD.4.8
Students will:

explore the concept of perimeter using a variety of tools and strategies.
E.g., geoboards, rubber bands, color tiles, graph paper, string, etc.





array
grid
irregular polygon
length
measure
perimeter
regular polygon
find the perimeter of a polygon (regular and irregular) that is located on a grid.
use an array model to determine perimeter of a rectangle (includes a square).
find the perimeter of a polygon when given the lengths of all sides.
identify and use properties of polygons to find the unknown side length(s) of a polygon given the perimeter without using a
grid.
solve word problems using perimeter.
HINT: Present problem situations involving perimeter, such as finding the amount of fencing needed to enclose a rectangularshaped park, or how much ribbon is needed to decorate the edges of a picture frame.

explain a method or strategy used to find the perimeter of a polygon.
Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
MAFS.3.MD.3.5
Students will:

define a unit square (i.e., a square with side length of 1 unit).
HINT: The side length of the square could be one customary unit (e.g., inch, foot), one metric unit (e.g., centimeter, meter) or
one non-standard unit.




area
column
length
measure
plane figure
row
square unit
describe area as the measure of space within a plane figure.
explain why area is measured in square units.
identify a situation where area measurement is applicable.
create a situation where area measurement is applicable.
one square unit
39
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
MAFS.3.MD.3.6
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Students will:


measure the area of a shape or flat surface by covering it with unit squares – with no gaps or overlaps – and counting the
number of unit squares used.
use an array model to determine the area of a rectangle.
1
2
3
4
E.g., To find the area one could count the unit squares.
5
6
7
8
9
10
11
12
Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by
multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical
problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c.
Use area models to represent the distributive property in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas
of the non-overlapping parts, applying this technique to solve real world problems.
MAFS.3.MD.3.7
Students will:


use square tiles to find the area of rectangles with whole number side lengths.
explain the relationship between tiling and multiplying side lengths to find the area of rectangles.
area
column
square feet
square inch
length
measure
square meter
plane figure
row
square unit
square centimeter
area
column
decompose
irregular polygon
length
measure
product
rectangle
regular polygon
row
square unit
width
HINT: Students need to discover that the length of one dimension of a rectangle tells how many unit squares are in each row
and the length of the other dimension of the rectangle tells how many unit squares are in each column.





solve real-world and mathematical area problems by multiplying length by width.
use appropriate labels to represent answers to area problems (e.g., 4 square meters).
use area models to explain the distributive property.
create area models to represent the distributive property for area of a rectangle.
decompose an irregular polygon into non-overlapping rectangles to find its area.
6 units
E.g.,
6 × (5 + 2) = (6 × 5) + (6 × 2)
5 units

40
2 units
solve real-world area problems involving irregular polygons formed by joining non-overlapping rectangles.
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an
unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Students will:



determine possible lengths and widths of a rectangle when given the area.
demonstrate how rectangles with the same perimeter can have different areas.
demonstrate how rectangles with the same area can have different perimeters.
MAFS.3.MD.4.8
area
length
perimeter
polygon
unknown
width
E.g.
A = 12, P = 16
A = 12, P = 14
41
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
Folding Flags
Lakeshore
Teacher Guide,
p. 24
Reproducibles,
p.13
G.1.2
Daily Math Practice
Journal,
pp. 64-66, 68, 70
MFAS
Four Parts of the Whole
Two Equal Parts
Teacher Guide,
pp. 11-12
Fraction
Block Out
Reproducibles,
p. 3
NF.1.1
Daily Math Practice
Journal,
pp. 30-32, 35-36, 45
Discovery Can: Fractions
Giant Magnetic Fraction
Circles and Bars
Fraction Circles Tub
How Did You Solve It?
Cards 33-35
Pick A Problem Cards
41,42,43,96,97,98,99,100
www.k5mathteachingresources.com
www.cpalms.org
Halves of an Irregular
Polygon
Fun with Fractions: Making and
Investigating Fraction Strips
Fractions Meet Pattern Blocks
Fun with Pattern block Fractions
hcpss.instructure.com/cours
es/97
Painting a Wall
Three Quarters of the Race
What Does One Fifth Mean
Which Shows One Third?
enVision
www.IXL.com/signin/volusia
W.5
13-1 SE
13-2 SE
G.2
Unit Fractions
How Did You Solve It?
Cards 81-90
Figuring
Fractions
Internet
https://learnzillion.com/
Unit: 4
Lesson 2: Partition and locate
unit fractions
Lesson 5: Use unit fractions
to understand the size of a
whole
G.2 Lessons
G.2 Formatives
http://achievethecore.org
www.k5mathteachingresources.com
NF.1
www.IXL.com/signin/volusia
W.1, W.2, W.3, W.4, W.5, W.7,
W.8, W.16, W.17, W.18
www.cpalms.org
Fraction Folding Part 1
It’s All About the Whole
https://learnzillion.com/
Unit: 10
Lesson: 6 - Express Whole
Numbers as Fractions
Lesson: 4 - Partition and
name fractions
hcpss.instructure.com/cours
es/97
NF.1 Lessons
NF.1 Formatives
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
42
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
NF.1.2
Fraction Fold
Up
(number line
goes past 1)
Fraction Line
Up
(number line
goes past 1)
Lakeshore
Teacher Guide,
pp. 13-14
Five-Eighths on the
Number Line
Reproducibles,
pp. 3, 9
Four-Sixths on the
Number Line
Daily Math Practice
Journal, pp. 30, 32, 34,
36, 38, 40, 42-44
One-Third on the Number
Line
Discovery Can: Fractions
Giant Magnetic Fraction
Circles and Bars
Fraction Circles Tub
How Did You Solve It?
Cards 36-40
What is the
One?
MFAS
Teacher Guide,
pp. 14-17
Three-Fourths on the
Number Line
NF.1.3
Daily Math Practice
Journal,
pp. 30-45
www.k5mathteachingresources.com
NF.2
Number Line Roll
Build a Hexagon
Make One
www.cpalms.org
Interactive Fractions Number
Line
Locating Fractions Less Than 1
on the Number Line
www.IXL.com/signin/volusia
W.9, W.10, W.11, W.12, W.13,
W.14
https://learnzillion.com/
Unit: 4
Lesson: 8 - Understand
fractions as a distance from
zero
Lesson: 9 – Use fractions to
show a distance from zero
http://achievethecore.org
Equivalent Fractions
Four Fourths
Reproducibles,
p. 3
enVision
Internet
How Many Fourths are in
Two Wholes
The Cake Problem
hcpss.instructure.com/cours
es/97
NF.2 Lessons
NF.2 Formatives
www.k5mathteachingresources.com
NF.3
Exploring Equivalent Fractions
Creating Equivalent Fractions
www.cpalms.org
Equivalent Fractions Dominoes
Match My Fraction
The Pizza Exchange
Twizzle the Fractions!
www.IXL.com/signin/volusia
X.1, X.2, X.3, X.5, X.7, X.8,
Y.1, Y.2, Y.3, Y.6, Y.10, Y.11
14-2 SE
14-4 SE
14-6A
https://learnzillion.com/
Unit: 10
Lesson: 2 - Generate
equivalent fractions
Lesson: 6 -Generate
equivalent fractions for whole
numbers
Unit: 11
Lesson: 6 - Comparing
fractions with like
denominators
Lesson: 3 - Comparing
fractions with like numerators
http://achievethecore.org
Discovery Can: Fractions
Giant Magnetic Fraction
hcpss.instructure.com/cours
Circles and Bars
es/97
Fraction Circles Tub
How Did You Solve It?
NF.3 Lessons
Cards 41-51
NF.3 Formatives
Pick A Problem Cards 44,
45, 46, 47, 48, 49, 50
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
43
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
Hook, Line
and Sticker
Lakeshore
Daily Math Practice
Journal,
pp. 55, 57, 58
MD.2.4
How Did You Solve It?
Cards 61-62
MFAS
Measuring Our Pencils Part
One
Measuring Our Pencils Part
Two
The Teacher’s Shoe-Part 1
The Teacher’s Shoe-Part 2
Internet
www.k5mathteachingresources.com
MD.4
www.cpalms.org
Measuring Up!
Measurement Fast Track
hcpss.instructure.com/cours
es/97
MD.4 Lessons
MD.4 Formatives
enVision
www.IXL.com/signin/volusia
U.3
4-3A
https://learnzillion.com/
Unit: 5
Lesson: 5 - Measure more
precisely by partitioning to a
smaller unit
Video: Interpret data on a line
plot
Author: Michelle Blackwell
http://achievethecore.org
Daily Math Practice
Journal, pp. 47, 59, 61,
63
MD.2.3
How Did You Solve It?
Cards 59-60
Pick-A-Problem, cards
62, 63, 64, 65, 66, 68
Collecting Cans For
Recycling
Favorite Activity After
School
Flowers in the Garden
www.k5mathteachingresources.com
MD.3
www.cpalms.org
Graphs Your Way!
Paper Airplanes Away
www.IXL.com/signin/volusia
T.5, T.9, T.6, T.10
4-3 SE
4-4 SE
4-5 SE
https://learnzillion.com/
Unit: 8
Lesson: 8 - Solve problems
with scale graphs
Lesson: 10 - Practice solving
problems using scaled graphs
hcpss.instructure.com/cours
es/97
http://achievethecore.org
MD.3 Lessons
MD.3 Formatives
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
Lunch Orders
44
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
MD.4.8
(perimeter)
Landmark
Logic
Wrecktangles
Ground
Cover
Lakeshore
Daily Math Practice
Journal, pp. 49, 51, 53,
62
Discovery Can:
Geometric Measurement
Area & Perimeter MatchUps (perimeter only)
Area Tiles
How Did You Solve It?
Cards 72, 73
Pick A Problem Cards
71-75, 81, 82, 83
(perimeter only)
Find All the Possible
Rectangles
Perimeter of Polygon w/
Missing sides
Perimeters with All sides
Known
Rectangles With Same
Perimeter
What’s the Missing Length?
Teacher Guide, p.18
Calculating Area
Reproducibles, p.10
Overlapping Tiles
Daily Math Practice
Journal, pp. 46, 52, 54,
62
Area Tiles
Discovery Can:
Geometric Measurement
How Did You Solve It?
Cards 63-65
MD.3.5
MFAS
Unit Square
Using Tiles of Different
Sizes
Internet
www.k5mathteachingresources.com
MD.8
www.cpalms.org
Finding Perimeter
Perimeter- It’s a Linear
Measurement
hcpss.instructure.com/cours
es/97
MD.8 Lessons
MD.8 Formatives
www.k5mathteachingresources.com
MD.5
www.cpalms.org
The Square Counting Shortcut
hcpss.instructure.com/cours
es/97
MD.5 Lessons
MD.5 Formatives
enVision
www.IXL.com/signin/volusia
V.8, V.9, V.16, V.18
https://learnzillion.com/
Unit: 3
Lesson: 12 - Find the
perimeter of polygons marked
with unit length markers
Lesson: 15 - Gwen’s Fence:
Create side lengths of a
rectangle given its perimeter
15-4 SE
15-5 SE
15-6 SE
15-7 SE
http://achievethecore.org
www.IXL.com/signin/volusia
V.10, V.11
15-9B
https://learnzillion.com/
Unit: 2
Lesson: 1 – Understand the
concept of area
Lesson: 2 – Understand that
area is measured in square
units
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
45
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
Sweet
Squares
Lakeshore
Teacher Guide, pp. 1920
Reproducibles, p. 11
MD.3.6
Daily Math Practice
Journal, pp. 46, 50, 52,
54, 62
MFAS
Area of a Right Trapezoid
Dawn’s Vegetable Garden
Fenced Dog Run
How Many Square Units
Area Tiles
Discovery Can:
Geometric Measurement
How Did You Solve It?
Cards 63-65
Pick A Problem Cards
Internet
www.k5mathteachingresources.com
MD.6
www.cpalms.org
Count Those Square Units
Area Designers
enVision
www.IXL.com/signin/volusia
V.10, V.11
15-9C
https://learnzillion.com/
Unit: 2
Lesson: 3 – Measure Area by
counting square units
hcpss.instructure.com/cours
es/97
MD.6 Lessons
MD.6 Formatives
http://achievethecore.org
www.k5mathteachingresources.com
MD.7
www.IXL.com/signin/volusia
V.12, V.13, V.14
MD.3.7
77, 78, 79, 80
Gardens By
Design
Teacher Guide, pp. 2021
Planning
Plots
Daily Math Practice
Journal, pp. 46, 48, 52,
56-60, 63
Polar Toy
Factory
Area Tiles
Discovery Can:
Geometric Measurement
How Did You Solve It?
Cards 66-69
Pick A Problem Cards
77, 78, 79, 80, 98
Area of a Butterfly Garden
Cover Me
Decompose Shapes to Find
Area
Using Arrays to Model the
Distributive Property
www.cpalms.org
Area Isn’t Just for Squares
Area: We Need to Know
Multiply and Conquer
hcpss.instructure.com/cours
es/97
MD.7 Lessons
MD.7 Formatives
15-9D
15-9E
https://learnzillion.com/
Unit: 2
Lesson: 7 – Understand that
the area of a rectangle can be
determined by multiplying side
lengths
Unit: 12
Lesson: 7 – Relate area to
multiplication and addition
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
46
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
Patches of
Pumpkins
Lakeshore
Teacher Guide, pp. 22
MD.4.8
(perimeter & area)
Reproducibles, pp. 12
Perimeter
and Area of
Rectangles
Book
47
Daily Math Practice
Journal, pp. 55, 60
MFAS
Internet
www.k5mathteachingresources.com
MD.8
www.cpalms.org
Area & Perimeter of Rectangles
Make a Mighty Monster
Same Perimeter Different Area
enVision
www.IXL.com/signin/volusia
V.8, V.9, V.16, V.18
15-9H
https://learnzillion.com/
Unit: 13
Lesson: 3 – Determine the
length of an unknown side
Lesson: 4 – Solve problems
by distinguishing between area
and perimeter
Area Tiles
Discovery Can:
hcpss.instructure.com/cours
Geometric Measurement
es/97
Area & Perimeter Match
http://achievethecore.org
Ups
MD.8 Lessons
How Did You Solve It?
MD.8 Formatives
Cards 70, 71, 74
Pick A Problem Cards
71-75, 77,78,79,80,81,
82,83
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Standards for Mathematical Practice
Students will:
(to be embedded throughout instruction as appropriate)
Make sense of
problems and
persevere in solving
them.
Reason abstractly
and quantitatively.
Construct viable
arguments and
critique the
reasoning of others.
Model with
mathematics.
Use appropriate
tools strategically.
Attend to precision.
Look for and make
use of structure.
Look for and
express regularity
in repeated
reasoning.
SMP.1
SMP.2
SMP.3
SMP.4
SMP.5
SMP.6
SMP.7
SMP.8
MAFS Domains:
Measurement and Data
Geometry
Number and Operations in Base Ten
Operations And Algebraic Thinking
Number and Operations- Fractions
Learning Targets
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply,
or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker
with a measurement scale) to represent the problem.
Pacing: Weeks 29-39
March 7 – May 26
Standards
MAFS.3.MD.1.2
Students will:





estimate masses of solid objects (grams and kilograms).
measure masses of solid objects (grams and kilograms).
estimate volumes of liquids (milliliters and liters).
measure volumes of liquids (milliliters and liters).
solve one-step word problems involving masses or volumes using addition, subtraction, multiplication, or division.
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time
intervals in minutes, e.g., by representing the problem on a number line diagram.
MAFS.3.MD.1.1
Students will:





tell and write time to the nearest minute using analog and digital clocks.
measure duration (intervals) of time in minutes (e.g., basketball practice is 45 minutes long).
record intervals of time in minutes (i.e. 75 minutes).
use clock models and number lines to solve word problems using time intervals in minutes.
solve one- and two-step word problems involving addition and subtraction of time durations (intervals) measured in minutes,
using a number line.
E.g., Tonya wakes up at 6:45 a.m. It takes her 5 minutes to shower, 15 minutes to get dressed, and 15 minutes to eat
breakfast. What time will she be ready for school?
48
Volusia County Schools
Mathematics Department
Vocabulary
estimate
grams
kilograms
liters
mass
measure
milliliters
volume
a.m. (AM)
analog
digital
duration
half-hour
half-past
hour
hour hand
measure
minute
minute hand
o’clock
p.m. (PM)
time
time interval
Grade 3 Math Curriculum Map
May 2016
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the
shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals,
and draw examples of quadrilaterals that do not belong to any of these subcategories.
MAFS.3.G.1.1
Students will:



understand that a quadrilateral is a closed figure with four straight sides.
analyze and compare the attributes of quadrilaterals (parallelogram, trapezoid, rectangle, rhombus, and square).
classify quadrilaterals by their attributes (number of sides, number of angles, whether the shape has a right angle, whether
the sides are the same length, and whether the sides are straight lines).
identify right angles.
sort geometric figures and identify different types of quadrilaterals.
draw quadrilaterals other than rhombuses, rectangles, and squares (e.g., trapezoid, parallelogram).
demonstrate an understanding of the hierarchy of quadrilaterals.




E.g.,
angle
attribute
diagonal
parallel sides
parallelogram
perpendicular sides
quadrilateral
rectangle
rhombus
right angle
side
square
trapezoid
vertex/vertices
HINT: All the
remaining standards in
the map are review
standards.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40,
one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
MAFS.3.OA.3.7
Students will:
HINT: By the end of Grade 3, students are to know from memory multiplication facts with factors 0 – 10.





demonstrate fluency with multiplication facts through 10.
multiply any two numbers with a product within 100 with ease by choosing and using strategies that will get to the answer
quickly.
determine factor pairs of a product with fluency.
understand the inverse relationship between multiplication and division.
divide whole numbers within 100 fluently (i.e., accurately, efficiently, and flexibly).
basic facts
dividend
division
divisor
factor
inverse operation
multiply
product
quotient
strategy
HINT: Fluency is knowing how a number can be composed and decomposed and using that information to be flexible (use a
variety of strategies) and efficient (use a reasonable number of steps and time).
49
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Use place value understanding to round whole numbers to the nearest 10 or 100.
MAFS.3.NBT.1.1
Students will:

identify possible answers (i.e. Step 1 below) and halfway points (i.e. Step 2 below) when rounding.
E.g., Round 138 to the nearest 10.



decrease
digit
estimate
halfway point
increase
place value
reasonable
rounding
round whole numbers to the nearest 10 through the use of a number line, hundred chart, place value chart, etc.
round whole numbers to the nearest 100 through the use of a number line, hundred chart, place value chart, etc.
determine possible starting numbers when given a rounded number.
E.g.,


understand that the purpose of rounding is to make mental math easier and to check the reasonableness of an answer.
explain the results of rounding.
HINT: Prior to implementing rules for rounding, students need to have opportunities to investigate place value. A strong
understanding of place value is essential when rounding numbers.
50
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.
Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
MAFS.3.OA.4.8
Students will:


use the four operations to solve two-step problem situations fluently using a variety of strategies.
choose the correct operation to perform the first computation, and choose the correct operation to perform the second
computation in order to solve two-step word problems.
represent problems using equations with an unknown quantity represented by letters or symbols (variable).
write equations to represent a two-step word problem.


E.g. Mike runs 2 miles a day. His goal is to run 25 miles. After 5 days, how many miles does Mike have left to run in order to
meet his goal? 5 × 2 = m 25 – m = ?
create a two-step word problem from an equation with a variable.
use mental computation and estimation strategies (including rounding) to determine the reasonableness of answers to one- and
two-step problems.


Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, (e.g., 1/2= 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a
visual fraction model.
c. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. E.g., Express 3 in the form 3 = 3/1;
recognize that 6/1 = 6, locate 4/4 and 1 at the same point of a number line diagram.
add
divide
equation
estimate
multiple
operation
subtract
symbol
variable
MAFS.3.NF.1.3
area model
denominator
eighths
equal parts
equivalent fractions
Students will:
fourths
fraction
 identify and represent equivalent fractions using visual models and linear models.
fractional parts
HINT: Expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.
halves
linear model
 locate equivalent fractions on a number line.
model
 explain fractional equivalence (i.e., same amount of the whole or same point on a number line).
number line
HINT: At this grade level, students only explore equivalent fractions using models, rather than using algorithms or procedures. numerator
partition
E.g.,
Using the number line and fraction strips to see
separate
fraction equivalence.
sixths
thirds
unit fraction
1
2
=1
1
1
1
whole
2
2
6
6
6
0


1
4
2
4
3
4
4
4
=1
1
2
use models to show and explain whole numbers as fractions.
express numerically whole numbers as a fraction with denominators 2, 3, 4, 6, 8.
E.g., 5/1 = 5, 7 = 7/1, 8/2 = 4, 6 = 12/2
HINT: On FSA items only whole number marks may be labeled on number lines.
51
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are
valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
MAFS.3.NF.1.3
Students will:


recognize that comparisons are valid only when the two fractions refer to the same whole.
compare two fractions with the same denominator with and without visual models (e.g., number lines, fraction strips, fraction
circles, color tiles, pattern blocks, drawings).
HINT: Student should be able to reason without visual models about the size of pieces (e.g., 3/8 of a pizza is less than 7/8 of
the same pizza).

compare two fractions with the same numerator with and without visual models.
HINT: Students should be able to reason without visual models about the size of pieces (e.g., 2/6 of a candy bar is more than
2/8 of the same candy bar).



use symbols (i.e., <, >, =) to compare fractions.
explain and justify the reasonableness of answers using a visual fraction model.
generate a fraction that falls between two given fractions with the same numerator or denominator.
compare
denominator
eighths
equal parts
equivalent fractions =
fourths
fraction
fractional parts
greater than >
halves
less than <
model
numerator
partition
separate
sixths
thirds
unit fraction
whole
HINT: Expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.
52
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MAFS
AIMS
The King’s
Containers
MD.1.2
Water In
Apples
Lakeshore
Daily Math Practice
Journal, pp. 46, 48, 50,
52, 54, 56, 62
How Did You Solve It?
Cards 56-58
MFAS
Estimating and Measuring
Mass
Estimating and Measuring
Volume
Pick A Problem Cards
59, 60, 61, 67, 84
Internet
www.k5mathteachingresources.com
MD.2
www.cpalms.org
Kick the Can Man
hcpss.instructure.com/cours
es/97
MD.2 Lessons
MD.2 Formatives
enVision
www.IXL.com/signin/volusia
U.16
https://learnzillion.com/
Unit: 6
Lesson: 7 - Add and subtract
to solve liquid volume
problems
Lesson: 10 – Solve addition
and subtraction problems
involving mass
16-6B
16-6C
http://achievethecore.org
Minute By
Minute
MD.1.1
Watch the
Time Fly
Turning Back
Time
Daily Math Practice
Journal, pp. 47, 48, 50,
51,54, 56, 61
Find The Time
Problem Solving
Strategy Puzzles
(Green)
How Did You Solve It?
Cards 52-55
Pick A Problem Cards
51,52,53,54,55,56,57,58
Time Spent
Telling Time
What Time Is It Now?
www.k5mathteachingresources.com
MD.1
www.cpalms.org
Are we there yet?
Cuts in a Rush
Rock Around the Clock
www.IXL.com/signin/volusia
S.2, S.3
https://learnzillion.com/
Unit: 6
Lesson: 2 – Measure time
intervals in minutes
Lesson: 3 – Add and subtract
to solve time problems
16-2 SE
hcpss.instructure.com/cours
http://achievethecore.org
es/97
MD.1 Lessons
MD.1 Formatives
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
Time Tellers
53
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MAFS
AIMS
Designing
With
Triangles
Lakeshore
Teacher Guide,
pp. 23-24
Daily Math Practice
Journal, pp. 64-67, 6971
G.1.1
Giant Magnetic Pattern
Blocks
How Did You Solve It?
Cards 75-80
Pick A Problem Cards
86,87,88,89,90,91,92,93
,94,95
OA.3.7
(review)
Salute to
Facts
Teacher Guide, p. 6
Reproducibles, p. 3
MFAS
Drawing Quadrilaterals
Identifying Quadrilaterals –
Part 1
Identifying Quadrilaterals –
Part 2
Internet
www.k5mathteachingresources.com
G.1
www.cpalms.org
Hoops for Quadrilaterals
Pretzel Quadrilaterals
hcpss.instructure.com/cours
es/97
G.1 Lessons
G.1 Formatives
enVision
www.IXL.com/signin/volusia
V.1, V.2, V.3, V.26
https://learnzillion.com/
Unit: 13
Lesson: 8 – Identify attributes
of quadrilaterals and use them
to compare shapes
Lesson: 9 – Categorize
shapes by analyzing attributes
Lesson: 10 – Classify shapes
into categories
11-1 SE
11-2 SE
11-3 SE
11-5 SE
11-8 SE
http://achievethecore.org
Fluency with Basic
Multiplication Facts
Daily Math Practice
Journal, pp. 8, 12, 14,
16, 18
Fluency with Division
How Did You Solve It?
Cards 15-16
Pick A Problem Cards
15, 17, 18
Using Flexible Strategies
Fluency with Multiplication
www.k5mathteachingresources.com
OA.7
www.cpalms.org
Skip Counting to Multiplying
Party Planning: Using
Multiplication
hcpss.instructure.com/cours
es/97
OA.7 Lessons
OA.7 Formatives
www.IXL.com/signin/volusia
Multiplication: F.1, F.2, F.3,
F.4, F.5, F.6, F.7, F.8, F.9,
G.1, G.2, G.3, G.5, G.6, G.7,
G.9, G.10, G.11, G.13, G.14,
G.20
Division: J.1, J.2, J.3, J.4, J.5,
J.6, J.7, J.8, J.9, K.1, K.2, K.3,
K.4, K.5, K.6, K.7, K.8, K.9,
K.10, K.11, K.12, M.3, M.4,
N.6, N.10
https://learnzillion.com/
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
54
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MAFS
AIMS
All Aboard for
Rounding
Lakeshore
Teacher Guide, pp. 8-9
MFAS
Mystery Number Rounding
Problem
Reproducibles, pp. 3, 7
NBT.1.1
(review)
Number Line
Round Up
Numbers in
the Round
Zoo Books
Daily Math Practice
Journal, pp. 22, 24, 26,
28, 29
Magnetic Place Value
Blocks
How Did You Solve It?
Cards 21-23
Pick A Problem Cards
26-30, 37, 40
Teacher Guide, p. 7
Daily Math Practice
Journal, pp. 3, 7, 9, 11,
12, 13, 15, 17, 19, 21
OA.4.8
(review)
How Did You Solve It?
Card 17, 18
Pick A Problem Cards 125
Rounding to the Nearest
Hundred
The Smallest and Largest
Numbers Possible
www.k5mathteachingresources.com
NBT.1
Estimating Sums
Estimating Differences
www.cpalms.org
What Decade is it?
Mystery Number Rounding
Problem
hcpss.instructure.com/cours
es/97
NBT.1 Lessons
NBT.1 Formatives
Party Beverages
Bake Sale
Zoo Field Trip
enVision
Internet
www.k5mathteachingresources.com
OA.8
www.cpalms.org
Water Park Fun Day
Books at the Book Fair
hcpss.instructure.com/cours
es/97
OA.8 Lessons
OA.8 Formatives
www.IXL.com/signin/volusia
B.1, B.2, B.4, B.5, B.7, B.8,
P.1
https://learnzillion.com/
Unit: 3
Lesson: 1 – Understand
rounding to the nearest 10
Lesson: 2 – Understand
rounding to the nearest 100
Lesson: 3 – determining
which values will round to a
specific number
http://achievethecore.org
www.IXL.com/signin/volusia
M.9, O.5 – One-step
M.11 – Multi-step
https://learnzillion.com/
Lesson: Interpreting a twostep word problem
Created by: Steve Lebel
Unit: 1
Lesson: 7 – use multiplication
and division to solve word
problems
Unit: 12
Lesson: 4 – Use the
properties of multiplication to
make multiplication easier
Unit: 15
Lesson: 3 – Choose the most
efficient strategy to solve a
word problem
Lesson: 10 – Solving two-step
word problems using more
than 1 variable
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
55
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MAFS
AIMS
What is the
One?
Lakeshore
Teacher Guide, pp. 1417
MFAS
Equivalent Fractions
Four Fourths
Reproducibles, p. 3
Daily Math Practice
Journal, pp. 30-45
How Many Fourths are in
Two Wholes
NF.1.3
(review)
The Cake Problem
Discovery Can:
Fractions
Giant Magnetic Fraction
Circles and Bars
Fraction Circles Tub
How Did You Solve It?
Cards 41-51
Pick A Problem Cards
44,45,46,47,48,49,50
Internet
www.k5mathteachingresources.com
NF.3
Pizza For Dinner
Build a Hexagon
www.cpalms.org
Comparing Fractions with
Brownies
Would You Rather?
hcpss.instructure.com/cours
es/97
NF.3 Lessons
NF.3 Formatives
enVision
www.IXL.com/signin/volusia
X.1, X.2, X.3, X.5, X.7, X.8,
Y.1, Y.2, Y.3, Y.6, Y.10, Y.11
https://learnzillion.com/
Unit: 10
Lesson: 2 - Generate
equivalent fractions
Lesson: 6 -Generate
equivalent fractions for whole
numbers
Unit: 11
Lesson: 6 - Comparing
fractions with like
denominators
Lesson: 3 - Comparing
fractions with like numerators
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
56
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Formative Assessment Strategies
Mathematics K-5
Name
A & D Statements
Agreement Circles
Annotated Student
Drawings
57
Description
A & D Statements analyze a set of “fact or fiction” statements. First,
students may choose to agree or disagree with a statement or identify
whether they need more information. Students are asked to describe
their thinking about why they agree, disagree, or are unsure. In the
second part, students describe what they can do to investigate the
statement by testing their ideas, researching what is already known, or
using other means of inquiry.
Agreement Circles provide a kinesthetic way to activate thinking and
engage students in mathematical argumentation. Students stand in a
circle as the teacher reads a statement. They face their peers still
standing and match themselves up in small groups of opposing beliefs.
Students discuss and defend their positions. After some students
defend their answers, the teacher can ask if others have been swayed.
If so, stand up. If not, what are your thoughts? Why did you disagree?
After hearing those who disagree, does anyone who has agreed want to
change their minds? This should be used when students have had
some exposure to the content.
Annotated Student Drawings are student-made, labeled illustrations that
visually represent and describe students’ thinking about mathematical
concepts. Younger students may verbally describe and name parts of
their drawings while the teacher annotates it for them.
Volusia County Schools
Mathematics Department
Additional Information
Statement
How can I find out?
9/16 is larger than 5/8.
__agree
__not sure
__disagree
__it depends on
My thoughts:
http://www.mathsolutions.com/documents/How_to_
Get_Students_Talking.pdf
There 20 cups in a gallon.
Agree or disagree?
2/3 equivalent to 4/6.
Agree or disagree?
A square is a rectangle.
Agree or disagree?
Additional Questioning:
Has anyone been swayed into new thinking?
What is your new thinking?
Why do you disagree with what you have heard?
Does anyone want to change their mind?
What convinced you to change your mind?
Use when students have had sufficient exposure to
content.
http://formativeassessment.barrow.wikispaces.net/A
greement+Circles
Represent 747 by drawing rods and cubes.
Represent 3x2=2x3 by drawing arrays.
Describe the meaning of 5.60.
http://formativeassessmen
t.barrow.wikispaces.net/A
nnotated+Student+Drawin
gs
Grade 3 Math Curriculum Map
May 2016
Name
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Card Sorts is a sorting activity in which students group a set of cards
with pictures or words according to certain characteristics or category.
Students sort the cards based on their preexisting ideas about the
concepts, objects, or processes on the cards. As students sort the
cards, they discuss their reasons for placing each card into a designated
group. This activity promotes discussion and active thinking.
Card Sorts
http://teachingmathrocks.blogspot.com/2012/09/voc
abulary-card-sort.html
Commit and Toss
Commit and Toss is a technique used to anonymously and quickly
assess student understanding on a topic. Students are given a
question. They are asked to answer it and explain their thinking. They
write this on a piece of paper. The paper is crumpled into a ball. Once
the teacher gives the signal, they toss, pass, or place the ball in a
basket. Students take turns reading their "caught" response.
Once all ideas have been made public and discussed, engage students
in a class discussion to decide which ideas they believe are the most
plausible and to provide justification for the thinking.
Stephanie eats 5 apple slices during lunch. When
she gets home from school she eats more. Which
statement(s) below indicates the number of apple
slices Stephanie may have eaten during the day?
a. She eats 5 apple slices.
b. She eats 5 apple slices at least.
c. She eats more than 5 apple slices.
d. She eats no more than 5 apple slices.
e. I cannot tell how many apple slices were eaten.
Explain your thinking. Describe the reason for
the answer(s) you selected.
Concept Card Mapping is a variation on concept mapping. Students are
given cards with the concepts written on them. They move the cards
around and arrange them as a connected web of knowledge. This
strategy visually displays relationships between concepts.
Concept Card
Mapping
58
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Name
Concept Cartoons
Four corners
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Concept Cartoons are cartoon drawings that visually depict children or
adults sharing their ideas about common everyday mathematics.
Students decide which character in the cartoon they agree with most
and why. This formative is designed to engage and motivate students to
uncover their own ideas and encourage mathematical argumentation.
Concept Cartoons are most often used at the beginning of a new
concept or skill. These are designed to probe students’ thinking about
everyday situations they encounter that involve the use of math.
Not all cartoons have one “right answer.” Students should be given
ample time for ideas to simmer and stew to increase cognitive
engagement.
Four Corners is a kinesthetic strategy. The four corners of the
classroom are labeled: Strongly Agree, Agree, Disagree and Strongly
Disagree. Initially, the teacher presents a math-focused statement to
students and asks them to go to the corner that best aligns with their
thinking. Students then pair up to defend their thinking with evidence.
The teacher circulates and records student comments. Next, the
teacher facilitates a whole group discussion. Students defend their
thinking and listen to others’ thinking before returning to their desks to
record their new understanding.

www.pixton.com (comic strip maker)
A decimal is a fraction.
Agree
Strongly
Agree
Strongly
Disagree
Disagree
http://debbiedespirt.suite101.com/four-cornersactivities-a170020
http://wvde.state.wv.us/teach21/FourCorners.html
Frayer Model
59
Frayer Model graphically organizes prior knowledge about a concept
into an operational definition, characteristics, examples, and nonexamples. It provides students with the opportunity to clarify a concept
or mathematical term and communicate their understanding.
For formative assessment purposes, they can be used to determine
students’ prior knowledge about a concept or mathematical term before
planning the lesson. Barriers that can hinder learning may be uncovered
with this assessment. This will then in turn help guide the teacher for
beneficial instruction.
Volusia County Schools
Mathematics Department
Frayer Model
Definition in your own words
A quadrilateral is a shape
with 4 sides.
Facts/characteristics
•4 sides
• may or may not be of equal
length
• sides may or may not be
parallel
Quadrilateral
Examples
• square
• rectangle
• trapezoid
• rhombus
Nonexamples
• circle
• triangle
• pentagon
• dodecahedron
Grade 3 Math Curriculum Map
May 2016
Name
Friendly Talk Probes
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Friendly Talk Probes is a strategy that involves a selected response
section followed by justification. The probe is set in a real-life scenario in
which friends talk about a math-related concept or phenomenon.
Students are asked to pick the person they most agree with and explain
why. This can be used to engage students at any point during a unit. It
can be used to access prior knowledge before the unit begins, or assess
learning throughout and at the close of a unit.
http://www.sagepub.com/upmdata/37758_chap_1_tobey.pdf
Human Scatterplots
I Used to Think…
But Now I Know…
60
Human Scatterplot is a quick, visual way for teacher and students to get
an immediate classroom snapshot of students’ thinking and the level of
confidence students have in their ideas. Teachers develop a selective
response question with up to four answer choices. Label one side of the
room with the answer choices. Label the adjacent wall with a range of
low confidence to high confidence. Students read the question and
position themselves in the room according to their answer choice and
degree of confidence in their answer.
I Used to Think…But Now I Know is a self-assessment and reflection
exercise that helps students recognize if and how their thinking has
changed at the end of a sequence of instruction. An additional column
can be added to include…And This Is How I Learned It to help students
reflect on what part of their learning experiences helped them change or
further develop their ideas.
Volusia County Schools
Mathematics Department
I USED TO THINK…
BUT NOW I KNOW…
AND THIS IS HOW I LEARNED IT
Grade 3 Math Curriculum Map
May 2016
Name
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Justified List begins with a statement about an object, process, concept
or skill. Examples and non-examples for the statement are listed.
Students check off the items on the list that are examples of the
statement and provide a justification explaining the rule or reasons for
their selections. This can be done individually or in small group. Small
groups can share their lists with the whole class for discussion and
feedback. Pictures or manipulatives can be used for English-language
learners.
Justified List
Example 1
Put an X next to the examples that represent 734.
___700+30+4
___730 tens 4 ones
___734 ones
___seventy-four
___7 tens 3 hundreds 4 ones
___7 hundreds 3 tens 4ones
___seven hundred thirty-four
___ 400+70+3
Explain your thinking. What “rule” or reasoning did
you use to decide which objects digit is another
way to state that number.
Example 2
K-W-L Variations
Learning Goals
Inventory (LGI)
61
K-W-L is a general technique in which students describe what they
Know about a topic, what they Want to know about a topic, and what
they have Learned about the topic. It provides an opportunity for
students to become engaged with a topic, particularly when asked what
they want to know. K-W-L provides a self-assessment and reflection at
the end, when students are asked to think about what they have
learned. The three phrases of K-W-L help students see the connections
between what they already know, what they would like to find out, and
what they learned as a result.
Learning Goals Inventory (LGI) is a set of questions that relate to an
identified learning goal in a unit of instruction. Students are asked to
“inventory” the learning goal by accessing prior knowledge. This
requires them to think about what they already know in relation to the
learning goal statement as well as when and how they may have
learned about it. The LGI can be given back to students at the end of
the instructional unit as a self-assessment and reflection of their
learning.
Volusia County Schools
Mathematics Department
K-This what I
already KNOW
W-This is what I
WANT to find out
L-This is what I
LEARNED
What do you think the learning goal is about?
List any concepts or ideas you are familiar with related
to this learning goal.
List any terminology you know of that relates to this
goal.
List any experiences you have had that may have
helped you learn about the ideas in this learning goal.
Grade 3 Math Curriculum Map
May 2016
Name
Look Back
Muddiest Point
Odd One Out
Partner Speaks
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Look Back is a recount of what students learned over a given
instructional period of time. It provides students with an opportunity to
look back and summarize their learning. Asking the students “how they
learned it” helps them think about their own learning. The information
can be used to differentiate instruction for individual learners, based on
their descriptions of what helped them learn.
Muddiest Point is a quick-monitoring technique in which students are
asked to take a few minutes to jot down what the most difficult or
confusing part of a lesson was for them. The information gathered is
then to be used for instructional feedback to address student difficulties.
Odd One Out combines similar items/terminology and challenges
students to choose which item/term in the group does not belong.
Students are asked to justify their reasoning for selecting the item that
does not fit with the others. Odd One Out provides an opportunity for
students to access scientific knowledge while analyzing relationships
between items in a group.
Partner Speaks provides students with an opportunity to talk through an
idea or question with another student before sharing with a larger group.
When ideas are shared with the larger group, pairs speak from the
perspective of their partner’s ideas. This encourages careful listening
and consideration of another’s ideas.
What I Learned
How I Learned it
Scenario: Students have been learning about the
attributes of three-dimensional shapes.
Teacher states, “I want you to think about the
muddiest point for you so far when it comes to
three-dimensional shapes. Jot it down on this
notecard. I will use the information you give to me
to think about ways to help you better understand
three-dimensional shapes in tomorrow’s lesson.”
Show students three figures and ask:
Which is the odd one out?
Explain your thinking.
Ask students to choose a different odd one out and
explain their thinking.
Today we are going to explore different ways to
add three-digit numbers together.
What different kinds of strategies
can you use to add 395+525?
Turn to your partner and take turns discussing
your strategies. Listen carefully and be prepared
to share your partner’s ideas.
62
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Name
A Picture Tells a
Thousand Words
Question Generating
Sticky Bars
63
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
A Picture Tells a Thousand Words, students are digitally photographed
during a mathematical investigation using manipulatives or other
materials. They are given the photograph and asked to describe what
they were doing and learning in the photo. Students write their
description under the photograph. The images can be used to spark
student discussions, explore new directions in inquiry, and probe their
thinking as it relates to the moment the photograph was snapped. By
asking students to annotate a photo that shows the engaged in a
mathematics activity or investigation helps them activate their thinking
about the mathematics, connect important concepts and procedures to
the experience shown in the picture and reflect on their learning.
Teachers can better understand what students are gaining from the
learning experience and adjust as needed.
Question Generating is a technique that switches roles from the teacher
as the question generator to the student as the question generator. The
ability to formulate good questions about a topic can indicate the extent
to which a student understands ideas that underlie the topic. This
technique can be used any time during instruction. Students can
exchange or answer their own questions, revealing further information
about the students’ ideas related to the topic.
Question Generating Stems:

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


Why does___?
Why do you think___?
Does anyone have a different way to
explain___?
How can you prove___?
What would happen if___?
Is___always true?
How can we find out if___?
Sticky Bars is a technique that helps students recognize the range of
ideas that students have about a topic. Students are presented with a
short answer or multiple-choice question. The answer is anonymously
recorded on a Post-it note and given to the teacher. The notes are
arranged on the wall or whiteboard as a bar graph representing the
different student responses. Students then discuss the data and what
they think the class needs to do in order to come to a common
understanding.
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Name
Thinking Log
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Thinking Logs is a strategy that informs the teacher of the learning
successes and challenges of individual students. Students choose the
thinking stem that would best describe their thinking at that moment.
Provide a few minutes for students to write down their thoughts using
the stem. The information can be used to provide interventions for
individuals or groups of students as well as match students with peers
who may be able to provide learning support.










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Think-Pair-Share
Three-Minute Pause
Traffic Light
Cards/Cups/Dots
64
I was successful in…
I got stuck…
I figured out…
I got confused when…so I…
I think I need to redo…
I need to rethink…
I first thought…but now I realize…
I will understand this better if I…
The hardest part of this was…
I figured it out because…
I really feel good about the way…
Think-Pair-Share is a technique that combines thinking with
communication. The teacher poses a question and gives individual
students time to think about the question. Students then pair up with a
partner to discuss their ideas. After pairs discuss, students share their
ideas in a small-group or whole-class discussion. (Kagan)
NOTE: Varying student pairs ensures diverse peer interactions.
Three-Minute Pause provides a break during a block of instruction in
order to provide time for students to summarize, clarify, and reflect on
their understanding through discussion with a partner or small group.
When three minutes are up, students stop talking and direct their
attention once again to the teacher, video, lesson, or reading they are
engaged in, and the lesson resumes. Anything left unresolved is
recorded after the time runs out and saved for the final three-minute
pause at the end.
Traffic Light Cards/Cups/Dots is a monitoring strategy that can be used
at any time during instruction to help teachers gauge student
understanding. The colors indicate whether students have full, partial,
or minimal understanding. Students are given three different-colored
cards, cups, or dots to display as a form of self-assessment revealing
their level of understanding about the concept or skill they are learning.
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Name
Two-Minute Paper
Two Stars and a Wish
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Two-Minute Paper is a quick way to collect feedback from students
about their learning at the end of an activity, field trip, lecture, video, or
other type of learning experience. Teacher writes two questions on the
board or on a chart to which students respond in two minutes.
Responses are analyzed and results are shared with students the
following day.




What was the most important thing you learned
today?
What did you learn today that you didn’t know
before?
What important question remains unanswered
for you?
What would help you learn better tomorrow?
Two Stars and a Wish is a way to balance positive and corrective
feedback. The first sentence describes two positive commendations for
the student’s work. The second sentence provides one
recommendation for revision. This strategy could be used teacher-tostudent or student-to-student.
Two-Thirds Testing provides an opportunity for students to take an
ungraded “practice test” two thirds of the way through a unit. It helps to
identify areas of difficulty or misunderstanding through an instructional
unit so that interventions and support can be provided to help them learn
and be prepared for a final summative assessment. Working on the test
through discussions with a partner or in a small group further develops
and solidifies conceptual understanding.
Two-Thirds Testing
65
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
Name
What Are You Doing
and Why?
Whiteboarding
3-2-1
66
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
What Are You Doing and Why? is a short, simple monitoring strategy to
determine if students understand the purpose of the activity or how it will
help them learn. At any point in an activity the teacher gets the students’
attention and asks “What are you doing and why are you doing it?”
Responses can be shared with the class, discussed between partners,
or recorded in writing as a One-Minute Paper to be passed in to the
teacher. The data are analyzed by the teacher to determine if the class
understands the purpose of the activity they are involved in.
Whiteboarding is a technique used in small groups to encourage
students to pool their individual thinking and come to a group consensus
on an idea that is shared with the teacher and the whole class. Students
work collaboratively around the whiteboard during class discussion to
communicate their ideas to their peers and the teacher.
Scenario: Students are decomposing a fraction
into the sum of two or more of its parts.
3-2-1 is a technique that provides a structured way for students to reflect
upon their learning. Students respond in writing to three reflective
prompts. This technique allows students to identify and share their
successes, challenges, and questions for future learning. Teachers
have the flexibility to select reflective prompts that will provide them with
the most relevant information for data-driven decision making.
Sample 1
Volusia County Schools
Mathematics Department
3
8
=
1
8
+
1
8
+
1
3
8
8
=
2
8
+
1
3
8
8
=
3
8
+
0
8
Teacher stops students in their tracks and asks,
“What are you do and why are you doing it?”
http://www.educationworl
d.com/a_lesson/02/lp251
-01.shtml


3 – Three key ideas I will remember
2 – Two things I am still struggling with
1 – One thing that will help me tomorrow

Sample 2
Grade 3 Math Curriculum Map
May 2016
Intervention/Remediation Guide
Resource
Location
Math Diagnosis and
Intervention Lessons
(Student and Teacher pages) Intervention System
Description
Use for pre-requisite skills or remediation. For grades K-2, the
lessons consist of a teacher-directed activity followed by
problems. In grades 3-5, the student will first answer a series of
questions that guide him or her to the correct answer of a given
problem, followed by additional, but similar problems.
Meeting Individual Needs
Planning section of each
Topic in the enVision Math
Teacher’s Edition
Provides topic-specific considerations and activities for
differentiated instruction of ELL, ESE, Below-Level and
Advanced students.
Differentiated Instruction
Close/Assess and
Differentiate step of each
Lesson in the enVision
Math Teacher’s Edition
Provides lesson-specific activities for differentiated instruction for
Intervention, On-Level and Advanced levels.
Error Intervention
Guided Practice step of
each Lesson in the
enVision Math Teacher’s
Edition
Provides on-the-spot suggestions for corrective instruction.
ELL Companion Lesson
Florida Interactive Lesson
Support for English
Language Learners
Includes short hands-on lessons designed to provide support for
teachers and their ELL students, useful for struggling students
as well
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Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016
GLOSSARY OF TERMS
The Mathematics Curriculum Map has been developed by teachers for ease of use during instructional planning.
Definitions for the framework of the curriculum map components are defined below.
Pacing: the recommended timeline determined by teacher committee for initial delivery of instruction in preparation for state assessments
Domain: the broadest organizational structure used to group content and concepts within the curriculum map
Cluster: a substructure of related standards; standards from different clusters may sometimes be closely related because mathematics is a
connected subject
Standard: what students should understand and be able to do
Learning Targets/Skills: the content knowledge, processes, and behaviors students should exhibit for mastery of the standards
Hints: additional information that serves to further clarify the expectations of the learning targets/skills to assist with instructional decision-making
processes
Vocabulary: the content vocabulary and other key terms and phrases that support mastery of the learning targets and skills; for teacher and
student use alike
Standards for Mathematical Practice: processes and proficiencies that teachers should seek to purposefully develop in students
Resource Alignment: a listing of available, high quality and appropriate materials, strategies, lessons, textbooks, videos and other media sources
that are aligned with the learning targets and skills; recommendations are not intended to limit lesson development
Common Addition and Subtraction/Multiplication and Division Situations: a comprehensive display of possible addition, subtraction,
multiplication and division problem solving situations that involve an unknown number in varied locations within an equation
Formative Assessment Strategies: a collection of assessment strategies/techniques to help teachers discover student thinking, determine
student understanding, and design learning opportunities that will deepen student mastery of standards
Intervention/Remediation Guide: a description of resources available within the adopted mathematics textbook resource (enVisionMATH) that
provides differentiated support for struggling learners—ESE, ELL, and General Education students alike
68
Volusia County Schools
Mathematics Department
Grade 3 Math Curriculum Map
May 2016