2016 – 2017
Second Grade
MATHEMATICS
Curriculum Map
Volusia County Schools
Mathematics Florida Standards
0
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2015
0
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2015
Table of Contents
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
Critical Areas for Mathematics in Grade 2……………………………....…2
Mathematics Florida Standards: Grade 2 Overview……………….….....3
Standards for Mathematical Practice ……………………………..…….....4
Common Addition and Subtraction Situations…………………..….……5
Common Strategies…………………………………………………….…..….6
5E Learning Cycle: An Instructional Model…………………………...….8
Instructional Math Block………………………………………….………......9
Units
A. Unit 1 ……………………………………………...………………..…....10
B. Unit 2 ……………………………..…………….……………………......19
C. Unit 3 …………………...…………………………………………..…....25
D. Unit 4 .……..………………………………………………………..…....34
IX. Appendices
Appendix A: Formative Assessment Strategies ……………………….....45
Appendix B: Intervention/Remediation Guide… ……………………….…55
X. Glossary of Terms for the Mathematics Curriculum Map…………......56
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Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Critical Areas for Mathematics in Grade 2
In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of
base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of
measure; and (4) describing and analyzing shapes.
(1) Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens,
and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including
comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing
that digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds +
5 tens + 3 ones).
(2) Student use their understanding of addition to develop fluency with addition and subtraction within 100.
They solve problems within 1000 by applying their understanding of models for addition and subtraction, and
they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and
differences of whole numbers in base-ten notation, using their understanding of place value and the
properties of operations. They select and accurately apply methods that are appropriate for the context and
the numbers involved to mentally calculate sums and differences for numbers with only tens or only
hundreds.
(3) Students recognize the need for standard units of measure (i.e., centimeter and inch) and they use rulers
and other measurement tools with the understanding that linear measure involves an iteration of units. They
recognize that the smaller the unit, the more iterations they need to cover a given length.
(4) Students describe and analyze shapes by examining their sides and angles. Students investigate, describe,
and reason about decomposing and combining shapes to make other shapes. Through building, drawing,
and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area,
volume, congruence, similarity, and symmetry in later grades.
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Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Grade 2 Overview
Domain: Operations and Algebraic Thinking
Cluster 1: Represent and solve problems involving addition and subtraction.
Cluster 2: Add and subtract within 20.
Cluster 3: Work with equal groups of objects to gain foundations for multiplication.
Domain: Number and Operations in Base Ten
Cluster 1: Understand place value.
Cluster 2: Use place value understanding and properties of operations to add and subtract.
Domain: Measurement and Data
Cluster 1: Measure and estimate lengths in standard units.
Cluster 2: Relate addition and subtraction to length.
Cluster 3: Work with time and money.
Cluster 4: Represent and interpret data.
Domain: Geometry
Cluster 1: Reason with shapes and their attributes.
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Volusia County Schools
Mathematics Department
Grade 2 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 2 examine problems (tasks), can make sense of the meaning of the task and find an entry point or a way to start the task. Grade 2 students also develop
a foundation for problem solving strategies and become independently proficient on using those strategies to solve new tasks. In Grade 2, students’ work still relies on concrete manipulatives and
pictorial representations as students solve tasks unless it refers to the word fluently, which denotes mental mathematics. Grade 2 students also are expected to persevere while solving tasks; that is,
if students reach a point in which they are stuck, they can reexamine the task in a different way and continue to solve the task. Lastly, mathematically proficient students complete a task by asking
themselves the question, “Does my answer make sense?”
Standards for Mathematical Practice
2. Reason abstractly and quantitatively. (SMP.2)
Mathematically proficient students in Grade 2 make sense of quantities and the relationships while solving tasks. This involves two processes- decontexualizing and contextualizing. In Grade 2,
students represent situations by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 25 children in the cafeteria and they are joined by 17 more children. Then, if
19 of those children then leave, how many are still there?” Grade 2 students are expected to translate that situation into the equation: 25 + 17 – 19 = __ and then solve the task. Students also
contextualize situations during the problem solving process.
3. Construct viable arguments and critique the reasoning of others. (SMP.3)
Mathematically proficient students in Grade 2 accurately use definitions and previously established solutions to construct viable arguments about mathematics. In Grade 2 during discussions about
problem solving strategies, students constructively critique the strategies and reasoning of their classmates. For example, while solving 74 + 18 – 37, students may use a variety of strategies, and
after working on the task, can discuss and critique each other’s reasoning and strategies, citing similarities and differences between strategies.
4. Model with mathematics. (SMP.4)
Mathematically proficient students in Grade 2 model real-life mathematical situations with a number sentence or an equation, and check to make sure that their equation accurately matches the
problem context. Grade 2 students still will rely on concrete manipulatives and pictorial representations while solving problems, but the expectation is that they will also write an equation to model
problem situations. Likewise, Grade 2 students are expected to create an appropriate problem situation from an equation. For example, students are expected to create a story problem for the
equation 24 + 17 – 13 = ___.
5. Use appropriate tools strategically. (SMP.5)
Mathematically proficient students in Grade 2 have access to and use tools appropriately. These tools may include place value (base ten) blocks, hundreds number boards, number lines, and
concrete geometric shapes (e.g., pattern blocks). Students should also have experiences with educational technologies, such as calculators and virtual manipulatives that support conceptual
understanding and higher-order thinking skills. During classroom instruction, students should have access to various mathematical tools as well as paper, and determine which tools are the most
appropriate to use. For example, while solving 28+17, students can explain why place value blocks are more appropriate than counters.
6. Attend to precision. (SMP.6)
Mathematically proficient students in Grade 2 are precise in their communication, calculations, and measurements. In all mathematical tasks, students in Grade 2 communicate clearly, using gradelevel appropriate vocabulary accurately as well as giving precise explanations and reasoning regarding their process of finding solutions. For example, while measuring objects iteratively
(repetitively), students check to make sure that there are no gaps or overlaps. During tasks involving number sense, students check their work to ensure the accuracy and reasonableness of
solutions.
7. Look for and make use of structure. (SMP.7)
Mathematically proficient students in Grade 2 carefully look for patterns and structures in the number system and other areas of mathematics. While solving addition and subtraction problems
students can apply the patterns of the number system to skip count by 10s off the decade. For example, Grade 2 students are expected to mentally reason that 33 + 21 is 33 plus 2 tens, which
equals 53 and then an addition one which equals 54. While working in the Numbers in Base Ten domain, students work with the idea that 10 ones equals ten, and 10 tens equals 1 hundred.
8. Look for and express regularity in repeated reasoning. (SMP.8)
Mathematically proficient students in Grade 2 begin to look for regularity in problem structures when solving mathematical tasks. For example, after solving two digit addition problems by
decomposing numbers by place (33+ 25 = 30 + 20 + 3 + 5), students may begin to generalize and frequently apply that strategy independently on future tasks. Further, students begin to look for
strategies to be more efficient in computations, including doubles strategies and making a ten. Lastly, while solving all tasks, Grade 2 students accurately check for the reasonableness of their
solutions during, and after completing the task.
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Volusia County Schools
Mathematics Department
Grade 2 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
Three red apples and two green apples are
on the table. How many apples are on the
table?
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
Difference Unknown
Bigger Unknown
Smaller Unknown
(“How many more?” version):
(Version with “more”):
(Version with “more”):
3+2=?
Lucy has two apples. Julie has five apples.
How many more apples does Julie have
than Lucy?
(“How many fewer?” version):
Julie has 3 more apples than Lucy. Lucy
has two apples. How many apples does
Julie have?
(Version with “fewer”):
Julie has three more apples than Lucy. Julie
has five apples. How many apples does
Lucy have?
(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.
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Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Addition Strategies
Name
Counting All
Counting On
Clarification
 student counts every number
 students are not yet able to add on from either addend, they must mentally
build every number
 transitional strategy
 student starts with 1 number and counts on from this point
 student recalls sums for many doubles
 student uses fluency with ten to add quickly
8 + (8 + 1)
(8 + 8) + 1
16 + 1= 17
8+9
Making Tens
Compensation
Breaking Each Number into its
Place Value
Adding Up in Chunks
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
8+9
Doubles/Near Doubles
Making Friendly Numbers/
Landmark Numbers
Student Work Sample
8+9
 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
 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
 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
 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
(7 +1) + 9
7 + (1 + 9)
7 + 10 = 17
23 + 48
23 + (48 + 2)
23 + 50= 73
73 – 2 = 71
8+6
8-1=7 6+1=7
7+7=14
24 + 38
(20 + 4) + (30 + 8)
20 + 30 = 50
4 + 8 = 12
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.
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Volusia County Schools
Mathematics Department
Grade 2 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.
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Volusia County Schools
Mathematics Department
Grade 2 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
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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 2 Math Curriculum Map
May 2016
Elementary Instructional Math Block
Time
5
minutes
Components
Opening:
Hook/Warm-up
(engage/explore)
Description
Teachers will engage students to create interest for the whole group
mini lesson or to review previous learning targets by posing a
hands-on minds-on 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.
5
minutes
Closure:
Summarize
(explain/evaluate)
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.
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.
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Volusia County Schools
Mathematics Department
Grade 2 Math CurriculumGrade
Map 2
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: Number and Operations in Base Ten
Operations and Algebraic Thinking
Pacing: Weeks 1-8
August 15 – October 7
Learning Targets
Standards
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones: e.g., 706 equals 7 hundreds, 0 tens, and 6
ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens – called a “hundred.”
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900, refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0
tens and 0 ones).
MAFS.2.NBT.1.1
Students will:
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identify the digit of a number to 999 that corresponds with a given place value with concrete materials and pictorial
representations.
represent the amount of a digit (i.e., 1-9 and 0) in a multi-digit numeral by its position within the number with models, words,
and numerals.
E.g.,
What is the amount of the underlined digit in 654? Answer: 600, or 6 hundreds
What is the amount of the underlined digit in 301? Answer: 0, or 0 tens
represent a hundred as ten groups of ten.
create bundles of 100s with or without leftovers using base ten blocks, cubes in towers of ten, and/or ten frames.
express a number up to 999 using place value in multiple ways.
Vocabulary
amount
base-ten numerals
bundles
decompose
digit
expanded form
hundreds flat
multi-digit
number line
number names
numeral
ones - unit
place value blocks
recompose
tens rod
E.g., 243 can be expressed in the following ways:
o 2 hundreds, 4 tens, 3 ones (i.e., 2 groups of hundred, 4 groups of ten, 3 ones)
o 2 hundreds, 43 ones (i.e., 2 groups of hundred, 43 ones)
o 24 tens, 3 ones (i.e., 24 groups of ten, 3 ones)
o 243 ones
E.g., 706 can be modeled with base ten blocks in the following ways:
7 hundreds and 6 ones
6 hundreds, 10 tens, and 6 ones
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Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2015
Count within 1000; skip-count by 5s, 10s, and 100s.
MAFS.2.NBT.1.2
count backward
count forward
count on/count back
fives
hundred chart
hundreds
number
number line
ones
tens
MAFS.2.NBT.1.3
base-ten numerals
decompose
digit
expanded form
hundreds flat
number line
number names/
word form
ones- unit
place value blocks/
base-ten blocks
recompose
tens rod
Students will:
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count forward and backward by ones from any given number up to 999.
identify missing numbers in a sequence on a number line, hundred chart, tape measure, etc.
E.g.,
346 347 348
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?
?
?
352
353 354 355
356
357
count forward and backward by fives, tens and hundreds from any given number up to 999.
HINT: Use a hundred chart to support this learning target.
E.g.,
Counting forward by tens starting with 23: “23, 33, 43…”
Counting backward by hundred starting with 825: “825, 725, 625, 525...”
Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Students will:
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read and write numbers using base-ten numerals (i.e., standard form) and number names (word form) through 999.
E.g., Standard form shows how to write numbers using the digits 0-9.
(e.g., eight hundred ninety-nine would be 899).
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model a number up to 999 in expanded form using appropriate tools (place value blocks, other concrete materials, or pictorial
representations).
write a number up to 999 in expanded form.
E.g., 328 is modeled concretely and numerically in expanded form below.
hundreds
300
11
tens
+
Volusia County Schools
Mathematics Department
20
ones
+
5
Grade 2 Math Curriculum Map
May 2016
Compare two three-digit numbers based on meanings of the hundreds, tens and ones digits, using >, =, and < symbols to record the results of
comparisons.
MAFS.2.NBT.1.4
Students will:


construct and communicate a comparison of two numbers up to 999 using place value blocks.
explain a process for determining whether a three-digit number is greater than, less than, or equal to another three-digit number.
HINT: Revisit analyzing and discussing a digit’s position and how it affects value.
E.g., 452 ___ 455
Student 1
452 has 4 hundreds 5 tens and 2 ones.
455 has 4 hundreds 5 tens and 5 ones.
They have the same number of
hundreds and the same number of tens,
but 455 has 5 ones and 452 only has 2
ones. 452 is less than 455.
452 < 455
Student 2
452 is less than 455. I know this
because when I count forward I say
452 before I say 455.
amount
digit
equal to (=)
greater than (>)
greatest
least
less than (<)
more than
most
place value blocks/
base ten blocks
same as/same value
HINT: Students should have ample experiences communicating their comparisons in words before using only symbols.
Comparative language includes but is not limited to:
more than, less than, greater than, most, greatest, least, same as, and equal to.


compare two numbers up to 999 using symbols, >, <, and =.
compare the magnitude of numbers by understanding the amount of the hundreds, tens, and ones digits.
12
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
MAFS.2.OA.2.2
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
Students will:
HINT: By the end of the year, students will know from memory all sums of two 1 digit numbers.

use a variety of visual tools (e.g., ten frame, number line, hundreds chart) to add or subtract numbers within 20.
E.g.,
14 – 5
7
15
8
15
9
10
11 12
13
+5
14
+4
5 + ___ = 14
4 5
6 7 8
9 10 11 12 13 14 15
HINTS: Students need to understand what the arrows mean on the ends of the number line. Numbers continue to count forward
or count backward beyond the numbers listed on the number line even though they cannot be seen.



add
addend
addition (+)
decompose
difference
double ten frame
doubles
equation
equivalent
hundred chart
inverse relationship
joining
number line
related facts
subtract
subtraction (-)
sum
ten frame
draw a visual representation of tools to add or subtract within 20.
apply different mental strategies to calculate with efficiency within 20 (e.g., count on, make tens, decompose a number leading to
a ten, fact families, doubles, doubles plus one, and the commutative and associative properties).
represent the inverse relationship between addition and subtraction.
E.g.,
Addition
For the addition equation 3 + 7 = 10,
the following equations are also true:
10 – 3 = 7 and 3 = 10 – 7.

Subtraction
For the subtraction equation 10 – 3 = 7,
the following equations are also true:
3 + 7 = 10 and 10 = 7 + 3.
recall, with fluency, basic addition facts with the addends zero through nine and the related subtraction facts.
HINTS: Fluency is knowing how a number can be composed and decomposed and using that information to be
flexible and efficient.
Research indicates that teachers can best support students’ memorization of sums and differences through
varied experiences such as, making 10, breaking numbers apart and working on mental strategies,
rather than repetitive timed tests.
Refer to pages 6-7 in the Grade 2 Mathematics Curriculum Map for clarification of Addition and Subtraction Strategies.
13
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an
equation to express an even number as a sum of two equal addends.
MAFS.2.OA.3.3
Students will:

show and explain how to pair manipulatives to demonstrate odd and even numbers (e.g. counters, cubes, tiles, etc).
E.g.,
decompose
doubles
equal addends
equal groups
equation
even
odd
sum
9 is odd because groups of 2 can be made with 1 leftover.

show and explain how an even number can be separated into two equal groups (without altering one of the objects) while an
odd number cannot be separated into two equal groups.
E.g.,
9 is odd because two equal groups cannot be made
(without altering one of the objects).

write an equation to express an even number as a sum of two equal addends, also known as doubles
(e.g., 10 = 5 + 5, 16 = 8 + 8).

identify numbers as odd or even and explain why.
HINT: After exploring odd and even numbers in a variety of ways, students should recognize that any number with a 0, 2, 4, 6, or
8 in the ones place is an even number.
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.
MAFS.2.NBT.2.8
Explain why addition and subtraction strategies work, using place value and the properties of operations.
MAFS.2.NBT.2.9
Students will:

mentally add and subtract 10 or 100 up to 900 using a variety of strategies.

apply their knowledge of place value to explain why mental math addition or subtraction strategies work.
E.g., Solve 10 + 47 and explain the strategy that you used.
ten
hundred
mental math
HINT: Refer to pages 6-7 in the Grade 2 Mathematics Curriculum Map for clarification of Addition and Subtraction Strategies.
14
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 1 Suggested Instructional Resources
MAFS
AIMS
Base-ic
Buildings
Lakeshore
Teacher Guide, pp. 7-10
Reproducibles pp. 3 – 7
NBT.1.1
Daily Math Practice
Journal pp. 22, 24, 25,
26, 28, 29
Pick A Problem Math
Warm Ups
Giant Magnetic Place
Value Blocks
MFAS
Can You Write the
Number?
How Many Hundreds, Tens,
and Ones?
Modeling Numbers with
Base Ten Blocks
Showing One Hundred
Equals Ten Tens
NBT.1.2
Counting Backward
Reproducibles pp. 8 –
13
Counting by Fives Within
1000
Daily Math Practice
Journal pp. 23, 24, 28,
31, 34, 38,
40
Counting by Ones Within
1000
Giant Magnetic Place
Value Blocks
www.k5mathteachingresources.com
NBT.1
www.IXL.com/signin/volusia
O.1, M.1, M.2, M.4, M.5, M.7,
M.8, M.10, M.13, M.15
www.cpalms.org
And the Number Is
Bundles and Combos
Hundreds, Tens, and Ones! Oh
My!
Place Value-3 digit Numbers
The Base Ten Block Shuffle
https://learnzillion.com
Unit 6
Lesson 1: Explore how many
bundles are in 100
Lesson 6: Use base ten
riddles
13-2
SE,POD,A&R
https://hcpss.instructure.com
/courses/106
NBT.1 Lessons
NBT.1 Formatives
Discovery Can: Place
Value
Teacher Guide, p. 10
Pick A Problem Math
Warm Ups
enVision
http://achievethecore.org
Whole Number Place
Value Magnets
Puzzling
Number
Patterns
Internet
Counting by Tens and
Hundreds Within 1000
www.k5mathteachingresources.com
NBT.2
www.IXL.com/signin/volusia
A.1, A.2, A.3, A.4, A.5, A.11,
A.12, A.13, A.14
www.cpalms.org
Skip Count by 10s and 100s
Skip Count by 5s
https://learnzillion.com
Unit 6
Lesson 3: Use skip counting
to order class party supplies
https://hcpss.instructure.com
/courses/106
NBT.2 Lessons
NBT.2 Formatives
13-1 RMC
13-5
SE,RMC
13-6A
Unit 8
Lesson 1: Add and subtract
10s and 100s mentally
http://achievethecore.org
Whole Number Place
Value Magnets
Discovery Can: Place
Value
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
15
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 1 Suggested Instructional Resources
MAFS
AIMS
NBT.1.3
Base-ic
Buildings
Lakeshore
MFAS
Teacher Guide, p. 10
Reading Numerals to 1000
Reproducibles pp. 8 –
13
Writing Numerals From
Expanded Form
Daily Math Practice
Journal pp. 22, 24, 30,
35
Writing Numerals From
Number Names
Pick A Problem Math
Warm Ups
Writing the Expanded Form
of a Number
Giant Magnetic Place
Value Blocks
Whole Number Place
Value Magnets
Dealing with
Digits
Discovery Can: Place
Value
Teacher Guide, pp. 12 14
Reproducibles pp. 14-16
Daily Math Practice
Journal pp. 25, 26, 32,
34, 36, 40
NBT.1.4
Pick A Problem Math
Warm Ups
Giant Magnetic Place
Value Blocks
Giant Magnetic Numbers
& Operations Kit
Inequalities Using Symbols
Missing Digits
Using Digits
Who Has More?
Internet
www.k5mathteachingresources.com
NBT.3
www.cpalms.org
Reading and Writing Number
Names
Different Ways to Represent 3digit Numbers
enVision
www.IXL.com/signin/volusia
M.13, C.3, C.4
https://learnzillion.com
Unit 6
Lesson 8: Represent 3 digit
numbers
Lesson 9: Use number
representations
https://hcpss.instructure.com
/courses/106
NBT.3 Lessons
NBT.3 Formatives
http://achievethecore.org
www.k5mathteachingresources.com
NBT.4
www.IXL.com/signin/volusia
B.1, B.2
www.cpalms.org
Less Than, Equal To, or
Greater Than?
How Can
You Compare Two 3-Digit
Numbers?
Symbol Spin
https://hcpss.instructure.com
/courses/106
NBT.4 Lessons
NBT.4 Formatives
13-3 SE,
RMC,POD,
A&R
13-6 SE,
RMC, A&R
13-7 POD
https://learnzillion.com
Unit 7
Lesson 6: Compare 3 digit
numbers with expanded form
and base ten sketches
Lesson 9: Use number cubes
to compare 3 digit numbers
http://achievethecore.org
Whole Number Place
Value Magnets
Discovery Can: Place
Value
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 2 Math Curriculum Map
May 2016
Unit 1 Suggested Instructional Resources
MAFS
AIMS
Blackout!
Book
Teacher Guide, pp. 5 - 6
Make it Even
Saluting
Subtraction
and Addition
OA.2.2
Lakeshore
Tic Tac Ten
and Twenty
Daily Math Practice
Journal pp. 3, 4, 5, 6, 8,
10, 12, 15, 16, 17, 18,
20
Pick A Problem Math
Warm Ups
Giant Magnetic Numbers
& Operations Kit
MFAS
Addition Facts From
Memory
Fluency for Addition Within
20
Fluency for Subtraction
Within 20
Fluency with Basic Addition
Facts
Math is a Snap Addition
& Subtraction
Internet
www.k5mathteachingresources.com
OA.2
www.cpalms.org
Let’s Learn Those Facts:
Addends Pairs to 12
Let’s Learn Those Facts: Some
Special Sums
https://hcpss.instructure.com
/courses/106
OA.2 Lessons
OA.2 Formatives
enVision
www.IXL.com/signin/volusia
E.1, E.2, E.3, E.4, E.5, E.7,
E.9, E.10, E.11, E.16, F.1, F.2,
F.3, F.5, F.6, F.7, L.5, L.2, K.1,
K.2, K.3
https://learnzillion.com
Unit 15
Lesson 12: Using mental
math to determine the
difference between given
numbers
Lesson 15: Mentally create
number combinations within
20
http://achievethecore.org
Odds and
Ends
Teacher Guide, p. 6
OA.3.3
Daily Math Practice
Journal pp. 2, 4, 7, 8, 10,
12, 13, 14,
16, 18, 20
Even Numbers as the Sum
of Two Equal Addends
How Do You Know if a
Number is Even or Odd?
Is it Even or Odd?
Pick A Problem Math
Warm Ups
Giant Magnetic Numbers
& Operations Kit
Showing a Collection as
Odd or Even
www.k5mathteachingresources.com
OA.3
www.cpalms.org
Bears Odd Bears Even
“Even” and “Odd” Go on a
Picnic
Is It Odd or Even?
https://hcpss.instructure.com
/courses/106
OA.3 Lessons
OA.3 Formatives
www.IXL.com/signin/volusia
A.6, A.7, A.8, A.9, A.10, A.11
https://learnzillion.com
Unit 12
Lesson 2: Decompose
numbers to decide if a number
is even or odd
Lesson 8: Write an equation
to prove that a give number is
even or odd
1-1 RMC
1-2 SE, A&R,
RMC
1-3 SE, A&R,
RMC, POD
1-4 POD
1-5 SE, A&R,
RMC
1-7 SE, A&R
2-3 SE, A&R,
RMC
2-4 SE, A&R,
RMC
2-5 SE, A&R,
POD
2-6 SE,RMC,
POD
2-7 SE/RMC
2-8 SE/RMC
Math Start
Readers:
Elevator
Magic
9-3 SE,
RMC, A&R
Math Start
Readers:
Missing
Mittens
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 2 Math Curriculum Map
May 2016
Unit 1 Suggested Instructional Resources
AIMS
NBT.2.8
MAFS
Lakeshore
MFAS
Daily Math Practice
Journal pp. 29, 32, 36,
38, 41
Add 100 Mentally
Pick A Problem Math
Warm Ups
Mentally Subtract 100
Mentally Add 10 More
Subtract 10 Mentally
Giant Magnetic Place
Value Blocks
Discovery Can: Place
Value
Daily Math Practice
Journal pp. 37, 41
Counting Up to Subtract
Using Place Value
NBT.2.9
Pick A Problem Math
Warm Ups
Internet
www.k5mathteachingresources.com
NBT.8
www.cpalms.org
Mental Math Mania
Tic Tac Toe by Ones, Tens and
Hundreds
Hop Up, Hop Down
enVision
www.IXL.com/signin/volusia
https://learnzillion.com
Unit 8
Lesson 2: Subtract 10 and
100 from various numbers
mentally
Lesson 4: Add 10 and 100
mentally
https://hcpss.instructure.com
/courses/106
NBT.8 Lessons
NBT.8 Formatives
http://achievethecore.org
www.k5mathteachingresources.com
NBT.9
www.IXL.com/signin/volusia
www.cpalms.org
Adding the “Fast Way” Using
the Hundred Grid
Subtracting the “Fast Way”
Using the Hundred Grid
https://hcpss.instructure.com
/courses/106
NBT.9 Lessons
NBT.9 Formatives
https://learnzillion.com
Unit 8
Lesson 1: Add and subtract
10s and 100s mentally
Lesson 3: Subtract 10 and
100 mentally
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
18
Volusia County Schools
Mathematics Department
Grade 2 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: Number and Operations in Base Ten
Operations and Algebraic Thinking
PACING: Weeks 9-19
October 10 – December 20
Learning Targets
Standards
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and
subtraction.
MAFS.2.NBT.2.5
Explain why addition and subtraction strategies work, using place value and the properties of operations.
MAFS.2.NBT.2.9
Students will:

add and subtract two 2-digit numbers (within 100) efficiently and accurately (fluently), using a variety of strategies.
Vocabulary
add
hundreds
ones
place value
strategy
subtract
tens
HINT: Refer to pages 6-7 in the Grade 2 Mathematics Curriculum Map for clarification of Addition and Subtraction Strategies.
Students are expected to choose strategies that assist them in solving problems efficiently and accurately.
Depending on the task, not all strategies would be considered efficient.
The standard algorithm for addition and subtraction will be taught in fourth grade.

apply knowledge of place value and the properties of operations to explain why addition or subtraction strategies work.
HINT: Students are NOT expected to identify the properties of operations by name.

justify and explain the chosen strategy .
E.g., Solve 38 + 47 and explain the strategy that you used.
Student 1
Place Value Strategy:
I broke both 38 and 47 into
tens and ones. 3 tens plus
4 tens equals 7 tens. 8
ones plus 7 ones equal 15
ones. I then combined the
7 tens and 15 ones and got
85.
19
Volusia County Schools
Mathematics Department
Student 2
Applying the Commutative
Property, Counting On and
Decomposing a Number
Leading to Ten:
I wanted to start with 47 and
break 38 apart. I counted on
from 47 to 50. That used 3
of the number 38 leaving 35.
Then it is easy to add 50 and
35 to get 85.
Student 3
Expanded form and
Commutative Property:
I wrote the expanded form
for 38 and 47 to get
30 + 8 + 40 + 7. It is easy to
do mental math when adding
the tens. So 30 and 40
make 70. Then I added 8 to
get 78. Finally I added 7
more to get 85.
Grade 2 Math Curriculum Map
May 2016
Add up to four two-digit numbers using strategies based on place value and properties of operations.
MAFS.2.NBT.2.6
Explain why addition and subtraction strategies work, using place value and the properties of operations.
MAFS.2.NBT.2.9
Students will:

add up to four two-digit numbers using a variety of strategies.
HINT: Refer to pages 6-7 in the Grade 2 Mathematics Curriculum Map for clarification of Addition and Subtraction Strategies.


justify the strategy chosen to solve a problem and explain thinking.
apply knowledge of place value and the properties of operation to explain why addition or subtraction strategies work.
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers,
one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or
hundreds.
MAFS.2.NBT.2.7
Explain why addition and subtraction strategies work, using place value and the properties of operations.
MAFS.2.NBT.2.9
composing
decomposing
equation
expression
hundreds
mental math
ones
place value
strategies
tens
thousands
Students will:







use concrete models to add and subtract two 3-digit numbers within 1000.
use drawings to add and subtract two 3-digit numbers within 1000.
use strategies based on place value to add and subtract two 3-digit numbers within 1000.
use properties of operation to add and subtract two 3-digit numbers within 1000.
use relationship between addition and subtraction to add and subtract two 3-digit numbers within 1000.
justify the strategy chosen to solve a problem and explain thinking.
apply knowledge of place value and the properties of operation to explain why addition or subtraction strategies work.
E.g., I started at 354 and jumped 200. I landed on 554. I then made 8 jumps of 10 and landed on 634. I then jumped 6 to
land on 640. I then jumped 1 more and landed on 641. 354 + 287 = 641
20
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together,
taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to
represent the problem.
MAFS.2.OA.1.1
Students will:


understand when to use addition and/or subtraction in a word problem.
solve one-step addition and subtraction word problems (i.e., difference unknown, bigger unknown and smaller unknown) using
objects, drawings, and equations (e.g., hundreds chart, place value blocks, etc.).
HINT: Refer to pages 5 in the Grade 2 Mathematics Curriculum Map for clarification of Common Addition and Subtraction
Situations.

justify your representation of how to solve the word problem.
Determine the unknown whole number in an equation relating four or more whole numbers. For example, determine the unknown number that
makes the equation true in the equations 37 + 10 + 10 = ______ + 18, ? – 6 = 13 – 4, and 15 – 9 = 6 + 
Students will:



understand that the equal sign means “is the same value as” or “ balances”.
(1st grade learning target)
determine an unknown number in an equation.
E.g. 36 + 23 + 10 = ____ + 48
MAFS.2.OA.1.a
add
addend
addend unknown
addition
balance
bigger unknown
difference
difference unknown
equal
equation
equivalent
result unknown
change unknown
smaller unknown
start unknown
subtract
sum
symbol
total unknown
balance (s)
same value/equal
quantity
equal to
equation
unknown
symbol
determine the unknown number that makes the equation true.
HINT: An equation is a number sentence stating that two quantities are equal.
(e.g., 5 + 2 = 3 + 4, 7 = 7, 7 = 6 + 1).

complete addition and subtraction equations using a symbol to represent the unknown number in any position.
21
__ + 5 + 25 = 12 + 32
49 + 7 = ? – 25
20 – p = 24 - 12
30 + 15 = ᴥ + 20.
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
MAFS
AIMS
Composing
with Codes
Lakeshore
Teacher Guide pp. 1418
Adding Within 100 Using
Place Value
Reproducibles pp.5, 6,
17-20
Fluently Subtract Within
100
Daily Math Practice
Journal pp.
22,23,26,28,30,31,33,36
Crossing a Decade
Pick A Problem Math
Warm Ups
NBT.2.5
MFAS
Using Properties and Place
Value to Add and Subtract
Giant Magnetic Place
Value Blocks
Internet
www.k5mathteachingresources.com
NBT.5
www.IXL.com/signin/volusia
G.2, G.7, G.8, H.3, H.6, H.7,
H.8, L.8, L.11, L.12
www.cpalms.org
Adding and Subtracting on a
Hundred Chart
Is it Most Magically Magical”?
What is Your New Number
When You Add or Subtract?
https://learnzillion.com
Unit 1
Lesson 1: Adding Within 100
Using Place Value
Understanding
Lesson 4: Subtracting Within
100 Using Place Value
Understanding
https://hcpss.instructure.com
/courses/106
NBT.5 Lessons
NBT.5 Formatives
Problem Solving
Strategy Puzzle
enVision
5-1 SE,
RMC, POD
A&R
5-2 SE, RMC
A&R
5-4 SE, RMC
A&R
5-5 SE, RMC
A&R
5-7 SE, A&R
5-8 SE, A&R
5-9 SE, A&R
15-2 POD
http://achievethecore.org
Pick a Problem Math
Warm Ups
Addition & Subtraction
Strategies Instant
Learning Center
Pick A Problem Math
Warm Ups
Using Place Values
Counting Up to Subtract
www.k5mathteachingresources.com
NBT.9
NBT.2.9
www.cpalms.org
Adding the “Fast Way” using a
Hundred Grid
Subtracting the “Fast Way”
Using a Hundred Grid
www.IXL.com/signin/volusia
https://learnzillion.com
Unit 1
Lesson 3: Solve Two-digit
addition problems using place
value knowledge
Lesson 6: Solve Two-Digit
Subtraction Using Place Value
and Decomposition
https://hcpss.instructure.com
/courses/106
http://achievethecore.org
NBT.9 Lessons
NBT.9 Formatives
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
22
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
NBT.2.6
MAFS
AIMS
Base Place:
The Pluses,
Use
operation
boards with
expanded
form.
Lakeshore
Teacher Guide, p. 19
MFAS
Adding Four Two-Digit
Numbers
Reproducibles p. 21
Daily Math Practice
Journal pp. 27, 30, 33,
35,
Pick A Problem Math
Warm Ups
Adding Two Digit Numbers
Using Place Value
Adding Two Digit Numbers
Using Properties of
Operation
Andy's Book
NBT.2.7
Base Place:
The Pluses,
Use
operation
boards with
expanded
form.
Base Place:
The Minuses,
Use
operation
boards with
expanded
form.
Composing
with Codes,
Giant Magnetic Place
Value Blocks
Teacher Guide, pp. 1920
Adding Within 1,000
Mr. Ford's Money
Internet
www.k5mathteachingresources.com
NBT.6
www.cpalms.org
Alternative Addition Strategies
Toll Bridge Puzzle
https://hcpss.instructure.com
/courses/106
NBT.6 Lessons
NBT.6 Formatives
www.k5mathteachingresources.com
NBT.7
Reproducibles, p. 22
Daily Math Practice
Journal pp. 27, 32, 34,
37, 38, 39, 40
Pick A Problem Math
Warm Ups
Giant Magnetic Place
Value Blocks
Discovery Can: Place
Value
Place Value Strategies for
Addition and Subtraction
Subtracting Within 1,000
www.cpalms.org
Pirate Party! – Let’s Make a
Ten
Roll and Add
Three Digit Numbers
How Much Do We Need to
Order?
Strategy-Based Instruction in 3
Digit Subtraction
enVision
www.IXL.com/signin/volusia
https://learnzillion.com
Unit 11
Lesson 13: Adding Three and
Four Two-Digit Addends Using
Various Strategies
Lesson 14: Practicing Finding
the Sum of Problems with Four
Two-Digit Addends
http://achievethecore.org
www.IXL.com/signin/volusia
https://learnzillion.com
Unit 11
Lesson 4 & 5: Three-digit
Addition with Regrouping
Lesson 7 & 9: Three-digit
Subtraction with Regrouping
15-1 SE,
RMC,A&R
15-2 SE,
RMC,A&R
16-1 SE,
RMC,A&R
POD
16-2 SE,
RMC,A&R
http://achievethecore.org
https://hcpss.instructure.com
/courses/106
NBT.7 Lessons
NBT.7 Formatives
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
23
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 2 Suggested Instructional Resources
MAFS
AIMS
Pond
Problems
OA.1.1
(one step word problems)
Pound
Pooches
Safari Sums
and
Differences
Lakeshore
Teacher Guide, pp. 3-4
Daily Math Practice
Journal pp. 2, 3, 4, 5, 7,
8, 9, 11, 13,
14, 15, 17, 18, 19, 20,
21
Pick A Problem Math
Warm Ups
Pick a Problem Math
Warm Ups
Monkey Math Balance
Giant Magnetic Number
& Operation Kit
OA.1.a
Pond
Problems
Saluting
Subtraction
and Addition
MFAS
Add to and Take From
(Start Unknown)
Word Problems with the
Result Unknown
Compare (Bigger Unknown)
Word Problems
Compare (Smaller
Unknown) Word Problems
Both Addends Unknown
How Many More and How
Many Fewer?
enVision
www.k5mathteachingresources.com
OA.1
www.IXL.com/signin/volusia
E.12, E.14, E.18, E.20, F.9,
F.11, H.9, H.11, L.3, L.9
www.cpalms.org
Are Your Numbers Equal to My
Numbers?
Let’s Do Some Solving
Math Doctor: Which Operation?
Words and Subtraction
https://learnzillion.com
Unit 1
Lesson 7: Finding Unknown
Values in Addition and
Subtraction Situations
http://achievethecore.org
https://hcpss.instructure.com
/courses/106
OA.1 Lessons
OA.1 Formatives
One, Two, Three Problems
to Solve
Math is a Snap Addition
& Subtraction
Pick A Problem Math
Warm Ups
What Number Makes the
Equation True?
Addition & Subtraction
Math is a Snap
Determine the Missing
Addend
Monkey Math
Relating Four Whole
Numbers
Giant Magnetic Numbers
& Operations
Internet
www.cpalms.org
Into the Unknown…
The Mystery of the Missing
Number
Creating a Balanced Equation
www.IXL.com/signin/volusia
F.12, E.15, H.12, G.12, L.10
https://learnzillion.com
Unit 1
Lesson 10: Solve Math
Stories by Identifying
Unknowns
1-7 POD
9-12 SE,
RMC,A&R
9-13 SE,
RMC,A&R
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
24
Volusia County Schools
Mathematics Department
Grade 2 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
Operations and Algebraic Thinking
Learning Targets
PACING: Weeks 20-28
January 4 – March 3
Standards
Measure the length of an object to the nearest inch, foot, centimeter, or meter by selecting and using appropriate tools such as rulers, yardsticks, meter
sticks, and measuring tapes.
MAFS.2.MD.1.1
Estimate lengths using units of inches, feet, yards, centimeters, and meters.
MAFS.2.MD.1.3
Vocabulary
benchmark
centimeter
Students will:
customary
estimate
 describe attributes of a standard linear measurement tool (e.g., inch ruler, centimeter ruler, yardstick, meter stick, measuring
foot
tapes) such as: equally spaced numbers, consecutive numbers (0, 1, 2, …), equally spaced markings between numbers,
inch
awareness of where the zero is located (i.e., the most appropriate place to begin measuring an object).
length
 understand that length tells how long, how tall, or how wide something is.
measure
 select an appropriate tool to measure the length of an object provided by the teacher.
measuring tape
meter
HINT: Select objects that have an exact whole number measurement when beginning this instruction.
meter stick
 measure and record the length of various objects provided by the teacher to the nearest inch, foot, centimeter, or meter (from any metric units
ruler
given number).
standard
units
HINT: Students must also be able to use appropriate abbreviations for inches (in), feet (ft), yards (yd), centimeters (cm),
yard
and meters (m).
yardstick
Students will:

discover useful benchmarks for the following measurements: inch, foot, yard, centimeter, and meter.
HINT: Students should be given the opportunity to find their own meaningful benchmarks.
E.g., The length from an adult’s elbow to wrist is about 1 foot.



estimate a reasonable length for a given object visually after seeing a benchmark unit.
estimate length using inch, foot, yard, centimeter, or meters. E.g., Is a book 8 inches or 8 feet long?
justify the reasoning for the estimate.
HINT: Students are NOT expected to convert units until 4th grade.
25
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Describe the inverse relationship between the size of a unit and number of units needed to measure a given object. E.g., Suppose the perimeter of a
room is lined with one-foot rulers. Now, suppose we want to line it with yardsticks instead of rulers. Will we need more or fewer yardsticks than rulers to
do the job? Explain your answer.
MAFS.2.MD.1.2
Students will:



discover what happens when different standard units are used to measure the same object (e.g., inches versus feet to measure a
desk).
explain that as the size of a unit increases, the number of units needed to measure an object decreases and vice versa (e.g., It
takes a greater number of inches than feet to measure an object).
determine an appropriate unit of measure.
HINTS: Students should not be limited to measuring within the same system of measurement. Multiple opportunities to explore
provide the foundation for relating metric units to customary units, as well as relating within customary (i.e., inches to feet
to yards) and within metric (i.e., centimeters to meters).
Students are NOT expected to calculate perimeter in second grade.
Students are NOT expected to calculate conversions in second grade.
Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
MAFS.2.MD.1.4
centimeter
customary
difference
foot
height
inch
length
measure
meter
meter stick
metric units
ruler
standard
units
width
yard
yard stick
Students will:


find the difference in length between two objects using standard units.
describe the difference between two objects with comparative phrases
E.g., The book is longer by 2 inches. The pencil is shorter by 5 centimeters.
26
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Represent whole numbers as length from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and
represent whole-number sums and differences within 100 on a number line diagram.
MAFS.2.MD.2.6
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as
drawing of rulers) and equations with a symbol for the unknown number to represent the problem.
MAFS.2.MD.2.5
centimeter
customary
Students will:
estimate
foot
 recognize the similarities between the number line and ruler.
height
 create a number line with whole-number units that are equally spaced and relevant to the addition or subtraction problem.
inch
 create a number line using numbers within 100 to solve addition and subtraction problems
length
E.g., use notebook or grid paper to make their own number line.
measure
 represent the addition or subtraction problem on the number line using curved line segments above and between the numbers.
meter
metric units
There were 27 students on the bus. 19 got off the bus. How many students are on the bus?
E.g.,
number line
ruler
I used a number line. I started at 27. I broke up 19 into 10 and 9. That way I could take a jump of 10. I landed on 17. Then I
standard
broke up 9 up into 7 and 2. I took a jump of 7, That got me 10. Then I took a jump of 2. That’s 8. So, there are 8 students now symbol
on the bus.
measuring tape
units
width
yard
Students will:



add and subtract lengths of the same unit within 100.
represent addition and subtraction word problems involving lengths of the same unit by using diagrams and equations with a
symbol for the unknown length.
solve for the unknown number in an equation from a word problem.
E.g., In P.E. class Chloe jumped 14 inches. Caleb jumped 23 inches. How much farther did Caleb jump than Chloe? Show your
work and write an equation to solve the problem.
Student B
My equation is 23 – 14 = ___. I thought about the difference
between Chloe and Caleb. I broke up the 14 into 10 and 4. I
know that 23 minus 10 is 13. Then, I broke up the 4 into 3 and
1. 13 minus 3 is 10. Then, I took one more away. That left me
with 9. So, Caleb jumped 9 more inches than Chloe. That
seems to make sense since 23 is almost 10 more than 14.
23 – 14 = 9.
27
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking
apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem.
MAFS.2.OA.1.1
Students will:

solve two-step word problems.
E.g.,

model and represent solutions with equations for all the Common Addition and Subtraction Situations on page 5 of the Grade 2
Mathematics Curriculum Map.
solve addition or subtraction real world problems with an unknown using drawings and equations.
E.g.,

28
Volusia County Schools
Mathematics Department
add
addend
addition
difference
equal
equation
subtract
sum
Grade 2 Math Curriculum Map
May 2016
MAFS.2.MD.3.8
Solve one- and two-step word problems involving dollar bills (singles, fives, tens, twenties, and hundreds) or coins (quarters, dimes, nickels, and
pennies) using $ and ¢ symbols appropriately. Word problems may involve addition, subtraction, and equal groups situations. E.g., The cash register
shows that the total for your purchase is 59¢. You gave the cashier three quarters. How much change should you receive from the cashier?
a. Identify the value of coins and paper currency.
b. Compute the value of any combination of coins within one dollar.
c. Compute the value of any combinations of dollars (e.g., If you have three ten-dollar bills, one five-dollar bill, and two one-dollar bills, how much
money do you have?).
d. Relate the value of pennies, nickels, dimes, and quarters to other coins and to the dollar (e.g., There are five nickels in one quarter. There are
two nickels in one dime. There are two and a half dimes in one quarter. There are twenty nickels in one dollar).
Students will:





identify and name the value of coins (i.e., pennies, nickels, dimes, and quarters) and bills (e.g., $1, $5, $10, $20, $50, $100).
skip count to find the value of a group of like coins up to $1 (e.g., using nickels, dimes, or quarters).
calculate the value of mixed coins up to $1 or mixed bills up to $100 (e.g. If you have two dimes and 3 pennies, how many cents
do you have?).
use the dollar ($) and cents (¢) symbols appropriately.
model and record different combinations of coins or bills from a given amount (e.g., $10 can be one $5 bill and five $1 bills or ten $1
add
bill
cent sign (¢)
cents
change
difference
dime
dollar
dollar bill
dollar sign ($)
money
nickel
penny
quarter
sum
bills or one $10 bill or five $2 bills or two $5 bills).


represent the value of pennies, nickels, dimes and quarters to other coins (e.g., five nickels in one quarter; 25 pennies in one
quarter, two nickels in one dime).
represent the value of pennies, nickels, dimes and quarters to one dollar (e.g., 10 dimes in 1 dollar; 4 quarters in one dollar, 100
pennies in one dollar).
HINT: Since students have not been introduced to decimals, money problems should involve only dollars or cents
(NOT a combination of dollars and cents).



represent one– and two-step word problems involving dollar bills or coins with objects, pictures, charts, tables, words, and/or
numbers.
solve one- and two-step word problems involving money finding both sums and differences .
communicate their mathematical thinking and justify their answers for one-and two-step word problem involving dollar bills or
coins.
E.g.,
o Brad spends $27 for a video game and some more money on batteries. If he spends a total of $36, how much did he spend on
the batteries?
o Anna saved $23. On her birthday, she received $15. She spent $26 on a necklace. How much money does Anna have now?
o Sandra went to the store and received 76¢ in change. What are three different sets of coins she could have received?
HINT: Students should have multiple opportunities to identify, count, recognize, and use coins and bills in and out of context.
29
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
What's in
Your Yard
Lakeshore
Teacher Guide, pp. 20 21
Measuring a Segment
Longer Than 12 Inches
Daily Math Practice
Journal pp. 42, 44, 48,
52
Measuring to the Nearest
Foot
Pick A Problem Math
Warm Ups
MD.1.1
MFAS
Measuring to the Nearest
Inch and Centimeter
Rulers and Meter Sticks
Discovery Can:
Measurement
Measuring a Curve
Internet
www.k5mathteachingresources.com
MD.1
enVision
www.IXL.com/signin/volusia
S.2, S.4, S.8, S.10
www.cpalms.org
Discovering Math: Beginning
Measurement
Best Vegetable Garden
Measure Both and Find Their
Difference
https://learnzillion.com
Unit 2
Lesson 1: Exploring Two
Standard Systems of
Measurement
Lesson 5: Practice Choosing
Measurement Tools
How Long? How Wide? How
Tall? How Deep?
http://achievethecore.org
11-1 RMC
11-2 RMC
11-3 RMC
11-4 POD
https://hcpss.instructure.com
/courses/106
MD.1 Lessons
MD.1 Formatives
Inching Along
Teacher Guide, pp. 2021
Estimating in Centimeters
Estimating In Feet
MD.1.3
Daily Math Practice
Journal pp. 42, 45, 47
Pick A Problem Math
Warm Ups
Estimating In Inches
Estimating In Meters
Estimating in Yards
Discovery Can:
Measurement
www.k5mathteachingresources.com
MD.3
www.cpalms.org
Can I Make a Reasonable
Guess?
Estimating Lengths & Distances
Measuring Mania
https://hcpss.instructure.com
/courses/106
MD.3 Lessons
MD.3 Formatives
www.IXL.com/signin/volusia
S.3, S.9
https://learnzillion.com
Unit 14
Lesson 1: Understanding
Ways to Estimate Length
Lesson 3: Practice Estimating
Length in Centimeters
11-1 SE,A&R
11-2 SE,A&R
11-3 SE,A&R
11-4
SE,A&R,
RMC
11-5 SE,A&R
11-6 POD
Unit 2
Lesson 7: Measurement Hunt
http://achievethecore.org
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 2 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
What's in
Your Yard
Lakeshore
Teacher Guide, pp. 20 21
MFAS
Centimeters and Meters
Feet and Inches
MD.1.2
Daily Math Practice
Journal pp. 45, 46
Discovery Can:
Measurement
Feet and Yards
Inches and Centimeters
Teacher Guide, pp. 20 21
Comparing Zigzag
Segments
Daily Math Practice
Journal pp. 43, 44, 46,
48
Dragonflies and
Grasshoppers
MD.1.4
How Much Longer?
Pick A Problem Math
Warm Ups
Discovery Can:
Measurement
Walking Ants
Internet
www.k5mathteachingresources.com
. MD.2
www.cpalms.org
Are They the Same Length?
How Long Is It?
How Many Inches, Feet, and
Yards?
https://hcpss.instructure.com
/courses/106
MD.2 Lessons
MD.2 Formatives
www.k5mathteachingresources.com
MD.4
www.cpalms.org
Comparing Inch by Inch
Measure Both and Find Their
Difference What’s the
Difference?
https://hcpss.instructure.com
/courses/106
MD.4 Lessons
MD.4 Formatives
enVision
www.IXL.com/signin/volusia
S.9
https://learnzillion.com
Unit 2
Lesson 8: Comparing Unit
Size and Measured Length
Lesson 9: Understanding Unit
and Measurement
Relationships
http://achievethecore.org
www.IXL.com/signin/volusia
S.4, S.10
11-9A
https://learnzillion.com
Unit 14
Lesson 6: Practice Comparing
Lengths
Lesson 7: Dev’s Sculpture:
Measure Differences in Length
Lesson 8: Connect Addition
and Subtraction to Finding
Length Differences
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 2 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
Lakeshore
Daily Math Practice
Journal pp. 47, 50, 53,
54, 56, 59, 60
Pick A Problem Math
Warm Ups
MFAS
Differences on a Number
Line
Representing Nine on the
Number Line
MD.2.6
Representing Numbers with
Length
Sums on a Number Line
Internet
www.k5mathteachingresources.com
MD.6
www.cpalms.org
Get Up and Go! With Addition
and Subtraction
https://hcpss.instructure.com
/courses/106
MD.6 Lessons
MD.6 Formatives
enVision
www.IXL.com/signin/volusia
6-6A
https://learnzillion.com
Unit 3
Lesson 1: Understand that
Whole Numbers Can be
Shown as Length on a
Number Line
Lesson 2: Create and
Complete Number Lines
Lesson 3: Add and Subtract
Lengths Using a Number Line
http://achievethecore.org
Inching
Along, Triple
Challenge
Cards
Daily Math Practice
Journal pp. 43, 44, 49,
51, 54, 55, 58, 61, 63
Adding Measures
Pick A Problem Math
Warm Ups
String for Bracelets
Heading Home
MD.2.5
Subtracting Measures
Discovery Can:
Measurement
www.k5mathteachingresources.com
MD.5
www.IXL.com/signin/volusia
www.cpalms.org
Where to Locate the Bus Stop
Wilbur’s Pig Pen Addition
https://learnzillion.com
Unit 3
Lesson 5: Use number lines
to find the difference between
lengths
https://hcpss.instructure.com
/courses/106
MD.5 Lessons
MD.5 Formatives
Unit 14
Lesson 8: Connect addition
and subtraction to finding the
length difference
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 2 Math Curriculum Map
May 2016
Unit 3 Suggested Instructional Resources
MAFS
AIMS
OA.1.1
(two step word problems)
Pond
Problems
Lakeshore
Teacher Guide, pp. 3-4
Daily Math Practice
Journal pp. 2, 3, 4, 5, 7,
8, 9, 11, 13, 14, 15, 17,
18, 19, 20, 21
Pound
Pooches
Safari Sums
and
Differences
MFAS
Solving a Two-Step Word
Problem: Eating Grapes
Solving a Two-Step Word
Problem: Going Fishing
www.k5mathteachingresources.com
OA.1
www.cpalms.org
Word Problems Galore!
Pick A Problem Math
Warm Ups
Pick a Problem Math
Warm Ups
enVision
Internet
www.IXL.com/signin/volusia
Third Grade: M.11
7-7 SE
8-8 SE
https://learnzillion.com
Unit 3
Lesson 10: Using a Number
Line to Solve 2-Step Addition
and Subtraction Problems
https://hcpss.instructure.com
/courses/106
OA.1 Lessons
OA.1 Formatives
http://achievethecore.org
www.k5mathteachingresources.com
MD.8
www.IXL.com/signin/volusia
P.1, P.2, P.3, P.4, P.6, P.8,
P.10, P.12, P.14, P.16, P.17,
P.19
Monkey Math Balance
Giant Magnetic Number
& Operation Kit
Pocket
Money
Change
Confusion
Math is a Snap Addition
& Subtraction
Teacher Guide, p. 22
Daily Math Practice
Journal, pp. 48, 50, 52,
54, 56, 57,
58, 60, 62
Fifty Cents is Your Change
Ninety Nine Cents
Combinations of Bills
Combinations of Coins
MD.3.8
Pick A Problem Math
Warm Ups
Problem Solving
Strategy Puzzle
Identifying the Value of
Paper Currency
Identifying the Value of
Coins
Discovery Can: Money
Relating Coins
School Store
www.cpalms.org
It Cost HOW Much?
Coin Combinations: How else
can you pay for that?
Creative Coin Collections
A Penny Saved is a Penny
Earned..Just Ask Alexander!
Party Anyone
https://hcpss.instructure.com
/courses/106
MD.8 Lessons
MD.8 Formatives
https://learnzillion.com
Unit 5
Lesson 2: Coin Race:
Practice Combining Coins
Lesson 5: Skip Count to Show
an Amount of Money in
Different Ways
Lesson 7: Understand How to
Use Addition and Subtraction
to Solve Story Problems
4-2 SE,RMC,
A&R
4-6 SE,RMC,
A&R
4-7 SE,RMC,
A&R, POD
4-8
SE,A&R,POD
4-9 RMC
10-1 POD
10-4 POD
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
33
Volusia County Schools
Mathematics Department
Grade 2 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
Operations and Algebraic Thinking
Learning Targets
Tell and write time from analog and digital clocks to the nearest five minutes.
PACING: Weeks 29-39
March 6 – May 26
Standards
MAFS.2.MD.3.7
Students will:




apply their understanding of fractional quarters, halves and wholes (1 st grade skill) when telling time on an analog clock.
skip count by 5’s to tell time in five-minute intervals on an analog clock.
determine the time on an analog clock and write the time as it would appear on a digital clock to the hour, half-hour, and fiveminute intervals.
determine the time on a digital clock and draw in the hands on an analog clock to the hour, half-hour, and five-minute intervals.
Vocabulary
analog clock
digital
half-hour
hour
hour hand
intervals
minute hand
minutes
quarter
HINT: The minute hand indicates the minutes in between each hour. As the students experience clocks with only hour hands, they
begin to realize that when the time is two o’clock, two-fifteen, or two forty-five, the hour hand’s position is different, but still
considered “two”. Using clocks with only hour hands helps develop students’ understanding of time.
All of these clocks indicate the hour of “two”, although the hour hand’s position is different. This is an important idea for
students as they learn to tell time.
34
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
MAFS.2.MD.4.10
Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart,
and compare problems using information presented in a bar graph.
Students will:


identify the parts of a picture graph (title, categories, category label, key, and data) and bar graph (title, scale, scale label,
categories, category label, and data).
interpret and explain data on a given picture graph and bar graph to solve put together, take-apart, and compare problems.


HINT: Refer to page 5 in the Second Grade Mathematics Curriculum Map for clarification of Common Addition and Subtraction
Situations.
use tally marks to collect and organize data.
create a picture graph and bar graph (with single-unit scale) from a set of data.
HINT: Students need to create both horizontal and vertical graphs.

represent up to four categories of data on single-unit scales.
MAFS.2.MD.4.9
Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same
object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
analyze
bar graph
category
category labels
data
horizontal
horizontal scale
interpret
key
line plot
picture graph
scale
scale labels
survey
tally mark
title
vertical
Students will:
Magnolia Leaves





measure and record the lengths of several objects to the nearest whole-number.
create a line plot with a horizontal scale marked off in whole-number units.
record length measurements on a line plot.
identify the parts of a line plot.
E.g.,
HINT: Line plots are used to display numerical data
for a set number of things (linear measurement)
0
E.g., height of 10 famous basketball players
A line plot can be thought of as plotting numeric data on a number line.
This is the first introduction to this type of data display.
35
Volusia County Schools
Mathematics Department
1
X
X
X
X
X
X
X
X
X
X
X
X
X
X
2
3
4
5
6
Leaf Lengths (in inches)
Grade 2 Math Curriculum Map
May 2016
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles,
quadrilaterals, pentagons, hexagons, and cubes.
MAFS.2.G.1.1
Students will:

identify and classify two-dimensional shapes as triangles, quadrilaterals (square, rectangle, trapezoid), pentagons, and
hexagons.
Triangles
Quadrilaterals
Pentagons
Hexagons
HINT: Students need to recognize that trapezoids, squares, and rectangles (taught in Grades K and 1) all belong to the group of
quadrilaterals.


angles
cube
defining attribute
faces
hexagon
non-defining
attributes
orientation
pentagon
quadrilateral
rectangle
square
three-dimensional
trapezoid
triangle
two-dimensional
vertex/vertices
identify and classify a cube as a three-dimensional shape.
explain which attributes define a shape or group of shapes (number of sides/vertices/angles).
E.g., Triangles: three sides, three vertices, three angles
Quadrilaterals: four sides, four vertices, four angles
Cubes: six equal faces
HINT: Non-defining attributes may include, but are not limited to, color, texture, size, and orientation. Shapes should be
presented in a variety of orientations and configurations.

construct two-dimensional shapes when given defining attributes.
E.g., use geoboards, popsicle sticks, toothpicks, pencil/paper
Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Students will:


differentiate between rows and columns.
partition a given rectangle into squares of equal size by drawing rows and columns.
E.g., Split a rectangle into 2 rows and 5 columns.
There are 10 equal-sized squares in the rectangle.

determine the number of equal-sized squares that result in the partitioned rectangle.
36
Volusia County Schools
Mathematics Department
MAFS.2.G.1.2
column
equal-sized
equivalent
horizontal
orientation
partition
row
sections
shares
split
vertical
Grade 2 Math Curriculum Map
May 2016
Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the
total as a sum of equal addends.
MAFS.2.OA.3.4
Students will:



organize a group of objects into rectangular arrays with up to 5 rows and up to 5 columns (i.e., equal amounts in each row and
equal amounts in each column).
use addition to find the total number of objects in an array.
represent the total number of objects with equations showing a sum of equal addends.
addends
columns
equal addends
equation
rectangular array
repeated addends
rows
E.g., 2 + 2 + 2 + 2 = 8

solve situational problems that involve two or more equal addends (i.e., repeated addition).
E.g.,
Pam arranges 12 pennies into a rectangular array as shown below. Write an equation to represent her arrangement.
Arrangement
Equation
4 + 4 + 4 = 12
HINT: Situational problems will be limited to rectangular arrays containing no more than 5 rows and 5 columns.


identify pictorial models of rectangular array arrangements.
record pictorial models (e.g., free drawing, graph/grid paper) of rectangular array arrangements that have been constructed with
tangible objects (e.g., counters, bears, square tiles, etc.).
37
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and
describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
MAFS.2.G.1.3
Students will:

partition/divide circles and rectangles into two, three, or four equal shares.
E.g., Partition a circle into three equal shares.
HINT: This will be difficult for Grade 2 students to
do at first. A clock face can make early attempts easier.
E.g., Show four different ways to partition a rectangle into 4 equal parts.
column
divide
equal shares
equal-sized
equivalent
fourths/a fourth of
half/halves/half of
horizontal
orientation
partition
pieces/parts
row
sections
shares
split
thirds/a third of
vertical
HINT: Students can partition circles and rectangles by folding, cutting, and drawing.


describe equivalent shares using words such as halves, thirds, fourths, half of, a third of, and a fourth of.
describe a whole as two of two equal parts, three of three equal parts, four of four equal parts, two halves, three thirds,
and four fourths.
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking
apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem.
MAFS.2.OA.1.1
Students will:



choose when to use addition or subtraction in a word problem.
add or subtract to solve one and two-step word problem situations within 100 using a variety of situations and strategies.
justify and explain the strategy chosen to solve a real world problem.
add
addition
difference
equal
equation
subtract
sum
HINT: Students should have ample experiences working on various types of two-step word problems that have
unknowns in all positions from the Common Addition and Subtraction Situations located on page 5.
Addition and Subtraction Strategies may include, but are not limited to the following from pages 6 and 7.
38
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
MAFS.2.OA.2.2
Students will:


apply different mental strategies to calculate with efficiency within 20 (e.g., count on, make tens, decompose a number leading to a
ten, fact families, doubles, doubles plus one, and use the commutative and associative properties).
recall from memory all sums of two one-digit numbers.
HINT: Fluency is knowing how a number can be composed and decomposed and using that information to be flexible
and efficient.
39
Volusia County Schools
Mathematics Department
add
addend
addition (+)
difference
equation
subtract
subtraction (-)
sum
Grade 2 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
AIMS
Lakeshore
MFAS
Double Time
Teacher Guide, p. 21
A Good Night's Sleep
Time by
Fives
Daily Math Practice
Journal, pp. 42, 46, 50,
52, 56, 58,
60, 62
Tell Time
Pick A Problem Math
Warm Ups
MD.3.7
MAFS
The Clock Says
Writing Times on Digital
Clocks
Discovery Can: Time
enVision
Internet
www.k5mathteachingresources.com
MD.7
www.IXL.com/signin/volusia
Q.1, Q.2, Q.3, Q.4, Q.5, Q.6,
Q.8
www.cpalms.org
Counting on a Clock
Time! Time! Time!
Excuse Me! Can You Please
Give Me the Time?
I’m Late! Telling Time to the 5
Minute Mark
Telling Time with “Ana Log and
Dig Ital Clock
https://learnzillion.com
Unit 4
Lesson 3: Connect skip
counting and telling time to the
nearest 5 minutes
Lesson 4: Practice telling time
to the nearest 5 minutes
10-7A
Math Start
Readers:
“Game
Time!”
http://achievethecore.org
https://hcpss.instructure.com
/courses/106
MD.7 Lessons
MD.7 Formatives
MD.4.10
Tuber Talk,
Part 2 and
Part 4
Teacher Guide, p. 23
Favorite Books
Daily Math Practice
Journal, pp. 49, 53, 57,
61, 63
Features of Our Shirts
Pick A Problem Math
Warm Ups
Shoe Sizes
Data & Graphing Instant
Learning Center
Number of Players
www.k5mathteachingresources.com
MD.10
www.cpalms.org
Class Pets
Drawing and Interpreting Data
on a Bar Graph
Setting the Bar: Representing
Data Sets Picture Graph
Pizazz!
Solid Graphing
https://hcpss.instructure.com
/courses/106
MD.10 Lessons
MD.10 Formatives
www.IXL.com/signin/volusia
R.2, R.3, R.4, R.5
3-7A
3-7B
https://learnzillion.com
Unit 9
Lesson 12: Field Day TShirts: Understand that picture
and bar graphs can be used to
represent the same data
Lesson 14: Let Us Eat Fruit!
Draw bar graphs to answer
questions
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
40
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MD.4.9
MAFS
AIMS
Tuber Talk,
Use data
from Part 2 to
build a line
plot.
Lakeshore
MFAS
Daily Math Practice
Journal, pp. 51, 55, 59
Measuring Hand Spans Part One
Pick A Problem Math
Warm Ups
Measuring Hand Spans Part Two
Measuring Our Pencils Part One
Measuring Our Pencils Part Two
G.1.1
On Board
with Shapes
Shapes All
Around Us,
pg. 1-3
Teacher Guide, p. 23
Figures with Five Sides
Daily Math Practice
Journal, pp. 64, 65, 66,
67, 68, 69, 70
Four Sided Figures
Pick A Problem Math
Warm Ups
Which of These are Cubes?
Giant Magnetic Pattern
Blocks
Pattern Blocks
Playground Math
Three Sided Figures
enVision
Internet
www.k5mathteachingresources.com
MD.9
www.cpalms.org
If the Shoe Fits…
X Marks the Spot!
https://hcpss.instructure.com
/courses/106
MD.9 Lessons
MD.9 Formatives
www.k5mathteachingresources.com
G.1
www.cpalms.org
Attributes of Geometric Shapes
Discovering Attributes of
Shapes
The Greedy Shapes
https://hcpss.instructure.com
/courses/106
G.1 Lessons
G.1 Formatives
www.IXL.com/signin/volusia
11-9B
https://learnzillion.com
Unit 9
Lesson 8: Staying Sharp:
Measuring pencil length in
inches
Lesson 9: Measure ones
cubes to create a line plot
http://achievethecore.org
www.IXL.com/signin/volusia
T.1, T.2, T.4, T.6
10-8C
https://learnzillion.com
Unit 10
Lesson 1: Understand that
shapes are defined by their
sides and angles
Lesson 2: Identify
quadrilaterals
Lesson 4: Draw shapes given
certain constraints
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
41
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MAFS
AIMS
Treasure
Trove
Lakeshore
MFAS
Teacher Guide, p. 24
Complete the Rectangle
Daily Math Practice
Journal, pp. 64, 66, 68,
71
Construct Rows and
Columns
G.1.2
How Many Units?
Pick A Problem Math
Warm Ups
Partition the Rectangle Into
Unit Squares
Playground Math
Pattern Blocks
Accounting
for Butterflies
OA.3.4
Treasure
Trove
Teacher Guide, p. 7
All Your Penquins in a Row
Daily Math Practice
Journal, pp. 2, 6, 9, 11,
12, 14, 16, 19, 21
Counting an Array
Pick A Problem Math
Warm Ups
Giant Magnetic Numbers
& Operations (use
counters from set to
make arrays)
Counting by Rows and
Columns
Writing an Equal Addends
Equation
enVision
Internet
www.k5mathteachingresources.com
G.2
www.cpalms.org
Which Rectangle is Bigger?
Chocolate Pieces
https://hcpss.instructure.com
/courses/106
G.2 Lessons
G.2 Formatives
www.k5mathteachingresources.com
OA.4
www.cpalms.org
Array Addition
Hooray Arrays
I Array+You Array=Arrays!
https://hcpss.instructure.com
/courses/106
OA.4 Lessons
OA.4 Formatives
www.IXL.com/signin/volusia
10-1A
https://learnzillion.com
Unit 13
Lesson 8: Partition rectangles
into rows and columns of
same-sized squares and count
to find the total number
http://achievethecore.org
www.IXL.com/signin/volusia
E.21, E.22, E.23, E.24
4-9A
https://learnzillion.com
Unit 13
Lesson 7: Create arrays
Lesson 9: Use skip counting
with arrays
http://achievethecore.org
Pattern Blocks
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 2 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MAFS
AIMS
Lakeshore
MFAS
Folding Flags
Teacher Guide, p. 24
Different Fourths
Fresh Baked
Fractions
Daily Math Practice
Journal, pp. 64-71
Different Halves
Halves, Thirds, and Fourths
G.1.3
Pick A Problem Math
Warm Ups
How Many Fourths are in a
Whole?
Pattern Blocks
Playground Math
OA.1.1
(one and two step word problems)
Pond
Problems
Teacher Guide, pp. 3-4
Daily Math Practice
Journal pp. 2, 3, 4, 5, 7,
8, 9, 11, 13, 14, 15, 17,
18, 19, 20, 21
Pound
Pooches
Safari Sums
and
Differences
Pick A Problem Math
Warm Ups
Pick a Problem Math
Warm Ups
Monkey Math Balance
www.k5mathteachingresources.com
G.3
www.cpalms.org
Fractions Action
Thirds
https://hcpss.instructure.com
/courses/106
G.3 Lessons
G.3 Formatives
Solving a Two-Step Word
Problem: Marbles in a Bag
enVision
Internet
www.IXL.com/signin/volusia
U.1, U.2
https://learnzillion.com
Unit 10
Lesson 5: Understand that
shapes can be partitioned into
equal parts
Lesson 6: Partition shapes
10-1 SE,
RMC,A&R
10-2 POD
10-3 SE,
RMC,A&R
10-7 POD
11-2 POD
http://achievethecore.org
www.k5mathteachingresources.com
OA.1
www.IXL.com/signin/volusia
E.12, E.14, E.18, E.20, F.9,
F.11, L.3, L.9, H.9, H.11
www.cpalms.org
Success with Story ProblemsAddition/Subtraction
Amazing Animal Athletes
https://learnzillion.com
Unit 1
Lesson 10: Solve math stories
by identifying unknowns
https://hcpss.instructure.com
/courses/106
OA.1 Lessons
OA.1 Formatives
Unit 15
Lesson 9: Create addition and
subtraction word problems
http://achievethecore.org
Giant Magnetic Number
& Operation Kit
Math is a Snap Addition
& Subtraction
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 2 Math Curriculum Map
May 2016
Unit 4 Suggested Instructional Resources
MAFS
AIMS
Blackout!
Book
Teacher Guide, pp.5-6
Make it Even
OA.2.2
Lakeshore
Saluting
Subtraction
and Addition
Tic Tac Ten
and Twenty
Daily Math Practice
Journal, pp. 3, 4, 5, 6, 8,
10, 12, 15,
16, 17, 18, 20
Pick A Problem Math
Warm Ups
Math Is A Snap Addition
& Subtraction
Giant Magnetic Number
& Operation Kit
MFAS
Addition Facts From
Memory
Fluency for Addition Within
20
Fluency for Subtraction
Within 20
Fluency with Basic Addition
Facts
enVision
Internet
www.k5mathteachingresources.com
OA.2
www.cpalms.org
Piece of Cake Mental Math
Show It Another Way
Number Facts Bingo
https://hcpss.instructure.com
/courses/106
OA.2 Lessons
OA.2 Formatives
www.IXL.com/signin/volusia
E.1, E.2, E.3, E.4, E.5, E.9,
E.10, E.11, E.16, F.1, F.2, F.3,
F.5, F.6, F.7, L.5, L.2, L.3, K.1,
K.2, K.3
https://learnzillion.com
Unit 15
Lesson 11: Fluently add and
subtract within 20 using mental
strategies
Lesson 14: Apply strategies to
add/subtract numbers mentally
1-1 RMC
1-2 RMC
1-3 RMC
1-5 RMC
2-3 RMC
2-4 RMC
2-6 RMC
2-7 RMC
2-8 RMC
http://achievethecore.org
enVisionMATH: SE = Student Edition; RMC= Ready-Made Centers; POD= Problem of the Day; A&R = Assessment and Reteaching Workbook
44
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Formative Assessment Strategies
Mathematics K-5
Name
Description
A & D Statements
Agreement Circles
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.
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.
Annotated Student
Drawings
http://formativeassessment.barrow.wikispaces.net/A
nnotated+Student+Drawings
45
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
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
46
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
Concept Cartoons
Four corners
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
47
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.
Examples
• square
• rectangle
• trapezoid
• rhombus
Facts/characteristics
•4 sides
• may or may not be of equal
length
• sides may or may not be
parallel
Quadrilateral
Nonexamples
• circle
• triangle
• pentagon
• dodecahedron
Grade 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
Friendly Talk Probes
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…
48
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 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
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
___7 tens 3 hundreds 4 ones
___730 tens 4 ones ___7 hundreds 3 tens 4ones
___734 ones
___seven hundred thirty-four
___seventy-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)
49
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.
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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 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
Look Back
Muddiest Point
Odd One Out
Partner Speaks
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.
50
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
A Picture Tells a
Thousand Words
Question Generating
Sticky Bars
51
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:







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 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
Thinking Log
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.











Think-Pair-Share
Three-Minute Pause
Traffic Light
Cards/Cups/Dots
52
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 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
Two-Minute Paper
Two Stars and a Wish
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
53
Volusia County Schools
Mathematics Department
Grade 2 Math Curriculum Map
May 2016
Formative Assessment Strategies/Mathematics K-5 (continued)
Description
Additional Information
Name
What Are You Doing
and Why?
Whiteboarding
Scenario: Students are decomposing a fraction
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 into the sum of two or more of its parts.
help them learn. At any point in an activity the teacher gets the students’
3
1
1
1
3
2
1
3
3
0
= + +
= +
= +
attention and asks “What are you doing and why are you doing it?”
8
8
8
8
8
8
8
8
8
8
Responses can be shared with the class, discussed between partners,
Teacher stops students in their tracks and asks,
or recorded in writing as a One-Minute Paper to be passed in to the
“What are you do and why are you doing it?”
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.
http://www.educationworld.com/a_lesson/02/lp
251-01.shtml
3-2-1
54
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.
Volusia County Schools
Mathematics Department
Sample 1


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 2 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 2 Math Curriculum Map
May 2016
GLOSSARY OF TERMS
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 sub-structure of related standards; standards from different clusters may sometimes be closely related because mathematics is a
connected subject.
Standard: a definition of what students should understand and be able to do.
Learning Targets: 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 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 Situations: a comprehensive display of possible addition and subtraction 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.
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Volusia County Schools
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Grade 2 Math Curriculum Map
May 2016