Third Grade Unit 3: Patterns in Addition and Multiplication (Extending Multiplication and Division)
9 Weeks
In this unit students will:
 Apply properties of operations (commutative, associative, and distributive) as strategies to multiply and divide
 Fluently multiply and divide within 100, using strategies such as the patterns and relationships between multiplication and division
 Understand multiplication and division as inverse operations
 Solve problems and explain their processes of solving division problems that can also be represented as unknown factor multiplication problems.
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Understand concepts of area and relate area to multiplication and addition.
Find the area of a rectangle with whole- number side lengths by tiling it.
Multiply side lengths to find areas of rectangles with whole-number side lengths in context of solving real world and mathematical problems.
Construct and analyze area models with the same product.
Describe and extend numeric patterns.
Determine addition and multiplication patterns.
Understand the commutative property’s relationship to area.
Create arrays and area models to find different ways to decompose a product.
Use arrays and area models to develop understanding of the distributive property.
Solve problems involving one and two steps and represent these problems using equations with letters such as “n” or “x” representing the unknown
quantity.
Create and interpret pictographs and bar graphs.
Unit Resources:
Unit 3 Overview Video
Vocabulary Cards
Parent Letter
Parent Guides
Number Talks Calendar
Prerequisite Skills Assessment
Sample Post Assessment
Topic 1: Patterns in Addition and Multiplication (Extending Multiplication and Division)
Big Ideas/Enduring Understandings:
 Multiplication and division can be modeled with arrays.
 The distributive property of multiplication allows us to find partial products and then find their sum.
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Area models are related to addition and multiplication.
When finding the area of a rectangle, the dimensions represent the factors in a multiplication problem.
Multiplication can be used to find the area of rectangles with whole numbers.
Area models of rectangles and squares are directly related to the commutative property of multiplication.
Rearranging an area such as 24 sq. units based on its dimensions or factors does NOT change the amount of area being covered (Van de Walle, pg 234). Ex.
A 3 x 8 is the same area as a 4 x 6, 2 x12, and a 1 x 24.
A product can have more than two factors.
Area in measurement is equivalent to the product in multiplication.
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Area models can be used as a strategy for solving multiplication problems.
Essential Questions:
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How does understanding the properties of operations help us multiply large numbers?
How can area be determined without counting each square?
How can the knowledge of area be used to solve real world problems?
How can the same area measure produce rectangles with different dimensions? (Ex. 24 square units can produce a rectangle that is a 3 x 8, 4 x 6, 1 x 24, 2 x
12)
How does understanding the distributive property help us multiply large numbers?
Student Relevance:
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Finding area of real world objects
Dividing up items into equal portions
Content Standards
Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections
that exist among mathematical topics.
MGSE3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities,‡ e.g.,
by using drawings and equations with a symbol for the unknown number to represent the problem.1 ‡See Glossary: Multiplication and Division Within 100.
MGSE3.OA.5 Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative
property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing
that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
MGSE3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one
knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
MGSE3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown
quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. ‡3
MGSE3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.‡ For
example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
MGSE3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of
operations.
MGSE3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units
MGSE3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
MGSE3.MD.7 Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
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See glossary, Table 2.
Students need not use formal terms for these properties.
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This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order where there are no parentheses to specify a
particular order (Order of Operations).
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b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent
whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to
represent the distributive property in mathematical reasoning
MGSE3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and
“how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5
pets.
Fluency: Procedural fluency is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Fluent problem solving does not
necessarily mean solving problems within a certain time limit, though there are reasonable limits on how long computation should take. Fluency is based on a deep
understanding of quantity and number.
Deep Understanding: Teachers teach more than simply “how to get the answer” and instead support students’ ability to access concepts from a number of
perspectives. Therefore students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual
understanding of foundational mathematics concepts by applying them to new situations, as well as writing and speaking about their understanding.
Memorization: The rapid recall of arithmetic facts or mathematical procedures. Memorization is often confused with fluency. Fluency implies a much richer kind of
mathematical knowledge and experience.
Number Sense: Students consider the context of a problem, look at the numbers in a problem, make a decision about which strategy would be most efficient in each
particular problem. Number sense is not a deep understanding of a single strategy, but rather the ability to think flexibly between a variety of strategies in context.
Fluent students:
 flexibly use a combination of deep understanding, number sense, and memorization.
 are fluent in the necessary baseline functions in mathematics so that they are able to spend their thinking and processing time unpacking problems and
making meaning from them.
 are able to articulate their reasoning.
 find solutions through a number of different paths.
For more about fluency, see: http://www.youcubed.org/wp-content/uploads/2015/03/FluencyWithoutFear-2015.pdf and: http://joboaler.com/timed-tests-andthe-development-of-math-anxiety/
Second Grade Standards
Vertical Articulation
Fourth Grade Standards
Fifth Grade Standards
MGSE2.NBT.2 Skip-count by 5s, 10s, and 100s, 10
to 100 and 100 to 1000.
MGSE2.OA.3 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
MGSE2.OA.4 Use addition to find the total number
MGSE4.OA.1 Understand that a multiplicative comparison is
a situation in which one quantity is multiplied by a specified
number to get another quantity.
a. Interpret a multiplication equation as a comparison e.g.,
interpret 35 = 5 × 7 as a statement that 35 is 5 times as
many as 7 and 7 times as many as 5.
MGSE4.NBT.5 Multiply a whole number of up to four digits
by a one-digit whole number, and multiply two two-digit
MGSE5.OA.3 Generate two numerical patterns
using two given rules. Identify apparent
relationships between corresponding terms.
Form ordered pairs consisting of corresponding
terms from the two patterns, and graph the
ordered pairs on a coordinate plane. For
example, given the rule “Add 3” and the
starting number 0, and given the rule “Add 6”
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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.
MGSE2.G.3 Partition a rectangle into rows and
columns of same-size squares and count to find
the total number of them.
numbers, using strategies based on place value and the
properties of operations. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or
area models.
MGSE4.NBT.6 Find whole-number quotients and
remainders with up to four-digit dividends and one-digit
divisors, using strategies based on place value, the
properties of operations, and/or the relationship between
multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or
area models
and the starting number 0, generate terms in
the resulting sequences, and observe that the
terms in one sequence are twice the
corresponding terms in the other sequence.
Explain informally why this is so.
MGSE5.NBT. 1 Recognize that in a multi-digit
number, a digit in one place represents
10 times as much as it represents in the place
to its right and 1/10 of what it represents in the
place to its left.
MGSE5.NBT.2 Explain patterns in the number
of zeros of the product when multiplying a
number by powers of 10, and explain patterns
in the placement of the decimal point when a
decimal is multiplied or divided by a power of
10. Use whole-number exponents to denote
powers of 10.
Instructional Strategies
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Students gain a full understanding of which operation to use in any given situation through contextual problems. Number skills and concepts are developed as
students solve problems. Problems should be presented on a regular basis as students work with numbers and computations.
Researchers and mathematics educators advise against providing “key words” for students to look for in problem situations because they can be misleading.
Students should use various strategies to solve problems. Students should analyze the structure of the problem to make sense of it. They should think through the
problem and the meaning of the answer before attempting to solve it.
Encourage students to represent the problem situation in a drawing or using manipulatives such as counters, tiles, and blocks. Students should determine the
reasonableness of the solution to all problems using mental computations and estimation strategies.
Students can use base–ten blocks on centimeter grid paper to construct rectangular arrays to represent problems involving area.
Students are to identify arithmetic patterns and explain these patterns using properties of operations. They can explore patterns by determining likenesses,
differences and changes. Use patterns in addition and multiplication tables.
What do you notice about the numbers highlighted in pink in the multiplication table? Explain a pattern using properties of operations.
When (commutative property) one changes the order of the factors they will still gets the same product, example 6 x 5 = 30 and 5 x 6 = 30.
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x 0 1 2 3 4 5 6 7
0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7
2 0 2 4 6 8 10 12 14
3 0 3 6 9 12 15 18 21
4 0 4 8 12 16 20 24 28
5 0 5 10 15 20 25 30 35
6 0 6 12 18 24 30 36 42
7 0 7 14 21 28 35 42 49
8 0 8 16 24 32 40 48 56
9 0 9 18 27 36 45 54 63
10 0 10 20 30 40 50 60 70
What pattern do you notice when 2, 4, 6, 8, or 10 are multiplied by any number (even or odd)?
2
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0 0
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16 18 20
24 27 30
32 36 40
40 45 50
48 54 60
56 63 70
64 72 80
72 81 90
80 90 100
The product will always be an even number.
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10 20 30 40 50 60 70 80 90 100
Geometric measurement– understand concepts of area and relate area to multiplication and to addition.
Students can cover rectangular shapes with tiles and count the number of units (tiles) to begin developing the idea that area is a measure of covering. Area describes
the size of an object that is two-dimensional. The formulas should not be introduced before students discover the meaning of area.
The area of a rectangle can be determined by having students lay out unit squares and count how many square units it takes to completely cover the rectangle
completely without overlaps or gaps. Students need to develop the meaning for computing the area of a rectangle. A connection needs to be made between the
number of squares it takes to cover the rectangle and the dimensions of the rectangle. Ask questions such as:
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What does the length of a rectangle describe about the squares covering it?
What does the width of a rectangle describe about the squares covering it?
The concept of multiplication can be related to the area of rectangles using arrays. Students need to discover that the length of one dimension of a rectangle tells
how many squares are in each row of an array and the length of the other dimension of the rectangle tells how many squares are in each column. Ask questions
about the dimensions if students do not make these discoveries. For example:
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How do the squares covering a rectangle compare to an array?
How is multiplication used to count the number of objects in an array?
Splitting arrays can help students understand the distributive property. They can use a known fact to learn other facts that may cause difficulty. For example,
students can split a 6 x 9 array into 6 groups of 5 and 6 groups of 4; then, add the sums of the groups.
The 6 groups of 5 is 30 and the 6 groups of 4 is 24. Students can write 6 x 9 as 6 x 5 + 6 x 4.
Students’ understanding of the part/whole relationships is critical in understanding the connection between multiplication and division.
Students should also make the connection of the area of a rectangle to the area model used to represent multiplication. This connection justifies the formula for the
area of a rectangle.
Represent and interpret data.
Representation of a data set is extended from picture graphs and bar graphs with single-unit scales to scaled picture graphs and scaled bar graphs. Intervals for the
graphs should relate to multiplication and division within 100 (product is 100 or less and numbers used in division are 100 or less). In picture graphs, use
multiplication fact values, with which students are having difficulty, as the icons. For example, one picture represents 7 people. If there are three pictures, students
should use known facts to determine that the three pictures represent 21 people. The intervals on the vertical scale in bar graphs should not exceed 100.
Pictographs: Scaled pictographs include symbols that represent multiple units. Below is an example of a pictograph with symbols that represent multiple units.
Graphs should include a title, categories, category label, key, and data. How many more books did Juan read than Nancy?
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Students are to draw picture graphs in which a symbol or picture represents more than one object. Bar graphs are drawn with intervals greater than one. Ask
questions that require students to compare quantities and use mathematical concepts and skills. Use symbols on picture graphs that students can easily represent
half of, or know how many half of the symbol represents.
Single Bar Graphs: Students use both horizontal and vertical bar graphs. Bar graphs include a title, scale, scale label, categories, category label, and data
**For additional assistance see the Unit Webinar at Georgiastandards.org.
Common Misconceptions
Evidence of Learning
Multiplication, Division and Data
● Describe and extend numeric patterns.
● Determine addition and multiplication patterns.
● Solve problems involving one and two steps and represent these problems using equations with letters such as “n” or “x” representing the unknown
quantity.
● Create and interpret pictographs and bar graphs.
Area
● Understand the commutative property’s relationship to area.
● Create arrays and area models to find different ways to decompose a product.
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Use arrays and area models to develop understanding of the distributive property.
Demonstrates Area models and how they are related to addition and multiplication.
When finding the area of a rectangle, understands the dimensions represent the factors in a multiplication problem.
Uses multiplication to find the area of rectangles with whole numbers.
Rearranges an area models and understands that the factors does NOT change the amount of area being
Understands Area in measurement is equivalent to the product in multiplication.
Uses Area models as a strategy for solving multiplication problems.
Additional Assessments:
Formative Assessment Lessons - (FAL) Interpret various multiplication strategies MGSE3.OA.1, MGSE3.OA.8, MGSE3.OA.9
This formative assessment is designed to be implemented approximately two-thirds of the way through the instructional unit.
http://ccgpsmathematicsk5.wikispaces.com/file/view/Multiplication%20Formative%20Assessment%20Lesson.pdf/437801992/Multiplication%20Formative%20Assessment%20Lesson.pdf
Adopted Resources
My Math:
Reminder: The Standard Algorithms for addition and
subtraction are taught in grade 4
Chapter 6: Multiplication and Division Patterns
6.1 Patterns in the Multiplication Table
6.2 Multiply by 2
6.3 Divide by 2
6.4 Multiply by 5
6.5 Divide by 5
6.6 Problem Solving
6.7 Multiply by 10
6.8 Multiples of 10
6.9 Divide by 10
Chapter 7: Multiplication and Division
7.1 Multiply by 3
7.2 Divide by 3
7.3 Double a known fact
7.4 Multiply by 4
7.5 Divide by 4
7.6 Problem Solve
7.7 Multiply by 0 and 1
7.8 Divide by 0 and 1
Chapter 8: Apply Multiplication and Division
Third Grade Unit 3
Adopted Online Resources
Think Math
My Math
Chapter 6: Rules and Patterns
6.1 Exploring Rules
6.2 Using Graphs to Find a Rule
Chapter 9: Multiplication Situations
9.1 Practice with Multiplication and
Division
9.2 Connecting Multiplication and
Division
9.4 Combining Multiplication and
Division
9.5 Separating Arrays
Chapter 12: Multiplication Strategies
12.1 Multiplication and Division
12.2 Using Sums to Multiply
12.3 Multiply with Base Ten Blocks
12.4 Multiply with Arrays
12.5 Separating Arrays to Multiply
12.7 Finding Missing Factors
12.8 Division
Chapter 15: Multiplication and Division
15.1 Multiply by 10
http://connected.mcgraw-hill.com/connected/login.do
Teacher User ID: ccsde0(enumber)
Password: cobbmath1
Student User ID: ccsd(student ID)
Password: cobbmath1
Exemplars
http://www.exemplarslibrary.com/
User: Cobb Email
Password: First Name
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Fish Dilemma
Great Pizza Dilemma
Equal Snacks
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8.1 Multiply by 6
8.2 Multiply by 7
8.3 Divide by 6 and 7
8.4 Multiply by 8
8.5 Multiply by 9
8.6 Divide by 8 and 9
8.7 Problem Solving
Chapter 9: Properties and Equations
9.1 Take apart to multiply
9.2 Distributive Property
9.4 Associative Property
9.5 Write equations
Chapter 12: Represent and Interpret Data
12.1 Collect and record data
12.2 Draw scaled picture graphs
12.3 Draw scaled bar graphs
Additional Web Resources:
National Council of Teachers of Mathematics, Illuminations:– Multiplication: It’s in the Cards - http://illuminations.nctm.org/Lesson.aspx?id=1267
Students skip-count and examine multiplication patterns. They also explore the commutative property of multiplication.
From the National Council of Teachers of Mathematics, Illuminations:– Multiplication: It's in the Cards: Looking for Calculator Patterns
http://illuminations.nctm.org/Lesson.aspx?id=1271
National Council of Teachers of Mathematics, Illuminations: Bar Grapher http://illuminations.nctm.org/Activity.aspx?id=4091
This is a NCTM site that contains a bar graph tool to create bar graphs.
National Council of Teachers of Mathematics, Illuminations: All About Multiplication – Exploring equal sets http://illuminations.nctm.org/Lesson.aspx?id=1254
National Council of Teachers of Mathematics, Illuminations: What’s in a Name? – Creating Pictographs. Students create pictographs and answer questions about the
data set. http://illuminations.nctm.org/Lesson.aspx?id=1254
Illustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources. http://illuminations.nctm.org/ActivityDetail.aspx?id=46
This website provides actives for measuring the area of rectangles
This website provides practice with measuring the area and perimeter of rectangles. http://www.mathplayground.com/area_
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Suggested Manipulatives
Vocabulary
sets of counters
open number lines
objects to share
multiplication chart
Geo-boards
square unit items (one inch tiles)
grid paper
area
area model
array
commutative property of multiplication
distributive property of multiplication
divide
equation
factor
multiply
operation
product
quotient
square unit
tiling
unknown/variable
Task Descriptions
Scaffolding Task
Constructing Task
Practice Task
Culminating Task
Formative Assessment
Lesson (FAL)
3-Act Task
Third Grade Unit 3
Suggested Literature
My Full Moon is Square Stacks of
Trouble
Too Many Kangaroos
The Best of Times
The Doorbell Rang
Bigger, Better, Best!
Sam’s Sneaker Squares Two of
Everything
Sea Squares
One Hundred Hungry Ants
Stay in Line
Clean Sweep Campers
Things that Come in 2’s, 3’s & 4’s
Amanda Bean’s Amazing Dream
Bats on Parade
Spunky Monkeys on Parade
Each Orange Had Eight Slices
Racing Around
Sam’s Sneaker Squares
Chickens on the Move
Task that build up to the learning task.
Task in which students are constructing understanding through deep/rich contextualized problem solving
Task that provide students opportunities to practice skills and concepts.
Task designed to require students to use several concepts learned during the unit to answer a new or unique situation.
Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key
mathematical ideas and applications.
Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and
solution seeking Act Two, and a solution discussion and solution revealing Act Three.
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Task Name
Task Type
Grouping Strategy
Skills
Standards
Analyze the concept of
area
MGSE3.MD.5
Description
Cover Me
Scaffolding Task
Partner/Small Group
Task
Fill Er’ Up
Constructing Task
Partner/Small Group
Task
Estimating area
MGSE3.MD.5
MGSE3.MD.6
Same But Different
Constructing Task
Partner/Small Group
Task
Same area, different
dimensions
MGSE3.MD.5
MGSE3.MD.6
Area Dimensions
MGSE3.MD.5
MGSE3.MD.6
MGSE3.MD.7
Area Dimensions
MGSE3.MD.5
MGSE3.MD.6
MGSE3.MD.7
In this task, students will watch a Vimeo and tell what they
noticed. Next, they will be asked to discuss what they wonder
about or are curious about. Students will then use
mathematics to answer their own questions.
Distributive Property of
Multiplication
MGSE3.MD.7
In this task, students will work through problems using
area models to understand that numbers can be
decomposed into “nice” numbers for multiplication and
addition.
One-digit by 2-digit
multiplication
MGSE3.MD.7
Count Me In
Paper Cut
Oops! I’m
Decomposing!
Multiplication W/
Base-Ten Blocks
Olympic Cola
Display
Constructing Task
Partner/Small Group
3-Act Task
Whole Group
Constructing Task
Partner/Small Group
Task
Practice Task
Individual/Partner
Task
3-Act Task
Whole Group
In this task, students investigate area using tangrams.
Distributive property of
multiplication
MGSE3.MD.7
Array Challenge
Practice Task
Partner/Small Group
Task
Practicing multiplication
facts using area models
MGSE3.MD.6
MGSE3.MD.7
Skip Counting
Constructing Task
Analyze patterns formed
MGSE3.OA.9
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In this task, students practice estimating and filling the area of
three different figures.
In this task, students will create different area models for a
given product.
In this task, students create area models and label them with
appropriate dimensions.
In this task, students will model multiplication of 2-digit
numbers using base-ten blocks to create partial products.
In this task, students will use their understanding of area
models to represent the distributive property to solve
problems associated with an Olympic cola display.
In this task, students will apply multiplication problems to the
matching area model/array
In this task, students look for number patterns relationship to
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Patterns
Partner/Small Group
when skip-counting on the
1-100 chart
Take The Easy Way
Out!
Practice Task
Partner/Small Group
Discovering patterns using
a multiplication chart
MGSE3.OA.9
In this task, students will identify patterns and their
relationship to multiplication and division.
Read All About It
Constructing Task
Small group/Partner
Applying area and problem
solving
MGSE3.OA.8
This task provides students with experiences solving multistep
real world problems.
MGSE3.OA.8
In this two part task, students will first work in groups to
solve two-step word problems. Student groups will then
create their own two-step word problems to present to
the class to solve.
Creating and interpreting
pictographs and bar graphs
MGSE3.MD.3
In the following task, students will organize data given to
create a picture graph. Students will use the graph to answer
word problems.
It Takes Two!
Subject To
Interpretation
Constructing Task
Individual/Partner
Constructing Task
Partner/Small Group
Write multiplication story
problems
multiplication.
Measure And Plot!
Constructing Task
Individual Task
Creating a line plot
MGSE3.MD.4
In this task, students measure their sitting height to
nearest whole inch and then use collected class results to
create a line plot graph.
Hooked On
Solutions!
Constructing Task
Individual Task
Writing two-step word
problems
MGSE3.OA.8
In this task, students will create word problems to match given
equations.
Area, multiplication,
problem solving, bar
graphs
MGSE3.OA.8
MGSE3.MD.3
MGSE3.MD.5
MGSE3.MD.6
MGSE3.MD.7
Students will create a flower garden representing 100 square
units. The garden is composed of five rectangular regions,
each with a different flower plant. A graph will be completed
to represent the number of plants used in the garden. Student
will compose word problems that can be answered by
analyzing the data in the graph.
Watch My Garden
Grow
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Culminating Task
Individual Task
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Unknown Product
36=?
There are 3 bags with 6 plums in each
bag. How many plums are there in all?
Equal Groups
Arrays4,
Area5
Measurement example. You need 3
lengths of string, each6 inches long.
How much string will you need
altogether?
There are 3 rows of apples with 6
apples in each row. How many apples
are there?
Area example. What is the area of a 3
cm by 6 cm rectangle?
A blue hat costs $6. A red hat costs 3
times as much as the blue hat. How
much does the red hat cost?
Compare
General
Measurement example. A rubber band
is 6 cm long. How long will the rubber
band be when it is stretched to be
3times as long?
a b = ?
Group Size Unknown
(“How many in each group? Division)
3  ? – 18, and 18 3 = ?
If 18 plums are shared equally into 3 bags, then
how many plums will be in each bag?
Measurement example. You have 18 inches of
string, which you will cut into 3 equal pieces. How
long will each piece of string be?
If 18 apples are arranged into 3equal rows, how
many apples will be in each row?
Area example. A rectangle has area 18 square
centimeters. If one side is 3 cm long, how long is a
side next to it?
Number of Groups Unknown
(“How many groups?” Division)
?  6 = 18, and 18  6 = ?
If 18 plums are to be packed 6to a bag, then
how many bags are needed?
Measurement example. You have 18 inches of
string, which you will cut into pieces that are6
inches long. How many pieces of string will you
have?
If 18 apples are arranged into equal rows of 6
apples, how many rows will there be?
Area example. A rectangle has area 18 square
centimeters. If one side is 6 cm long, how long
is a side next to it?
A red hat costs $18 and that is3 times as much as a
blue hat costs. How much does a blue hat cost?
A red hat costs $18 and a blue hat costs $6.
How many times as much does the red hat cost
as the blue hat?
Measurement example. A rubber band is stretched
to be18 cm long and that is 3 times as long as it
was at first. How long was the rubber band at first?
Measurement example. A rubber band was 6
cm long at first. Now it is stretched to be18 cm
long. How many times as long is the rubber
band now as it was at first?
a ? = p, and pa = ?
?b = p, and pb = ?
4
The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in
there? Both forms are valuable.
5
Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement
situations. The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples .
Third Grade Unit 3
13
2015-2016