Third Grade

MATHEMATICS Curriculum Map

2017 – 2018

Volusia County Schools

Mathematics Florida Standards

1 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

2 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

Elementary Instructional Math Block

Time Components Description

5-15 minutes

Number Talks

Short, daily fluency routine that engages students in meaningful conversations around purposefully crafted computation problems that are solved using number relationships and the structure of numbers. Students are asked to communicate their thinking when presenting and justifying solutions to problems they solve mentally while the teacher records their ideas with mathematical precision. These exchanges lead to the development of more accurate, efficient, and flexible strategies.

5 minutes

Opening: Hook/Coherence Connection

The teacher will engage students to create interest for the whole group lesson or review prerequisite standards to prepare students to make explicit connections that will allow students to apply and extend previous learning when interacting with the lesson’s grade-level content.

15 minutes

Whole Group: Mini Lesson/Guided Practice

Used prior to small group to introduce/practice new knowledge and skills or after small group to refine/practice strategies discovered by students.

The lesson focuses on the depth of grade-level cluster(s), grade-level content standard(s), or part(s) thereof, intentionally targeting the aspect(s) of rigor (conceptual understanding, procedural skill and fluency, application) called for by the standard(s) being addressed.

During this time, the teacher makes the mathematics of the lesson explicit using clear and correct explanations, representations, tasks, and/or examples. The teacher provides opportunities for all students to work with and practice grade-level problems and exercises, deliberately checking for understanding throughout the lesson and adapting the lesson according to student understanding. The teacher poses high-quality questions and problems that prompt students to share their developing thinking about the content of the lesson. Class created anchor charts are constructed by strategically adding key concepts throughout the topic’s lessons.

30-40 minutes

Small Collaborative Groups/ Independent Practice

The teacher encourages reasoning and problem solving by posing challenging problems that offer opportunities for student choice of appropriate tools and promote productive struggle. Students work in small, flexible collaborative groups to engage in mathematical tasks while the teacher circulates and asks questions to elicit thinking, providing support or extensions as needed. The teacher asks students to explain and justify work, connecting and developing students’ informal language to precise mathematical language appropriate to their grade, and provides feedback that helps students revise initial work. The teacher makes observations to select and sequence appropriate strategies for students to share during the class discussion.

5 minutes

Closure: Summarize

The teacher strengthens all students’ understanding of the content by strategically sharing a variety of students’ representations and solution methods. The teacher facilitates the summary of the mathematics with references to student work and by creating the conditions for student conversations where students are encouraged to talk about each other’s thinking in order to reinforce the purpose of the lesson.

Formative techniques occur throughout the framework to drive instruction, guide collaborative grouping, and evaluate which students will need intervention/enrichment.

Grade 3 Math Curriculum Map July 2017

3 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Year At A Glance

Unit 1: August 14 – October 2

Topic 1: Exploring equal groups as a foundation for multiplication and division Topic 2: Developing conceptual understanding of area Topic 3: Developing strategies for addition and subtraction

Unit 2: October 3 – November 21

Topic 4: Understanding unit fractions Topic 5: Using fractions in measurement and data Topic 6: Solving addition and subtraction problems involving measurement

Unit 3: November 27 – March 2

Topic 7: Understanding the relationship between multiplication and division Topic 8: Investigating patterns in number and operations Topic 9: Developing strategies for multiplication and division Topic 10: Understanding equivalent fractions Topic 11: Comparing fractions

Unit 4: March 5 – May 30

Topic 12: Solving problems involving area Topic 13: Solving problems involving shapes Topic 14: Using multiplication and division to solve measurement problems Topic 15: Demonstrating computational fluency in problem solving Topic 16: Revisiting solving problems involving area Topic 17: Revisiting using multiplication and division to solve measurement problems

4 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Unit 1 PACING: August 14 – October 2

Topic 1: Exploring equal groups as a foundation for multiplication and division Pacing: August 14 – 25

In Grade 2 students have added groups of objects by skip-­‐counting and using repeated addition (2.OA.3.4). In this topic students connect these concepts to

multiplication and division by interpreting and representing products and quotients. Students begin developing these concepts by working with numbers

with which they are more familiar, such as 2s, 5s, and 10s, in addition to numbers that are easily skip counted, such as 3s a nd 4s. Since multiplication is a

critical area for Grade 3, students will build on these concepts throughout the year, working towards fluency by the end of t he year.

Standards Academic Language

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.

MAFS.3.OA.1.1 array column dividend divisor equal groups equation expression factors groups of inverse operation partition product quotient row shares symbol

Students will:

• interpret a situation requiring multiplication using objects, pictures, words, and expressions.

• describe a context that could be represented with multiplication.

E.g., Jim purchased 5 packages of muffins. Each package contained 3 muffins. 5 groups of 3. Describe another situation where there would be 5 groups of 3 or 5 x 3.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MAFS.3.OA.1.2

Students will:

• interpret a situation requiring division using objects, pictures, words, and expressions.

• describe a context that could be represented with division.

E.g., 50 ÷ 10; can be 50 items divided into 10 equal groups, or 50 items divided into equal groups of 10. Represent a context that could be described as the quotient of two whole numbers (e.g., 8 ÷ 2 is a way to show the equal sharing of 8 cookies between 2 boys).

5 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent a problem.

MAFS.3.OA.1.3

Students will:

• use the following situations to solve real-world and mathematical problems related to multiplication by numbers that are easily skip counted (e.g., 2s, 3s, 4s, 5s, and 10s).

o equal groups: Stan has 4 bags of cookies with 5 cookies in each bag. How many cookies does he have? Hector has 12 wrenches. He puts 4 in each compartment in his tool box. How many compartments does it take to hold all of his wrenches?

o array model: Mrs. Smith arranges the desks in her classroom. She has 4 rows with 3 desks in each row. How many desks are in her classroom? A marching band has 28 members. The director puts the members into equal columns of 7. How many columns does it take to arrange all of the band members?

• represent multiplication and division word problems involving numbers that are easily skip counted (e.g., 2s, 3s, 4s, 5s, and 10s). using objects, drawings, and equations using a symbol for the unknown number.

NOTE: See Common Multiplication and Division Situations Table on page 61.

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

MAFS.3.OA.3.7

Students will: NOTE: By the end of Grade 3, students are to know from memory all products of two one-digit numbers.

Computational fluency is defined as accuracy, efficiency, and flexibility. Research indicates that teachers can best support students’ knowledge of sums and differences through varied experiences with mental strategies rather than using repetitive timed tests.

• multiply by numbers that are easily skip counted (e.g., 2s, 3s, 4s, 5s, and 10s) choosing and using strategies such as the relationship between multiplication and division or properties of operations.

• divide by numbers that are easily skip counted (e.g., 2s, 3s, 4s, 5s, and 10s), leading to one-digit quotients by choosing and using strategies such as the relationship between multiplication and division or properties of operations. NOTE: Students are NOT expected to identify the properties of operations by name.

6 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics

MAFS.K12.MP.1.1 MAFS.K12.MP.2.1 MAFS.K12.MP.4.1

Topic Comments:

In 3.OA.1.1 situations with discreet objects should be explored first when developing a conceptual understanding of multiplication, followed by measurement examples involving area models.

3.OA.1.3 will be readdressed in topic 7 in order to provide students the opportunity to develop computational strategies as they extend the range of numbers with which they compute. It will be finalized in topic 14 to include measurement quantities in order to provide students multiple opportunities to develop and practice these concepts.

3.OA.3.7 will be readdressed in topic 7 and topic 15 in order to provide students the opportunity to develop computational

strategies as they extend the range of numbers with which they compute. Fluency will also be developed through Number Talks

throughout the year and finalized in topic 15, allowing students time to work towards learning products of two 1-digit numbers

from memory.

Students use concrete objects or pictures to help conceptualize and solve problems (MP.1). They use arrays and other

representations to model multiplication and division (MP.4) and contextualize given expressions (MP.2).

Topic 1 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.1

.1

Topic 1 Accounting for Butterflies Figuring Fingers and Tallying Toes

Teacher Guide, p. 4

Daily Math Practice Journal, pp. 2, 4, 6, 8, 18, 20

Problem Solving Strategy Puzzles (purple) Discovery Can: Algebraic Thinking Cards 6-20 Discovery Can: Operations Cards 6, 11-22 How Did You Solve It? Cards 1-3

Interpreting Multiplication What Does 21 Mean?

www.cpalms.org

Cheesy Arrays

Circle and Stars

Array to Multiply

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3: E2, E3

https://learnzillion.com/ The Carrot Patch: Use equal groups to understand multiplication

Practice representing multiplication in different ways

http://achievethecore.org No aligned resources

7 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 1 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.1

.2

Topic 1 Camp Fair Shares Boxing Bags and Matches

Teacher Guide, p. 3

Reproducibles, p. 3

Daily Math Practice Journal, pp. 3, 5, 7, 9, 15

Discovery Can: Operations Cards 2, 7, 21-25 Discovery Can: Algebraic Thinking Cards 17-20 How Did You Solve It? Cards 1-3

Interpreting Division What Does the Six Mean?

www.cpalms.org No aligned resources

https://www.illustrativemathematics.org/content-standards

Fish tanks

Markers in Boxes

https://www.ixl.com/math/grade-3 : I1

https://learnzillion.com/

Practice representing division in different ways

http://achievethecore.org No aligned resources

3.O

A.1

.3

Topic 1 No aligned resources

Teacher Guide, pp. 3-4

Daily Math Practice Journal, pp. 3, 5, 7, 9, 11, 13, 17, 19

Problem Solving Strategy Puzzles (purple) Discovery Can: Algebraic Thinking Cards 6-20 Discovery Can: Operations Cards 6, 11-22 How Did You Solve It? Cards 3, 6-7

Finding the Number of Groups

Finding the Group Size the Group Size

Writing Multiplication Word Problem

Writing a Problem With a Quotient

www.cpalms.org

https://www.illustrativemathematics.org/content-standards:

https://www.ixl.com/math

/grade-3 : E4, E5, E6, E7,

H6, H7, I4, L5

https://learnzillion.com/

Use multiplication and division representations to solve problems Understand how to use drawings and equations to solve multiplication and division problems Cards 1,2,3,6 and 8

http://achievethecore.org

8 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 1 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.3

.7

Topic 1 Salute to Facts Daily Math Practice Journal, pp. 8, 12, 14, 18 Discovery Can: Operations Cards 1, 6, 11-22

Fluency With Division

www.cpalms.org

Area isn’t just for squares

https://www.illustrativemathematics.org/content-standards

Kiri's Multiplication Matching Game

https://www.ixl.com/math/grade-3 F1-F11

I3, I5

https://learnzillion.com/

Understand properties of multiplication and division Cards 1-3

http://achievethecore.org No aligned resources

9 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 2: Developing conceptual understanding of area Pacing: August 28 – September 14 This topic provides ample time, and should include multiple experiences, for students to explore the connections among counting tiles, skip counting the number of tiles in rows or columns, and multiplying the side lengths of a rectangle to determine area. Students’ understanding of these connections is critical content at this grade, and must occur early in the school year, thereby allowing time for understanding and fluency to develop across future topics.

Standards Academic Language

Apply properties of operations as strategies to multiply and divide. E.g., If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative Property of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 – 30. (Associate Property of multiplication.) Knowing that 8 x 5 = 40, and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive Property).

MAFS.3.OA.2.5

attribute equation equivalent expression factor inverse operation product area column length plane figure product row square unit width

Students will:

• represent expressions using various objects, pictures, and words in order to develop understanding of the commutative property of multiplication.

• apply the commutative property as a strategy to multiply. o Commutative Property of multiplication: E.g., 3 × 2 is the same value as 2 × 3

NOTE: Students are NOT expected to identify the properties by name.

Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

MAFS.3.MD.3.5

Students will:

• define a unit square (i.e., a square with side lengths of 1 unit) and understand that it is used to measure the attribute of area.

NOTE: The side length of the square could be one customary unit (e.g., inch, foot), one metric unit (e.g., centimeter, meter) or one non-standard unit. Exponential notation for unit abbreviations (e.g., cm2 ) is not introduced until Grade 5.

• describe area as the measure of space within a plane figure.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). MAFS.3.MD.3.6

Students will:

• measure the area of a shape by covering it with unit squares – with no gaps or overlaps – and counting the number of unit squares used.

• use an array model to determine the area of a rectangle by counting the unit squares.

• use appropriate labels to represent answers to area problems (e.g., 4 square meters).

10 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

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.

MAFS.3.MD.3.7

Students will:

• use square tiles to find the area of rectangles with whole number side lengths.

• discover the relationship between tiling and multiplying side lengths to find the area of rectangles.

• explain the relationship between tiling and multiplying side lengths to find the area of rectangles. NOTE: Students need to discover that the length of one dimension of a rectangle tells how many unit squares are in each row

and the length of the other dimension of the rectangle tells how many unit squares are in each column. Students will not use the formula a = l × w until Grade 4.

• use appropriate labels to represent answers to area problems (e.g., 4 square meters).

2. Reason abstractly and quantitatively 6. Attend to precision 7. Look for and make use of structure

MAFS.K12.MP.2.1 MAFS.K12.MP.6.1 MAFS.K12.MP.7.1

Topic Comments: 3.OA.2.5 will be readdressed in topic 9 with a focus on the distributive property and in topic 12 with a focus on the associative property. 3.MD.3.7 will be readdressed in topic 9 to extend the understanding of using area models to represent the distributive property and recognize that area is additive and in topic 12 to solve real world and mathematical problems involving area. Students analyze the structure of multiplication (MP.7) through their work with arrays (MP.2) and work towards precisely expressing their understanding of the connection between area and multiplication (MP.6).

11 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 2 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.2

.5

Topic 2 No aligned resources

Teacher Guide, p. 5

Reproducibles, p. 3

How Did You Solve It? Cards 10-14

Meeting the Reading Goal

www.cpalms.org

Efficient Multiplication

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 No aligned

resources

https://learnzillion.com/

Understand properties of multiplication and division Cards 4-8 Video: Understand properties of multiplication and division (Communicative)

http://achievethecore.org

3.M

D.3

.5 (

a, b

)

Topic 2 Ground Cover Teacher Guide, p.18

Reproducibles, p.10

Daily Math Practice Journal, pp. 46, 52, 54, 62 Area Tiles Discovery Can: Geometric Measurement How Did You Solve It? Cards 63-65

Unit Square

Using Tiles of Different Sizes

www.cpalms.org No aligned resources

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 : FF6 https://learnzillion.com/

Measure area by counting square units You will need to stop the video early and eliminate some questions from the practice

http://achievethecore.org No aligned resources

12 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 2 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3. M

D.3

.6

Topic 2 Sweet Squares Teacher Guide, pp. 19-20

Reproducibles, p. 11

Daily Math Practice Journal, pp. 46, 50, 52, 54, 62

Area Tiles Discovery Can: Geometric Measurement How Did You Solve It? Cards 63-65 Pick A Problem Cards 77, 78, 79, 80

Dawn’s Vegetable Garden Fenced Dog Run

How Many Square Units

www.cpalms.org

Count those Square Units

https://www.illustrativemathematics.org/content-standards

Finding the Area of Polygons

https://www.ixl.com/math/grade-3 FF7, FF8

https://learnzillion.com/ No aligned resources

http://achievethecore.org No aligned resources

3.M

D.3

.7 (

a)

Topic 2 Gardens By Design

Teacher Guide, pp. 20-21

Daily Math Practice Journal, pp. 46, 48, 52, 56-60, 63

Area Tiles Discovery Can: Geometric Measurement How Did You Solve It? Cards 66-69 Pick A Problem Cards 77, 78, 79, 80, 98

Area of a Butterfly Garden Cover Me

www.cpalms.org

Area isn’t just for squares

https://www.illustrativemathematics.org/content-standards

India’s bathroom Tiles

https://www.ixl.com/math/grade-3 FF10

https://learnzillion.com/

Understand that area is measured in square units

Understand that the area of a rectangle can be determined by multiplying side lengths

Multiply to find the area of rectangles and explore the commutative property Links 3.7 with OA.2.5

http://achievethecore.org No aligned resources

13 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 3: Developing strategies for addition and subtraction Pacing: September 15 – October 2 In Grade 2 students used addition and subtraction within 1000 using concrete objects and strategies. In this topic students increase the sophistication of computation strategies for addition and subtraction that will be finalized by the end of the year. This topic introduces the concept of rounding, which provides students with another strategy to judge the reasonableness of their answers in addition and subtraction situations. Perimeter provides a context in which students can practice both rounding and addition and subtraction (e.g. estimating the perimeter of a polygon).

Standards Academic Language

Use place value understanding to round whole numbers to the nearest 10 or 100. MAFS.3.NBT.1.1 compose decompose decrease difference distance estimate increase inverse length perimeter reasonable rounding sum

Students will:

• round whole numbers to the nearest 10 through the use of a number line, hundred chart, place value chart, etc.

• round whole numbers to the nearest 100 through the use of a number line, hundred chart, place value chart, etc.

• determine possible starting numbers when given a rounded number

• understand that the purpose of rounding is to make mental math easier and to check the reasonableness of an answer.

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

MAFS.3.NBT.1.2

Students will:

• add and subtract within 1000, using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

NOTE: The Standards distinguish strategies from algorithms. From the Standards glossary:

Computation strategy- Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. Computation algorithm- A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly. Work with computation begins with use of strategies and “efficient, accurate, and generalizable methods.” For addition and subtraction, the culmination of this work is signaled in the Grade 4 Standards by use of the term “standard algorithm.”

14 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

MAFS.3.MD.4.8

Students will:

• explore the concept of perimeter as a measure of distance, using a variety of tools (e.g., geoboards, rubber bands, color tiles, graph paper, string, etc.).

• find the perimeter of a polygon (regular and irregular) that is located on a grid by counting the units.

• find the perimeter of a polygon when given the lengths of all sides.

• identify and use properties of polygons to find the unknown side length(s) of a polygon given the perimeter without using a grid.

• solve real world and mathematical problems involving perimeter.

6. Attend to precision. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.6.1 MAFS.K12.MP.8.1

Topic Comments: 3.NBT.1.1 introduces the concept of rounding, which is new to students and will be revisited in topic 8 in the context of multiplication. 3.NBT.1.2 will be revisited in topic 15 and finalized in topic 18 in order to give students time to reach fluency in addition and subtraction within 1000 by the end of the year. 3.MD.4.8 is the first time perimeter appears in MAFS. Students are not expected to use formulas until Grade 4 (4.MD.1.3). 3.MD.4.8 will be addressed in full in topic 13 after students have been introduced to and worked with the concept of area. Students use precise language to make sense of their solution in the context of a problem and the magnitude of the numbers (MP.6). Students also generalize algorithms and strategies and look for shortcuts (MP.8).

15 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 3 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

BT

.1.1

Topic 3 All Aboard for Rounding Number Line Round Up Numbers in the Round

Teacher Guide, pp. 8-9

Reproducibles, pp. 3, 7

Daily Math Practice Journal, pp. 22, 24, 26, 28, 29

Magnetic Place Value Blocks

How Did You Solve It? Cards 21-23

Pick A Problem Cards 26-30, 37, 40

Mystery Number Rounding Problem Rounding to the Nearest Hundred The Smallest and Largest Numbers Possible Rounding to the Nearest Ten

www.cpalms.org

Rockin’ Round Number line lesson 1 & 2

Rounding for Decades

https://www.illustrativemathematics.org/content-standards

Rounding to 50 or 500

Rounding to the Nearest 10 and 100

https://www.ixl.com/math/grade-3 : B2, P1, P2

https://learnzillion.com/

Understanding rounding to the nearest ten

Understanding rounding to the nearest hundred

Determining which values will round to a specific number

Use rounding to determine if a sum or difference is reasonable

http://achievethecore.org No aligned resources

Origo One Video: Rounding - Using Number Lines to Round Numbers

16 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 3 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

BT

.1.2

Topic 3 Base Place: The Pluses String Bead Subtraction

Teacher Guide, p. 9

Reproducibles, p. 3

Daily Math Practice Journal, pp. 22, 24, 26, 28, 29

How Did You Solve It? Cards 24-27

Pick A Problem Cards 31-36, 38

Discovery Can: Operations Cards 3-5, 8-10

Problem Solving Strategy Puzzles (blue)

Adding and Subtracting Using Properties Addition Within 1000 Subtraction Within 1000 Wanda’s Method

www.cpalms.org

Decoding Decomposing

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 D1

https://learnzillion.com/

Use decomposition and regrouping to add

Decomposing to add on a number line

Counting up and decomposing to solve a subtraction problem

Comparing strategies of addition and subtraction to look for efficiency

http://achievethecore.org No aligned resources

3.M

D.4

.8

Topic 3 Landmark Logic Wreck-tangles

Daily Math Practice Journal, pp. 49, 51, 53, 62

Discovery Can: Geometric Measurement Area & Perimeter Match-Ups (perimeter only) Area Tiles How Did You Solve It? Cards 72, 73 Pick A Problem Cards 71-75, 81, 82, 83 (perimeter only)

Find All the Possible Rectangles

Rectangles With Same Perimeter

What’s the Missing Length?

www.cpalms.org No aligned resources

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 FF1, FF2, FF3, FF4, FF5

https://learnzillion.com/

Add side lengths to get perimeter

Find the perimeter of polygons marked with unit length markers

Find the perimeter of polygons marked with side lengths

Gwen's Fence: Create side lengths of a rectangle given its perimeter

http://achievethecore.org No aligned resources

17 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Unit 2 PACING: October 3 - November 21

Topic 4: Understanding unit fractions Pacing: October 3 – 17 In previous grades students have had experience partitioning shapes into fair shares (1.G.1.3 and 2.G.1.3), using words to describe the quantity (one-half). In this topic students extend this understanding to partition shapes and number lines, representing these fair shares using fraction notation with a horizontal fraction bar

(e.g., 1

2). Similar to how students view 1 as the building block of whole numbers, students learn to view unit fractions as building blocks—understanding that every

fraction is a combination of unit fractions.

Standards Academic Language

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example,

partition a shape into 4 parts with equal area, and describe the area of each part as 1

4 of the area of the shape.

MAFS.3.G.1.2

area model denominator equal parts linear model (number line) numerator partition unit fraction whole

Students will:

• partition shapes into 2, 3, 4, 6, or 8 parts with equal-sized areas.

NOTE: Shapes may include: quadrilateral, equilateral triangle, isosceles triangle, hexagon, octagon, and circle. (Students do not need to identify triangles as equilateral or isosceles).

• describe the area of each part as a unit fraction of the whole.

E.g., This figure was partitioned/divided into four equal parts. Each part is 1

4 of the total area of the figure.

1

4 is the unit fraction of the

whole (e.g., 4

4).

18 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Understand a fraction 1

𝑏 as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a

fraction 𝑎

𝑏 as the quantity formed by a parts of size

1

𝑏.

MAFS.3.NF.1.1

Students will:

• determine the number of equal parts that make a whole from a given model.

• identify the area of one of the equal parts of a partitioned shape as a unit fraction represented as 1

𝑏.

NOTE: Shapes may include: quadrilateral, equilateral triangle, isosceles triangle, hexagon, octagon, and circle. (Students do not need to identify triangles as equilateral or isosceles).

• understand a fraction 𝑎

𝑏 as the quantity formed by a parts of size

1

𝑏, and that every fraction is a combination of unit fractions.

E.g.,

NOTE: Set models (e.g., There are two boys and three girls. 2

5 of the group are boys.) are not explored in third Grade 3.

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

a. Represent a fraction 1

𝑏 on a number line diagram by defining the interval from 0 to 1 as the whole and

partitioning it into b equal parts. Recognize that each part has size 1

𝑏 and that the endpoint of the part based at 0

locates the number 1

𝑏 on the number line.

MAFS.3.NF.1.2

Students will:

• partition the interval from 0 to 1 on a number line (i.e., linear model) into 2, 3, 4, 6, or 8 equal-length segments.

• identify one of the equal parts as a unit fraction represented as 1

𝑏.

• recognize that a fraction’s location on a number line is based on its distance from zero.

3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics 6. Attend to precision

MAFS.K12.MP.3.1 MAFS.K12.MP.4.1 MAFS.K12.MP.6.1

Topic Comments:

The focus of 3.NF.1.1 and 3.NF.1.2 in this topic is on fractions between 0 and 1. 3.NF.1.2 will be revisited in Topic 5 and will extend students’ learning beyond the unit fraction . Fractions greater than 1 will also be introduced in topic 5.

Students use number lines to represent fractions in a new way (MP.4). It is key for students to have meaningful conversations around this concept to develop precise language about the components of fractions and location on the number line (MP.3, MP.6).

19 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 4 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.G

.1.2

Topic 4 Folding Flags Teacher Guide, p. 24

Reproducibles, p.13

Daily Math Practice Journal, pp. 64-66, 68, 70

How Did You Solve It? Cards 81-90

Four Parts of the Whole

Two Equal Parts

Unit Fractions

Halves of an Irregular Polygon What Does One Fifth Mean

www.cpalms.org

Fun with Pattern Block Fractions

https://www.illustrativemathematics.org/content-standards

Halves, Thirds, Sixths

https://www.ixl.com/math/grade-3 : W1, W2, W3, W4,

W5, W6, W8

https://learnzillion.com/

Understand fractions as the partitioning of a whole

Partition wholes and locate unit fractions

http://achievethecore.org No aligned resources

Origo One Video: Partitioning – Interpreting Fractions as Part of a Whole

3.N

F.1

.1

Topic 4 Figuring Fractions

Fraction Block Out

Teacher Guide, pp. 11-12

Reproducibles, p. 3

Daily Math Practice Journal, pp. 30-32, 35-36, 45

Discovery Can: Fractions Giant Magnetic Fraction Circles and Bars Fraction Circles Tub How Did You Solve It? Cards 33-35 Pick A Problem Cards 41,42,43,96,97,98,99,100

Painting a Wall

Three Quarters of the Race

What Does One Fifth Mean

Which Shows One Third?

www.cpalms.org

Fraction Folding Part 1

It Is all About The Whole

https://www.illustrativemathematics.org/content-standards

Halves, Thirds, Sixths

Naming the Whole for a Fraction

https://www.ixl.com/math/grade-3 : W7 https://learnzillion.com/

Partition and name fractions

http://achievethecore.org No aligned resources Origo One Video: Fractions – Exploring the Area Model of Fractions

Exploring the Length Model of Fractions (stop video at 0:50) - also introduces number lines briefly

Introducing Fraction Models

20 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 4 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

F.1

.2 (

a)

Topic 4 Fraction Fold Up (number line goes past 1)

Fraction Line Up (number line goes past 1)

Teacher Guide, pp. 13-14

Reproducibles, pp. 3, 9

Daily Math Practice Journal, pp. 30, 32, 34, 36, 38, 40, 42-44

Discovery Can: Fractions Giant Magnetic Fraction Circles and Bars Fraction Circles Tub How Did You Solve It? Cards 36-40

Five-Eighths on the Number Line

Four-Sixths on the Number Line

One-Third on the Number Line

Three-Fourths on the Number Line

www.cpalms.org

Interactive Fraction Number Lines

Locating Fractions Less than One on A number Line

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 : W9, W11

https://learnzillion.com/

Combine unit fractions to create new fractions

Create new fractions using unit fractions

Understand fractions as a distance from zero

Use fractions to show a distance from zero

http://achievethecore.org No aligned resources

21 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 5: Using fractions in Measurement and Data Pacing: October 18 – November 2 In this topic students extend their work with measurement and data involving whole numbers to include fractional quantities. Measurement and data are used as a context to support students’ understanding of fractions as numbers. In students’ work with data, context is important, because data are not just numbers; they are numbers with meaning. Through experience with measurement, students realize fractions allow us to represent data much more accurately than just representing data with whole numbers

Standards Academic Language

Understand a fraction 1

𝑏 as the quantity formed by 1 part when a whole is partitioned into b equal parts;

understand a fraction 𝑎

𝑏 as the quantity formed by a parts of size

1

𝑏.

MAFS.3.NF.1.1 area model data denominator distance endpoint equal parts fraction greater than 1 horizontal scale interval linear model (number line) line plot numerator partition unit fraction whole

Students will:

• determine the number of equal parts that make a whole from a given model.

• identify the area of one of the equal parts of a partitioned shape as a unit fraction represented as 1

𝑏.

NOTE: Shapes may include: quadrilateral, equilateral triangle, isosceles triangle, hexagon, octagon, and circle. (Students do not

need to identify triangles as equilateral or isosceles).

• understand a fraction 𝑎

𝑏 as the quantity formed by a parts of size

1

𝑏, and that every fraction is a combination of unit fractions.

E.g.,

NOTE: Set models (e.g., There are two boys and three girls. 2

5 of the group are boys.) are not explored in third grade.

22 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Understand a fraction as a number on the number line; represent fractions on a number line diagram

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1

𝑏 from 0. Recognize that

the resulting interval has size 𝑎

𝑏 and that its endpoint locates the number

𝑎

𝑏 on the number line.

MAFS.3.NF.1.2

Students will:

• represent a fraction 𝑎

𝑏 on a number line by marking off multiple copies of a unit fraction from 0.

E.g.,

• represent fractions greater than 1 on a number line.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole number, halves, or quarters.

MAFS.3.MD.2.4

Students will:

• use a ruler to measure lengths of objects in whole, half, and quarter inches.

• make a line plot with the horizontal scale marked off in whole number, half, or quarter units to display the data that is collected.

2. Reason abstractly and quantitatively. 5. Use appropriate tools strategically.

MAFS.K12.MP.2.1 MAFS.K12.MP.5.1

Topic Comments:

3.NF.1.1 is repeated here to include fractions greater than 1.

Students use tools to generate measurement data (MP.5) and make connections among different representations of the quantities and their relation to the given data context (MP.2).

23 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 5 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

F.1

.1

Topic 5 Figuring Fractions

Fraction Block Out

Teacher Guide, pp. 11-12

Reproducibles, p. 3

Daily Math Practice Journal, pp. 30-32, 35-36, 45

Discovery Can: Fractions Giant Magnetic Fraction Circles and Bars Fraction Circles Tub How Did You Solve It? Cards 33-35 Pick A Problem Cards 41,42,43,96,97,98,99,100

Painting a Wall

Three Quarters of the Race

What Does One Fifth Mean

Which Shows One Third? How Many Fourths are in Two Wholes?

www.cpalms.org

Fraction Folding Part 1

It Is all About The Whole

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 : No aligned

resources https://learnzillion.com/ Partition and name fractions

http://achievethecore.org No aligned resources

3.N

F.1

.2 (

b)

Topic 5 Fraction Fold Up (number line goes past 1)

Fraction Line Up (number line goes past 1)

Teacher Guide, pp. 13-14

Reproducibles, pp. 3, 9

Daily Math Practice Journal, pp. 30, 32, 34, 36, 38, 40, 42-44

Discovery Can: Fractions Giant Magnetic Fraction Circles and Bars Fraction Circles Tub How Did You Solve It? Cards 36-40

Five-Eighths on the Number Line

Four-Sixths on the Number Line

One-Third on the Number Line

Three-Fourths on the Number Line Four Fourths

www.cpalms.org

Interactive Fraction Number Lines Locating Fractions Less than One on A number Line

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 : W10, W12, W13, W14

https://learnzillion.com/

Combine unit fractions to create new fractions

Create new fractions using unit fractions

Understand fractions as a distance from zero

Use fractions to show a distance from zero

http://achievethecore.org No aligned resources

Origo One Video: Fractions on a Number Line - Exploring the Number Line Model of a Fractions

24 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 5 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.M

D.2

.4

Topic 5 Hook, Line and Sticker

Daily Math Practice Journal, pp. 55, 57, 58 How Did You Solve It? Cards 61-62

Measuring Our Pencils Part One Measuring Our Pencils Part Two The Teacher’s Shoe-Part 1 The Teacher’s Shoe-Part 2

www.cpalms.org No aligned resources

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math

/grade-3 : No aligned

resources

https://learnzillion.com/

Measuring objects using whole, half, and quarter inches

http://achievethecore.org No aligned resources

25 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 6: Solving addition and subtraction problems involving measurement Pacing: November 3 – November 21 The focus of this topic is to develop a conceptual understanding of measuring mass, liquid volume, intervals of time, and using measurement as a context for the development of fluency in addition and subtraction (See Common Addition and Subtraction Situations Table on page 60).

Standards Academic Language

Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

MAFS.3.MD.1.1 a.m. analog digital duration half-hour half-past liquid volume mass p.m. time interval

Students will:

• tell and write time to the nearest minute using analog and digital clocks.

• measure duration (intervals) of time in minutes (e.g., basketball practice is 45 minutes long).

• record intervals of time in minutes (i.e. 75 minutes).

• use clock models and number lines to solve word problems using time intervals in minutes.

• solve one- and two-step word problems involving addition and subtraction of time durations (intervals) measured in minutes, using a number line. E.g., Tonya wakes up at 6:45 a.m. It takes her 5 minutes to shower, 15 minutes to get dressed, and 15 minutes to eat breakfast. What time will she be ready for school?

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

MAFS.3.MD.1.2

Students will:

• estimate masses of solid objects (grams and kilograms).

• measure masses of solid objects (grams and kilograms).

• estimate volumes of liquids (milliliters and liters).

• measure volumes of liquids (milliliters and liters).

• solve one-step word problems involving masses or volumes using addition and subtraction.

1. Make sense of problems and persevere in solving them. 5. Use appropriate tools strategically. 4. Model with mathematics.

MAFS.K12.MP.1.1 MAFS.K12.MP.5.1 MAFS.K12.MP.4.1

Topic Comments:

3.MD.1.1 is included here as an opportunity to model addition and subtraction situations with time as the context. 3.MD.1.2 is addressed in full in topic 14 to include multiplication and division situations.

Students can apply the mathematics they know to persevere in solving problems arising in everyday life, society, and the workplace (MP.1, MP.4). Selecting and using appropriate tools supports the development of measurement concepts by asking students to reason about which tools are appropriate and how to use tools efficiently (MP.5).

26 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 6 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.M

D.1

.1

Topic 6 Minute By Minute Watch the Time Fly Turning Back Time Time Tellers

Daily Math Practice Journal, pp. 47, 48, 50, 51,54, 56, 61

Problem Solving Strategy Puzzles (Green) How Did You Solve It? Cards 52-55 Pick A Problem Cards 51,52,53,54,55,56,57,58

Find The Time Telling Time Time Spent What Time Is It Now?

www.cpalms.org

Are we there yet?

Cut in a rush

https://www.illustrativemathematics.org/content-standards

Dajuana’s Homework

https://www.ixl.com/math/grade-3 : T1, T2, T3, T6,

T7

https://learnzillion.com/ Reading the exact minute on a clock

Solving elapsed time word problems to the nearest minute

Identifying the start time, change of time, and end time in real-world elapsed time problems

http://achievethecore.org No aligned resources

3.M

D.1

.2

Topic 6 The King’s Containers Water In Apples

Daily Math Practice Journal, pp. 46, 48, 50, 52, 54, 56, 62

How Did You Solve It? Cards 56-58

Pick A Problem Cards 59, 60, 61, 67, 84

Estimating and Measuring Mass Estimating and Measuring Volume Addition and Subtraction with Mass and Volume

www.cpalms.org

Is that Estimate Correct?

https://www.illustrativemathematics.org/content-standards

How Heavy?

https://www.ixl.com/math/grade-3 : BB6, BB14, BB15

https://learnzillion.com/

Understand mass and how mass is measured

Find the volume of liquids

Find the mass of an object using a balance scale

http://achievethecore.org No aligned resources

27 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Unit 3 PACING: November 27 – March 2

Topic 7: Understanding the relationship between multiplication and division Pacing: November 27 – December 12 The emphasis of this topic is for students to develop a solid understanding of the connection between multiplication and division. Students recognize that multiplication strategies can be used to make sense of and solve division problems. This topic provides students a solid foundation in solving problems with equal groups and arrays, which is necessary to support future success with measurement problems.

Standards Academic Language

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MAFS.3.OA.1.2

array column dividend divisor equal groups equation expression factors groups of inverse operation partition product quotient row shares symbol unknown-factor

Students will:

• interpret a situation requiring division using objects, pictures, words, and expressions.

• describe a context that could be represented with division.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent a problem.

MAFS.3.OA.1.3

Students will:

• use the following situations to solve real-world and mathematical problems related to multiplication within 100. o equal groups: Stan has 4 bags of cookies with 5 cookies in each bag. How many cookies does he have?

Hector has 12 wrenches. He puts 4 in each compartment in his tool box. How many compartments does it take to hold all of his wrenches?

o array model: Mrs. Smith arranges the desks in her classroom. She has 4 rows with 3 desks in each row. How many desks are in her classroom? A marching band has 28 members. The director puts the members into equal columns of 7. How many columns does it take to arrange all of the band members?

• represent multiplication and division word problems involving numbers within 100 using objects, drawings, and equations using a symbol for the unknown number.

NOTE: See Common Multiplication and Division Situations Table on page 61.

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

MAFS.3.OA.2.6

Students will:

• demonstrate the relationship between multiplication and division using a variety of strategies and tools as a foundation for understanding division as an unknown-factor problem.

• demonstrate and explain how a division equation can be rewritten as a related multiplication equation with an unknown factor.

• determine the unknown number in division problems using the relationship between multiplication and division.

28 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

MAFS.3.OA.3.7

Students will: NOTE: By the end of Grade 3, students are to know from memory all products of two one-digit numbers.

Computational fluency is defined as accuracy, efficiency, and flexibility. Research indicates that teachers can best support students’ knowledge of sums and differences through varied experiences with mental strategies rather than using repetitive timed tests.

• multiply within 100 choosing and using strategies such as the relationship between multiplication and division or properties of operations.

• divide within 100 by choosing and using strategies such as the relationship between multiplication and division or properties of operations.

NOTE: Students are NOT expected to identify the properties of operations by name.

1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure.

MAFS.K12.MP.1.1 MAFS.K12.MP.7.1

Topic Comments: 3.OA.1.2 and 3.OA.3.7 are revisited in this topic to extend the range of numbers to include all numbers within 100 when multiplying and dividing. 3.OA.1.3 will be finalized in topic 14 to include measurement quantities. Note that multiplicative comparison problems are introduced in Grade 4 (4.OA.1.2). 3.OA.3.7 is finalized in topic 18. This gives students the opportunity to develop and practice strategies in order to achieve fluency by the end of the year. Students make sense of and solve various types of multiplication and division problems (MP.1) by using the relationship between the two operations (MP.7).

29 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 7 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.1

.2

Topic 7 Camp Fair Shares Boxing Bags and Matches

Teacher Guide, p. 3

Reproducibles, p. 3

Daily Math Practice Journal, pp. 3, 5, 7, 9, 15

Discovery Can: Operations Cards 2, 7, 21-25 Discovery Can: Algebraic Thinking Cards 17-20 How Did You Solve It? Cards 1-3

Interpreting Division Using a Number Line to Solve a Division Problem What Does the Six Mean? Writing a Problem With a Quotient

www.cpalms.org

Pet Store Partitive Division

https://www.illustrativemathematics.org/content-standards

Markers in Boxes

https://www.ixl.com/math/grade-3 No aligned

resources

https://learnzillion.com/

Understand that quotients are shares or groups

Fluently divide to find equal or shares

http://achievethecore.org

3.O

A.1

.3

Topic 7 No aligned resources

Teacher Guide, pp. 3-4 Daily Math Practice Journal, pp. 3, 5, 7, 9, 11, 13, 17, 19 Problem Solving Strategy Puzzles (purple) Discovery Can: Algebraic Thinking Cards 6-20 Discovery Can: Operations Cards 6, 11-22 How Did You Solve It? Cards 3, 6-7

Finding an Unknown Product Bake Sale Books at the Book Fair

www.cpalms.org

Interpret meaning of

division

Two interpretations of division

https://www.illustrativemathematics.org/content-standards

Analyzing Word Problem Involving Multiplication

Gifts From Grandma

Two Interpretations of Division

https://www.ixl.com/math/grade-3 : No aligned resources https://learnzillion.com/ No aligned resources

http://achievethecore.org No aligned resources

30 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 7 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.2

.6

Topic 7 No aligned resources

Teacher Guide, p. 6 Reproducibles, p. 5 Daily Math Practice Journal, pp. 8, 10, 13

Alien Math Changing Division Equations into Multiplication Equations Using Multiplication to Solve Division Problems Multiplication as the Inverse of Division

www.cpalms.org

Grandma wants to know

Three is not a crowd

https://www.illustrativemathematics.org/content-standards

Finding the Unknown in a Division Equation

https://www.ixl.com/math/grade-3 : K15, K16

https://learnzillion.com/

Understand multiplication and division relationships

http://achievethecore.org No aligned resources

3.O

A.3

.7

Topic 7 No aligned resources

Daily Math Practice Journal, pp. 8, 12, 14, 18

Discovery Can: Operations Cards 2, 7, 23-25 Pick A Problem Cards 15, 17, 18

Fluency With Division

www.cpalms.org No aligned resources

https://www.illustrativemathematics.org/content-standards

Kiri's Multiplication Matching Game

https://www.ixl.com/math/grade-3 : N10, J1-J10

https://learnzillion.com/

Apply the relationship between the multiplication and division to multiply within 100

http://achievethecore.org No aligned resources

31 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 8: Investigating patterns in number and operations Pacing: December 13 – January 12 The focus of this topic is for students to identify arithmetic patterns in order to develop a deeper understanding of number and number relationships. In subsequent topics, students will use the understanding of pattern developed in this unit to strengthen their computational strategies and skills.

Standards Academic Language

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding

MAFS.3.OA.4.8 bar graph category category labels column data estimate even generate horizontal interpret key odd pattern picture graph represent row reasonable round scale scale labels title vertical

Students will:

• use the four operations to solve two-step word problems.

• use mental computation and estimation strategies, including rounding (prior to solving), to determine the reasonableness of answers to two-step word problems.

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

MAFS.3.OA.4.9

Students will:

• discover and identify patterns that occur in addition tables.

• explain addition patterns, including patterns that are not explicit, using properties of operations.

E.g., o Any sum of two even numbers is even. o Any sum of two odd numbers is even. o Any sum of an even number and an odd number is odd. o Changing the order of the addends does not change the sum.

• discover and identify patterns that occur in multiplication tables.

• explain multiplication patterns, including patterns that are not explicit, using properties of operations. E.g.,

All even numbers can be divided by 2. A skip counting pattern occurs in each row and column. Changing the order of the factors does not change the product. The product of two even numbers is always even. The product of two odd numbers is always odd. The product of one even and one odd number is always even.

32 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Use place value understanding to round whole numbers to the nearest 10 or 100 MAFS.3.NBT.1.1

Students will:

• round whole numbers to the nearest 10 through the use of a number line, hundred chart, place value chart, etc.

• round whole numbers to the nearest 100 through the use of a number line, hundred chart, place value chart, etc.

• determine possible starting numbers when given a rounded number

• understand that the purpose of rounding is to make mental math easier and to check the reasonableness of an answer.

Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

MAFS.3.NBT.1.3

Students will:

• use concrete tools or drawings to multiply one-digit numbers by multiples of 10.

• apply place value understanding to multiply by multiples of 10. E.g., 4 x 50 is 4 groups of 5 tens or 20 tens. Twenty tens has the same value as 200.

• recognize patterns in multiplying by multiples of 10. E.g., “When you multiply a number by 10, the digits shift and the value becomes10 times greater.”

• multiply one-digit numbers by multiples of 10 in the range of 10-90 using strategies based on place value and properties of operation. E.g., 9 x 80 = 9 x (8 x 10) or (9 x 8) x 10

NOTE: This standard expects that students explain and reason about their products rather than “just adding zeroes”.

33 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

MAFS.3.MD.2.3

Students will:

• create a bar graph representing up to 6 categories of data using the parts of a bar graph (title, scale, scale label, categories, category label, and data and bar graph).

• solve one- and two-step “how many more” and “how many less” problems using information presented in bar graphs.

• create a picture graph using the parts of a scaled picture graph (title, categories, category label, key, and data).

NOTE: Students need to create both horizontal and vertical graphs.

1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure.

MAFS.K12.MP.1.1 MAFS.K12.MP.7.1

Topic Comments: 3.OA.4.8 will be revisited in topic 15 and topic 18 to address the use of equations and letters for unknown quantities. 3.NBT.1.1 is revisited in this topic to give students opportunities to make sense of rounding in multiplication situations. Students examine patterns in arithmetic (MP.7) and discuss what they discover (MP.3).

Topic 8 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.4

.8

Topic 8 Picturing a Solution

Teacher Guide, p. 7 How Did You Solve It? Card 17 Pick A Problem Cards 7,9

Multiplication and Division with Mass and Volume

www.cpalms.org

Getting the hang of two-step word problems

https://www.illustrativemathematics.org/content-standards

The Class Trip

The Stamp Collection

https://www.ixl.com/math/grade-3 : M9, M12

https://learnzillion.com/ No aligned resources

http://achievethecore.org No aligned resources

34 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 8 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.4

.9

Topic 8 No aligned resources

Teacher Guide, p. 8

Daily Math Practice Journal, pp. 10, 14, 16

Discovery Can: Algebraic Thinking Cards 1-4, 21-25 How Did You Solve It? Card 20

Adding Odd Numbers Adding Odds and Evens Patterns within the Multiplication Table Multiplication of Even Numbers

www.cpalms.org

Power of Patterns

https://www.illustrativemathematics.org

Addition Patterns

Symmetry of the Addition

table

Making a Ten

https://www.ixl.com : No aligned resources

https://learnzillion.com/ No aligned resources

http://achievethecore.org No aligned resources

35 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 8 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

BT

.1.1

Topic 8 All Aboard for Rounding Number Line Round Up Numbers in the Round

Teacher Guide, pp. 8-9

Reproducibles, pp. 3, 7

Daily Math Practice Journal, pp. 22, 24, 26, 28, 29

Magnetic Place Value Blocks

How Did You Solve It? Cards 21-23

Pick A Problem Cards 26-30, 37, 40

Mystery Number Rounding Problem

Rounding to the Nearest Hundred

Rounding to the Nearest Ten

The Smallest and Largest Numbers Possible

www.cpalms.org

Rockin’ Round Number line lesson 1 & 2

Rounding for Decades

https://www.illustrativemathematics.org/content-standards

Rounding to 50 or 500

Rounding to the Nearest 10 and 100

https://www.ixl.com/math/grade-3 P1, P2

https://learnzillion.com/

Video: Round to the nearest ten using a number line

Video: Round to the nearest hundred using a number line

http://achievethecore.org No aligned resources

3.N

BT

.1.3

Topic 8 No aligned resources

Teacher Guide, pp. 10-11

Reproducibles, p. 3

Daily Math Practice Journal, pp. 22, 23, 24, 25, 26, 27

How Did You Solve It? Cards 28-32 Magnetic Place Value Blocks

Explaining Multiplication Using Multiples of Ten How Are These Two Problems Related? Multiplying by Multiples of Ten

Packages of 50

www.cpalms.org

Fishing for multiples of 10

Ten, Ten, and more ten

Ten Ten we all win

https://www.illustrativemathematics.org/content-standards

How many Colored Pencils

https://www.ixl.com/math

/grade-3 : F11, H1

https://learnzillion.com/

Fluently multiply one digit numbers by multiples of 10

http://achievethecore.org No aligned resources

36 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 8 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.M

D.2

.3

Topic 8 No aligned resources

Daily Math Practice Journal, pp. 47, 59, 61, 63 How Did You Solve It? Cards 59-60 Pick-A-Problem, cards 62, 63, 64, 65, 66, 68

Collecting Cans For Recycling Favorite Activity After School Flowers in the Garden Lunch Orders

www.cpalms.org

Graphs your way

Paper Air Planes away

https://www.illustrativemathematics.org/content-standards

Classroom Supplies

https://www.ixl.com/math

/grade-3 : U10, U11, U5,

U6, U7

https://learnzillion.com/

Use graphs with scales other than one

Practice solving problems using scaled graphs

Video: Draw Bars on A Graph

http://achievethecore.org No aligned resources

37 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 9: Developing strategies for multiplication and division Pacing: January 16 – 31 The focus for this unit is developing a conceptual understanding of decomposing multiplication problems through the use of the distributive property and the concept of area. Students are not required to use the properties explicitly, but are encouraged to discuss this concept and use area diagrams to support their reasoning.

Standards Academic Language

Apply properties of operations as strategies to multiply and divide. E.g., If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative Property of multiplication). (3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 =30. (Associate Property of multiplication.) Knowing that 8 x 5 = 40, and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive Property).

MAFS.3.OA.2.5

additive area column decompose length row square unit width

Students will:

• represent expressions using various objects, pictures, and words in order to develop understanding of the commutative and distributive properties of multiplication.

• apply properties of operations as strategies to multiply. o Commutative Property of multiplication: E.g., 3 × 2 is the same value as 2 × 3 o Distributive Property of multiplication: E.g., 5 × 7 is the same value as (5 × 5) + (5 × 2)

Relate area to the operations of multiplication and addition. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping

rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

MAFS.3.MD.3.7

Students will:

• use square tiles to connect the area of rectangles to the distributive property.

• explain the relationship between tiling and multiplying decomposed side lengths to find the area of rectangles.

• create area models to represent the distributive property for the area of a rectangle.

• recognize area as additive. E.g.,

• solve real-world area problems involving composite polygons that can be decomposed into non-overlapping rectangles.

3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

MAFS.K12.MP.3.1 MAFS.K12.MP.7.1

Topic Comments: 3.OA.2.5 will be revisited in topic 12 to address the associative property of multiplication. 3.MD.3.7 will be finalized in topic 12 to solve real world and mathematical problems involving area. Students use area diagrams and tiling (MP.5) to model the distributive property and generalize this experience to calculations (MP.7, MP.8).

38 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 9 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.2

.5

Topic 9 No aligned resources

Teacher Guide, p. 5 Reproducibles, p. 3 How Did You Solve It? Cards 10-14 Pick A Problem Cards 7, 9, 10, 14, 23, 24, 25

Break Apart Put Together

Meeting the Reading Goal

Using Arrays to Model the Distributive Property

Decomposing into Equal Addends

www.cpalms.org

Efficient Multiplication

Amazing Arrays

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 : N6, N7 https://learnzillion.com/

Video: Understand commutative property by naming arrays

http://achievethecore.org No aligned resources

Origo One Video: Division Property of Zero – Can I Divide By 0?

3.M

D.3

.7 (

c, d

)

Topic 9 Gardens By Design Planning Plots Polar Toy Factory

Teacher Guide, pp. 20-21

Daily Math Practice Journal, pp. 46, 48, 52, 56-60, 63

Area Tiles Discovery Can: Geometric Measurement How Did You Solve It? Cards 66-69 Pick A Problem Cards 77, 78, 79, 80, 98

Area of a Butterfly Garden Cover Me Decompose Shapes to Find Area Using Arrays to Model the Distributive Property Dawn’s Vegetable Garden

www.cpalms.org

Area we need to know

https://www.illustrativemathematics.org/content-standards

Introducing the Distributive Property

Finding the Area of Polygons

Three Hidden Rectangles

https://www.ixl.com/math/grade-3 FF13, FF14

https://learnzillion.com/ No aligned resources

http://achievethecore.org No aligned resources

39 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 10: Understanding equivalent fractions Pacing: February 1 - 14 In this topic students develop a conceptual understanding of equivalence. Multiple types of models and representations should be used to help students develop this understanding. Students will apply their understanding of equivalence in the next topic as they learn to compare fractions. Through repeated experience locating fractions on the number line, students will recognize that many fractions label the same point and use this to support their understanding of equivalency.

Standards Academic Language

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, (e.g., 1/2= 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. E.g., Express 3 in the form 3 = 3/1; recognize that 6/1 = 6, locate 4/4 and 1 at the same point of a number line diagram.

MAFS.3.NF.1.3 area model denominator equivalent fractions linear model numerator partition unit fraction whole

Students will:

• identify and represent equivalent fractions using area models and linear models. E.g.,

NOTE: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

• recognize and generate simple equivalent fractions.

• explain fraction equivalence (i.e., same area of the whole or same point on a number line).

NOTE: Grade 3 students only explore equivalent fractions using continuous models, rather than using:

algorithms: 1

2 ×

3

3 =

3

6 (multiplying by a fraction equivalent to 1)

procedures: such as cross multiplying (the butterfly method)

• use models to show and explain whole numbers as fractions.

• express whole numbers as fractions, and fractions as whole numbers.

E.g., 5

1 = 5 7 =

7

1

8

2 = 4 3 =

12

4 1 =

6

6

4. Model with mathematics. 6. Attend to precision.

MAFS.K12.MP.4.1 MAFS.K12.MP.6.1

Topic Comments: (3.NF.1.3) The focus of this unit is around equivalence. Although the cluster heading includes comparison of fraction, fraction comparisons (3.NF.1.3d) will be addressed in topic 11. Students develop understanding of equivalence by modeling fractions (MP.4) and communicating their understanding of what it means for fractions to be equivalent (MP.6).

40 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 10 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

F.1

.3 (

a, b

, c)

Topic 10 What is the One? Teacher Guide, pp. 14-17 Reproducibles, p. 3 Daily Math Practice Journal, pp. 30-45 Discovery Can: Fractions Giant Magnetic Fraction Circles and Bars Fraction Circles Tub How Did You Solve It? Cards 41-51 Pick A Problem Cards 44, 45, 46, 47, 48, 49, 50

Equivalent Fractions Four Fourths How Many Fourths are in Two Wholes The Cake Problem Generating Equivalent Fractions

www.cpalms.org

Equivalent fraction dominoes

Match my fractions

The pizza exchange

Twizzle the fractions

https://www.illustrativemathematics.org/content-standards

Jon and Charlie’s Run

https://www.ixl.com/math/grade-3 X1, X2, X3, X4,

X7, X8

https://learnzillion.com/

Generating equivalent fractions

Recognize fractions that are equivalent to whole numbers

http://achievethecore.org No aligned resources

41 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 11: Comparing fractions Pacing: February 15 – March 2 In this topic students build on their prior work with fractions to reason about fraction size and structure to compare quantities. This topic focuses on a single standard to provide time for students to develop conceptual understanding of fraction comparisons and practice reasoning about size. Students defend their reasoning and critique the reasoning of others using both visual models and their understanding of the structure of fractions. This reasoning is important to develop a solid understanding of fraction magnitudes.

Standards Academic Language

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

MAFS.3.NF.1.3

area model denominator equal parts equivalent fractions linear model numerator partition unit fraction whole < (less than) > (greater than) = (equal to)

Students will:

• recognize that fraction comparisons are valid only when the two fractions refer to the same whole.

• compare two fractions with the same denominator with and without visual models.

E.g., 3

8 of a pizza is less than

7

8 of the same size pizza. The pieces are the same size, so 3 of the

1

8 sized pieces is less than 7 of

the 1

8 sized pieces.

• compare two fractions with the same numerator with and without visual models.

E.g., 2

6 of a candy bar is more than

2

8 of the same size candy bar. Cutting the candy bar into 6 pieces results in bigger pieces than

cutting it into 8 pieces. Therefore 2 of the 1

6 sized pieces is more candy than 2 of the

1

8 sized pieces.

• record the results of comparisons with the symbols >, =, or <, and justify the conclusion. NOTE: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically. 7. Look for and make use of structure.

MAFS.K12.MP.3.1 MAFS.K12.MP.5.1 MAFS.K12.MP.7.1

Topic Comments: Students will use their understanding of structure (i.e., the role of the numerator and denominator) (MP.7) to reason about relative sizes of fractions (MP.3). Students use various tools to justify their comparisons, paying particular attention to the same-­‐sized wholes (MP.5).

42 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 11 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

F.1

.3 (

d)

Topic 11 What is the One? Teacher Guide, pp. 14-17 Reproducibles, p. 3 Daily Math Practice Journal, pp. 30-45 Discovery Can: Fractions Giant Magnetic Fraction Circles and Bars Fraction Circles Tub How Did You Solve It? Cards 41-51 Pick A Problem Cards 44, 45, 46, 47, 48, 49, 50

Equivalent Fractions Four Fourths How Many Fourths are in Two Wholes The Cake Problem

www.cpalms.org

Comparing fractions with brownies

https://www.illustrativemathematics.org/content-standards

Comparing Fractions Game

Comparing Fractions with a different Whole

Comparing Fractions with the same Denominator

Comparing Fractions with the same numerator

Fraction Comparisons with pictures

https://www.ixl.com/math/grade-3 Y1, Y6

https://learnzillion.com/

Comparing fractions with like numerators

Comparing fractions with like numerators using number line and area models

Farming fractions- comparing fractions with like denominators

http://achievethecore.org No aligned resources

43 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Unit 4 PACING: March 5 – May 30

Topic 12: Solving problems involving area Pacing: March 5 – 23

The focus of this topic is to use area as a context to further develop multiplicative thinking. In this work, students bridge between concrete and abstract thinking, and use strategies to solve problems. This includes solving problems involving rectangular areas by multiplying side lengths and solving for an unknown number in related multiplication and division equations.

Standards Academic Language

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = __ ÷ 3, 6 x 6 = ?.

MAFS.3.OA.1.4

additive area dividend divisor factor inverse operation non-overlapping polygon product quotient

Students will:

• solve multiplication and division equations where the unknown number is represented by a symbol.

Apply properties of operations as strategies to multiply and divide. E.g., If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative Property of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 – 30. (Associate Property of multiplication.) Knowing that 8 x 5 = 40, and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive Property).

MAFS.3.OA.2.5

Students will:

• represent expressions using various objects, pictures, and words in order to develop understanding of the commutative, distributive and associative properties of multiplication.

• apply properties of operations as strategies to multiply.

o Commutative Property of multiplication: E.g., 3 × 2 is the same value as 2 × 3 o Distributive Property of multiplication: E.g., 5 × 7 is the same value as (5 × 5) + (5 × 2) o Associative Property: E.g., 7 × 6 = 7 x (3 x 2), which is the same value as (7 x 3) x 2

44 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Relate area to the operations of multiplication and addition. 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.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

MAFS.3.MD.3.7

Students will:

• solve real-world and mathematical area problems by multiplying length by width.

• use appropriate labels to represent answers to area problems (e.g., 4 square meters).

• decompose a composite polygon into non-overlapping rectangles to find its area by recognizing area as additive. E.g.,

• solve real-world area problems involving composite polygons that can be decomposed into non-overlapping rectangles.

2. Reason abstractly and quantitatively. 6. Attend to precision. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.2.1 MAFS.K12.MP.6.1 MAFS.K12.MP.8.1

Topic Comments: 3.OA.2.5 introduces the associative property explicitly for the first time. This property is fundamental for developing higher-level computation strategies. In topic 9, students used various strategies to solve area problems. In 3.MD.3.7b students recognize that they can find area in real-world situations by multiplying side lengths—without necessarily using a rectangular array. In 3.MD.3.7d students use the understanding that area is additive to find the area of composite polygons by decomposing the polygon into non-overlapping rectangles. Students move in and out of context to solve these types of problems (MP.2) and use their repeated experience with area models to recognize that area problems can be solved using multiplication (MP.8). Students also explain precisely how an array corresponds to an expression (MP.6).

45 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 12 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.1

.4

Topic 12 No aligned resources

Daily Math Practice Journal, pp. 2, 4, 6, 10, 16, 20

Discovery Can: Algebraic Thinking Cards 6-10

Find the Unknown Number

Missing Number In Division Equations

Missing Numbers in Multiplication Equations

Multiplication and Division Equations

Changing Multiplication Equations into Division Equations

www.cpalms.org

Tasty Algebra using toasted O’s

Discovering the Mystery Factor

https://www.illustrativemathematics.org/content-standards

Finding the unknown in a division equation

https://www.ixl.com/math/grade-3 : G12, K12

https://learnzillion.com/

Video: Use inverse operations to find unknowns in multiplication & division problems

Video: Practice using inverse operations to multiply within 100

http://achievethecore.org No aligned resources

3.O

A.2

.5

Topic 12 No aligned resources

Teacher Guide, p. 5 Reproducibles, p. 3 How Did You Solve It? Cards 10-14 Pick A Problem Cards 7, 9, 10, 14, 23, 24, 25

Break Apart Put Together

Meeting the Reading Goal

Using the Associative Property of Multiplication

Decomposing into Equal Addends Does it work for Division?

www.cpalms.org

Efficient Multiplication

https://www.illustrativemathematics.org/content-standards

Valid Equalities (Part 2)

https://www.ixl.com/math/grade-3 : N8

https://learnzillion.com/

No aligned resources

http://achievethecore.org No aligned resources

3.M

D.3

.7 (

b, d

)

Topic 12 Gardens By Design Planning Plots Polar Toy Factory

Teacher Guide, pp. 20-21

Daily Math Practice Journal, pp. 46, 48, 52, 56-60, 63

Area Tiles Discovery Can: Geometric Measurement How Did You Solve It? Cards 66-69 Pick A Problem Cards 77, 78, 79, 80, 98

Area of a Butterfly Garden

Cover Me

Decompose Shapes to Find Area

Using Arrays to Model the Distributive Property

Fenced Dog Run

Dawn’s Vegetable Garden

www.cpalms.org

Area isn’t just for squares

Area we need to know

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 FF11, FF14, FF9

https://learnzillion.com/

No aligned resources

http://achievethecore.org No aligned resources

46 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 13: Solving problems involving shapes Pacing: March 26– April 6 The focus of this topic is reasoning with shapes and their attributes, including area and perimeter. The standards in this topic strongly support one another because perimeter, like area, is an attribute of shape. Prior work with area and perimeter allows students to differentiate between the two measures in this unit.

Standards Academic Language

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

MAFS.3.MD.4.8

angle area attribute category length linear perimeter polygon quadrilateral side vertex/vertices width

Students will:

• find the perimeter of a polygon that is located on a grid by counting the units.

• find the perimeter of a polygon when given the lengths of all sides.

• identify and use properties of polygons to find the unknown side length(s) of a polygon given the perimeter without using a grid.

• solve real world and mathematical problems involving perimeter.

• demonstrate how rectangles with the same perimeter can have different areas.

• demonstrate how rectangles with the same area can have different perimeters.

• distinguish between linear (perimeter) and area measures and when each measure is appropriate to use

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

MAFS.3.G.1.1

Students will:

• understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category (e.g., all closed plane figures with four straight sides belong to the category of quadrilaterals).

• analyze and compare the attributes of quadrilaterals (i.e., general quadrilaterals, parallelogram, trapezoid, rectangle, rhombus, and square).

• classify quadrilaterals by their attributes (number of sides, number of angles, whether the shape has a right angle, whether the sides are the same length, and whether the sides are straight lines).

• draw quadrilaterals other than rhombuses, rectangles, and squares (i.e., general quadrilaterals, trapezoid, parallelogram).

1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

MAFS.K12.MP.1.1 MAFS.K12.MP.3.1 MAFS.K12.MP.7.1

Topic Comments: 3.MD.4.8 is addressed in full in this topic and focuses on distinguishing between linear and area measures and examining their relationship. Students look for and make use of structure (MP.7) as they determine categories and subcategories of shapes by identifying and reasoning about their attributes. Students make conjectures involving the attributes and measures of shapes and analyze various ways of approaching problems (MP.1, MP.3)

47 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 13 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.M

D.4

.8

Topic 13 Patches of Pumpkins Perimeter and Area of Rectangles Book

Teacher Guide, pp. 22 Reproducibles, pp. 12 Daily Math Practice Journal, pp. 55, 60 Area Tiles Discovery Can: Geometric Measurement Area & Perimeter Match Ups How Did You Solve It? Cards 70, 71, 74 Pick A Problem Cards 71-75, 77,78,79,80,81, 82,83

Rectangles with the same perimeter

Find all the Possible Rectangles

www.cpalms.org

Getting the hang of two-step word problems

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 FF18, FF16,

FF17 https://learnzillion.com/

Solve Real World Area Problems using multiplication and division.

Video: Using a Chart to Understand that rectangles can have the same perimeter with a different area

http://achievethecore.org No aligned resources

3.G

.1.1

Topic 13 Designing With Triangles

Teacher Guide, pp. 23-24

Daily Math Practice Journal, pp. 64-67, 69-71

Giant Magnetic Pattern Blocks How Did You Solve It? Cards 75-80 Pick A Problem Cards 86,87,88,89,90,91,92,93,94,95

Drawing Quadrilaterals Identifying Quadrilaterals – Part 1 Identifying Quadrilaterals – Part 2

www.cpalms.org

Pretzel Quadrilaterals

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 : CC4, CC1, CC6, DD3

https://learnzillion.com/

Video: Sort Quadrilaterals by their Attributes

http://achievethecore.org No aligned resources

48 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 14: Using multiplication and division to solve measurement problems Pacing: April 9 – April 20

This unit extends students’ work in unit 6 to include multiplication and division to solve problems involving measurement quantities.

Standards Academic Language

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent a problem.

MAFS.3.OA.1.3 array equal groups estimate mass volume

Students will:

• use the following situations to solve real-world and mathematical problems related to multiplication within 100. o equal groups: Stan has 4 bags of cookies with 5 cookies in each bag. How many cookies does he have?

Hector has 12 wrenches. He puts 4 in each compartment in his tool box. How many compartments does it take to hold all of his wrenches?

o array model: Mrs. Smith arranges the desks in her classroom. She has 4 rows with 3 desks in each row. How many desks are in her classroom? A marching band has 28 members. The director puts the members into equal columns of 7. How many columns does it take to arrange all of the band members?

o measurement quantities: these problems will focus on multiplication situations involving units of measure.

• represent multiplication and division word problems involving numbers within 100 using objects, drawings, and equations using a symbol for the unknown number.

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

MAFS.3.MD.1.2

Students will:

• estimate masses of solid objects (grams and kilograms).

• measure masses of solid objects (grams and kilograms).

• estimate volumes of liquids (milliliters and liters).

• measure volumes of liquids (milliliters and liters).

• solve one-step word problems involving masses or volumes using addition, subtraction, multiplication, or division.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 5. Use appropriate tools strategically.

MAFS.K12.MP.1.1 MAFS.K12.MP.2.1 MAFS.K12.MP.5.1

Topic Comments: 3.OA.1.3 includes the use of all of the problem types in the Common Multiplication and Division Situations Table (see pg. 61) except for multiplicative compare problems—which will be introduced in Grade 4. Students use strategies for multiplication and division to conceptualize and solve measurement problems (MP.1, MP.2). Students select appropriate tools and justify their selection for measuring different quantities (MP.5).

49 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 14 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.1

.3

Topic 14 No aligned resources

Teacher Guide, pp. 3-4 Daily Math Practice Journal, pp. 3, 5, 7, 9, 11, 13, 17, 19 Problem Solving Strategy Puzzles (purple) Discovery Can: Algebraic Thinking Cards 6-20 Discovery Can: Operations Cards 6, 11-22 How Did You Solve It? Cards 3, 6-7

Finding the Number of Groups

Finding the Group Size the Group Size

Writing Multiplication Word Problem

Writing a Problem With a Quotient

Bake Sale

Books at the Book Fair

www.cpalms.org

Chip Chip Array

Cookies for All

https://www.illustrativemathematics.org/content-standards

Analyzing Word

Problems using

Multiplication

Two Interpretations of Division

https://www.ixl.com/math/grade-3 : H6, H7, H13, O5,

L5

https://learnzillion.com/

No aligned resources

http://achievethecore.org No aligned resources

3.M

D.1

.2

Topic 14 The King’s Containers Water In Apples

Daily Math Practice Journal, pp. 46, 48, 50, 52, 54, 56, 62

How Did You Solve It? Cards 56-58

Pick A Problem Cards 59, 60, 61, 67, 84

Estimating and Measuring Mass

Estimating and Measuring Volume

Addition and Subtraction with Mass and Volume Multiplication and Division with Mass and Volume

www.cpalms.org

Is that Estimate Correct?

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 : BB14, BB15,

BB16 https://learnzillion.com/

Using Multiplication to solve Measurement word problems

The Potato Family

Using Division to solve measurement word problems

Lemonade Split

http://achievethecore.org No aligned resources

50 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 15: Demonstrating computational fluency in problem solving Pacing: April 23 – May 15 This is a culminating topic in which students focus on problem solving in order to demonstrate fluency with addition and subtraction to 1000 and demonstrate

fluency for multiplication and division within 100.

Standards Academic Language

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

MAFS.3.OA.3.7

digit difference dividend division divisor equation factor inverse operation multiply product quotient sum

Students will:

• multiply within 100 choosing and using strategies such as the relationship between multiplication and division or properties of operations.

• divide within 100 by choosing and using strategies such as the relationship between multiplication and division or properties of operations.

• know from memory all products of two one-digit numbers. NOTE: Computational fluency is defined as accuracy, efficiency, and flexibility. Research indicates that teachers can best

support students’ knowledge of sums and differences through varied experiences with mental strategies rather than using repetitive timed tests.

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

MAFS.3.OA.4.8

Students will:

• use the four operations to solve two-step word problems representing the problems using equations with a letter standing for the unknown quantity.

• use mental computation and estimation strategies, including rounding (prior to solving), to determine the reasonableness of answers to two-step word problems.

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

MAFS.3.NBT.1.2

Students will:

• fluently add and subtract within 1000, using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

NOTE: The Standards distinguish strategies from algorithms. From the Standards glossary:

Computation strategy- Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. Computation algorithm- A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly.

51 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Work with computation begins with use of strategies and “efficient, accurate, and generalizable methods.” For addition and subtraction, the culmination of this work is signaled in the Grade 4 Standards by use of the term “standard algorithm.”

2. Reason abstractly and quantitatively. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.2.1 MAFS.K12.MP.8.1

Topic Comments: 3.OA.4.8 was introduced in topic 8 and is finalized in this topic to include the use of letters to represent unknown quantities in equations.

Students demonstrate fluency in multiplication and division within 100 using various strategies and the properties of these operations (MP.8). They also represent these calculations and problem situations abstractly using letters (MP.2).

Topic 15 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.3

.7

Topic 15

Daily Math Practice Journal, pp. 8, 12, 14, 18

Discovery Can: Operations Cards 2, 7, 23-25 Pick A Problem Cards 15, 17, 18

Fluency With Division Using Flexible Strategies

www.cpalms.org

Area isn’t just for squares

Area we need to know

https://www.illustrativemathematics.org/content-standards

Kiri’s Multiplication Matching Game

https://www.ixl.com/math/grade-3 G1, G2, G4, G5, G6, G8, G9, G10, G12-14 G-20

https://learnzillion.com/

Multiplying and Dividing within 100

http://achievethecore.org No aligned resources

52 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 15 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.O

A.4

.8

Topic 15 Picturing a Solution

Teacher Guide, p. 7 How Did You Solve It? Card 17 Pick A Problem Cards 7,9

Zoo Field Trip

Bake Sale

Books at the Book Fair

Party Beverages

www.cpalms.org

Getting the hang of two-step word problems

https://www.illustrativemathematics.org/content-standards See previous resources

https://www.ixl.com/math/grade-3 M7, M8, M9,

M12, O5 https://learnzillion.com/

Solving two step problems with unknown quantity

http://achievethecore.org No aligned resources

3.N

BT

.1.2

Topic 15 Base Place: The Pluses String Bead Subtraction

Teacher Guide, p. 9

Reproducibles, p. 3

Daily Math Practice Journal, pp. 22, 24, 26, 28, 29

How Did You Solve It? Cards 24-27 Pick A Problem Cards 31-36, 38 Discovery Can: Operations Cards 3-5, 8-10 Problem Solving Strategy Puzzles (blue)

Adding and Subtracting Using Properties Addition Within 1000 Subtraction Within 1000 Wanda’s Method

www.cpalms.org

Decoding Decomposing

https://www.illustrativemathematics.org/content-standards See previous resources

https://www.ixl.com/math/grade-3 D2, D3, D4, C2, C3, C4, C6, C7

https://learnzillion.com/

Solving two-step word problems using a variable and more complex story structure

Understanding the relationship between addition and subtraction with 1000

http://achievethecore.org No aligned resources

53 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 16: Revisiting linear and area measurement Pacing: May 16 – 22

These standards are revisited from topic 12 in order to further develop multiplicative thinking and solidify student understanding of area and perimeter prior to Grade 4.

Learning Intentions Standards Academic Language

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

MAFS.3.MD.4.8

area perimeter polygon product quotient Students will:

• demonstrate how rectangles with the same perimeter can have different areas.

• demonstrate how rectangles with the same area can have different perimeters.

• distinguish between linear (perimeter) and area measures and when each measure is appropriate to use

Apply properties of operations as strategies to multiply and divide. E.g., If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative Property of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 – 30. (Associate Property of multiplication.) Knowing that 8 x 5 = 40, and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive Property).

MAFS.3.OA.2.5

Students will:

• apply properties of operations as strategies to multiply and divide.

54 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 16 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.M

D.4

.8

Topic 16 Patches of Pumpkins Perimeter and Area of Rectangles Book

Teacher Guide, pp. 22 Reproducibles, pp. 12 Daily Math Practice Journal, pp. 55, 60 Area Tiles Discovery Can: Geometric Measurement Area & Perimeter Match Ups How Did You Solve It? Cards 70, 71, 74 Pick A Problem Cards 71-75, 77,78,79,80,81, 82,83

Rectangles with the same perimeter

Find all the Possible Rectangles

www.cpalms.org

Getting the hang of two-step word problems

https://www.illustrativemathematics.org/content-standards No aligned resources

https://www.ixl.com/math/grade-3 FF18, FF16, FF17 https://learnzillion.com/ See previous videos http://achievethecore.org No aligned resources

3.O

A.2

.5

Topic 16 No aligned resources

Teacher Guide, p. 5 Reproducibles, p. 3 How Did You Solve It? Cards 10-14 Pick A Problem Cards 7, 9, 10, 14, 23, 24, 25

Break Apart Put Together

Meeting the Reading Goal

Using the Associative Property of Multiplication

Decomposing into Equal Addends Does it work for Division?

www.cpalms.org

Efficient Multiplication

https://www.illustrativemathematics.org/content-standards

Valid Equalities (Part 2)

https://www.ixl.com/math/grade-3 : N8, N6, N7, N10

https://learnzillion.com/ See previous videos http://achievethecore.org No aligned resources

55 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 17: Revisiting understanding equivalent fractions Pacing: May 23 - 30 These standards are revisited from topic 14 in order to solidify student understanding of equivalent fractions prior to work with adding and subtracting fractions in Grade 4.

Standards Academic Language

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

b. Recognize and generate simple equivalent fractions, (e.g., 1

2 =

2

4,

4

6 =

2

3). Explain why the fractions

are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. E.g.,

Express 3 in the form 3 = 3

1; recognize that

6

1 = 6, locate

4

4 and 1 at the same point of a number line

diagram.

MAFS.3.NF.1.3

equivalent

Students will:

• identify and represent equivalent fractions using area models and linear models.

NOTE: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

• recognize and generate simple equivalent fractions.

• explain fraction equivalence (i.e., same area of the whole or same point on a number line).

NOTE: Grade 3 students only explore equivalent fractions using continuous models, rather than using:

algorithms: 1

2 ×

3

3 =

3

6 (multiplying by a fraction equivalent to 1)

procedures: such as cross multiplying (the butterfly method)

• use models to show and explain whole numbers as fractions.

• express whole numbers as fractions, and fractions as whole numbers.

56 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Topic 17 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

3.N

F.1

.3 (

a, b

, c)

Topic 17 What is the One?

Teacher Guide, pp. 14-17 Reproducibles, p. 3 Daily Math Practice Journal, pp. 30-45 Discovery Can: Fractions Giant Magnetic Fraction Circles and Bars Fraction Circles Tub How Did You Solve It? Cards 41-51 Pick A Problem Cards 44, 45, 46, 47, 48, 49, 50

Equivalent Fractions Four Fourths How Many Fourths are in Two Wholes The Cake Problem Generating Equivalent Fractions

www.cpalms.org

Equivalent fraction dominoes

Match my fractions

The pizza exchange

Twizzle the fractions

https://www.illustrativemathematics.org/content-standards

Jon and Charlie’s Run

https://www.ixl.com/math/grade-3 : X1, X2, X3, X4, X7,

X8

https://learnzillion.com/ No aligned resources

http://achievethecore.org No aligned resources

57 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Critical Areas for Mathematics in Grade 3

rigor

In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

(1) Students develop understanding of the meanings of multiplication and division of whole numbers through activities and problems

involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.

(2) Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to and less than. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.

(3) Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.

(4) Students describe, analyze, and compare properties of two-dimensional shapes (i.e., quadrilaterals). They compare and classify

shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.

58 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Grade 3 Major, Supporting, and Additional Work

Topic Title Major Work Supporting Work Additional Work

1 Exploring equal groups as a foundation for multiplication and division

3.OA.1.1, 3.OA.1.2, 3.OA.1.3, 3.OA.3.7

2 Developing conceptual understanding of area 3.OA.2.5,

3.MD.3.5 (a, b), 3.MD.3.6, 3.MD.3.7 (a)

3 Developing strategies for addition and subtraction 3.NBT.1.1,

3.NBT.1.2, 3.MD.4.8

4 Understanding unit fractions 3.NF.1.1, 3.NF.1.2 (a) 3.G.1.2

5 Using fractions in measurement and data 3.NF.1.1, 3.NF.1.2 (b)

3.MD.2.4

6 Solving addition and subtraction problems involving measurement

3.MD.1.1, 3.MD.1.2

7 Understanding the relationship between multiplication and division 3.OA.1.2, 3.OA.1.3,

3.OA.2.6, 3.OA.3.7

8 Investigating patterns in number and operations 3.OA.4.8, 3.OA.4.9

3.MD.2.3 3.NBT.1.1, 3.NBT.1.3

9 Developing strategies for multiplication and division 3.OA.2.5,

3.MD.3.7 (c, d)

10 Understanding equivalent fractions

3.NF.1.3 (a, b, c)

11 Comparing fractions

3.NF.1.3 (d)

12 Solving problems involving area 3.OA.1.4, 3.OA.2.5,

3.MD.3.7 (b, d)

13 Solving problems involving shapes

3.G.1.1 3.MD.4.8

14 Using multiplication and division to solve measurement problems

3.OA.1.3, 3.MD.1.2

15 Demonstrating computational fluency in problem solving 3.OA.3.7, 3.OA.4.8

3.NBT.1.2

16 Revisiting linear and area measurement

3.OA.2.5 3.MD.4.8

17 Revisiting understanding equivalent fractions

3.NF.1.3 (a,b,c)

59 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Standards for Mathematical Practice Grade 3 students will:

1. Make sense of problems and persevere in solving them. (SMP.1) Mathematically proficient students in Grade 3 know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a

problem and look for ways to solve it. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does

this make sense?” They listen to the strategies of others and will try different approaches. Students in Grade 3 will often use another method to check their answers.

2. Reason abstractly and quantitatively. (SMP.2) Mathematically proficient students in Grade 3 recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem

at hand, considering both the appropriate units involved and the meaning of quantities. This involves two processes- decontexualizing and contextualizing. In Grade 3, students represent situations

by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 8 bags of cookies with the same amount of cookies in each bag. If there are 48 cookies how many cookies

are in each bag?” Grade 3 students are expected to translate that situation into the equation: 8 × __ = 48 or 48 / 8 = __ and then solve the task. Students also contextualize situations during the

problem solving process. For example, while solving the task above, students can refer to the context of the task to determine that they were given the number of bags, and the total number of

cookies, but they need to find the number of cookies in each bag.

3. Construct viable arguments and critique the reasoning of others. (SMP.3) Mathematically proficient students in Grade 3 may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they

participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. For example,

when comparing the fractions 1/3 and 1/5, students may generate their own representation of both fractions and then critique each others’ reasoning in class, as they connect their arguments to the

representations that they created.

4. Model with mathematics. (SMP.4) Mathematically proficient students in Grade 3 experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects,

acting out, making a chart, list, or graph, creating equations, etc. Students should have ample opportunities to connect the different representations and explain the connections. Grade 3 students

should evaluate their results in the context of the situation and reflect on whether the results make sense.

5. Use appropriate tools strategically. (SMP.5) Mathematically proficient students in Grade 3 consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance,

they may use graph paper to find all the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table, and determine whether they have all the

possible rectangles.

6. Attend to precision. (SMP.6) Mathematically proficient students in Grade 3 develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning.

They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle they record their answers in square

units.

7. Look for and make use of structure. (SMP.7) Mathematically proficient students in Grade 3 look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to multiply and divide (commutative and

distributive properties).

8. Look for and express regularity in repeated reasoning. (SMP.8) Mathematically proficient students in Grade 3 notice repetitive actions in computation and look for more shortcut methods. For example, students may use the distributive property as a strategy for

using products they know to solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x

8 to arrive at 40 + 16 which equals 56. In addition, third graders continually evaluate their work by asking themselves, “Does this make sense?”

60 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Common Addition and Subtraction Situations Table

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

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?

2 + ? = 5

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?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Total Unknown Both Addends Unknown1 Addend Unknown2

Put Together/

Take Apart

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = ? + ? 5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5 5 – 3 = ?

Difference Unknown Bigger Unknown Smaller Unknown

Compare

“How many more?” version:

Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

“How many fewer?” version:

Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie?

2 + ? = 5 5 – 2 = ?

“More” version suggests operation:

Julie has 3 more apples than Lucy. Lucy has two apples. How many apples does Julie have?

“Fewer” version suggests operation:

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

“Fewer” version suggests wrong operation:

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ? 3 + 2 = ?

“More” version suggests wrong operation: Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

5 – 3 = ? ? + 3 = 5

Darker shading indicates the four Kindergarten problem subtypes. Grade 1 and 2 students work with all subtypes and variants. Unshaded (white) problems are the four difficult subtypes or variants that students should work with in Grade 1 but need not master until Grade 2. Adapted from CCSS, p. 88, which is based on Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity, National Research Council, 2009, pp. 32–33.

1 This can be used to show all decompositions of a given number, especially important for numbers within 10. Equations with totals on the left help children understand that = does not always mean “makes” or “results in” but always means “is the same number as.” Such problems are not a problem subtype with one unknown, as is the Addend Unknown subtype to the right. These problems are a productive variation with two unknowns that give experience with finding all the decompositions of a number and reflecting on the patterns involved.

2 Either addend can be unknown; both variations should be included.

61 Volusia County Schools Grade 3 Math Curriculum Map Mathematics Department July 2017

Common Multiplication and Division Situations Table1

Unknown Product

Group Size Unknown (“How many in each group?” Division)

Number of Groups Unknown (“How many groups?” Division)

3 × 6 = ? 3 × ? = 18 and 18 ÷ 3 = ? ? × 6 = 18 and 18 ÷ 6 = ?

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

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 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays2, Area3

Unknown Product Unknown Factor Unknown Factor 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?

If 18 apples are arranged into 3 equal 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?

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?

Compare4

Larger Unknown Smaller Unknown Multiplier Unknown A blue hat costs $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does the blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

Smaller Unknown 1

3 x 18 = ?

Larger Unknown 1

3 x ? = 6

Multiplier Unknown ? x 18 = 6

A red hat costs $18. A blue hat costs 1

3 as

much as the red hat. How much does the blue hat cost?

A blue hat costs $6 and that is 1

3 of the cost of a

red hat. How much does a red hat cost?

A red hat costs $18 and a blue hat costs $6. What fraction of the cost of the red hat is the cost of the blue hat?

General a × b = ? a × ? = p and p ÷ a = ? ? × b = p and p ÷ b = ?

1 The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. 2 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. 3 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. 4 Multiplicative Compare problems appear first in Grade 4, with whole-number values for A, B, and C, and with the “times as much” language in the table. In Grade 5, unit fractions language such as “one third as much” may be used. Multiplying and unit fraction language change the subject of the comparing sentence, e.g., “A red hat costs A times as much as the blue hat” results in the same comparison as “A blue hat

costs 1

𝑎 times as much as the red hat,” but has a different subject.