3rd Math Unit 3 - Georgia Standards

Georgia

Standards of Excellence

Curriculum Frameworks

Mathematics

GSE Third Grade

Unit 3: Patterns in Addition and

Multiplication

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Georgia Department of Education

Georgia Standards of Excellence Framework

GSE Patterns in Addition and Multiplication ? Unit 3

TABLE OF CONTENTS

Overview ..............................................................................................................................3

Standards for Mathematical Practice ...................................................................................3

Content Standards ................................................................................................................4

Big Ideas ..............................................................................................................................6

Essential Questions ..............................................................................................................6

Concepts and Skills to Maintain ..........................................................................................6

Strategies for Teaching and Learning ..................................................................................7

Selected Terms and Symbols ...............................................................................................9

Tasks ..................................................................................................................................11

Intervention Table ..............................................................................................................16

Formative Assessment Lessons .........................................................................................17

¡ñ Cover Me ..................................................................................................................19

¡ñ Fill Er¡¯ Up .................................................................................................................22

¡ñ The Same But Different ............................................................................................26

¡ñ Count Me In! .............................................................................................................29

¡ñ Paper Cut ...................................................................................................................35

¡ñ Oops! I¡¯m Decomposing ..........................................................................................45

¡ñ Multiplication W/Base Ten Blocks ...........................................................................48

¡ñ Olympic Cola Display...............................................................................................54

¡ñ Array Challenge ........................................................................................................64

¡ñ Skip Counting Patterns .............................................................................................72

¡ñ Take The Easy Way Out ...........................................................................................78

¡ñ Read All About It ......................................................................................................89

¡ñ It Takes Two .............................................................................................................93

¡ñ Subject To Interpretation ..........................................................................................98

¡ñ Measure and Plot.....................................................................................................106

¡ñ Hooked on Solutions ...............................................................................................111

Culminating Task

¡ñ Watch My Garden Grow! .......................................................................................119

IF YOU HAVE NOT READ THE THIRD GRADE CURRICULUM OVERVIEW IN ITS

ENTIRETY PRIOR TO USE OF THIS UNIT, PLEASE STOP AND CLICK HERE:

Return to the use of this unit once you¡¯ve completed reading the Curriculum

Overview. Thank you.

Mathematics ? GSE Third Grade ? Unit 3: Patterns in Addition and Multiplication

Richard Woods, State School Superintendent

July 2021 ? Page 2 of 122

All Rights Reserved

Georgia Department of Education

Georgia Standards of Excellence Framework

GSE Patterns in Addition and Multiplication ? Unit 3

UNIT OVERVIEW

In this unit, students will:

¡ñ Understand concepts of area and relate area to multiplication and addition.

¡ñ Find the area of a rectangle with whole- number side lengths by tiling it.

¡ñ Multiply side lengths to find areas of rectangles with whole-number side lengths in

context of solving real world and mathematical problems.

¡ñ Construct and analyze area models with the same product.

¡ñ Describe and extend numeric patterns.

¡ñ Determine addition and multiplication patterns.

¡ñ Understand the commutative property¡¯s relationship to area.

¡ñ Create arrays and area models to find different ways to decompose a product.

¡ñ Use arrays and area models to develop understanding of the distributive property.

¡ñ Solve problems involving one and two steps and represent these problems using

equations with letters such as ¡°n¡± or ¡°x¡± representing the unknown quantity.

¡ñ Create and interpret pictographs and bar graphs.

The understanding of and ability to use multiplication and division is the basis for all further

mathematics work and its importance cannot be overemphasized. As students move through

upper elementary grades and middle school, the foundation laid here will empower them to work

with fractions, decimals, and percents.

Area is a measure of the space inside a region or how much it takes to cover a region. As with

other attributes, students must first understand the attribute of area before measuring.

The concept of multiplication can be related to the area of rectangles using arrays. Students need

to discover that the length of one dimension of a rectangle tells how many squares are in each

row of an array and the length of the other dimension of the rectangle tells how many squares are

in each column.

Using this model, students should be able to create arrays to solve real-life problems involving

multiplication and apply this concept with addition, subtraction, and division to solve equations

involving two steps or more to find the solution.

Adapted from NC Dept of Public Instruction, Teaching Resources

STANDARDS FOR MATHEMATICAL PRACTICE (SMP)

This section provides examples of learning experiences for this unit that support the development

of the proficiencies described in the Standards for Mathematical Practice. The statements

provided offer a few examples of connections between the Standards for Mathematical Practice

and the content Standards of this unit. The list is not exhaustive and will hopefully prompt

further reflection and discussion.

Mathematics ? GSE Third Grade ? Unit 3: Patterns in Addition and Multiplication

Richard Woods, State School Superintendent

July 2021 ? Page 3 of 122

All Rights Reserved

Georgia Department of Education

Georgia Standards of Excellence Framework

GSE Patterns in Addition and Multiplication ? Unit 3

Students are expected to:

1. Make sense of problems and persevere in solving them. Students make sense of problems

involving area.

2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning by

connecting area with multiplication and arrays.

3. Construct viable arguments and critique the reasoning of others. Students construct and

critique arguments regarding area by creating or drawing arrays or area models to prove

answers.

4. Model with mathematics. Students use arrays or area models to find area.

5. Use appropriate tools strategically. Students use tiles and drawings to solve area problems.

6. Attend to precision. Students use vocabulary such as area, array, area model, and

dimensions with increasing precision to discuss their reasoning when solving area problems.

7. Look for and make use of structure. Students compare rectangles with the same area but

different dimensions and look for patterns in the shapes of the rectangles.

8. Look for and express regularity in repeated reasoning. Students will notice that arrays

and multiplication can be used to solve area problems.

****Mathematical Practices 1 and 6 should be evident in EVERY lesson. ***

CONTENT STANDARDS

Solve problems involving the four operations, and identify and explain patterns in

arithmetic.

MGSE3.OA.8. Solve two-step word problems using the four operations. Represent these

problems using equations with a letter standing for the unknown quantity. Assess the

reasonableness of answers using mental computation and estimation strategies including

rounding.1

1

See Glossary, Table 2

Mathematics ? GSE Third Grade ? Unit 3: Patterns in Addition and Multiplication

Richard Woods, State School Superintendent

July 2021 ? Page 4 of 122

All Rights Reserved

Georgia Department of Education

Georgia Standards of Excellence Framework

GSE Patterns in Addition and Multiplication ? Unit 3

MGSE3.OA.9. Identify arithmetic patterns (including patterns in the addition table or

multiplication table), and explain them using properties of operations.2 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.

?

See Glossary, Table 3

Represent and interpret data.

MGSE3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with

several categories. Solve one- and two-step ¡°how many more¡± and ¡°how many less¡± problems

using information presented in scaled bar graphs. For example, draw a bar graph in which each

square in the bar graph might represent 5 pets.

MGSE3.MD.4. 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¡ª whole numbers, halves, or quarters.

Geometric Measurement: understand concepts of area and relate area to multiplication

and to addition.

MGSE3.MD.5. Recognize area as an attribute of plane figures and understand concepts of area

measurement.

a. A square with side length 1 unit, called ¡°a unit square,¡± is said to have ¡°one square unit¡±

of area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to

have an area of n square units.

MGSE3.MD.6. Measure areas by counting unit squares (square cm, square m, square in, square

ft, and improvised units).

MGSE3.MD.7. Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the

area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole number side lengths in the

context of solving real world and mathematical problems, and represent whole-number

products as rectangular areas in mathematical reasoning.

c. Use tiling to show, in a concrete case, that the area of a rectangle with whole-number side

lengths a and b + c is the sum of a ¡Á b and a ¡Á c. Use area models to represent the

distributive property in mathematical reasoning.

2

See Glossary, Table 3

Mathematics ? GSE Third Grade ? Unit 3: Patterns in Addition and Multiplication

Richard Woods, State School Superintendent

July 2021 ? Page 5 of 122

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