Third Grade - MATH
5: Math
Unit 1: Multiplication and Division I
Lesson 1
Getting Ready to Multiply
Students practice skip counting and identifying patterns on number grids by coloring multiples (activities for counting by 2, 3, 4, 5, 6, 7, 8, 9, 10 and skip-counting worksheets). Students create and interpret arrays and write repeated-addition sentences (e.g., 2+2+2+2+2+2=12 and 6+6=12) and make multiple arrays to show the same total (examples for 24). The Math Strategies Review explicitly presents the commutative property of addition (turn-around facts), and students are asked to explain how they found totals and to match arrays to addition facts.
Lesson 2
What Is Multiplication?
Students practice representing equal groups, arrays, and repeated addition (e.g., drawing 4 groups of 5 and writing 4×5=20) and create multiplication sentences from pictured scenarios. Students use skip counting and interpret products of whole numbers as totals of equal groups. The answer key text also notes equivalent fact orders (e.g., 5×6 or 6×5), which shows at least an incidental recognition of the relationship between factor order and product.
Lesson 3
Arrays and Equal Groups
Students draw arrays and equal groups and write corresponding repeated-addition, word, and number sentences (e.g., 3+3+3+3+3+3 OR 6+6+6; 3 groups of 6; 3×6 or 6×3). Students use skip counting by 2, 5, and 10 to find products and match arrays to multiplication sentences and products (e.g., circle groups of 5 in a 5×6 array and count by 5s to get 30). Students are asked to write multiplication in both orders (3×6 and 6×3), showing the turn-around/commutative relationship in specific examples.
Lesson 5
Multiplication and the Abacus
Students build arrays on the abacus (e.g., 4 by 5, 3 groups of 5, 10 groups of 4) and write the corresponding multiplication sentences and products. Students are asked to model either 6×3 or 3×6, showing both orders of factors, and to check products on the abacus. Students are prompted to look for chances to count by 2, 5, and 10 and to make 10 by trading beads to figure out products.
Lesson 6
The Commutative Property of Multiplication
Students create and compare arrays (for example 2×5 and 5×2) and match multiplication sentences with their array representations to show that swapping factors does not change the product. Students roll dice, record the two-factor order as Sentence #1 and the switched order as Sentence #2, and compute the product to observe that the product is the same. Students generate all multiplication sentences with product 20 (4×5, 5×4, 2×10, 10×2) and are prompted to consider commutativity when listing possibilities.
Lesson 7
Multiples of 2 and 3
Students draw and use a 0–20 number line to count by 2s and interpret 1×2, 2×2, etc., showing multiples of 2. Students color multiples of 2 and 3 on an interactive multiplication table and are prompted to notice patterns (for example, two straight lines that begin with 3). Students answer questions such as "Are the multiples of 2 odd or even?" and are reminded to use the commutative property to find symmetric products on the table.
Lesson 8
More Practice With 2 and 3
Students practice and identify multiples of 2 and 3 using number lines and skip-counting tasks (drawing jumps to show multiples up to 20 and 30). The introduction explicitly prompts students to use the commutative property (e.g., 2×4 and 4×2) and the skills list includes applying properties of operations as strategies to multiply and divide. Activities include missing-factor problems that require students to use the number line to determine how many equal jumps produce a given product.
Lesson 9
Multiples of 4 and 5
Students color multiples of 4 on an interactive 10×10 multiplication table and complete worksheets that highlight the products 4, 8, 12, …, 40. They compare multiples of 2 and 4, observe that those multiples are all even, and are prompted to explain how a multiple of 4 is twice a multiple of 2. The lesson explicitly guides students to see that multiplying by 4 is like doubling twice (e.g., if 2×5 = 10 then 4×5 = double 10 = 20) and has students draw number-line jumps of 4 to show repeated addition.
Lesson 10
More Practice With 2, 3, 4, and 5
Students cut out numbers and sort them into groups labeled Multiples of 2, 3, 4, and 5, placing numbers (e.g., 8 and 10) with more than one factor when appropriate. Students glue lists of multiples into their Interactive Notebook and repeat timed sorting to build fluency with these multiplication patterns. During practice and wrapping up, students are prompted to use arrays, number lines, and the abacus to think about products and to discuss "tricks," including that multiplying by 2 is doubling, multiplying by 4 is doubling twice, and multiplying by 5 yields products ending in 0 or 5.
Lesson 11
Multiples of 10
Students make and count groups of ten with counters and an abacus and write multiplication sentences such as 3×10=30 and 10×3=30, with an explicit reference to the commutative property. Students complete worksheets that ask them to observe that multiplying by 10 adds a zero, list the first ten multiples of 10, and color multiples of 10 in a multiplication table. Students practice producing products by multiplying sums from dice by 10, test their rule with a calculator, and solve application problems (e.g., fingers, octopus legs) using multiplication by 10.
Lesson 12
Problem Solving With Multiplication
Students generate and use multiples of 2, 3, 4, 5, and 10 in the Multiplication Targets activity by filling products and missing factors. Students apply and recognize multiplication rules in the Input/Output Machine activity (e.g., ×2, ×3, ×4, ×5, ×10) and deduce a rule when given input/output pairs. Students solve word problems and compare group totals using arrays, equal groups, repeated addition, and number lines, providing repeated practice with multiplicative patterns.
Lesson 13
What Is Division?
Students complete a "Connecting Multiplication and Division" sheet in which they write matching multiplication and division sentences (e.g., 4 x 6 = 24 and 24 ÷ 6 = 4; 4 x 5 = 20 and 5 x 4 = 20) and draw arrays/dots to make groups. Students use arrays and division sentences in the IXL "Write Division Sentences for Arrays" activity to link grouping with multiplication facts. Students also model division problems with dots and boxes (e.g., 12 ÷ 4 = 3, 24 ÷ 4 = 6) to see numeric relationships between factors and quotients.
Lesson 14
Multiplication and Division Fact Families
Students are asked to write a multiplication sentence (5×4=20) and then write the "switched" version (4×5=20) and name the commutative property of multiplication. Students use a domino to create two multiplication sentences and then write the corresponding two division sentences, demonstrating fact-family relationships. Students make and use triangular fact-family cards (for factors 2, 3, 4, 5, and 10) and practice covering one number to determine the missing number, with an explicit skill statement to "apply properties of operations as strategies to multiply and divide."
Lesson 15
Unit Test
Students write and extend lists of multiples (Multiples of 2, 3, 4, 5, 10) and practice skip-counting patterns from their Interactive Notebook. Students complete an input/output table with rule ×4 and write multiplication and division fact-family sentences, and they identify the commutative property in given multiplication sentences. Students use the multiplication strategies mat to represent products as arrays, equal groups, repeated addition, and number-line jumps.
Final Project
Multiples Mini-Posters
Students are asked to represent a given multiple (e.g., 16) in five different ways including arrays, equal groups, repeated addition, number lines, and multiplication sentences. The Steps to Success explicitly require a demonstration of the Commutative Property of Multiplication, and the Skills list includes applying properties of operations as strategies to multiply and divide. Students are prompted to identify which numbers a given number is a multiple of and to explain how they chose to show each multiple.
Unit 2: Place Value
Lesson 1
Three-Digit Place Value Review
Activity 4 has students write sequences (280, 300, 330, 290, 310, 320), put them in order, and identify the counting interval (10), and students complete a "Skip Counting Within 1000" worksheet that practices sequences and additive steps. The Skills section requires students to "Know from memory all products of two one-digit numbers," and the Wrap-Up directs students to work with multiplication flashcards and multiplication/division fact family cards for factors 2, 3, 4, 5, and 10.
Lesson 2
Numbers to 10,000
The lesson states as a skill that students should "know from memory all products of two one-digit numbers" and provides Activity 6 with practice on times tables using the "Hit the Button" game. The Option 2 activity has a "Which Numbers?" sheet that asks students to identify which two numbers produce given products, prompting work with factor pairs and products. Students also complete mixed times-table practice (tables up to 10) in both "Hit the Answer" and "Hit the Question" formats.
Lesson 5
Adding Four-Digit Numbers
Students are asked to list and use multiples (e.g., Activity 4 asks "What are the multiples of 1000?" and students practice 1000, 2000, 3000, etc.). Students complete sequences for multiples of 10 and 100 in the fill-in-the-blank activity and use place-value reasoning to explain how adding 2000 changes the thousands place. Students also use expanded form to decompose numbers (Activity 1) which can reveal additive structure.
Lesson 7
Unit Test
Students complete a multiplication-pattern input/output table where they identify the rule 'multiply by 3' and produce outputs for given inputs, demonstrating identification of an arithmetic rule. Students also circle numbers that are multiples of 2 AND 3, practicing recognition of multiplicative patterns (common multiples). The skills list and multiplication review require knowing products of one-digit numbers, indicating practice with multiplication facts and patterns.
Unit 3: Measurement
Lesson 6
Exploring Volume
Students repeatedly identify and use multiplicative relationships between units (e.g., find that 1 pint = 2 cups, 1 quart = 4 cups, 1 gallon = 16 cups) by measuring and counting cups to fill larger containers. Students complete a foldable showing how cups, pints, quarts, half gallons, and gallons relate and answer conversion questions (e.g., how many pints in a gallon; how many cups in a quart). Students are asked to use a known fact (16 tablespoons = 1 cup) to compute larger measures (How many tablespoons in 1 pint? 1 quart?) and to practice multiplication fact families for factors 2, 3, 4, 5, and 10.
Lesson 7
More Work With Volume
The lesson provides time for students to work with multiplication flashcards and multiplication and division fact family cards for factors 2, 3, 4, 5, and 10. Activity 4 (Basic Skills Review) and the mention of fact family cards give students practice with basic multiplication and related division facts. The multiplication practice reinforces numerical relationships among specific factors.
Lesson 8
Some Weighty Problem Solving
Students compute totals for repeated equal items (e.g., "If you have 2 blocks that are the same weight, how many total ounces do the blocks weigh?" and 5 blocks problems), which requires repeated addition or simple multiplication. Students add and subtract weights in the "Reading Scales" and "Packing My Lunch" problems to find new weights and differences. In "What Do They Weigh?" students use sums of several shapes to deduce individual shape weights, applying numerical relationships across multiple equations.
Unit 4: Multiplication and Division II
Lesson 1
Mastering More Multiplication Facts
Students are asked to use a multiplication table to locate products and to name the terms "factor" and "product," practicing reading patterns in the table. Students physically model and fill in problems that show the zero property (showing zero groups, completing a worksheet of products with zero, and creating fact-family cards with zero). Students model and write multiplication sentences for multiplying by one (drawing groups of one, completing 1×1 through 5×1, and answering the prompt "What pattern do you see, and how might you explain it?"). The lesson also prompts review of the commutative property when comparing 2×5 and 5×2.
Lesson 2
Multiples of 6 and 7
Students are directed to color multiples of 6 and 7 on an interactive 1–10 multiplication table, which makes the rectangular patterns in the multiplication chart visible. Students list the multiples of 6 to 60 and are asked to circle those that are also multiples of 4, and they are explicitly asked whether 48 is a multiple of 4 and to explain why. Students use an abacus to show problems as groups (e.g., 6×7 as 6 rows of 7) and complete input/output ×7 tables, reinforcing group structure of multiplication.
Lesson 3
Multiples of 8 and 9
Students identify arithmetic patterns by coloring multiples of 8 and 9 on a 1–100 multiplication table and by completing fill-in-the-blank problems for 8× and 9× facts. Students write both the multiplication sentence and the "turn-around" sentence (e.g., 3×8 and 8×3), and they are prompted to note factors versus products. For multiples of 9, students are instructed to add the digits of each highlighted multiple and observe that the digits sum to 9, and they are shown a three-step "trick" for multiplying by 9.
Lesson 4
Practicing All of the Multiples
Students play Zap Multiples, which provides practice with multiples described as number patterns. Students create and use multiplication and division fact family cards, covering products and missing factors to reveal relationships among factors and products. Students play Multiplication Blocks where they select factors that multiply to a given product, reinforcing recognition of factor patterns in the multiplication array.
Lesson 5
Associative Property of Multiplication
Students repeatedly group three factors with and without parentheses (e.g., (3×2)×4 and 3×(2×4)) and compute both products to verify equality. Students use letters for unknowns in multiplication sentences (e.g., (2×10)×1 = 2×(n×1) and solve for n), showing they apply the associative property to maintain equality. Students complete worksheets that show and match grouped products (e.g., 1×6×3 = 1×(6×3)) and answer reflective questions about multiplication by zero.
Lesson 6
Distributive Property of Multiplication
Students create arrays and physically break a 6×4 array into two smaller arrays and write corresponding multiplication sentences (for example, 6×4 = (2×4)+(4×4)). Students rewrite problems like 8×9 as 8×(4+5) and expand to (8×4)+(8×5), then add the products to get 72. Students practice multiple decompositions of the same factor (e.g., 12 = 5+7 and 12 = 10+2) and record the expanded forms and sums on worksheets and sticky notes.
Lesson 7
Reviewing Properties of Multiplication
Students identify and match written number sentences to named properties (commutative, zero, one/identity, associative, distributive) and write their own examples. Students create a foldable by placing example boxes under flaps labeled with each property, directly matching equations (for example, 5×9=(5×4)+(5×5) and 6×9=(6×4)+(6×5)) to properties. In the TRUE/FALSE activity, students sort multiplication statements, place them in True/False piles, and explain why true statements (e.g., 7×8=(7×4)+(7×4)) follow particular properties or why false statements do not.
Lesson 8
Revisiting Division
Students create and use multiplication/division fact families, saying four related number sentences (e.g., 2×3=6, 3×2=6, 6÷3=2, 6÷2=3), which highlights commutativity and relationships in the multiplication table. Students use number lines and repeated jumps to represent division and link repeated addition/subtraction to multiplication facts. Students work with multiples and missing-factor problems (e.g., hiding a factor from 2, 8, 16 and asking what number multiplies by 8 to make 16), prompting recognition of multiplicative patterns.
Lesson 9
Multiplication and Division Facts Practice
Students practice and articulate specific multiplication patterns: they use the ×9 trick (products digits sum to 9; subtract 1 from the non-9 factor to get the tens digit) during the input/output machine activity. Students are asked to observe and state the ×11 pattern (single-digit ×11 doubles the digit) and use repeated addition and the distributive property to explain and extend it (e.g., 6×11 as (6×5)+(6×6), and 6×12 by adding another 6). Students build and read multiplication/division fact families with dominoes and match missing factors in the Factor Family Reunion game, reinforcing pattern structure in tables of facts.
Lesson 10
Problem Solving Using Multiple Operations
Students are asked to treat the "Snail Parade" picture as an array and to decompose a 5×5 array and subtract missing snails (5×5 − 3 = 22), and to write an explanation of how they got the answer. In the Chinese Checkerboard activity, students group dots (e.g., groups of 10), multiply to find totals (10×12 + 1 = 121), and are prompted to try multiple grouping strategies and write about each. The Dividend Challenge has students generate multiple division sentences (factor pairs) for given dividends, and the "Make a Number" and web game activities require students to use multiplication and the other operations within problems.
Lesson 11
Multiplying by Multiples of 10
Students are asked to recite multiples of 10 and to examine paired multiplication sentences (e.g., 3×40=120 and 60×2=120) to look for patterns. Students rewrite problems like 3×40 as 3×4×10 and are prompted to use the associative property, writing (3×4)×10 and 3×(4×10), and to choose the easier grouping. Students model with base-ten rods and practice converting a tens-multiple problem into a simpler multiplication fact plus a factor of 10 (adding a zero).
Lesson 12
Unit Test
Students are asked to generate and identify multiples (e.g., write the first 10 multiples of a chosen number, write multiples of 6, and circle multiples of 8), and to complete items on the Unit Test that require recognizing patterns in products. Students match multiplication sentences to named properties (associative, commutative, zero, one/identity, distributive) and are given explicit decomposition using a property (e.g., 9×8 = (9×4)+(9×4)). The introduction prompts students to explain how to find unknowns while using and naming properties of multiplication and to point out examples of each property as they solve problems.
Final Project
Planning a Picnic
Students are explicitly asked to "Apply properties of operations as strategies to multiply and divide" in the Skills list, and Step 2 explicitly suggests using the distributive property to break down numbers when multiplying. Students perform multiple contextual multiplication/division tasks (calculating packages of supplies, eggs, sacks, and seating capacities) where they compute and may draw or decompose numbers on a whiteboard. The Wrapping Up section encourages students to replay factor-based web games and "select as many factors as he can," reinforcing factor and multiplicative reasoning.
Unit 5: Area and Perimeter
Lesson 1
Review of Plane Shapes
Students are asked to compute totals and write number sentences in tasks such as "How many sides do 8 rectangles have? (32)", "How many vertices do 6 triangles have? (18)", and "How many vertices do 4 squares and 3 hexagons have? Write a number sentence to show your answer. (16+18=34)". The materials remind students that letters can represent missing numbers as seen "when multiplying and dividing," and several activity pages require writing number sentences to justify answers. These items require students to use repeated addition or multiplication to find totals of sides and vertices.
Lesson 2
What Is Perimeter?
Students use addition to find the perimeter of polygons (stated: "We use addition to find the perimeter of polygons"). Students use multiplication as a shortcut for regular polygons (stated: "We can use multiplication as a shortcut to find the perimeter of regular polygons") and practice this by modeling shapes (e.g., creating a 4×4 tile square with perimeter 16 and building 6 by 4 and 3 by 8 rectangles and computing 6+4+6+4=20 and 3+8+3+8=22). Students physically label side lengths twice and compute repeated-addend sums when finding perimeters of rectangles made from tiles.
Lesson 3
Calculating Perimeter
Students are asked to use multiplication to find the perimeter of regular polygons ("multiply the number of sides by the length of one side") and shown example number sentences such as 4 × 6 = 24 and 3 + 5 + 3 + 5 = 16. The lesson explicitly tells students they may use repeated addition instead of multiplication for squares (e.g., add 13 four times rather than using multiplication). Activities require students to write number sentences for perimeters (e.g., 2+6+2+6=16) and complete basic multiplication problems on the review sheet.
Lesson 4
More Work With Perimeter
Students use multiplication as repeated addition when finding perimeters of regular polygons (e.g., the prompt to write 6(x) = 24 and to multiply the number of sides by the length of one side). Students add side lengths around irregular shapes and use addition and subtraction to find missing side lengths (e.g., finding the missing side of a triangle by adding known sides and subtracting from the total perimeter). Students compute perimeters of pentomino shapes and compare largest and smallest perimeters by summing unit side lengths.
Lesson 6
What Is Area?
In Activity 3 students use pentominoes to create shapes with 2, 3, 4, and 5 pieces and are asked, "What do you notice about the areas of these shapes?" The lesson then directs the teacher to help the student see that every area will be a multiple of 5 because every pentomino is made up of 5 square units. The Basic Skills Review includes explicit multiplication practice (e.g., 80×9=720 and a 7×8 context in the answer key) that gives students opportunities to work with products.
Lesson 7
Calculating Area
Students create rectangles (3×4, 5×6, 2×6, etc.) and the teacher records the side lengths and areas (e.g., 3, 4, 12) and asks how the first two numbers relate to the third. Students tile rectangles and are asked to count unit squares and then multiply side lengths to show the same area, explicitly writing multiplication sentences (e.g., 2×6=12). Activity 4 asks students to make two different four-sided polygons with the same area (e.g., 2×6 and 3×4 for area 12) and write the equations for each.
Lesson 9
Creating With Perimeter and Area
Students multiply whole-number side lengths to find areas of rectangles as stated in the Skills and used when they compute area for names and creature body parts. Students decompose rectilinear figures into non-overlapping rectangles and add the areas of the parts when they break a creature into body parts and compute each part's area and total area. Students compute perimeters by counting side lengths for letters and creature parts, recording perimeter and area values on their grids and worksheets.
Lesson 10
Problem Solving With Perimeter and Area
Students are asked to multiply side lengths to find areas of rectangles (Skills and Activity 1). The lesson explicitly models decomposing a multiplication problem using the distributive property: for 15×3 it shows (8×3)+(7×3)=24+21=45. Several activities (Area Builder, Area Blocks, and robot/food court tasks) require students to compute products and break larger multiplications into simpler parts for computation.
Lesson 11
Unit Test
Students are asked to relate area to the operations of multiplication and addition and to multiply side lengths to find areas of rectangles; the skills list explicitly includes "Relate area to the operations of multiplication and addition" and "Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas." The activities require students to divide composite shapes into simpler rectangles, calculate each area, and add those areas together (Composite Shapes Review and composite shape problems on the activity pages).
Unit 9: Skills Review
Lesson 1
Reviewing Multiplication and Division
Students watch a video and complete a cut-and-paste activity that presents and practices the commutative, associative, distributive, zero, and identity properties of multiplication. Students use an input/output machine to repeatedly multiply by 10 and are explicitly asked to explain the quick rule for multiplying by 10 (add a zero). Students also use knowledge of multiplication facts (fact families) to work backwards on ÷3 and ÷5 problems, connecting multiplication and division relationships.
Lesson 3
Reviewing Perimeter and Area
Students are asked to write number sentences using multiplication for regular polygons and the answer key shows perimeters calculated with expressions like 3 × 8, 4 × 7, 6 × 5, and 8 × 4. Students are prompted to explain a square's perimeter by adding all sides (repeated addition) or by multiplying because all sides are the same length. In the area activity, students generate rectangles with given areas and are told that a 3 cm by 5 cm shape is the same as a 5 cm by 3 cm shape, reinforcing multiplication fact pairs and commutativity.