Third Grade - MATH
5: Math
Unit 1: Multiplication and Division I
Lesson 1
Getting Ready to Multiply
Students use arrays and repeated addition to represent multiplication (e.g., drawing 3 rows of 4 or 4 rows of 3 and writing 4+4+4=12 and 6+6=12). The egg-carton example has students state a 2 by 6 array and explicitly note they can make 12 by adding 6 groups of 2 or 2 groups of 6. The Arrays and Repeated Addition answer key shows paired arrays (2x12 and 12x2, 3x8 and 8x3, etc.), which students write addition sentences for.
Lesson 2
What Is Multiplication?
Students interpret products from equal groups, arrays, and repeated addition (students draw groups like 4×5 and count by 5 to get 20). Student activities ask them to create multiplication sentences from pictures (e.g., 6×4, 7×3, 4×8) and to draw representations for scenarios such as 5 bags of 6 donuts and 3 spiders with 8 legs. The answer-key descriptions explicitly show some problems written in both orders (5×6 or 6×5; 3×8 or 8×3), indicating recognition that factor order can represent the same total.
Lesson 3
Arrays and Equal Groups
Students model multiplication with arrays, equal groups, repeated addition, and number lines (Activities 1–4 and Day 2), interpret products (e.g., 5×4=20), and write multiplication in word and number form (e.g., 3 groups of 6 and 3×6 or 6×3). Students create arrays (3×6 or 6×3), write repeated-addition sentences, and match arrays to multiplication sentences on multiple activity pages. Students use skip counting by 2, 5, and 10 to find products from arrays (Day 2) and use counters to make equal groups and find products (Activity 6).
Lesson 5
Multiplication and the Abacus
Students model multiplication on the abacus by creating arrays and writing multiplication sentences (e.g., showing 4 rows of 5 or 5 rows of 4), and they are asked to model either 6×3 or 3×6 when using dominoes. Students count by 2s, 5s, and 10s and are shown that they can count by 10 by counting beads in columns rather than rows (e.g., 10 groups of 4 shown as 4 columns of 10). The materials instruct students to trade beads to make tens to figure out products, reinforcing strategies for computing products.
Lesson 6
The Commutative Property of Multiplication
The lesson provides an explicit definition of the commutative property of multiplication and has multiple student tasks that require switching factors (e.g., creating 2×5 and 5×2 arrays, grouping matching multiplication sentences and arrays, and the Rolling for Products activity where students write Sentence #1 and the switched Sentence #2). Students use manipulatives (counters, abacus) and representations (arrays, dot grids, dice) to show that changing the order of factors does not change the product. The Wrapping Up task has students generate all multiplication sentences for 20 and explicitly notes commutative pairs (4×5 and 5×4, 2×10 and 10×2).
Lesson 7
Multiples of 2 and 3
Students use a number line to interpret products (for example, identifying 1×2 and 2×2 as jumps of 2) and practice forming multiplication sentences from arrays on the number line. Students identify and mark symmetric entries on a multiplication chart (e.g., noting 1×2 and 2×1 are both 2) and are prompted to use the commutative property when coloring multiples. Students practice many multiplication facts for 2 and 3 (coloring multiples, completing multiplication problems, and reciting products in order and in random order).
Lesson 8
More Practice With 2 and 3
The skills list explicitly includes "Apply properties of operations as strategies to multiply and divide," and the Introduction tells students to "use what she knows about the commutative property of multiplication" while giving paired facts (2×4 and 4×2, 3×5 and 5×3). Students practice paired multiplication facts, write products and solve missing-factor problems (e.g., __ x 2 = 14) using number lines, and complete timed quizzes and flashcard work focused on the 2 and 3 fact families.
Lesson 9
Multiples of 4 and 5
Students are asked to "consider switching the order of the factors" when finding multiples of 4 on the multiplication table, supporting use of the commutative property. Students use a number line showing increments of 4 and repeated addition to model multiplication as groups. Students are guided to see that multiplying by 4 can be done by doubling twice (using known 2× facts to get 4× facts) and to relate 2× and 4× products as a strategy.
Lesson 10
More Practice With 2, 3, 4, and 5
The Skills section explicitly lists "Apply properties of operations as strategies to multiply and divide," and students are asked to practice multiplication facts for 2, 3, 4, and 5. In Activity 1 students sort numbers into "Multiples of 2/3/4/5," and are told some numbers (for example, 8 and 10) can be matched to more than one factor, so students identify overlapping factor relationships. The Wrapping Up asks students to describe "tricks" (doubling for ×2, doubling twice for ×4, products ending in 0 or 5 for ×5) and encourages using arrays, number lines, and the abacus as strategies while working timed quizzes.
Lesson 11
Multiples of 10
Students are explicitly prompted to write and say both 3×10=30 and 10×3=30, and are reminded that this is due to the commutative property of multiplication. Students set up and read 10×0 and 0×10 and provide the product zero, practicing the zero property of multiplication. The skills list also states "Apply properties of operations as strategies to multiply and divide," indicating an intended focus on using properties.
Lesson 12
Problem Solving With Multiplication
The lesson's skills list explicitly names "Apply properties of operations as strategies to multiply and divide," and multiple activities ask students to use strategies for multiplication (e.g., use multiples of 2, 3, 4, 5, and 10). In the Getting Started riddle students are prompted to group humps by 5s to avoid counting each one, and Activity 1 (Multiplication Targets) asks students to find missing factors from known products. Activity 3 directs students to use arrays, equal groups, repeated addition, and number lines as strategies when solving word problems.
Lesson 13
What Is Division?
Students practice matching multiplication and division sentences on the "Connecting Multiplication and Division" page (for example, 4 x 5 = 20 and 5 x 4 = 20 are shown), and they draw groups of dots to represent equal groups and write corresponding division sentences. The introduction prompts students to create different equal-group factorizations of 24 (e.g., 6 groups of 4, 4 groups of 6, 3 groups of 8), which exposes them to swapping factors and different groupings. Activities ask students to convert multiplication sentences to division sentences and to make groups from totals, reinforcing the relationship between factors and quotients.
Lesson 14
Multiplication and Division Fact Families
Students are asked to switch 5×4 to 4×5 and explicitly name the commutative property of multiplication. Students model division with 20 counters to show 20÷4=5 and 20÷5=4, reinforcing division as an unknown-factor/partition problem. In Activity 1 and the Rolling for Fact Families sheet, students generate two multiplication sentences from rolled numbers and then write corresponding division sentences, practicing the relationship between multiplication and division. In Activity 2, students make triangular fact family cards and cover a number to determine the missing factor, practicing retrieval and use of multiplication/division relationships.
Lesson 15
Unit Test
Students are asked to use fact-family cards and to write both multiplication and division sentences (for example, 3×7=21 and 7×3=21, and the related division sentences), and the Unit Review explicitly lists "Commutative Property of Multiplication." Students complete a laminated multiplication strategies mat for 6×5 showing a 6 by 5 or 5 by 6 array, 6 groups of 5, repeated addition, and a number line. The unit test includes items that ask students to identify which sentences show the commutative property and to model multiplication using multiple strategies.
Final Project
Multiples Mini-Posters
Students are asked to represent a number (16) in multiple multiplication ways including arrays, equal groups, repeated addition, number lines, and multiplication sentences (e.g., 2×8, 8×2, 4×4). The Steps to Success explicitly requires each poster to include a demonstration of the Commutative Property of Multiplication, and evaluation questions prompt students to identify where the commutative property appears on their posters. The sample poster and activity examples show students writing and interpreting multiplication sentences and swapping factors (2×8 and 8×2).
Unit 2: Place Value
Lesson 2
Numbers to 10,000
The Skills list explicitly requires students to "Know from memory all products of two one-digit numbers." Activity 6 directs students to practice times tables (factors 2, 3, 4, 5, and 10) using the Hit the Button game and to complete a mixed-times activity. The "Which Numbers?" activity asks students to identify pairs whose product equals given numbers and to use multiplication within combined operations (multiply then add/subtract).
Unit 3: Measurement
Lesson 6
Exploring Volume
Students measure and count cups to determine that 1 pint = 2 cups, 1 quart = 4 cups, and 1 gallon = 16 cups through hands-on activities and the foldable. Students answer conversion questions (e.g., How many cups are in a gallon? How many pints in a quart?) and record estimates and actual capacities on the measurement sheet. An additional challenge asks students to compute that 1 pint = 32 tablespoons and 1 quart = 64 tablespoons given 16 tbsp = 1 cup, requiring multiplicative calculation. The lesson also directs students to practice multiplication flashcards and multiplication/division fact family cards for factors 2, 3, 4, 5, and 10.
Lesson 8
Some Weighty Problem Solving
Students are asked to find total weight for multiple identical items (Reading Scales problems 4 and 5 ask for the weight of 2 blocks and 5 blocks respectively), which requires multiplying a single-item weight by 2 or 5. Packing My Lunch includes problems with repeated items (e.g., 2 bags of chips, 2 cookies) that require computing totals by repeated addition or simple multiplication. Activity 1 has students combine weights of shapes and use additive reasoning to deduce individual weights, which can involve repeated-addition thinking.
Unit 4: Multiplication and Division II
Lesson 1
Mastering More Multiplication Facts
Students explore and practice the zero property of multiplication using counters, a student activity page with problems where zero is a factor, and by creating fact-family cards that include zero. Students investigate the one (identity) property by using plates and counters to generate and write multiplication sentences such as 1×1=1, 2×1=2, etc., and by answering rapid-fire 1×n and n×1 problems. Students also review the commutative property by being asked whether order matters (e.g., 2×5 vs. 5×2) and by using multiplication tables and fact families to locate products in different orders.
Lesson 2
Multiples of 6 and 7
Students are asked to color and fill multiplication facts showing pairs like 8×6 = 48 or 6×8 = 48 and are explicitly told that because they know multiples of 2 they already know 2×6 and 6×2, which demonstrates using the commutative property. Students use an abacus to model ‘6 rows with 7 beads each' and are prompted to read 6×7 as 6 groups of 7, supporting use of grouping as a multiplication strategy. Students complete input/output ×7 tasks and practice finding missing factors and products, encouraging use of known facts to produce other products.
Lesson 3
Multiples of 8 and 9
Students turn over dominoes and for each pair of numbers draw an array or picture, write a multiplication sentence, then write the "turn-around" multiplication sentence and the product, which makes the commutative property explicit. Students complete fill-in-the-blank multiplication and division problems (e.g., __ x 8 = 16, 8 x __ = 32, __ ÷ 8 = 7) and color multiples on a multiplication table, giving repeated-practice with facts and with reading products and factors. Students also use a trick for multiplying by 9 and practice times tables through 10, reinforcing strategies for computing products.
Lesson 4
Practicing All of the Multiples
Students create multiplication and division fact family cards (product at top, × and ÷ included) and use those cards to hide a number and determine the missing factor, practicing relationships between multiplication and division. Students play Multiplication Blocks where they must select two or three adjacent factors that multiply to a given product, requiring them to multiply multiple factors and identify factor combinations. Optional games (Happy Burger, Multiplication War) and the Zap Multiples activity give repeated practice with multiples and fluent multiplication and division within 100.
Lesson 5
Associative Property of Multiplication
Students are given an explicit definition of the associative property of multiplication and asked to compute grouped products such as (3×2)×4 and 3×(2×4), finding both products equal. Students place parentheses in multiplication sentences, compute products, and complete worksheets that require rewriting expressions with different groupings (e.g., 3×5×2 with 5 and 2 multiplied first) and matching grouped expressions to products. Students also use letters for unknowns in grouped multiplication problems (e.g., (2×10)×1 = 2×(n×1)) and justify why grouped expressions are equal.
Lesson 6
Distributive Property of Multiplication
Students roll a die and write three numbers, then write and evaluate expressions showing the associative property (e.g., (2×3)×5 = 2×(3×5)) and compare which grouping is easier. Students build arrays (e.g., 6×4) and physically split them with a straw, then write equivalent sums of smaller products to show the distributive property (e.g., 6×4 = (2×4)+(4×4)). Students practice breaking factors (12 into 5+7 and 10+2) and use (a×b)+(a×c) to find products, and worksheets prompt use of the commutative property as a hint for rewriting factors.
Lesson 7
Reviewing Properties of Multiplication
Students are asked to identify and write examples for named properties (commutative, zero, one/identity, associative, distributive) using explicit equations such as 6×4=4×6, (2×6)×1=2×(6×1), and 5×9=(5×4)+(5×5). In Activity 1 students physically match and glue example boxes under flaps for each property, creating a foldable that shows each property with a corresponding equation. In Activity 2 students watch a properties song, complete an online practice, and sort true/false multiplication statements (including distributive and associative examples), then explain why each true statement demonstrates a property or why false ones are incorrect.
Lesson 8
Revisiting Division
Students create and use multiplication–division fact families (e.g., turning a 2, 3, 6 card into 2×3=6, 3×2=6, 6÷3=2, 6÷2=3) and are asked to say and write the four related sentences. Students are encouraged to use what they know about multiplication to find division answers on number lines and to use multiplication facts to solve missing-factor division problems. The activities have students write multiplication sentences to represent equal groups (e.g., 3×6=18) and then write the corresponding division sentence (18÷3=6).
Lesson 9
Multiplication and Division Facts Practice
Students are explicitly asked to "apply properties of operations as strategies to multiply and divide" in the Skills section. In Day 3 students are shown and asked to use the distributive property with concrete examples (e.g., 6×11 as (6×5)+(6×6), 7×12 as (7×6)+(7×6)). In multiple activities (domino fact families, Input/Output Machine, division games) students create multiplication and division fact families and use multiplication knowledge to find unknowns, practicing commutativity and the inverse relationship between multiplication and division.
Lesson 10
Problem Solving Using Multiple Operations
Students are asked to treat pictures as arrays and then use multiplication and subtraction to solve riddles (e.g., treat a 5×5 array as 25 then subtract 3 to get 22). In the Chinese Checkerboard activity students circle equal groups (e.g., groups of 10), multiply to find totals for the groups (10×12) and then add extra dots, showing use of grouping and multiplication with addition. The "More Problems to Solve" item gives number sentences such as (5×4)+(3×4) to compute total legs, which has students combine multiplication facts to solve composite situations.
Lesson 11
Multiplying by Multiples of 10
The lesson has students rewrite 3×40 as 3×4×10 and explicitly asks them to use parentheses to model the associative property (e.g., (3×4)×10 and 3×(4×10)). Students model multiplication with base-10 rods (drawing groups of ten rods) to show 3 groups of 4 tens = 120 and are asked to choose the grouping that is easier (associative strategy). Multiple practice problems (e.g., 7×30, 60×5, 7×40) and the index-card/die activity require students to multiply one-digit numbers by multiples of 10, often by multiplying the nonzero factors then adding a zero.
Lesson 12
Unit Test
Students are asked to name and talk about multiplication properties (commutative, zero, one/identity, associative, distributive) while solving number sentences and identifying factors, products, dividends, divisors, and quotients. The Multiplication Properties Review activity and answer key present explicit examples (e.g., (6×2)×2 = 6×(2×2); 9×8 = (9×4)+(9×4); 5×4 = 4×5; 5×0 = 0; 1×9 = 9) and require students to match sentences to properties. Unit test items and class activities ask students to identify the associative and distributive properties, produce fact families, and use related multiplication/division equations (e.g., 63, 7, 9 fact family; 63÷7=9; 63÷9=7).
Final Project
Planning a Picnic
The lesson explicitly instructs students to "use what you know about addition, subtraction, multiplication, and division" and tells them they "can use the distributive property of multiplication to break down numbers to make multiplying easier." Students are asked to compute numbers of packages (e.g., packages of 15 plates for 60 people) and to use whiteboards to draw and keep track of computations, which requires multiplying and dividing within 100. Game and food tasks (finding numbers of eggs, ropes, sacks, packages, and seating capacities) require students to apply multiplication and division strategies to real problems.
Unit 5: Area and Perimeter
Lesson 5
Problem Solving With Perimeter
Students solve multiplication and division problems in the Basic Skills Review (e.g., 7 boxes of 6 cookies → 7×6, 90×7=630, 50÷8 word problem). Students use one-inch colored tiles to model grouping and counts in Activity 1 (e.g., start with eight tables that seat 32, push tables together and recount seats; use 16 tables as 4 groups of 4). Students use tiles to form shapes and count side units to find perimeters, which requires repeated addition and implicit multiplication (e.g., regular polygons with equal side lengths and squares with each side repeated).
Lesson 7
Calculating Area
Students create rectangles with given whole-number side lengths, count tiles, and then write multiplication sentences to find area (e.g., 3×4=12, 5×6=30, 2×6=12). Students make different rectangles that produce the same area and write the corresponding equations (e.g., tasks asking for two different 4-sided polygons with area 12 using 2×6 and 3×4). Students measure real objects and draw shapes, label side lengths, and record multiplication equations to compute areas during games and hands-on activities.
Lesson 8
More Work With Area
Students multiply whole-number side lengths to find areas of rectangles in multiple activities (dice activity, Making More Areas items like 8×5 = 40, and Design Your Garden). Students decompose rectilinear and composite figures into non-overlapping rectangles and add the areas of the parts to find total area (Activity 2 composite shapes, Activity 3 and 4 worksheets asking to break shapes into simpler rectangles and add areas; answer keys show sums such as 16+36 = 52 and combinations like 12+15+16 = 43). The Basic Skills Review includes solving multiplication equations with unknown factors (60×b = 540, a×7 = 420) and division word problems, giving practice with multiplication and division facts.
Lesson 9
Creating With Perimeter and Area
Students are asked to multiply side lengths to find areas of rectangles with whole-number side lengths (Skills and Activity instructions). Students decompose rectilinear figures into non-overlapping rectangles and add the areas of the parts (Skills and the "Getting To Know My Creature" total-area activity). Students compute area and perimeter for multiple body parts and then find total area by adding the areas of component parts (Activity 3).
Lesson 10
Problem Solving With Perimeter and Area
Students multiply side lengths to find areas of rectangles throughout the activities (Activity 1 lists several rectangle dimensions and has students find each area). Students are instructed to break a large rectangle into two smaller ones to make multiplication easier, with an explicit example using the distributive property: 15×3 = (8×3)+(7×3)=45. Students also count squares to determine area and use multiplication in the robot and Food Court activities to compute areas from given side lengths or grid counts.
Lesson 11
Unit Test
Students multiply side lengths to find areas of rectangles and use multiplication when finding area or perimeter of regular polygons (e.g., computing area = length × width, finding side lengths from a given area). Students decompose rectilinear and composite shapes into non-overlapping rectangles and add the areas of those parts, which requires using multiplication for each sub-rectangle and addition to combine results. Students draw or choose four-sided shapes to match given area or perimeter values, which requires using factor pairs and multiplicative reasoning to produce dimensions that satisfy the area/perimeter.
Unit 6: Fractions
Lesson 6
Fractions on Number Lines
Students solve multiplication and division problems in the Basic Skills Review (e.g., 5×8=40 and 31÷7=4 remainder 3) and practice multiplication facts for 30 minutes. Students also solve for unknown factors in equations (40×b=360 and a×3=270) and complete word problems that require multiplying and dividing whole numbers.
Unit 9: Skills Review
Lesson 1
Reviewing Multiplication and Division
Students view a properties-of-multiplication video and complete a cut-and-paste activity that asks them to match examples to the Commutative, Associative, and Distributive properties. The provided answer-key image explicitly shows commutative examples (e.g., 6×7 = 7×6), associative examples ((3×4)×2 = 3×(4×2)), and distributive examples (8×12 = (8×2) + (8×10)). In Activity 2 students practice multiplication (x10) and use inverse relationships and fact-family reasoning to find missing dividends for ÷3 and ÷5, applying multiplication knowledge to division problems.
Lesson 3
Reviewing Perimeter and Area
Students write multiplication number sentences for regular polygons when finding perimeters (e.g., 3 × 8 for an equilateral triangle, 6 × 5 for a hexagon) and complete perimeter problems using multiplication. Students compute area by multiplying length and width (e.g., 10 cm × 7 cm = 70 cm²) and create rectangles with given areas, listing factor pairs such as 3 × 5 and 5 × 3. Students are asked to recognize that a shape that is 3 cm by 5 cm is the same as one that is 5 cm by 3 cm, which implies interchangeability of factors.