Third Grade - MATH
5: Math
Unit 1: Multiplication and Division I
Lesson 1
Getting Ready to Multiply
Students practice skip counting by 2, 3, 4, 5, 6, 7, 8, 9, and 10 using number lines, grids, and online activities. Students model multiplication as repeated addition with arrays (egg carton 2 × 6, drawing arrays for 4+4+4, and the "Arrays and Repeated Addition" sheet) and write corresponding addition sentences. Students identify equal groups (e.g., gloves/hands example and the "Equal Groups" sheet) and use picture arrays from The Grapes of Math to find totals by grouping, and the unit text explicitly states students will "explore the relationship between multiplication and division" and "begin to memorize his multiplication facts."
Lesson 2
What Is Multiplication?
Students interpret products and factors as shown in the Skills section and in activities where they write and read multiplication sentences such as 4×5=20 and 2×3. Students create multiplication sentences from visual scenarios (cookies, donuts, spiders) and draw arrays or equal groups to represent problems. Students use skip counting (counting by 5) and grouping to find totals and watch videos that reinforce multiplication as counting equal groups.
Lesson 3
Arrays and Equal Groups
Students model multiplication with arrays, equal groups, repeated addition, and number lines (Activities 1–3). They draw arrays and write repeated-addition sentences, word forms, number sentences, and compute products for problems such as 3×6, 5×4, 10×4, and other problems up to 10×4 (Activities 2, 4, and Amanda Bean activities). Students use skip counting by 2, 5, and 10 to find products and match arrays to multiplication sentences and products (Day 2 and Activity 4).
Lesson 4
Repeated Addition and Number Lines
Students practice multiple multiplication strategies: they create repeated addition sentences (e.g., 6+6 for 2×6), represent products with number lines (showing jumps and spaces for 4×3, 3×6, 5×4, etc.), draw arrays and equal groups, and use skip counting. The domino activity has students draw two numbers (including 7, 8, 9) and write and model multiplication sentences in four ways, and the mat activity requires producing the product (e.g., 4×3 = 12) after modeling.
Lesson 5
Multiplication and the Abacus
Students model multiplication with arrays on the abacus (e.g., showing 4×5, 3×5, 10×4, 7×2) and count beads by 2, 5, and 10 to find products. Students use domino prompts to model both 6×3 and 3×6, write multiplication sentences, and check products using the abacus. Worksheets titled "Finding Products on the Abacus" and "Arrays on the Abacus" require students to compute many one-digit × one-digit products within 100. Instructions to trade beads to make tens support using place-value strategies to find products.
Lesson 6
The Commutative Property of Multiplication
Students compute specific products such as 7×8 and 9×5 and check answers with an abacus and calculator. Students build and compare arrays (2×5 vs 5×2, 4×7 vs 7×4, etc.) and group multiplication sentences with matching arrays to demonstrate the commutative property. In the Rolling for Products activity, students roll dice to generate factor pairs, write the multiplication sentence and its switched version, and record the product. In the Wrapping Up task, students generate all multiplication sentences with a given product (20) using counters and arrays.
Lesson 7
Multiples of 2 and 3
Students use a 0–20 number line to interpret multiplication (e.g., 1×2 as one jump of 2 and 2×2 as two jumps of 2). Students color multiples of 2 and 3 on an interactive multiplication table, using the commutative property to find symmetric products (e.g., 2×3 and 3×2). Students practice memorizing the 2s and 3s with music videos, online games, worksheet problems (including word problems like horses and tricycles), and timed/random-order drills with number cards.
Lesson 8
More Practice With 2 and 3
Students practice and are prompted to recall specific multiplication facts for the 2 and 3 fact families (e.g., 2×4, 3×5, listed facts). Students complete number-line activities that show skip-counting and use jumps to find products and missing factors (e.g., __ x 2 = 14, __ x 3 = 21). Students use flashcards and timed online quizzes targeted to the 2 and 3 families and are encouraged to use strategies (arrays, number lines, commutative property, abacus) and to solve missing-factor problems that reflect the multiplication/division relationship.
Lesson 9
Multiples of 4 and 5
Students practice multiplying using an interactive multiplication table and worksheets that ask them to color and find multiples of 4 and 5, fill in multiplication sentences (e.g., 1×4 through 10×4, 1×5 through 10×5), and draw number lines showing repeated addition. Students are prompted to use properties of operations and strategies: they are reminded to switch factor order (commutative property), to view multiplication as equal groups, and to use doubling twice to get multiples of 4 (a properties/strategy explanation). Students are given flashcards and online games to practice facts for factors 2, 3, 4, and 5 and are asked to interpret and write multiplication sentences from pictorial problems (cats' legs, cars' wheels).
Lesson 10
More Practice With 2, 3, 4, and 5
The Skills section explicitly lists fluently multiply and divide within 100 and know from memory all products of two one-digit numbers. Students practice multiplication facts for factors 2, 3, 4, and 5 with flashcards, timed quizzes (Learning Gates), and number-card drills that ask them to name products quickly. Activities also ask students to sort and glue multiples and to discuss strategies (doubling for 2, doubling twice for 4, endings for 5), which engages properties of operations and pattern reasoning.
Lesson 11
Multiples of 10
Students use counters and an abacus to represent equal groups and write multiplication sentences such as 3×10=30 and 10×3=30, explicitly applying the commutative property. Students complete worksheets and activities that require computing single-digit times 10 (e.g., 2×10 through 10×10), listing multiples of 10 to 100, and applying the rule of 'add a zero' when multiplying by 10. Students practice selected multiplication facts using flashcards and online games with factors 2, 3, 4, 5, and 10, and the skills list explicitly names fluently multiply and divide within 100 and knowing all products of two one-digit numbers.
Lesson 12
Problem Solving With Multiplication
The lesson's Skills list explicitly includes fluently multiplying and dividing within 100 and knowing from memory all products of two one-digit numbers. Students complete Multiplication Targets and Input/Output activities where they write multiplication sentences, find missing factors (e.g., cover-up tasks), and apply rules like ×2, ×3, ×4, ×5, and ×10. Students solve word problems using arrays, equal groups, repeated addition, and number lines, and they are instructed to practice with flashcards.
Lesson 13
What Is Division?
Students use counters and drawing (dots and arrays) to model division and create equal groups (e.g., dividing 24 into 4 groups, drawing 24 dots and making groups of 8). They identify parts of division sentences (dividend, divisor, quotient) and write/read division equations (e.g., 8÷2=4, 15÷5=3). Students complete a "Connecting Multiplication and Division" sheet that has them write multiplication sentences and matching division sentences (for example, 4×6=24 paired with 24÷6=4) and interpret unknowns in related facts.
Lesson 14
Multiplication and Division Fact Families
Students practice the commutative property by writing 5×4=20 and switching to 4×5=20, and they model division with counters when converting 20÷4=5 and 20÷5=4. The Rolling for Fact Families activity has students generate two multiplication sentences from dice rolls and turn them into two division sentences, explicitly using the relationship between multiplication and division. The triangular fact-family cards and the "Multiplication and Division Fact Families Set 1" page have students create and practice multiplication and division sentences for factors 2, 3, 4, 5, and 10.
Lesson 15
Unit Test
The Skills list explicitly states that students should "Fluently multiply and divide within 100" and "Know from memory all products of two one-digit numbers." Students practice the relationship between multiplication and division with fact-family card activities that ask them to cover a number, name the missing number, and state multiplication and division sentences. Students use and practice strategies (arrays, equal groups, repeated addition, number line, input/output machine ×4) in the multiplication strategies mat and in Unit Test items that require multiplying and dividing within 100.
Final Project
Multiples Mini-Posters
Students are asked to represent target multiples in five different ways (arrays, equal groups, repeated addition, number lines, and multiplication sentences) and to demonstrate the Commutative Property of Multiplication on each poster. Students must create multiplication word problems where the multiple is the answer and are encouraged to practice multiplication facts with flash cards, online games, and timed quizzes. The Skills list explicitly names fluently multiplying and dividing within 100 and knowing from memory all products of two one-digit numbers.
Unit 2: Place Value
Lesson 1
Three-Digit Place Value Review
The lesson's Skills list explicitly states that students should "Know from memory all products of two one-digit numbers." At the end of the lesson students are given time to work with multiplication flashcards and multiplication and division fact family cards for factors 2, 3, 4, 5, and 10, which provides direct practice of multiplication facts.
Lesson 2
Numbers to 10,000
The lesson's Skills list explicitly states students should "Know from memory all products of two one-digit numbers." Activity 6 provides direct practice: students play the "Hit the Button" times-tables games (tables up to 10, selectable mixed) to rehearse multiplication facts. The "Which Numbers?" activity asks students to identify pairs whose product is a given number and includes a quotient question, so students practice both multiplication and some division within the provided number sets.
Lesson 3
Rounding to 10 and 100
The lesson's Skills list explicitly states that students should "Know from memory all products of two one-digit numbers." In Wrapping Up, students are given time to work with multiplication flashcards and multiplication and division fact family cards for factors 2, 3, 4, 5, and 10. The materials prompt students to practice some multiplication facts and to use fact family cards that include both multiplication and division relationships for those specific factors.
Lesson 6
Subtracting Four-Digit Numbers
The Skills section explicitly lists "Know from memory all products of two one-digit numbers." The Wrapping Up section directs that students be given time to work with multiplication flashcards and multiplication/division fact family cards for factors 2, 3, 4, 5, and 10. These items indicate that students are expected to practice and review multiplication facts.
Unit 3: Measurement
Lesson 2
Telling Time to the Minute
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. The inclusion of fact family cards gives students practice linking specific multiplication facts with their related division facts for those factors.
Lesson 4
Working With Weight
Students are given time to work with multiplication flashcards and with multiplication and division fact-family cards for factors 2, 3, 4, 5, and 10 (Wrapping Up). This indicates students practice both multiplication and division facts and some fact-family relationships for those specific factors. The instruction explicitly pairs multiplication and division practice materials, implying practice of the relationship between the operations for those fact families.
Lesson 5
More Work With Weight
The introduction directs students to divide their weight by the weight of comparison items (e.g., 51 ÷ 2 to find how many 2-lb cartons fit into 51 lb) and to multiply their weight by the number of items that make a pound (e.g., 3 × 51 when 3 shoes = 1 lb). The "Weighty Things" activity has students compute equivalents (e.g., I weigh the same as ___ tires at 15 lb each, ___ chickens at 6 lb each, ___ bowling balls at 10 lb each, ___ bananas when 4 bananas = 1 lb, and ___ ping pong balls when 168 = 1 lb). Activity 3 and the "Using My Scale" sheet have students compare objects as less than, same as, or more than a known weight, prompting arithmetic comparisons that involve multiplication or division in context.
Lesson 6
Exploring Volume
Students are given time to work with multiplication flashcards and multiplication and division fact family cards for factors 2, 3, 4, 5, and 10, which provides direct practice with some multiplication and related division facts. The wrap-up challenge uses unit conversions (16 tablespoons = 1 cup; then 32 in a pint; 64 in a quart) that require students to use multiplication to find related totals. Throughout activities students count and record repeated measures (e.g., counting cups to find capacities), which practices repeated-addition/multiplication thinking.
Lesson 7
More Work With Volume
Students physically add 10 milliliters ten times and are asked to determine the total (recognizing 10 groups of 10 = 100 and 10 groups of 100 = 1000), which connects repeated addition to multiplication. The wrap-up directs students to work with multiplication flashcards and multiplication/division fact family cards for factors 2, 3, 4, 5, and 10. The activity with tally marks while filling the 1-liter bottle has students count equal groups to find a total.
Lesson 8
Some Weighty Problem Solving
Students compute totals for multiple identical items (e.g., Reading Scales problems: "If you have 2 blocks that are the same weight, how many total ounces do the blocks weigh?" and "If you have 5 blocks that are the same weight, how many total pounds do the blocks weigh?"). In Packing My Lunch students find totals that require combining repeated items (e.g., "2 bags of chips"), so they practice calculating multiples and repeated addition. Activity 1 asks students to deduce individual shape weights from scales that show sums of several identical shapes, which requires reasoning with repeated quantities.
Lesson 9
Unit Test
The lesson's skills list explicitly includes "Add, subtract, multiply, or divide to solve one-step word problems involving weights or volumes that are given in the same units," and the student activity asks students to compute the total weight of three identical blocks (3 objects weighing 8 oz each → 24 oz). The test items ask students to compute aggregated weights and compare weights (e.g., an object 10 ounces more than a block), which requires students to perform multiplication or repeated addition in context.
Unit 4: Multiplication and Division II
Lesson 1
Mastering More Multiplication Facts
The Skills list explicitly includes "Fluently multiply and divide within 100" and "Apply properties of operations as strategies to multiply and divide," and students are directed to practice facts for 2, 3, 4, 5, and 10 using the Learning Gates and timestables links. Activities have students practice and explain the zero and one properties of multiplication (showing groups with counters, filling in worksheets, and creating fact-family cards that include × and ÷). Students also practice products quickly using dominoes (factors 0–5) and timed/untimed quizzes to build speed and accuracy.
Lesson 2
Multiples of 6 and 7
The Skills section explicitly lists "Fluently multiply and divide within 100" and "Determine the unknown whole number in a multiplication or division equation," and activities have students fill in missing factors and products on the Multiples of 6 and 7 sheets. Students use concrete strategies: they model 6×7 on an abacus, read 6×7 as "6 groups of 7," and are encouraged to use the commutative property (e.g., knowing 2×6 helps with 6×2). Timed games (Hit the Button, SpuQ Balloons), input/output machine practice (×7), skip-counting videos, and flashcard sorting are provided to build recall of multiplication facts.
Lesson 3
Multiples of 8 and 9
Students turn over dominoes and for each pair of one-digit numbers draw an array or picture, write a multiplication sentence, write the "turn-around" multiplication sentence, and write the product. Students color multiples of 8 and 9 on a 1–100 multiplication table, complete fill-in-the-blank problems that include both multiplication (e.g., 8×5=__) and division (e.g., __ ÷ 8 = 7), and use a 9s trick to find products. Students practice times tables through 10 using the Learning Gates Multiplication Practice tool and watch skip-counting songs to reinforce fluency.
Lesson 4
Practicing All of the Multiples
The skills list explicitly notes that students will "Determine the unknown whole number in a multiplication or division equation relating three whole numbers" and "Fluently multiply and divide within 100." In Activity 1 students create and use multiplication and division fact-family cards to cover a number and determine the missing factor, directly practicing the relationship between multiplication and division. Activity 2 has students select two or three factors that multiply to a given product in the Multiplication Blocks game, providing repeated practice identifying factor pairs for products under 100. The optional Multiplication War game has students rapidly name products of two one-digit numbers, supporting recall practice.
Lesson 5
Associative Property of Multiplication
Students compute single-digit products such as 5×6, 9×3, 6×3 and complete worksheets with multiplication problems within 100. Students apply the associative property by rewriting and evaluating expressions like (3×2)×4 and 3×(2×4), add parentheses to indicate which factors to multiply first, and solve problems that use a letter for an unknown factor. Students practice multiple three-factor multiplication problems and play a multiplication game to reinforce skills.
Lesson 6
Distributive Property of Multiplication
Students create and break arrays (Activity 1) and write multiplication sentences such as 6×4 = (2×4)+(4×4) to show the distributive property. They work through examples that use the distributive property to find products (8×9 broken into 8×4 + 8×5, 6×9 as (6×4)+(6×5), 12×5 broken into 5×5+7×5 and 10×5+2×5). The lesson explicitly lists the skill "Fluently multiply and divide within 100" and provides practice problems and worksheets (Option 1 and Option 2) that ask students to use the distributive property on multiplication problems within 100 (e.g., 14×3, 15×6, 4×12, 7×9).
Lesson 7
Reviewing Properties of Multiplication
Students identify and write examples of the commutative, associative, distributive, zero, and one/identity properties by matching and creating number sentences (e.g., 6×4=4×6, 5×9=(5×4)+(5×5)). Students make a foldable that places example boxes under property flaps, and they sort TRUE/FALSE multiplication statements, explaining why each is true or false. Students practice fact families by hiding one number on a card and finding the missing factor or product.
Lesson 8
Revisiting Division
Students use counters and plates to model equal groups and write corresponding multiplication and division sentences (e.g., 3×6=18 and 18÷3=6). They watch a video and explain the relationship between multiplication and division, then represent division on number lines and act out division sentences (e.g., 12÷4 by taking jumps). Students work with fact-family cards to produce four related sentences (two multiplication, two division) and complete "What's Missing?" problems that frame division as an unknown-factor problem.
Lesson 9
Multiplication and Division Facts Practice
Students create multiplication and division fact families from domino draws and write and read the four related sentences, practicing the relationship between multiplication and division. Students complete an input/output activity multiplying by 8 and 9 (with an explicit '×9' trick) and reverse the process for ÷2 and ÷3, using multiplication to find missing dividends. Students use flashcards, targeted online games (including factors through 12), explicit distributive-property examples (e.g., breaking 6×11 into (6×5)+(6×6)), and a × and ÷ facts worksheet that includes problems up to 12×12.
Lesson 10
Problem Solving Using Multiple Operations
Students play a Multiplication 4 in a Row game and complete web-based multiplication/division problem sets to practice facts within 100. Students use arrays and subtraction in the Grapes of Math activity (e.g., treat a 5×5 array as 25 then subtract 3) and use grouping strategies on the Chinese Checkerboard (e.g., 10×12+1=121). Students generate and record division sentences in the Dividend Challenge (listing fact pairs like 8÷2=4 and 8÷4=2), and solve multi-step word problems that combine multiplication and division (e.g., (5×4)+(3×4)).
Lesson 11
Multiplying by Multiples of 10
Students practice multiplying one-digit numbers by multiples of 10 (for example turning 3×40 into 3×4×10 and computing 7×30 by first finding 7×3 then adding a zero). They use the associative property explicitly (writing (3×4)×10 and 3×(4×10)) and model problems with base-10 rods. Students also solve division contexts that use the relationship between multiplication and division (for example 400 ÷ 10 = 40 and word problems that ask for equal shares such as 42 ÷ 7).
Lesson 12
Unit Test
The lesson explicitly lists fluency with multiplication and division within 100 as a skill and provides many practice items (fill-in-the-blank products, division problems, word problems, and fact-family questions) that require computing within 100. Students match and explain multiplication properties (commutative, associative, distributive, zero, identity) with example equations and use those properties when solving problems. The materials include fact-family items showing multiplication/division relationships (e.g., 7×9=63, 63÷9=7) and prompt students to name products quickly and play times-tables games and use flashcards for quick recall.
Final Project
Planning a Picnic
Students solve multi-step word problems that require multiplying and dividing quantities within 100 (e.g., determining how many packages are needed for 60 people: plates 15 per package, forks 20 per package). Students apply properties of operations as strategies, including an explicit example of using the distributive property to break numbers apart for easier multiplication. Students compute team sizes, numbers of ropes, dozens of eggs, cornhole boards and beanbags, and sacks—tasks that require both multiplication and division within 100.
Unit 5: Area and Perimeter
Lesson 1
Review of Plane Shapes
Students solve questions that require multiplying one-digit numbers such as "How many sides do 8 rectangles have?" (8×4=32) and "How many vertices do 6 triangles have?" (6×3=18). Students write number sentences combining products, for example "4 squares and 3 hexagons" shown as 16+18=34 and "3 rectangles and 7 pentagons" shown as 12+35=47. Students are reminded that letters can represent missing numbers "when multiplying and dividing," linking the polygon problems to multiplication/division notation.
Lesson 3
Calculating Perimeter
Students calculate perimeters using multiplication for regular polygons, shown by examples such as 3×5=15 ft, 4×6=24 cm, and 8×5=40 in. Students solve contextual multiplication and division word problems (e.g., 4 boxes of 8 cookies → 4×8, and 30 pieces shared among 5 friends → 30÷5). Students are asked to write number sentences for perimeters and may use repeated addition or multiplication when finding perimeters of squares and rectangles.
Lesson 4
More Work With Perimeter
Students set up and solve multiplication equations for perimeters of regular polygons (example: teacher prompts writing 6(x) ___ cm = 24 cm). Students divide a total perimeter to find an individual side (square with perimeter 16 leads to sides of length 4) and solve for missing side lengths using arithmetic and algebraic reasoning (e.g., 6 in. + ? + ? = 32 in.). Students label side lengths, compute perimeters for pentomino shapes, and use repeated addition or multiplication to total side lengths.
Lesson 5
Problem Solving With Perimeter
Students match shape problems to perimeter answers that require computing products of one-digit numbers (e.g., regular pentagon with sides 8 → 40, square with sides 7 → 28, octagon with sides 8 → 64, hexagon with sides 6 → 36). Students use colored tiles to model groupings (e.g., one tile = one table that seats 4 people so 8 tables seat 32), and they complete Basic Skills Review items that include multiplication and division within 100 (e.g., 7×6, 50÷8, 90×7). Students also form squares and rectangles with given perimeters and label side lengths, which requires dividing a total perimeter among sides or multiplying side length by number of sides.
Lesson 6
What Is Area?
Students build and fill arrays of tiles (e.g., a 6 by 4 box filled with 24 one-inch tiles) and explicitly state areas as products ("24 square inches"). In Activity 3, students roll two dice, color a rectangle with the rolled dimensions (e.g., 2 across and 3 down) and say/write its area ("6 square centimeters"), using the rectangular array to find the product. The Basic Skills Review asks multiplication and division problems (e.g., 7×8 in a word problem and 45 ÷ 6) so students practice computing products and quotients.
Lesson 7
Calculating Area
Students create rectangles with whole-number side lengths and compute their areas by multiplying one side by the other (examples given: 3×4=12, 5×6=30, 2×6=12). Students write multiplication sentences for area problems and complete worksheets with problems such as 5×3, 7×2, 6×6, 9×7, 9×9, and 8×4. Students build shapes, record number sentences (e.g., 2×5=10, 3×4=12, 2×6=12), and solve a ‘‘Think About It'' item that reverses a multiplication fact (square area 25 ⇒ side 5).
Lesson 8
More Work With Area
Students roll two dice and multiply the two one-digit results to find the area of a rectangle, practicing multiplication of side lengths. Students draw and label rectangles and squares on grid paper and write areas for items such as 4×4=16, 8×5=40, 7×7=49, and 6×6=36, directly using multiplication to compute areas. Students complete Basic Skills problems that include multiplication and division (e.g., 9×8=72, 39÷7=5 R4, solve 60×b=540, a×7=420) and use inverse reasoning in at least one problem.
Lesson 9
Creating With Perimeter and Area
The Skills section explicitly states that students will "Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems." In Activities 1 and 3, students trace shapes on centimeter grids, count filled squares to determine area, and compute perimeter values for letters and creature body parts. The "Getting to Know My Creature" sheet requires students to find area and perimeter for multiple body parts and compute totals.
Lesson 10
Problem Solving With Perimeter and Area
Students multiply side lengths to find areas of rectangles (Activity 1 lists nine rectangles such as 9×9, 10×8, 12×6 with areas like 81, 80, 72) and are instructed to find each shape's area and write it on the shape. The lesson explicitly models using the distributive property to make multiplication easier (example: 15×3 = (8×3)+(7×3) = 45). Students also compute areas for robot parts and food court stands, counting squares and using multiplication to fill tables of areas (e.g., areas like 72, 41, 38).
Lesson 11
Unit Test
The lesson has students multiply side lengths to find areas of rectangles (e.g., problems asking for area of 4 ft x 10 ft, 9 ft x 5 ft, and drawing a 5x5 shape for area 25). Students solve for a missing side given area (e.g., area 48 with one side 6 leads to finding the other side is 8), which requires using the inverse relationship between multiplication and division. The skills list explicitly states students will "Multiply side lengths to find areas of rectangles" and identifies relating area to multiplication.
Final Project
Shapesville
The Skills section explicitly requires students to "Multiply side lengths to find areas of rectangles with whole-number side lengths" and to solve perimeter problems. In Step 5 students compute side lengths and areas using division and multiplication (e.g., Building #2: perimeter 40 cm gives each side 10 cm; Building #3: area 30 sq. in and width 3 in gives height 10 in; Building #4: area 40 sq. in and height 8 in gives width 5 in). Day 2 asks students to explain how they found perimeters and areas for their own buildings, prompting use of multiplication and division calculations within the given measurements.
Unit 6: Fractions
Lesson 2
Naming Fractions
Students solve multiplication and division problems in the Basic Skills Review, e.g., computing 10 × 6 = 60 and then dividing 55 ÷ 9 = 6 remainder 1. The review also asks students to solve unknowns in multiplication equations (4 × b = 320 and a × 30 = 270) and includes an instruction that Karl needs to practice his multiplication facts for 25 minutes. These items require students to perform multiplication and division computations and to apply inverse relationships in a word problem context.
Lesson 3
Fraction Parts
Students solve multiplication and division problems in the Basic Skills Review (e.g., 9×6=54 and 43÷8=5 R3) and work equations involving unknowns in multiplication (4×b=120 and a×30=180). Students are instructed to use multiplication flashcards and sort them into piles to show which facts they recall easily and which need more practice. The review items and flashcard practice give students opportunities to work with products and quotients within 100.
Lesson 4
More Fraction Exploration
Students solve multiplication and division problems on the Basic Skills Review #17, including 9 × 6 = 54 and using division to find 44 ÷ 7 = 6 R2. Students also solve simple equations involving multiplication such as 60 × b = 360 (b = 6) and a × 9 = 270 (a = 30). These items require students to compute products and quotients and to use multiplication to solve for unknowns.
Lesson 5
Fractions, Division, and Groups
Students write and interpret division expressions such as 24 ÷ 4 = x and model 24 ÷ 4 with real objects (donut holes). Students convert division to fraction notation (24/4) and name fractions as division (e.g., 1/2 as one divided into two groups). Students divide counters and tiles into equal groups (12 ÷ 2 = 6; dividing 12 into 3 or 4 groups) and complete a Shapes–Fraction–Division table that expresses fractions as division statements.
Lesson 6
Fractions on Number Lines
Activity 4 (Basic Skills Review) directs students to compute 5 × 8 = 40 and then divide 31 ÷ 7 = 4 R3, and includes equations such as 40 × b = 360 and a × 3 = 270 that require using multiplication and division. The review sheet also asks students to practice multiplication facts for 30 minutes and to solve multi-step word problems that combine multiplication and subtraction, giving some practice with operations within 100.
Unit 7: Geometry
Lesson 3
What Is a Quadrilateral?
Students complete the Basic Skills Review which includes multiplication and division computations: 8 × 10 = 80, 68 ÷ 7 = 9 R5, and 8 × 8 = 64. Students also solve a related multiplication equation a × 5 = 450 and apply multiplication to area (8 × 8 = 64) and sharing/division in word problems.
Lesson 4
Getting To Know Specific Quadrilaterals
Students solve multiplication and subtraction in Basic Skills Review #21 (Lonny had 5 bags of cookies, each with 8 cookies; 5×8=40 and 40−7=33). Students then perform a division of a non-multiple in the same set (33÷5=6 remainder 3), showing they compute a division related to the prior multiplication. The review also includes an equation involving multiplication by 8 (a×8=400), which requires solving for a.
Lesson 6
Dividing Shapes
Students solve multiplication and division problems in the Basic Skills Review (e.g., 9×8=72 and then 52÷6=8 R4). Students use multiplication to find area (3×4=12) and then use division to split that area into equal parts (12÷2=6, 12÷3=4, 12÷4=3), so they practice the link between multiplication and division in contextual tasks. Several worksheet activities require creating and reasoning about equal shares, which involves dividing whole areas into equal parts.
Unit 8: Graphing Data
Lesson 2
Pictographs
Students read scaled pictographs and convert between picture counts and actual counts (e.g., one book icon = 10 so Monday with 2 icons = 20; apples: 30 apples -> 3 icons; 65 apples -> 6 1/2 icons). Students determine fractional values of symbols (half = 5 when one symbol = 10; quarter and three-fourths examples for tennis balls) and answer "how many more/how many less" questions using graph values. Students create pictographs from given numeric data using a key (each square = 5 books) which requires dividing totals by the scale and placing the correct number of symbols.
Lesson 3
Bar Graphs
Students complete Basic Skills Review problems that require multiplying and dividing within 100, including 10×6=60, 36÷6=6, and 6×4=24. The review also includes a division word problem that follows a multiplication calculation (finding how many cookies each friend receives after computing total cookies). Activity prompts about choosing a scale ask students to consider common factors (e.g., 5) when deciding a scale.
Lesson 4
Line Plots
Students solve multiplication and division problems in Activity 4 (e.g., 7×8=56 used in a word problem, 41÷5=8 remainder 1, and 8×4=32 in the fencing problem). The Basic Skills Review also includes solving 60×b=420 to find b. These items require students to compute products and quotients within and near the range of 100.
Lesson 5
More Work With Graphing
Students solve multiplication and division problems in the Basic Skills Review (examples: 8×4=32 used to check fencing, 9×10=90 in the cookie problem, and 73÷8=9 R1). In the Money in the Bank activity students use multiplicative relationships to find counts (twice as many pennies as dimes → 2×10=20; multiplying the number of half-dollars by 3 equals the number of quarters). The clue-based coin task and the division problem 7×b=420 (solved as 420÷7=60) require students to apply multiplication and division within the context of word problems.
Unit 9: Skills Review
Lesson 1
Reviewing Multiplication and Division
Students are asked to apply properties of operations and to "fluently multiply and divide within 100" in the Skills list. In Activity 1, students sort and match examples of commutative, associative, distributive, zero, and identity properties using concrete multiplication examples (e.g., 6×7, 5×9, 8×5). In Activity 2, students use an input/output machine with rules like "÷3" and "÷5," drawing number cards and using multiplication facts to find missing numbers, explicitly linking multiplication and division. Multiple web games for practicing multiplication and division facts are provided for additional rehearsal.
Lesson 3
Reviewing Perimeter and Area
Students are asked to write number sentences using multiplication for regular polygons and to calculate perimeters with multiplication (examples shown: 3 × 8 = 24, 4 × 7 = 28, 8 × 4 = 32). Students calculate area by multiplying side lengths (e.g., 10 cm × 7 cm = 70 cm²) and are prompted to draw rectangles with given areas using factor pairs (12: 1×12, 2×6, 3×4; 15: 1×15, 3×5; 16: 1×16, 2×8, 4×4). Students complete worksheets that require computing perimeters and areas, providing practice multiplying whole numbers related to geometry tasks.