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, and 10 through multiple activities and number grids, which supports building multiplication facts. Students create and interpret arrays (egg carton example, drawing arrays for 4+4+4, and the "Arrays and Repeated Addition" page) and write repeated-addition sentences for each array (e.g., 2+2+2+2+2+2=12 and 4+4+4+4+4+4=24). Students use equal-group reasoning in tasks such as determining how many hands 8 people have and listing real-world items that come in groups (Equal Groups sheet). The Grapes of Math activities ask students to use arrays and grouping to count items (fish and grapes) rather than counting one-by-one.
Lesson 2
What Is Multiplication?
Students interpret multiplication as repeated addition and as equal groups, for example by representing 4 groups of 5 counters and writing 4×5=20 and counting by 5 to get the product. Students create multiplication sentences and draw pictures for word problems such as "Each bag has 6 donuts. You buy 5 bags" and "Each spider has 8 legs. There are 3 spiders." Students identify arrays and equal groups from the read-aloud (cookies, window panes, etc.) and complete activity pages that ask them to draw situations and write corresponding multiplication equations.
Lesson 3
Arrays and Equal Groups
Students draw arrays and write repeated addition, word form (___ groups of ___), and number form (___ × ___) for given totals (Activities 2 and 4). Students model equal groups with counters and plates, write multiplication sentences (e.g., 4×6), and find the product by counting or skip counting (Activity 6 and Showing Equal Groups). Students find arrays and equal-group situations in the Amanda Bean read-aloud and write multiplication sentences and compute products from those story contexts (Activities 5 and 7).
Lesson 4
Repeated Addition and Number Lines
Students model multiplication as repeated addition (Activity 1) by writing addition sentences such as 6+6 for 2×6 and finding products using skip counting. Students use number lines to represent multiplication (Activity 3) with tasks showing jumps (e.g., 4×3 shown as four jumps of three to reach 12). Students create and model multiplication sentences in multiple formats (Activity 4) by drawing arrays, showing equal groups, writing repeated addition, and drawing number-line jumps for problems like 4×3 and for domino-generated multiplication pairs.
Lesson 5
Multiplication and the Abacus
Students model multiplication as equal groups and arrays using an abacus (e.g., showing 4×5, 3 groups of 5, 10×4, 7×2) and write the corresponding multiplication sentences. Students complete worksheets that ask them to write multiplication sentences for given arrays and to find products for multiplication sentences (many products are within 100). Students are prompted to use strategies such as counting by 2, 5, and 10 and trading beads to make tens to determine products.
Lesson 6
The Commutative Property of Multiplication
Students create and interpret arrays and equal groups (e.g., making 2×5 and 5×2 arrays with 20 counters, matching dot grids to multiplication sentences). Students write multiplication sentences and their switched versions (Rolling for Products) and compute products using an abacus, whiteboard, or calculator; the Skills section explicitly lists interpreting products of whole numbers and applying properties of operations. Students use arrays and drawings repeatedly to represent multiplication situations.
Lesson 7
Multiples of 2 and 3
Students draw jumps on a 0–20 number line to represent repeated addition and write multiplication sentences such as 2×2 to show equal groups. Students solve two explicit equal-group word problems (How many legs do 3 horses have? How many wheels are on 5 tricycles?), draw pictures to find answers, and write the corresponding multiplication sentences. Students use a 10×10 multiplication table and color multiples of 2 and 3 and complete multiplication problems on worksheets, reinforcing multiplication within 100.
Lesson 8
More Practice With 2 and 3
Students practice multiplying within 100 using number lines for multiples of 2 and 3 and by writing and solving multiplication problems (e.g., 6×2, 10×3) and timed quizzes for fluency. Students use visual models and skip-counting (frog and pogo-stick illustrations, arrays/abacus suggestions) to represent multiplication and understand equal groups. Students solve missing-factor equations with a blank (e.g., __ × 2 = 14, __ × 3 = 21), using the number line to find the unknown.
Lesson 9
Multiples of 4 and 5
Students solve equal-group word problems by drawing and writing multiplication sentences (e.g., "How many legs do 5 cats have? Draw a picture and write the multiplication sentence"; "How many wheels are on 4 cars?"). Students use number lines to represent repeated addition/multiples (draw a number line showing jumps from 0 to 28). Students practice multiplying within 100 using multiplication tables and fill-in products up to 40, and the lesson lists as a skill "Determine the unknown whole number in a multiplication or division equation relating three whole numbers."
Lesson 11
Multiples of 10
Students represent equal groups using manipulatives (abacus and counters) and write multiplication sentences such as 3×10=30 and 10×3=30. Students solve real-world word problems by drawing pictures and writing multiplication equations (e.g., how many fingers 5 people have; how many legs 10 octopuses have). Students practice multiplying within 100 on worksheets and games, list multiples of 10 up to 100, and color multiples in a multiplication table to identify patterns.
Lesson 12
Problem Solving With Multiplication
Students solve multiple word problems that require multiplication within 100 (Activity 3: Sandy, Randy, Mandy) and compare multiplicative situations (Activity 2: panes, chocolate chips, wheels). Students are explicitly asked to draw pictures, use arrays, equal groups, repeated addition, number lines, and to write multiplication sentences to represent and solve problems. Students practice finding missing factors and outputs (Activity 1: Multiplication Targets and Activity 4: Input/Output Machine), which requires working backward from a product or output.
Lesson 13
What Is Division?
Students solve carnival-themed word problems (Divide and Ride) that require finding how many seats/chairs/cars are filled when groups of children are arranged, using numbers like 14, 24, and 30. Students draw dots to model division sentences and complete division equations (e.g., 24 ÷ 4 = 6; blanks provided for missing answers), and they complete a Connecting Multiplication and Division page that has students write division sentences corresponding to arrays and multiplication facts. Students also practice creating equal groups and writing division sentences using an online IXL activity focused on arrays.
Lesson 14
Multiplication and Division Fact Families
Students model division as equal groups with 20 counters (e.g., making 4 groups of 5 and 5 groups of 4) and write the corresponding division and multiplication sentences. Students create and write multiplication and division fact families from dominoes and dice (e.g., 3×4=12, 12÷4=3) and make triangular fact-family cards for factors 2,3,4,5,10, covering facts through 10×10. The lesson also lists the skill "Determine the unknown whole number in a multiplication or division equation relating three whole numbers," which prompts students to find missing numbers in fact families.
Lesson 15
Unit Test
Students model multiplication problems with arrays, equal groups, repeated addition, and number lines (for example, the task to model 3×8 with an array, equal groups, repeated addition, and a number line). Students solve measurement word problems by drawing pictures and writing equations (e.g., How many legs do 5 dogs have? How many fingers do 8 people have? How many hotdogs in 2 packages?). Students write and interpret multiplication and division sentences and fact families (e.g., 3×7=21, 21÷7=3; fact family tasks for 4, 9, 36) and complete input/output tables using a ×4 rule, all within 100.
Final Project
Multiples Mini-Posters
Students are asked to represent chosen multiples in five different ways including arrays, equal groups, repeated addition, number lines, and multiplication sentences (several activity pages and the sample poster show these representations). Each poster must include a multiplication word problem where the multiple is the answer, and the sample poster includes a word problem with the equation 2 × 8 = 16. The skills list explicitly names determining the unknown whole number in a multiplication or division equation and fluently multiplying and dividing within 100.
Unit 2: Place Value
Lesson 1
Three-Digit Place Value Review
The Skills section states that students should "Know from memory all products of two one-digit numbers," indicating explicit practice of basic multiplication facts. The closing activity asks students to work with multiplication flashcards and multiplication and division fact family cards for factors 2, 3, 4, 5, and 10, providing additional practice with multiplication and simple division facts.
Lesson 2
Numbers to 10,000
Students practice multiplication fact fluency in Activity 6 by using the 'Hit the Button' times-tables games (tables up to 10, including mixed practice). Students also complete the 'Which Numbers?' sheet, which asks them to find pairs of one-digit numbers from a given set whose products equal targets (e.g., 12, 40, 30) and to perform small multiplication-based calculations.
Unit 3: Measurement
Lesson 5
More Work With Weight
Students are asked to compute how many of an item equal their weight using division when an item weighs more than a pound (example: 51 ÷ 2 to find cartons of milk) and to use multiplication when an item weighs less than a pound (example: 3 × 51 for shoes). The "Weighty Things" activity requires students to fill blanks such as "I weigh the same as ___ tires" (tire = 15 lb) and "These 4 bananas together weigh 1 pound. I weigh the same as ___ bananas," which directly prompt multiplication or division with measurement quantities. The lesson also gives items with unit relationships (e.g., 168 ping pong balls = 1 lb) that require students to compute counts of equal groups to match a given weight.
Lesson 6
Exploring Volume
Students measure liquid volumes by filling containers with a 1-cup measure to determine how many cups are in a pint, quart, and gallon. Students create a foldable that records relationships (e.g., 2 cups = 1 pint, 4 cups = 1 quart, 16 cups = 1 gallon) and answer questions such as how many cups or pints are in a gallon. Students estimate and then measure capacities of several containers and compute differences in capacity, and are asked extended multiplication tasks (e.g., how many tablespoons in a pint or quart) and given time with multiplication/division fact family cards.
Lesson 7
More Work With Volume
Students use a 10-milliliter syringe to add 10 ml ten times and determine there are 100 milliliters in the cup, and they add 100-ml pours ten times to fill a 1-liter bottle, making and counting equal groups and using tally marks to track pours. The materials prompt students to compare groups (20 drops = 1 ml; 1000 ml = 1 liter) and to answer "What does 10 groups of 100 equal?" which elicits multiplying equal measurement groups. The wrap-up also directs students to practice with multiplication and division fact family cards for factors 2, 3, 4, 5, and 10.
Lesson 8
Some Weighty Problem Solving
Students read scale drawings and compute new weights when a single block is made heavier or lighter, including problems that ask for the total weight of 2 identical blocks and of 5 identical blocks (Reading Scales problems 4 and 5). Students deduce individual shape weights from totals of equal groups (e.g., three identical rectangular prisms total 9 lb) in the "What Do They Weigh?" activity, which requires dividing or reasoning about equal groups. Students compute combined measurement quantities in Packing My Lunch, including items repeated (e.g., 2 bags of chips), requiring repeated addition or simple multiplication within 100.
Lesson 9
Unit Test
Students are asked to "add, subtract, multiply, or divide to solve one-step word problems involving weights or volumes that are given in the same units," which explicitly engages measurement word problems. Students answer a question that asks what 3 objects with the same weight weigh altogether, requiring them to compute a total from equal groups (e.g., 3 × 8 oz). Several measurement conversion and quantity questions (e.g., cups in a gallon = 16) involve numerical work with measurement quantities within the same-unit context.
Unit 4: Multiplication and Division II
Lesson 1
Mastering More Multiplication Facts
Students practice interpreting products as equal groups when the Skills section asks them to "interpret 5×7 as the total number of objects in 5 groups of 7 objects each," and Activity 2 has students make groups with paper plates and counters and write multiplication sentences (e.g., 1×1=1, 2×1=2). Students complete fill-in-the-blank multiplication equations on the Student Activity Page (e.g., 5×0=__) and solve missing-factor problems (e.g., __×10=0). The lesson also has students create fact-family cards (including division facts) and includes a skills statement to "determine the unknown whole number in a multiplication or division equation relating three whole numbers."
Lesson 2
Multiples of 6 and 7
Students draw pictures and write multiplication sentences to find the number of legs for 6 and 9 ants and the total sides of 8 hexagons, directly modeling equal groups. Students use the multiplication chart and abacus to create and interpret arrays (rows and columns) and to compute products such as 6×7, 4×6, and 9×6. Students solve measurement word problems by converting weeks to days and by determining how many weeks are in 35 or 49 days, and they fill in blanks in equations (e.g., 7 x __ = 42) to determine unknown factors or products.
Lesson 3
Multiples of 8 and 9
Students draw pictures (arrays or object groups) for domino numbers and write multiplication sentences, turn-around sentences, and products as they flip dominoes. Students solve contextual word problems that use equal groups and measurement quantities (e.g., how many legs 5 spiders have; how many packages of 8 hot dogs are needed for 32 hot dogs; how many sides 7 octagons have). Students complete fill-in-the-blank multiplication and division equations (e.g., __ × 8 = 16, __ ÷ 8 = 7, __ ÷ 8 = 48) and color multiples on a 1–100 multiplication table, keeping work within 100.
Lesson 4
Practicing All of the Multiples
The Skills section explicitly tells students to determine the unknown whole number in a multiplication or division equation relating three whole numbers and to fluently multiply and divide within 100. In Activity 1, students create and use fact family cards, covering a corner to hide one number (e.g., the 8, 7, 56 card) and then turn the card over to figure out the missing factor. Activity 2 and the linked games require students to select factors that multiply to a given product, giving repeated practice with multiplication and division facts within 100.
Lesson 5
Associative Property of Multiplication
Students practice using letters for unknowns and solving for n in multiplication sentences (examples: 3×n=9; (6×1)×2=6×(1×n) with n=2). Students compute products within 100 in multiple exercises and worksheets (examples: 5×6=30, 9×3=27, 5×5×2=50). Students use parentheses and the associative property to regroup and evaluate products (examples: (3×2)×4 and 3×(2×4) showing both equal 24).
Lesson 6
Distributive Property of Multiplication
Students create and label arrays (e.g., 6×4, 5×6) and physically break them into smaller arrays, then write the corresponding multiplication sentences and add them to show equality. Students use drawings and step-by-step equations to decompose multiplication facts (e.g., 8×9 into 8×4 + 8×5; 6×9 into (6×4)+(6×5)) and compute the sums. Students complete activity pages with problems like 14×3, 15×6, 4×12, and are asked to use the distributive property and array representations to find products within and near the 100 range.
Lesson 8
Revisiting Division
Students use counters and paper plates to make equal groups and write matching multiplication and division sentences (e.g., 3×6=18 and 18÷3=6). Students represent division on number lines and physically act out division sentences by taking jumps on a 0–20 number line. Students find missing factors and write equations with a symbol for the unknown (e.g., 18 ÷ q = 2, q × 2 = 18) and create contextual examples such as dividing 35 pennies among 7 people or 16 cookies among 8 people.
Lesson 9
Multiplication and Division Facts Practice
Students practice multiplication and division facts within 100 through repeated activities such as the input/output machine (writing ×8, ×9 and ÷2, ÷3 rules) and flashcards/games that include facts through 12. Students use manipulatives (counters and small plates) to model division sentences like 3 ÷ 3, 4 ÷ 4, and 3 ÷ 1, reinforcing division as splitting into equal groups. Students build and write fact families from domino numbers, creating multiplication and division sentences that relate three whole numbers.
Lesson 10
Problem Solving Using Multiple Operations
The Skills list explicitly states that students will "Use multiplication and division within 100 to solve word problems" and to "Solve two-step word problems using the four operations." In Activity 1 students read Grapes of Math riddles and are guided to treat the "Snail Parade" as an array and write 5×5−3 to find 22, explaining the array strategy. Activity 2 has students group dots on a Chinese checkerboard into equal groups (e.g., circle groups of 10 and compute 10×12+1) and describe their grouping strategies. Day 2 problems and the Dividend Challenge require students to write and use multiplication and division number sentences ((5×4)+(3×4), 16÷4, many division sentences for 8,12,15,16,24), and Activity 4 has students construct equations using the four operations to reach target numbers.
Lesson 11
Multiplying by Multiples of 10
Students solve word problems that use multiplication and division in equal-group and measurement contexts (e.g., "Tanner bought 6 boxes of pencils. There are 30 pencils in each box. How many pencils did he buy?" and "If Callie wants to split her candy up among 10 friends... 400 ÷ 10 = 40"). Students model multiplication by tens using base-10 rods and drawings (e.g., drawing groups of ten rods for 3 × 40) and write and manipulate equations such as 3×4×10 and (3×4)×10 to apply the associative property. Students complete worksheets and activities that require computing products and quotients involving multiples of 10 and write number sentences for division word problems.
Lesson 12
Unit Test
The skills list explicitly includes "Use multiplication and division within 100 to solve word problems" and "Determine the unknown whole number in a multiplication or division equation". Students are asked to write number sentences using n for missing numbers (e.g., 4×6=n; 16÷4=n) and then solve them. The instructions tell students they may "create arrays, draw pictures, or use recall of facts" and require a number sentence before solving, and multiple Unit Test and activity problems (e.g., candy sharing, buckets of water, pepperoni problem) ask students to solve equal-group and measurement problems within 100.
Final Project
Planning a Picnic
Students compute how many packages or servings are needed for 60 people on the "Picnic Food" page (e.g., packages of plates, forks, cups, hot dogs, chips, cookies, ice cream), explicitly using multiplication and division and breaking numbers apart with the distributive property. Students divide the 24 children into pairs and teams for games and compute numbers of ropes, eggs (dozens), cornhole boards and beanbags, and sacks on the "Picnic Games" page, practicing equal-group and measurement-quantity reasoning. Students design seating arrangements using given capacities (blankets seat 4, small tables 6, large tables 10) and compute whether arrangements provide exact seating for 60 people, using drawings and written computations on a whiteboard.
Unit 5: Area and Perimeter
Lesson 1
Review of Plane Shapes
Students answer questions that require multiplying equal groups, for example: "How many sides do 8 rectangles have?" (answer 32) and "How many vertices do 6 triangles have?" (answer 18). The activity asks students to write number sentences for combined groups, e.g., "How many vertices do 4 squares and 3 hexagons have? Write a number sentence to show your answer. (16+18=34)" and "How many sides do 3 rectangles and 7 pentagons have? Write a number sentence to show your answer. (12+35=47)." The materials also remind students they have seen letters representing missing numbers when multiplying and dividing.
Lesson 2
What Is Perimeter?
Students model perimeters by building rectangles with straws and pipe cleaners and by making squares and rectangles with tiles, then measure or count side lengths to find total perimeter. Students compute perimeters by adding side lengths (e.g., 6+4+6+4=20) and are told that multiplication can be used as a shortcut for regular polygons. Students solve a measurement-context problem (how much fencing for a garden) and create multiple rectangles (4x4, 6x4, 3x8) and find their perimeters.
Lesson 3
Calculating Perimeter
Students calculate perimeters using repeated addition and multiplication (examples: 3+5+3+5=16 cm, 4×6=24 in.) and are instructed to use multiplication for regular polygons (e.g., hexagon with sides 4 cm, octagon with sides 5 in.). The Basic Skills Review includes word problems that require multiplication and division within 100 (e.g., 4 boxes of 8 cookies => 4×8=32; 30 pieces of gum shared among 5 friends => 30÷5=6). Students are asked to write number sentences/equations and label units for perimeter and other problems.
Lesson 4
More Work With Perimeter
Students count tile sides and add lengths to find perimeters of irregular shapes and use units when working with pentominoes and composed shapes. Students set up and solve equations with a symbol for an unknown side (e.g., 3 + 4 + n = 12) and use letters on rectangles and triangles to find missing lengths. Students write and solve multiplicative equations for regular polygons (example shown: 6(x) = 24) and use perimeter ÷ number of sides to find an individual side length (square with perimeter 16 → side 4).
Lesson 5
Problem Solving With Perimeter
Students solve multiplication and division word problems in the Basic Skills Review (e.g., Carlota: 7 boxes × 6 cookies = 42; Gregory: 50 ÷ 8 = 6 remainder 2). In Activity 1 students use one-inch tiles to model seating arrangements and to reason about equal groups and arrays for seating 32, 24, and other numbers. In the Perimeter Problems and Practicing Perimeter activities students compute perimeters of regular polygons and rectangles by multiplying side length by number of sides and by arranging tiles to measure perimeter (measurement quantities).
Lesson 6
What Is Area?
Students solve word problems that require multiplication and division within 100 (e.g., Carney has 7 boxes of 8 crayons each and Hans shares 45 candies among 6 friends). Students use arrays and measurement contexts to compute products by filling rectangles with unit tiles (e.g., filling a 6 by 4 box with 24 one-inch tiles and creating 4 across by 6 down to get 24). Students interact with grid drawings (coloring grids after dice rolls, using the Area Builder simulation) to represent and count area as repeated groups of unit squares.
Lesson 7
Calculating Area
Students create rectangles on an interactive grid, count unit tiles, and then multiply one side by the other to find area (examples: 3×4=12, 5×6=30). Activities have students find areas of given measurement quantities (inches, feet, centimeters) and write multiplication number sentences on activity pages. Students tile rectangles and draw polygons with unit squares and then write the equations that represent the area (e.g., 2×5=10), and they label units such as "sq. ft." or "sq. in.".
Lesson 8
More Work With Area
Students roll two dice to make rectangles and compute the area by multiplying the rolled side lengths, using the grid to visualize the array. Students draw shapes on centimeter grid paper, shade them, and compute areas by multiplying side lengths (examples include 8×5=40, 7×5=35, 6×6=36) and by decomposing composite figures into rectangles and adding areas. Students complete word problems that require multiplication and division (e.g., 9×8=72; 39÷7=5 R4) and solve equations with symbols for unknowns (e.g., 60×b=540, a×7=420).
Lesson 9
Creating With Perimeter and Area
Students are asked to find area by multiplying side lengths (skill: "Multiply side lengths to find areas of rectangles with whole-number side lengths") and to compute area and perimeter for block-letter names by counting squares and recording perimeter and area in cm and sq. cm. In Activity 3 students identify six body parts of a grid creature and find area and perimeter for each part and total the areas and perimeters. The Getting to Know My Creature page requires students to calculate and record numeric areas and perimeters for multiple parts.
Lesson 10
Problem Solving With Perimeter and Area
Students multiply whole-number side lengths (e.g., 17×1, 16×2, …, 9×9) to find areas of rectangles and use the distributive property to break larger multiplications into smaller ones. Students draw rectangles and other parts on centimeter grid paper (array-like drawings) to compute area and perimeter. Students answer measurement word problems (Food Court questions) that ask for areas, comparisons, and combined areas of stands.
Lesson 11
Unit Test
Students are asked to multiply side lengths to find areas of rectangles (e.g., problems asking for area of 9 ft by 5 ft and 4 ft by 10 ft) and to divide to find an unknown side when area is given (e.g., a rectangle with area 48 sq ft and one side 6 ft, and a rectangle with area 32 sq ft and one side 4 ft). Students use laminated grid paper to draw shapes with specified areas and perimeters (e.g., draw an area of 25 as a four-sided shape and draw perimeters of 10 and 16), supporting array and drawing representations. A perimeter problem labels an unknown as n (triangle with sides 5 in, 7 in, and n, perimeter 22 in), showing use of a symbol for an unknown in an equation context.
Final Project
Shapesville
Students multiply side lengths to find areas of rectangles (Skills and Step 2). Students solve for unknown side lengths and perimeters when they determine building widths and heights from given areas or perimeters (Step 3, Step 4, and Step 5 list specific dimensions students must find for Buildings #1–#6). Students arrange windows in rows (e.g., 3 rows of 2 windows, 2 rows of 2 windows), which has them reason about equal groups and arrays while measuring and cutting paper shapes.
Unit 6: Fractions
Lesson 2
Naming Fractions
Students solve word problems that use multiplication and division within 100: the donut problem uses 10 × 6 = 60 and 60 − 5 = 55, and the sharing problem uses 55 ÷ 9 = 6 with a remainder. Students solve a measurement problem by computing the garden area (6 × 6 = 36) and comparing it to a bag coverage of 25 sq ft. The Basic Skills Review also includes symbolic multiplication equations (4 × b = 320 and a × 30 = 270), showing use of an unknown symbol in some equations.
Lesson 3
Fraction Parts
Students solve multiplication and division word problems such as computing 9×6=54 and then 43÷8=5 remainder 3 when sharing donuts, showing use of multiplication and division within 100 in equal-groups contexts. Students compute area from side lengths (4 ft × 4 ft = 16 sq ft) and compare it to a bag coverage (25 sq ft), showing use of multiplication in a measurement-quantity context. Students also work with equations that include unknown symbols (for example 4×b=120 and a×30=180) and practice multiplication facts with flashcards.
Lesson 4
More Fraction Exploration
Students solve word problems that use multiplication and division in the Basic Skills Review (#17), e.g., Marco had 9 bags of donuts with 6 donuts each (9×6=54) and then shares the remaining 44 donuts equally with 7 friends (44÷7=6 R2). A measurement problem asks whether a 7×9 rug (area 63) fits in a 60 sq. ft. room, requiring multiplication to compare areas. The review also includes equations with unknowns such as 60×b=360 and a×9=270 for students to solve.
Lesson 5
Fractions, Division, and Groups
Students set up and solve equal-group division situations such as 24 ÷ 4 = x (donut holes) and sharing pizzas among 2, 3, and 4 people. Students physically divide counters into equal groups (12 counters into 2, 3, 4, 6 groups) and identify the fraction each group represents. Students write division statements and convert fractions to division language (e.g., shapes with shaded parts and a corresponding division column).
Lesson 6
Fractions on Number Lines
Students solve word problems that use multiplication and division, e.g., Landon had 5 boxes of candy with 8 pieces each (5×8=40) and then share 31 pieces equally among 7 friends (31÷7=4 remainder 3). The Basic Skills Review also presents equations with unknowns (40×b=360 and a×3=270) and measurement/time problems (30-minute practice, rug area) that require multiplication/division reasoning.
Lesson 7
Equivalent Fractions
The Basic Skills Review #19 includes a word problem where students compute 7 × 10 = 70, subtract one box to get 60, and then divide 60 ÷ 7 to share markers (equal groups). The review also contains numeric equations with unknowns (50 × b = 450 and a × 7 = 420) that require solving for a symbol representing an unknown.
Unit 7: Geometry
Lesson 3
What Is a Quadrilateral?
The Basic Skills Review includes Deena's jellybean problem that requires multiplication (8 × 10 = 80) and a follow-up division problem sharing 68 jellybeans equally among 7 friends (68 ÷ 7 = 9 remainder 5). The rhino enclosure question asks students to use multiplication to find area (8 × 8 = 64), a measurement quantity. One item presents an equation with a symbol for an unknown (a × 5 = 450), showing use of an equation format with a variable.
Lesson 4
Getting To Know Specific Quadrilaterals
Students solve word problems that use multiplication and division within 100: e.g., Lonny had 5 bags of cookies with 8 cookies each (5×8=40, then 40−7=33) and then share 33 cookies with 5 friends (33÷5=6 R3). Students also use multiplication to compare measurement quantities (room area 42 sq. ft. and a 7×7 rug = 49 sq. ft.). The review sheet includes an equation with a symbol (a×8=400), showing use of an unknown in an equation.
Lesson 6
Dividing Shapes
Students solve multiplication and division word problems in the Basic Skills Review (e.g., 9×8=72 then 72−20=52; 52÷6=8 remainder 4). Students compute area by multiplication (finding area of a 3×4 rectangle as 12 square centimeters) and use grid/tiles to model area and partition it into equal parts. The review also includes an equation with a symbol for the unknown (a×4=320).
Unit 8: Graphing Data
Lesson 2
Pictographs
Students interpret and create scaled pictographs that require dividing totals by a scale (e.g., 30 apples → 3 apple icons when each icon = 10; 65 apples → 6 1/2 icons). Students use fractional parts of symbols to represent quantities (quarters and halves of a tennis ball representing 20 games: 20/4 = 5, half = 10, 3/4 = 15). Students convert given counts into pictogram units using a key (Library Pictograph uses a key of 5 books per square and students must divide counts like 25, 40, 15, etc., by 5 to draw the graph). The wrap-up asks students to choose a scale and show what each picture equals, reinforcing using division or multiplication to relate pictures to totals.
Lesson 3
Bar Graphs
The Basic Skills Review includes word problems that require multiplication and division (e.g., Lisa had 10 bags of 6 cookies: 10×6=60 and then 36÷6=6). A perimeter item uses multiplication for a measurement quantity (square pen: 6×4=24 feet). The review also shows an equation with a symbol for an unknown (6×b=420) that asks students to solve for the unknown.
Lesson 4
Line Plots
Students solve word problems that require multiplication and division within 100, for example by computing 7 × 8 = 56 for Mark's boxes of candy and then dividing 41 ÷ 5 to share remaining pieces. Students compute a measurement-related product when determining perimeter (8 × 4 = 32) to decide if there is enough fencing. A problem asking to solve 60 × b = 420 presents an equation with a symbol for an unknown number.
Lesson 5
More Work With Graphing
Students solve the cookie word problem using multiplication and subtraction (9×10=90, 90−17=73) and then use division to share the remainder (73÷8=9 R1), showing use of multiplication and division to solve a contextual equal-groups problem. The "Money in the Bank" activity requires students to use multiplicative relationships ("twice as many pennies as dimes," "half as many quarters as nickels," and "multiply the number of half-dollars by 3") to determine counts of coins. The Basic Skills Review also includes an equation with an unknown (7×b=420), indicating practice with writing or solving equations that include a symbol for an unknown.
Lesson 6
Unit Test
Students interpret scaled pictographs and bar graphs to find totals and compare amounts (e.g., questions: "How many boxes were sold on Monday?" and "How many more boxes were sold on Friday than on Saturday?"). On the Unit 8 Test students determine the value represented by one picture in a pictograph ("If Mark read 35 books in May, how many books does a picture of one book equal? (10)") and use that scale to find another month's total ("How many books did Mark read in August? (30)"). Students also combine values from graphs (e.g., June and July combined, or July and August combined) and read scaled axes on a miles-hiked graph.
Unit 9: Skills Review
Lesson 3
Reviewing Perimeter and Area
Students draw rectangles and other shapes and compute perimeters by adding side lengths or by writing multiplication number sentences for regular polygons (e.g., 3 × 8 for an equilateral triangle, 4 × 7 for a square). Students find areas by multiplying side lengths (e.g., 10 cm × 7 cm = 70 cm²) and practice making rectangles/squares with given areas (e.g., 12, 15, 16 cm²). Students label units and use grid paper and an area-blocks activity to represent measurement quantities.
Lesson 4
Reviewing Geometry
Students draw a rectangle of area 15 square centimeters on grid paper and are told its sides should be 3 and 5 centimeters, creating a 3-by-5 array. Students divide that rectangle into thirds and identify that each third is made up of five square centimeters, and they repeat similar tasks for one-fourth of a 16-square-centimeter square and two-thirds of a 9-square-centimeter square. These activities have students work with measurement quantities, arrays, and equal groups of unit squares.