Third Grade - MATH
5: Math
Unit 1: Multiplication and Division I
Lesson 1
Getting Ready to Multiply
The lesson has students practice skip counting by 2, 3, 4, 5, and 10 and complete number-grid and web-based skip-counting activities that connect to multiplication. Students model arrays and repeated addition (e.g., writing 2+2+2+2+2+2=12 and 6+6=12, drawing arrays for 4+4+4) and create multiple arrays to show totals such as 24. The text also states that students will "explore the relationship between multiplication and division" and includes an "Equal Groups" activity that has students group items into sets (2, 3, 4, 5, 8, 10).
Lesson 3
Arrays and Equal Groups
Students draw and interpret arrays and equal groups, then write multiplication sentences in number form (___ × ___ = ___), word form (___ groups of ___), and repeated addition, e.g., creating arrays for 18 as 3 rows of 6 and writing 3×6 and 6×3. Students use counters and plates to model equal groups and compute products (e.g., 4×6=24, 3×5=15) and complete worksheets that match arrays to multiplication sentences and find products. Activities ask students to find products from given multiplicative situations (Amanda Bean tasks, Arrays and Products sheet) and to use skip-counting to determine products.
Lesson 4
Repeated Addition and Number Lines
Students practice representing multiplication as repeated addition (Activity 1) and use number lines to show multiplication sentences (Day 2, Activity 3). Students write multiplication sentences from number-line diagrams (e.g., completing 6×2=12) and model given multiplication sentences in multiple ways (Activity 4: arrays, equal groups, repeated addition, number line). Students also create and solve multiplication sentences drawn from domino values and record the product.
Lesson 5
Multiplication and the Abacus
The lesson explicitly lists the skill "Determine the unknown whole number in a multiplication or division equation relating three whole numbers" in the Skills section. Students write multiplication sentences for given arrays, use the abacus to model multiplication (e.g., showing 3 groups of 5, 10 rows of 4), and complete worksheets that require finding products for multiplication sentences. Students also model and check products from domino-drawn factor pairs using the abacus.
Lesson 6
The Commutative Property of Multiplication
The lesson's Skills section explicitly lists "Determine the unknown whole number in a multiplication or division equation relating three whole numbers," which states the target skill. Students roll dice and write factors, two multiplication sentences (switched order), and the product in the "Rolling for Products" activity, giving practice creating multiplication sentences and finding products. Students also match multiplication expressions to arrays and generate all multiplication sentences with product 20, practicing interpretation of products and factor pairs.
Lesson 7
Multiples of 2 and 3
The Skills section explicitly lists "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." Students complete multiple worksheets and table activities where they fill in products (e.g., 2×2=4, 2×7=14) and color multiples of 2 and 3. Students also use the interactive multiplication chart and games where they select products and recite multiplication sentences (e.g., "two times one is two").
Lesson 8
More Practice With 2 and 3
The Skills list explicitly includes "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." The Student Activity Pages give multiple missing-factor multiplication problems (e.g., "__ x 2 = 14", "__ x 3 = 21") and instruct students to use number lines to find the missing factor. Activities require students to write products and complete missing-factor tasks for both the 2 and 3 fact families, and timed quizzes reinforce finding products quickly.
Lesson 9
Multiples of 4 and 5
The Skills list explicitly includes "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." Students color and identify multiples of 4 on an interactive multiplication table and complete sheets where they "provide the missing products" (e.g., fill in products like 1×4, 4×3, 9×4). Students complete the "Practicing Multiples of 4" and "Multiples of 5" sheets and "complete the multiplication sentences" at the top of the pages, using tools (abacus, charts) to find missing products.
Lesson 10
More Practice With 2, 3, 4, and 5
The Skills section explicitly lists "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." Students sort numbers into "Multiples of 2/3/4/5," draw multiples and match them to factor cards, and complete timed multiplication quizzes and product-naming with number cards. Activities ask students to use arrays, number lines, and the abacus and to practice fluently multiplying within 100, which builds related multiplication and division knowledge.
Lesson 11
Multiples of 10
The lesson's Skills list explicitly includes "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." In Activity 2 the teacher says a multiple of 10 (for example, "sixty") and asks the student to say the number being multiplied by 10 (the student responds "six"), which has the student find a missing factor given a product and one factor. Multiple student pages present blanks for products and ask students to write multiplication sentences from pictures (e.g., legs of octopuses, toes of babies), giving further practice relating factors and products.
Lesson 12
Problem Solving With Multiplication
The lesson explicitly lists "Determine the unknown whole number in a multiplication or division equation relating three whole numbers" in the Skills section. In Activity 1 (Multiplication Targets) students cover numbers and are asked "What should you multiply by 2 to get this product?", requiring them to find missing factors. In Activity 4 (Input/Output Machine) students deduce the multiplication rule from a given input and output (e.g., 5 → 25 leading to ×5) and complete tables where outputs or inputs are missing on the "Multiplication Input/Output #1" sheet.
Lesson 13
What Is Division?
The Skills list explicitly names determining the unknown whole number in multiplication or division equations and understanding division as an unknown-factor problem. In Activity 3 (Connecting Multiplication and Division) students fill blanks in both multiplication and division sentences (for example, "___ ÷ 6 = 4" and writing division sentences that match given multiplication sentences). The "Showing Division" activity asks students to write missing answers in division equations (for example, 24 ÷ 4 = ____ and 30 ÷ 5 = ____), and Activity 1 includes writing multiplication sentences (for example, 3×3=9) tied to groupings.
Lesson 14
Multiplication and Division Fact Families
Students are explicitly asked to "Determine the unknown whole number in a multiplication or division equation relating three whole numbers" in the Skills list. Students model division as an unknown-factor problem with counters (e.g., using 20 counters to show 20 ÷ 4 = 5 and 20 ÷ 5 = 4). Students create multiplication sentences from rolled numbers and then turn those multiplication sentences into corresponding division sentences during the Rolling for Fact Families activity. Students cover one number on triangular fact-family cards and determine which number is missing (e.g., covering 5 on the 2, 5, 10 card and identifying 5).
Lesson 15
Unit Test
Students practice finding a missing number by using multiplication/division fact-family cards where one number is covered and they are asked, "What number is missing from this family?" and to explain how they figured it out (repeated six times). Students complete activity and test items with blanks such as 2 x __ = 8 and 3 x __ = 18 and write the fact-family sentences for sets like 4, 9, 36 (including 36 ÷ 9 = 4), which requires determining unknown factors and quotients. Students model and represent multiplication and division relationships (for example, writing multiplication and division sentences for 3, 7, 21 and using input/output tables with rule ×4) that reinforce solving equations relating three whole numbers.
Final Project
Multiples Mini-Posters
The lesson's Skills list explicitly includes "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." Students are required to create multiplication sentences and demonstrate the commutative property on each poster, and the sample poster shows multiplication equations (e.g., 2×8=16, 4×4=16). Students must also write word problems where the multiple is the answer, which requires linking three-number multiplication/division situations to a numerical result.
Unit 2: Place Value
Lesson 2
Numbers to 10,000
The lesson lists as a skill that students should "know from memory all products of two one-digit numbers," and Activity 6 has students practice times tables (individual factors and mixed) using the Hit the Button game. The "Which Numbers?" activity asks students to identify which two numbers produce a given product (e.g., "The product of which two numbers is 12?") and which two produce a given quotient (e.g., "The quotient of which two numbers is 4?"). These tasks require students to find factor pairs and divisor/dividend pairs from a provided set of whole numbers.
Lesson 3
Rounding to 10 and 100
The lesson lists as a skill that students should "Know from memory all products of two one-digit numbers," and the Wrapping Up section directs students to work with multiplication flashcards and multiplication and division fact family cards for factors 2, 3, 4, 5, and 10. Students practice multiplication facts and fact families, which builds fluency with related multiplication and division relationships.
Lesson 7
Unit Test
Students are asked to complete a 'Multiplication Review' including an input/output table with rule 'multiply by 3' (inputs 2, 4, 6 -> outputs 6, 12, 18) and to circle numbers that are multiples of 2 and 3 (8, 18, 9, 12, 16, 24, 21). The lesson's Skills section also states that students should 'know from memory all products of two one-digit numbers.' The Unit Test description says it will include items related to multiplication and division from Unit 1.
Unit 3: Measurement
Lesson 2
Telling Time to the Minute
The lesson asks students to work with multiplication flashcards and multiplication and division fact family cards for factors 2, 3, 4, 5, and 10, which engages them with multiplication and division relationships. The wrapping up section explicitly directs time for practicing multiplication and division fact families, connecting three-number relationships (e.g., x × y = z and related division facts).
Lesson 5
More Work With Weight
Students record their own weight and compute how many of a given item equal that weight by dividing their weight by the item weight (example: 51 ÷ 2) or by multiplying the number of items per pound by their weight (example: 3 × 51). Students complete fill-in-the-blank problems on the "Weighty Things" page such as "I weigh the same as ___ tires" (tire = 15 lb) and compute the number of items for cases like 168 ping pong balls per pound. Students set up and calculate both multiplication and division equations in these real-world comparisons.
Lesson 6
Exploring Volume
Students use multiplication to relate units (e.g., finding that 1 pint = 2 cups, 1 quart = 4 cups, 1 gallon = 16 cups) when they measure and convert capacities. Students complete challenge questions that require multiplying unit counts (for example, using 16 tablespoons per cup to compute 16 × 2 = 32 tablespoons in a pint and 16 × 4 = 64 in a quart). The lesson also provides time to work with multiplication and division fact family cards for factors 2, 3, 4, 5, and 10.
Lesson 7
More Work With Volume
The lesson explicitly provides time for students to work with multiplication flashcards and "multiplication and division fact family cards" for factors 2, 3, 4, 5, and 10, which addresses relationships among multiplication and division facts. The Basic Skills Review sheet includes arithmetic practice, and the curriculum mentions practicing multiplication and division facts as part of wrap-up activities.
Lesson 8
Some Weighty Problem Solving
Students work on the "What Do They Weigh?" activity where scales show totals for multiple identical shapes (for example, three identical shapes total 9 lb), requiring them to determine each shape's weight. Several Reading Scales and Packing My Lunch problems ask for totals of repeated items (e.g., "If you have 2 blocks that are the same weight, how many total ounces?" and computing weight of 5 identical blocks), which requires multiplying a single-item weight by a whole-number count. The activity guidance explicitly directs students to use trial-and-error and subtraction/addition strategies to deduce individual weights from totals, which results in solving for unknown whole-number weights.
Lesson 9
Unit Test
The skills list explicitly states students will "add, subtract, multiply, or divide to solve one-step word problems involving weights or volumes that are given in the same units." The Unit Test includes a weight problem that asks, "What will 3 objects with this same weight weigh altogether? (24 oz)," which requires students to compute a product (3 × 8 = 24). The test also includes other one-step arithmetic questions about weights (e.g., adding 10 ounces to a block).
Unit 4: Multiplication and Division II
Lesson 1
Mastering More Multiplication Facts
The lesson's Skills list explicitly includes "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." The Student Activity Page contains many multiplication items with blanks (e.g., 5 x __ = 0, __ x 10 = 0, 5 x 0 = __) that require students to fill missing factors or products. Activity 2 has students draw groups and complete 5×1=____ and other multiplication sentences, giving students practice finding missing numbers in multiplication equations.
Lesson 2
Multiples of 6 and 7
Students complete practice problems with blanks in multiplication sentences (e.g., 7 × __ = 42, __ × 7 = 56) and are asked to provide missing products on the "Multiples of 6" and "Multiples of 7" sheets. The materials explicitly tell students to note when they are filling in factors versus products and to find missing factors and products. Students solve word problems that require grouping/dividing (e.g., finding how many weeks are in 35 or 49 days), which requires determining an unknown whole number by dividing by 7.
Lesson 3
Multiples of 8 and 9
The lesson's Skills list explicitly states that students will "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." Student activity pages include multiple fill-in-the-blank equations such as "__ x 8 = 16," "8 x __ = 32," and "__ ÷ 8 = 8 / __ ÷ 8 = 7 / __ ÷ 8 = 48," requiring students to find missing factors, products, or dividends. The worksheet descriptions and answer key note that students will provide missing factors and products and complete incomplete multiplication equations.
Lesson 4
Practicing All of the Multiples
The Skills section explicitly lists "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." In Activity 1, students create multiplication/division fact family cards, place × and ÷ on each card, and repeatedly cover one corner of a triangle (hiding one number) and use the two visible numbers to determine the missing number (example: 8, 7, 56). In Activity 2, students play Multiplication Blocks where they must select two or three adjacent factors that multiply to equal a given product, directly practicing finding unknown factors that make an equation true. The Student Activity Page and Multiplication War extension also have students produce products and identify missing factors/products from given numbers.
Lesson 5
Associative Property of Multiplication
Students replace blanks with a letter (n) and solve multiplication sentences such as 5×6=n, 9×3=n, and 3×n=9. Students set up and solve three-factor multiplication equations using grouping, for example finding n in (2×10)×1 = 2×(n×1) and in (3×2)×3 = n×(2×3). The student activity pages include items that ask students to fill missing numbers in expressions like (2×3)×_ = (3×5) and to write multiplication sentences using three numbers (1, 6, 3).
Lesson 7
Reviewing Properties of Multiplication
The Wrapping Up activity instructs the student to use fact family cards, hide one number, and "figure out the missing factor or product," which requires finding an unknown in multiplication relationships. The Getting Started skills list includes "Apply properties of operations as strategies to multiply and divide" and "Fluently multiply and divide within 100," indicating practice with multiplication and division facts. Multiple activity pages and true/false exercises present multiplication equations and fact families that give students practice with factors and products.
Lesson 8
Revisiting Division
The lesson explicitly lists the skill "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." Students practice finding missing factors on the "What's Missing?" triangular cards and sheets (e.g., □ × 6 = 36 and 49 ÷ □ = 7). Students use fact-family activities to write four related sentences (e.g., 2×3=6, 3×2=6, 6÷3=2, 6÷2=3) and complete problems that give quotient/divisor and ask for the missing dividend or divisor (e.g., exercises where the quotient is 4 and divisor is 5).
Lesson 9
Multiplication and Division Facts Practice
The Skills list explicitly states that students will "Determine the unknown whole number in a multiplication or division equation relating three whole numbers." In the domino activity, students draw two numbers and write four fact-family sentences, using a drawn number as a product or factor (for example using 2 and 6 to write 2×3=6), which requires finding a missing factor. Activity 1 has students complete an input/output table with rules like "÷2" where they are given the divisor and quotient (output) and must determine the dividend (input). The Factor Family Reunion game and the "× and ÷ Facts Practice" worksheet give repeated practice matching or filling in missing factors and quotients.
Lesson 10
Problem Solving Using Multiple Operations
Students practice multiplication and division within 100 as stated in the Skills section and play a Multiplication 4 in a Row game to answer multiplication facts. In Activity 2 (Chinese Checkerboard) students create equal groups, multiply to find totals (example: 10×12+1=121) and explain their strategies. The Dividend Challenge has students write many division sentences for given dividends (e.g., 8÷2=4, 12÷3=4) and the More Problems to Solve tasks require writing number sentences such as 16÷4=4.
Lesson 11
Multiplying by Multiples of 10
Students compute products of one-digit numbers and multiples of ten (e.g., 7×30=210, 8×40=320) and complete practice problems on the activity pages that require finding products. Students set up number sentences and find answers for division word problems (e.g., Jonathan: 42 ÷ 7 = ?, Callie: 400 ÷ 10 = 40), determining unknown quotients. Students use multiplication and division in contextual problems (boxes of pencils, buckets of rocks) so they practice relating three whole numbers in word-problem settings.
Lesson 12
Unit Test
Students are given explicit number sentences with a symbol n for the unknown (e.g., 7×n=0, 1×n=5, 3×2×n=24, n÷3=6, 9÷9=n, 10÷n=10) and are asked to explain how to find the unknown. Students write number sentences with n from word problems (e.g., 4×6=n and 16÷4=n) and then compute the answers. The Unit Test and answer key include multiple items that require finding unknowns in multiplication and division equations and fact families (e.g., 6×4=n, 36÷4=n, 63÷9=7, 63÷7=9, and fill-in-the-blank multiplication/division problems).
Final Project
Planning a Picnic
Students compute numbers that require finding an unknown in multiplication/division relationships: e.g., determining packages for 60 people given 15 plates per package (60 ÷ 15 = 4), finding 12 ropes for 24 children paired in a two-legged race (24 ÷ 2 = 12), dividing children into teams of 4 for the egg toss (24 ÷ 4 = 6) and computing eggs needed (6 × 2 = 12 → 1 dozen), and finding 5 cornhole sets for 10 players (10 ÷ 2 = 5). The activity directions ask students to "fill in the blanks" on the Picnic Food and Picnic Games sheets, prompting them to produce the missing numbers by using multiplication and division within 100.
Unit 5: Area and Perimeter
Lesson 2
What Is Perimeter?
The lesson explicitly states that students can use multiplication as a shortcut to find the perimeter of regular polygons (Facts and Answer Key). In Activity 2 students create squares and rectangles and are encouraged to use multiplication and addition to find perimeters of larger shapes. The student activity sheet includes the sentence "We can use multiplication as a shortcut to find the perimeter of regular polygons," which students fill in and thus read and acknowledge.
Lesson 4
More Work With Perimeter
Students are asked to represent missing side lengths with letters and solve for them (e.g., triangle with sides 3 in., 4 in., and n with perimeter 12, so n = 5). The teacher models a regular polygon with the equation 6(x) ___ cm = 24 cm, prompting students to set up and solve the multiplication equation 6×x = 24. Students find side lengths from a total perimeter (e.g., square with perimeter 16 → each side 4), which requires dividing the perimeter by the number of sides. Multiple activities (Something's Missing, pentomino perimeter tasks) require students to write unknowns and compute their values from multiplication/division relationships.
Lesson 5
Problem Solving With Perimeter
Students cut out and match perimeter problem cards that require multiplying the number of sides by a side length (e.g., regular pentagon: 5 × 8 = 40; regular octagon: 8 × 8 = 64; regular hexagon: 6 × 6 = 36). Students use the "Practicing Perimeter" tasks to find unknown side lengths from a given perimeter (e.g., identifying each side of a square given its total perimeter). The Basic Skills Review and Spaghetti and Meatballs activity ask students to perform division in sharing contexts (e.g., 50 ÷ 8 and arranging tables to seat people), providing practice with division with remainders and equal groups.
Lesson 6
What Is Area?
Students compute multiplication and division facts in the Basic Skills Review (e.g., 7×8=56, 80×9=720, 45÷6=7 R3). Students use arrays and counting tiles to find areas (e.g., filling a 6 by 4 box with 24 one-inch tiles and saying "24 square inches") and create rectangles from dice rolls (e.g., 2 across × 3 down = 6). Students reason about multiples when combining pentominoes (every pentomino has area 5, so combined areas are multiples of 5).
Lesson 7
Calculating Area
Students create rectangles and write multiplication sentences linking two side lengths to the area when using the Area Builder, recording examples such as 3 × 4 = 12 and 5 × 6 = 30. In the "Make These Areas!" activities students are given a target area and must produce side lengths and write equations (e.g., 2 × 5 = 10; 2 × 6 = 12; 3 × 4 = 12). The "Think About It!" question asks students to find the side length of a square with area 25, requiring them to determine the unknown whole number (5) that makes the multiplication sentence true.
Lesson 8
More Work With Area
Students find missing side lengths when given an area and one side (e.g., rectangle with area 12 sq. cm and one side 2 cm, square with area 36 sq. cm -> side 6). The Basic Skills Review includes explicit unknown-factor equations (60 × b = 540 and a × 7 = 420) that students solve for the unknown. The division word problem (39 ÷ 7 = 5 remainder 4) and area tasks requiring division to find side lengths give students practice relating multiplication and division to find unknown whole numbers.
Lesson 10
Problem Solving With Perimeter and Area
The Skills section tells students to "multiply side lengths to find areas of rectangles with whole-number side lengths," and Activity 1 has students compute areas of rectangles (e.g., 15×3=45) using multiplication and the distributive property. Activity 2 (Assemble/Draw a Robot) asks students to use given area and perimeter measures to draw parts (e.g., Head: area 20, perimeter 18), which requires choosing whole-number side lengths whose product equals the given area and that meet perimeter constraints. The Food Court and other activities have students compute areas and perimeters and combine areas, reinforcing multiplication and division reasoning with whole-number areas.
Lesson 11
Unit Test
Students are asked to find missing side lengths given area (e.g., a rectangle has an area of 48 sq. ft. and one side is 6 ft; students choose 6 ft and 8 ft as the sides; a rectangle with area 32 sq. ft. and one side 4 ft asks students to find the other side). Students find side lengths of squares given area (square area 36 → side 6) and compute areas by multiplying given side lengths (examples: square side 7 → area 49; square side 8 → area 64). The Unit Test items and practice problems require students to solve for an unknown factor in equations that model area (interpreting and solving x × known = area).
Final Project
Shapesville
Students are asked to find unknown side lengths from area and perimeter information (Step 3 and Step 4). Step 5 lists explicit computations students perform: Building #2 each side is 10 cm (40 ÷ 4), Building #3 height is 10 in (30 ÷ 3), Building #4 width is 5 in (40 ÷ 8), Building #5 height is 3 in from perimeter 28 and width 11, and Building #6 width is 2 in from perimeter 18 and height 7. The Skills section explicitly states students will practice "finding an unknown side length."
Unit 6: Fractions
Lesson 2
Naming Fractions
Students solve multiplication equations with an unknown in Basic Skills Review #15 (e.g., "What is b? 4 × b = 320" and "What is a? a × 30 = 270"). Students perform division to find a quotient and remainder in a word problem (Sharon shares 55 donuts with 9 friends, 55 ÷ 9 = 6 remainder 1). The review answers show students obtaining unknown factors and quotients from given multiplication and division relationships.
Lesson 3
Fraction Parts
Students are given explicit multiplication and division equations to solve on the Basic Skills Review #16 (for example, 4 × b = 120 and a × 30 = 180) and are expected to find the unknown whole numbers. Students also solve division in a word problem (43 ÷ 8 = 5 remainder 3) when sharing donuts equally. The lesson asks students to practice multiplication facts with flashcards, providing additional practice that supports finding unknowns in multiplication equations.
Lesson 4
More Fraction Exploration
Students complete the Basic Skills Review #17, which includes multiplication and division equation problems such as 60 × b = 360 and a × 9 = 270, and they solve word problems that require computing 9 × 6 = 54 and 44 ÷ 7 = 6 R2. The answer key explicitly shows solving for the unknowns b and a in the multiplication equations. Students also perform division to find quotients and remainders in the donut-sharing problem.
Lesson 5
Fractions, Division, and Groups
Students are asked to solve 24 ÷ 4 = x explicitly (asked "What is x?"), and they compute quotients in similar contexts (e.g., "What's 12 divided by 2?" and dividing counters into equal groups). Students write division as fractions (24/4) and express fractions as division statements (e.g., 3/5 described as "3 divided into 5 groups").
Lesson 6
Fractions on Number Lines
Students solve multiplication and division problems in the Basic Skills Review, including solving for unknowns in equations such as 40 × b = 360 and a × 3 = 270. Students compute multiplication in context (e.g., 5 boxes × 8 pieces = 40 then 40 − 9 = 31) and perform the division 31 ÷ 7 to find how many pieces each friend gets and the remainder. Students also practice basic arithmetic fact fluency (multiplication and division) through timed or practice activities referenced in the review.
Lesson 7
Equivalent Fractions
Students complete the "Basic Skills Review #19" problems that include multiplication and division equations with unknowns (e.g., 50 × b = 450 and a × 7 = 420). The marker word problem requires students to compute 60 ÷ 7 to find how many markers each friend receives and the remainder. The student activity page lists solving for b and a as explicit tasks for students to perform.
Unit 7: Geometry
Lesson 3
What Is a Quadrilateral?
The Basic Skills Review includes the equation a × 5 = 450, requiring students to determine an unknown factor in a multiplication equation. The same review has a division problem (68 ÷ 7 = 9 remainder 5) and an equal-sharing word problem, which gives students practice with whole-number division and interpreting quotients and remainders.
Lesson 4
Getting To Know Specific Quadrilaterals
The Basic Skills Review #21 includes the explicit equation a × 8 = 400 and expects the student to find a (answer key: 50). The same review asks students to divide 33 by 5 to determine how many cookies each friend gets and the remainder (33 ÷ 5 = 6 R3). The review also has a two-step multiplication/subtraction word problem (5 × 8 = 40 then 40 − 7 = 33), giving students practice with multiplication in contextual problems.
Lesson 6
Dividing Shapes
The Basic Skills Review #22 includes explicit multiplication and division computations (9×8=72 and 52÷6=8 R4) in a cookie-sharing context, so students compute products and quotients in real problems. The review also includes a literal equation with an unknown, a×4=320, asking students to solve for a, which requires finding an unknown whole number in a multiplication equation. The rug and area items (6×6=36 and area/division tasks) provide additional multiplication/division practice in contextual problems.
Unit 8: Graphing Data
Lesson 2
Pictographs
Students are asked to compute how many picture symbols represent a total (e.g., "If the shop sells 30 apples in May, how many apples should the graph show? (3)") and to compute the value each symbol represents given a total (e.g., "If there were 40 books sold on Monday, how many books does one book image represent? (10)"). Students also compute totals from symbols (e.g., "How many books were sold on Tuesday? (60)") and must create their own scaled pictograph and state what each picture equals.
Lesson 3
Bar Graphs
Students solve an explicit multiplication equation with an unknown in Basic Skills Review #23 (6 × b = 420, b = 70). Students perform multiplication and subsequent division to find unknown answers in word problems (10 × 6 = 60 then 36 ÷ 6 = 6 when sharing cookies). Students complete other arithmetic problems involving multiplication and division (e.g., computing 10×6, 36÷6) that practice the operations relevant to finding unknowns.
Lesson 4
Line Plots
The Basic Skills Review includes an explicit equation with an unknown: "60 × b = 420. What is b? (7)", which requires finding the missing whole number in a multiplication equation. The review also has division work where students compute 41 ÷ 5 = 8 remainder 1 to share candy, so students practice division with whole-number quotients and remainders. Other problems require multiplication facts (7 × 8) and using multiplication to solve a word problem, reinforcing multiplication and division computations.
Lesson 5
More Work With Graphing
The Basic Skills Review #25 includes the equation 7 × b = 420 for which students find b = 60, directly requiring them to determine an unknown in a multiplication equation. The Bess cookie problem has students compute 73 ÷ 8 to share cookies equally, requiring division to find how many each friend receives and the remainder. The "Money in the Bank" clues require students to use multiplicative relationships (e.g., multiply the number of half-dollars by 3 to get the number of quarters; twice as many pennies as dimes) to determine unknown counts and complete a table and bar graph.
Unit 9: Skills Review
Lesson 1
Reviewing Multiplication and Division
In Activity 2, students draw number cards and, with the rule "÷3" or "÷5," write the drawn number as the output (quotient) and then figure out and write the input (dividend) by using multiplication (divisor × quotient = dividend). The activity explicitly prompts students to think, "If you know the divisor and the quotient, how might you figure out the dividend?" Students also practice multiplication facts (for example, x10 input/output) and play multiplication/division games to rehearse fact fluency.
Lesson 3
Reviewing Perimeter and Area
Students are asked to write number sentences using multiplication for regular polygons and compute perimeters with multiplication (e.g., 3 × 8 = 24, 4 × 7 = 28, 8 × 4 = 32). Students are reminded to find area by multiplying length by width and then asked to draw rectangles with given areas, with factor-pair possibilities provided (e.g., for area 12: 1×12, 2×6, 3×4). Students complete perimeter and area problems that require using multiplication to calculate side totals and to select side lengths that produce a specified area.