Third Grade - MATH
5: Math
Unit 1: Multiplication and Division I
Lesson 1
Getting Ready to Multiply
Students model equal groups with an egg carton shown as a 2 by 6 array and write two addition sentences (2+2+2+2+2+2=12 and 6+6=12) to represent the total. Students draw arrays for given repeated-addition problems (for example, 4+4+4 as 3 rows of 4 or 4 rows of 3) and complete an Arrays and Repeated Addition sheet where arrays corresponding to totals (e.g., various ways to make 24) are written as repeated addition. Students solve contextual equal-groups problems (e.g., finding how many hands 8 people have, listing items that come in groups of 2,3,4,5,8,10) and use Grapes of Math riddles to group objects and determine totals (e.g., grouping grapes into 5 groups of 10 for 50 grapes).
Lesson 2
What Is Multiplication?
Students are asked to interpret products in the Skills section, which explicitly lists "Interpret products of whole numbers (for example, interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each)." In Activity 2, students view and count 4 groups of 5 counters, write 4×5=20, and are asked to write 2×3 for 2 groups of 3 counters. The Student Activity Pages require students to create multiplication sentences from contextual images (cookies/chips, bags of donuts, spiders' legs) and draw pictures to represent equal groups. The Wrapping Up task has students label a multiplication sentence, point to its parts, and explain how they know the product (e.g., counting by groups or counting all dots).
Lesson 3
Arrays and Equal Groups
The Skills section explicitly states students will "Interpret products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each)." Students make arrays and write word form and number form ("___ groups of ___" and "___ × ___") in Activities 2 and 4. Students use manipulatives to create equal groups (e.g., placing 24 counters on 4 plates to show 4×6=24) and analyze story contexts (Amanda Bean) to write multiplication sentences and find the product.
Lesson 4
Repeated Addition and Number Lines
The Skills section explicitly lists interpreting products of whole numbers and using repeated addition and number lines. In Activity 1, students convert multiplication sentences (e.g., 2×6, 4×6, 7×3) into repeated addition and find the products. Activity 3 has students represent multiplication sentences on number lines (e.g., 4×3 shown as four jumps of three) and create their own number-line/multiplication pairs. Activity 4 requires students to model a multiplication sentence by drawing an array, showing equal groups, writing repeated addition, and drawing a number line, and then repeat this modeling for randomly drawn domino pairs.
Lesson 5
Multiplication and the Abacus
Students model multiplication sentences as arrays and equal groups using the abacus (e.g., the introduction has students represent 5×6 and 7×4 and may use an array or equal groups). Activity 1 has students create a 4 by 5 array, make 3 groups of 5 (3×5), show 10 groups of 4 (10×4), and represent sentences such as 7×2, 10×6, and 5×8 on the abacus to find products. Student pages ask learners to color beads to show 9×2, write the multiplication sentence for given abacuses, and complete sheets of multiplication problems by using the abacus or counting by 2, 5, and 10.
Lesson 6
The Commutative Property of Multiplication
Students use counters, an abacus, and arrays to create equal groups (for example making 2×5 and 5×2 arrays) and count the total, matching multiplication sentences to dot grids. The Skills list explicitly names interpreting products of whole numbers and gives the 5×7 example. Activities have students roll dice, write factor pairs as multiplication sentences and switched sentences, and record the product, and the Wrapping Up task has students break 20 counters into equal groups and list multiplication sentences that produce 20.
Lesson 7
Multiples of 2 and 3
The Skills list explicitly states students will "Interpret products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each)." Students use a number line to represent multiplication (jumps and spaces) and write multiplication sentences (e.g., 1×2, 2×2). The student pages give contextual problems asking students to draw pictures and write multiplication sentences for situations (How many legs do 3 horses have? How many wheels are on 5 tricycles?), requiring students to express totals as products.
Lesson 8
More Practice With 2 and 3
The lesson's Skills list explicitly names interpreting products of whole numbers and gives the example 5×7 as 5 groups of 7. Students are prompted to consider equal groups ("2 groups of 4") and to picture arrays or an abacus. Number-line activities tell students that the first number in a multiplication sentence tells how many jumps to make, and missing-factor problems (__ x 2 = 14, __ x 3 = 21) require students to use the number line to find how many groups (jumps) produce a given product.
Lesson 9
Multiples of 4 and 5
The lesson's skill list explicitly includes "Interpret products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each)." In the Introduction students answer real-world equal-group questions (e.g., sides of three squares, mittens for 6 people, days in three weeks) and are asked to prove answers by drawing or writing. Student pages ask students to draw pictures and write multiplication sentences for contexts (e.g., "How many legs do 5 cats have?" and "How many wheels are on 4 cars?") and to show multiples on number lines and fingers (counting by 5s and relating fingers shown to 9×5 = 45).
Lesson 10
More Practice With 2, 3, 4, and 5
The skills list explicitly names "Interpret products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each)." In Activity 1 students sort numbers by factor cards (2, 3, 4, 5), drawing multiples from a bag and placing them with the appropriate factor, which has students match numbers to multiplicative groupings. Activity 2 instructs students to think about arrays, number lines, and the abacus while finding products, and the wrapping-up discussion asks students to explain tricks (e.g., multiplying by 2 as doubling), linking multiplication to repeated addition or grouping.
Lesson 11
Multiples of 10
Students use counters and an abacus to make and count equal groups (e.g., one group of 10, two groups of 10, three groups of 10) and are asked to state multiplication sentences such as 3×10=30 and 10×3=30. The student worksheets and activities ask students to draw pictures and write multiplication sentences for real contexts (e.g., how many fingers 5 people have; how many legs 10 octopuses have). The skills list explicitly states that students will "Interpret products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each)."
Lesson 12
Problem Solving With Multiplication
Students read and solve word problems that describe equal groups (e.g., Sandy made 5 cakes and on Tuesday she made 3 times that number, written as 3×5=15). Students complete the "Which Has More?" page where they compare scenarios given as rows × items per row (e.g., 3 rows of 5 panes vs. 4 rows of 2 panes). Activities ask students to draw arrays, use equal groups, repeated addition, and write multiplication sentences, and students are asked to make up their own problems that can be expressed with multiplication.
Lesson 13
What Is Division?
Students write and interpret multiplication sentences tied to real contexts (for example, the activity asks "What is the multiplication sentence to show 3 children per chair and 3 full chairs? (3×3=9)"). The Connecting Multiplication and Division sheet explicitly states and practices statements like "4 x 6 = 24 means 4 groups of 6 is 24" and has students draw dots and make groups to represent products. Students convert between arrays, drawings, and multiplication sentences (e.g., draw 24 dots, make groups of 8, fill in 8×3=24).
Lesson 14
Multiplication and Division Fact Families
Students write and evaluate multiplication sentences (e.g., teacher writes 5×4= and student finds 20 and writes the switched sentence 4×5=20). Students use 20 counters to model grouping: they make 4 groups of 5 counters and then make 5 groups of 4 counters, and they are asked to explain what the division sentence 20÷5=4 means. Students create multiplication sentences from a domino (3×4 and 4×3) and then write corresponding division sentences (12÷3=4 and 12÷4=3).
Lesson 15
Unit Test
The skills list explicitly states interpreting products of whole numbers (for example, interpret 5×7 as the total number of objects in 5 groups of 7 objects each). Students are asked to complete a multiplication strategies mat for 6×5 by showing an array, equal groups, repeated addition, a number line, and the product. Multiple assessment items require students to model 3×8 using an array, equal groups, repeated addition, and a number line, and several word problems (dogs' legs, fingers, hotdogs, spiders) ask students to write multiplication sentences that represent totals of equal groups.
Final Project
Multiples Mini-Posters
Students are instructed to represent a target number (for example, 16) using arrays, equal groups, repeated addition, number lines, and multiplication sentences. Students create posters that must show each multiple in five different ways and include a multiplication word problem where the multiple is the answer (for example, 2×8 = 16 or 'How many eyes do 8 people have?'). Students are asked to demonstrate the commutative property by showing factor pairs in both orders (e.g., 2×8 and 8×2).
Unit 2: Place Value
Lesson 7
Unit Test
The lesson's skills list states that students should "know from memory all products of two one-digit numbers." The student pages include a Multiplication Review with an input/output table whose rule is "multiply by 3" and a task asking students to circle numbers that are multiples of 2 and 3. These items require students to compute products and recognize multiples.
Unit 3: Measurement
Lesson 5
More Work With Weight
Students are instructed to multiply when a comparison item weighs less than a pound, with the explicit example "if 3 shoes together weigh one pound, then the problem would be 3 (x) 51." The "Weighty Things" activity asks students to compute blanks such as "These 4 bananas together weigh 1 pound. I weigh the same as ___ bananas," and the ping-pong-ball item requires using 168 × (student pounds). Multiple items (tires, chickens, bowling balls, bags of rice, bananas, ping-pong balls) require students to compute totals using multiplication related to their own weight.
Lesson 6
Exploring Volume
Students physically fill larger containers with 1-cup measures in Activity 1 to determine how many cups are in a pint, quart, and gallon, counting repeated groups of cups to find totals. The foldable (Activity 2) displays stacked representations of cups, pints, quarts, half-gallons, and gallons, allowing students to see repeated units (e.g., multiple cups making a pint/quart). The wrapping-up questions ask students to use known unit quantities to compute larger totals (e.g., 16 tablespoons in 1 cup then find tablespoons in a pint and quart), and the lesson directs students to practice multiplication fact cards for factors 2, 3, 4, 5, and 10.
Lesson 7
More Work With Volume
Students repeatedly add equal groups of volume (they put 10 milliliters into a cup 10 times and are asked "how many milliliters of water are in the cup in all?"). Students count and record pours and make tally marks while adding 100-milliliter pours to a 1-liter bottle and are asked "What does 10 groups of 100 equal?" Students are prompted to estimate, measure how many cups fill a bottle, and use multiplication flashcards/fact-family cards for practice with repeated groups.
Lesson 8
Some Weighty Problem Solving
Students are asked in the Reading Scales activity to find the total weight when given 2 identical blocks and when given 5 identical blocks, which requires computing totals for equal groups. Activity 1 presents scales with three identical shapes totaling 9 lb, and students must reason that each of the three shapes is 3 lb, which reflects 3 × (shape weight) = 9. The lesson skills list explicitly includes multiplying to solve one-step word problems involving weights.
Lesson 9
Unit Test
Students are asked to use multiplication in measurement contexts, as shown in the Skills list: "Add, subtract, multiply, or divide to solve one-step word problems involving weights or volumes that are given in the same units." A specific test question asks students to find the total weight of "3 objects with this same weight" (answer 24 oz), which requires multiplying 8 oz × 3. Several weight and volume items require choosing appropriate units and ordering units, giving contexts where multiplication could be applied to combine equal groups of a measured quantity.
Unit 4: Multiplication and Division II
Lesson 1
Mastering More Multiplication Facts
The Skills section explicitly lists "Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each." In the Introduction students are asked to use a multiplication table and to point to factors and the product while using the terms "factor" and "product." In Activity 2 students place counters on plates, draw the plates and counters for multiplication sentences (e.g., 5×1) and write corresponding multiplication equations to show totals of equal groups.
Lesson 2
Multiples of 6 and 7
The Skills list explicitly names the target: "Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each." Activity 2 directs students to use an abacus and states, "Remember that we can read 6 times 7 as 6 groups of 7," asking students to model problems like 6×7, 4×6, and 9×6. Multiple student pages ask students to draw pictures and write multiplication sentences for contextual tasks (e.g., number of legs for 6 ants and 9 ants, sides of 8 hexagons, days in weeks), and Activity 4 has students use an input/output machine with rule "×7" to produce contextual outputs.
Lesson 3
Multiples of 8 and 9
The Skills list explicitly includes "Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each." In the Introduction, students turn over dominoes and are instructed to "show multiplying the numbers using a picture (for example, an array... )", write a multiplication sentence and the turn-around sentence, and write the product; an example has the student draw three spiders each with 8 legs and record 3×8 = 24. Student activity pages include context problems that ask for totals from equal groups (e.g., "how many legs 5 spiders have," "how many packages of hot dogs are needed if each package contains 8 hot dogs and you need 32 hot dogs," and how many sides 7 octagons have).
Lesson 6
Distributive Property of Multiplication
Students create physical arrays (e.g., a 6×4 array with counters) and label them with multiplication sentences such as "6×4." They break large arrays into smaller arrays and write the corresponding multiplication expressions (for example, 5×3 = 2×3 + 3×3) to show the same total number of counters. Students are asked to picture multiplication facts as arrays (e.g., 8×9) and to use counters, drawings, or calculators to verify products. The wrap-up asks students to explain equality of expressions like 5×12 = (5×10)+(5×2), reinforcing the interpretation of products as totals of grouped objects.
Lesson 8
Revisiting Division
Students physically model equal groups with counters and plates (place 18 counters on 3 plates) and write the corresponding multiplication sentence 3×6=18, reading it aloud. The introduction repeats this process with other numbers (for example, dividing 15 counters among 5 plates and writing 5×3=15) and allows students to choose numbers and create matching multiplication sentences. Fact family activities require students to state multiplication sentences (e.g., 2×3=6, 3×2=6) and connect those products to group contexts. The Language of Division mini-book and Using Division Vocabulary pages include pages and prompts about making groups and using arrays, reinforcing multiplication as total objects in groups.
Lesson 9
Multiplication and Division Facts Practice
Students draw dominoes and write multiplication and division fact-family sentences (for example, using a domino showing 2 and 6 to create 2×6=12 or 2×3=6). Students complete input/output tables applying rules like ×8 and ×9, and are prompted to use strategies (including the rule for multiplying by 9 and the idea that multiplication is repeated addition). Students also use counters and plates to model division into equal groups, reinforcing the relationship between multiplication and grouping.
Lesson 10
Problem Solving Using Multiple Operations
Students are prompted to treat pictorial arrays as equal groups and use multiplication to solve (Snail Parade: treat picture as a 5 by 5 array = 25 then subtract 3). Students are asked to circle equal groups of 10 on the Chinese Checkerboard and compute 10×12+1 to find the total number of dots. Word problems require writing number sentences that map contexts to products, e.g., (5×4)+(3×4) for legs of animals, and activity pages ask students to write explanations of how they found answers.
Lesson 11
Multiplying by Multiples of 10
Students draw dominoes, add the two ends, and multiply that sum by 10 (e.g., draw 4 and 5, get 9, then compute 9×10=90). Students are asked to rephrase 3×40 as "3 times 4 groups of 10 equals 12 groups of 10 or 120" and to write and manipulate 3×4×10 and (3×4)×10, explicitly linking multiplication to groups. Students model multiplication with base-10 rods by drawing "3 groups of 4 ten rods" and counting the total by tens, and they solve multiple context-based word problems (e.g., 6 boxes of 30 pencils → 6×30) that require writing number sentences and finding total objects.
Lesson 12
Unit Test
Students translate contextual situations into multiplication sentences (e.g., "Chuck has 4 bags of donuts. Each bag has 6 donuts. How many donuts does Chuck have in all? (4×6=n)"). Students write number sentences and solve word problems that explicitly map equal groups to products (e.g., Sarah made 5 snacks with 4 crackers each → 5×4; Daniel picked 6 flowers with 4 leaves each → 6×4). Students are prompted to draw arrays or pictures and to use correct multiplication vocabulary (factor, product, multiple) as they explain and solve problems.
Final Project
Planning a Picnic
Students calculate how many packages are needed given a package size and 60 people on the Picnic Food sheet (for example, using 15 plates per package to determine 4 packages for 60 people). Students compute supplies for games by forming pairs and teams (for example, dividing 24 children into 12 pairs and determining 12 ropes, or forming 6 teams of 4 for the egg toss). Students use the Seating Arrangements activity to multiply numbers of blankets/tables by their seating capacities (for example, x blankets × 4 seats each plus y tables × seats each to total 60). The instructions ask students to use multiplication and to explain how they arrived at their answers, and allow drawing/grouping on a whiteboard to track computations.
Unit 5: Area and Perimeter
Lesson 1
Review of Plane Shapes
Students are asked to compute totals for multiple shapes (e.g., "How many sides do 8 rectangles have?" with answer 32 and "How many vertices do 6 triangles have?" with answer 18). Students are prompted to write number sentences for combined groups of shapes (e.g., "How many vertices do 4 squares and 3 hexagons have? Write a number sentence to show your answer." and "How many sides do 3 rectangles and 7 pentagons have? Write a number sentence to show your answer.", with answers shown as 12+35=47). These tasks place multiplication-like group contexts (multiple shapes each having the same number of sides/vertices) into student work.
Lesson 2
What Is Perimeter?
Students build a 4-inch by 4-inch square with tiles and count the perimeter to be 16 inches. The Facts and Definitions state that to find the perimeter of a regular polygon, multiply the number of sides by the length of one side. The answer key and lesson text explicitly state, "We can use multiplication as a shortcut to find the perimeter of regular polygons."
Lesson 3
Calculating Perimeter
Students are asked to use multiplication to find perimeters of regular polygons, with the explicit formula "number of sides × length of sides = perimeter" and an example showing 4 × 6 = 24 in for a square. The provided answer-key and activity images show repeated-group multiplications such as 3 × 5 = 15 ft (equilateral triangle), 6 × 4 = 24 cm (hexagon), 8 × 5 = 40 in (octagon), and 4 × 10 = 40 ft, tying multiplication to totals. The Basic Skills Review includes a real-world grouping problem (Matt has 4 boxes of 8 cookies: 4 × 8 = 32) that has students interpret a product as total items in equal groups.
Lesson 4
More Work With Perimeter
Students use one-inch tiles to build shapes and count or add the sides of tiles to find perimeters, practicing counting equal-length units around shapes. The pentomino activity highlights that each pentomino is made up of 5 squares, and students work with units when making shapes with 2 or more pentominoes. The teacher models finding the perimeter of a regular polygon by multiplying the number of sides by the side length and writes 6(x) = 24 on the board to solve for a side length.
Lesson 5
Problem Solving With Perimeter
Students use one-inch tiles to model tables that seat four people each and demonstrate that eight separate tables seat 32 people (modeling 8 groups of 4). Activities ask students to create arrangements with 16 and 12 tables and to describe how many seats each grouped arrangement provides, prompting grouping and repeated-counting reasoning. The Basic Skills Review includes word problems solved with multiplication, e.g., Carlota has 7 boxes of 6 cookies (worked as 7×6=42) and the arithmetic problem 90×7=630.
Lesson 6
What Is Area?
Students fill a 6 by 4 box with one-inch tiles and count 24 tiles to find area, and they create shapes of a chosen number of tiles (e.g., 15) and recognize each shape has area equal to that total number of tiles. Students roll two dice to make rectangles (e.g., 2 across and 3 down) and then count and state the total number of unit squares (e.g., 6 square centimeters). A Basic Skills problem describes Carney with 7 boxes of 8 crayons, and the answer key shows 7 × 8 = 56, providing a real-world grouping context.
Lesson 7
Calculating Area
Students build rectangles on an interactive grid, count unit squares (tiles) to find area, and then are asked to multiply the side lengths to get the same total (e.g., create 3 by 4 rectangle, count 12 tiles, then write 3 × 4 = 12). The Make These Areas activity requires students to construct rectangles with given areas and write number sentences such as 2 × 5 = 10 and 3 × 4 = 12. Outdoor/real-world tasks ask students to draw whole-number-sided rectangles (e.g., 4 ft by 3 ft), measure sides, compute area by multiplying, and record the total number of square units for objects found in the house.
Lesson 8
More Work With Area
Students roll two dice to make rectangles and are asked to find the area (length × width). The Skills list explicitly says to "relate area to the operations of multiplication and addition" and to "multiply side lengths to find areas of rectangles with whole-number side lengths." Activity 1 and later composite-shape activities require students to find side lengths that produce given areas (e.g., 2 and 6 for area 12, 5 and 7 for area 35). Activity 6 includes a multiplication word problem about boxes of crayons (9 boxes of 8 crayons) where students compute 9 × 8 and 5 × 8 to find totals.
Lesson 9
Creating With Perimeter and Area
Students are asked to find area and perimeter for shapes they create (e.g., block-letter names and creatures) and to record areas and perimeters on provided sheets. The Skills list explicitly states that students will "Multiply side lengths to find areas of rectangles with whole-number side lengths". The "Getting To Know My Creature" page requires students to compute area for six body parts and a total area, and an illustrated example gives an area value (109 sq cm) and a perimeter value (98 cm).
Lesson 10
Problem Solving With Perimeter and Area
Students multiply whole-number side lengths to find areas of rectangles (Skills: "Multiply side lengths to find areas of rectangles with whole-number side lengths"). Activity 1 lists explicit rectangle dimensions (e.g., 17×1, 15×3, 9×9) and instructs students to find areas for each shape. The lesson shows students using grid paper to count unit squares and decomposing a 15×3 rectangle into (8×3)+(7×3) to compute area, demonstrating multiplication and the distributive approach.
Lesson 11
Unit Test
Students are asked to relate area to multiplication and to multiply side lengths to find areas of rectangles (Skills list). Several tasks have students draw areas on a 5x5 grid (e.g., draw a four-sided shape with area 25 and with area 28 as a 4 by 7 shape), and worked examples show a square with side 7 labeled and area 49 and rectangles where area is found by multiplying side lengths. The answer key and activity pages require students to represent specific area totals as dimensions (for example, representing 28 as 4 by 7).
Final Project
Shapesville
Students multiply side lengths to find areas of rectangles (Skills list and Step 6 asking students to explain how they found areas). Students physically arrange windows into rows (e.g., "There should be 3 rows of 2 windows," "2 rows of 2 windows," "3 rows with 1 window each"), which requires counting total objects by equal groups. Students measure and cut rectangles with whole-number side lengths (Step 2 and Building construction steps), then use those measurements to compute totals for windows and area.
Unit 6: Fractions
Lesson 2
Naming Fractions
The Basic Skills Review problem about Sharon gives a real-world multiplication context: "Sharon had 10 bags of donuts. Each bag had 6 donuts." The answer key explicitly shows 10×6=60 and interprets that as the total number of donuts before subtracting the eaten donuts. Additional arithmetic problems include multiplication equations (e.g., 4×b=320, a×30=270) that require working with products of whole numbers.
Lesson 3
Fraction Parts
Students solve a word problem involving multiplication: "Jenny had 9 bags of donuts. Each bag had 6 donuts... (9×6=54, 54−11=43 donuts)", which frames a total as groups of equal size. The lesson also includes multiplication practice (multiplication flashcards) and equations to solve such as 4×b=120 and a×30=180, giving students opportunities to compute products and use them in context.
Lesson 4
More Fraction Exploration
Students solve a word problem in Basic Skills Review #17 where Marco has 9 bags of donuts with 6 donuts in each bag and the solution shows 9×6=54, then uses that product to find the remaining donuts after Carly ate 10. The review also includes multiplication equations such as 60×b=360 and a×9=270 that require students to work with products and understand the multiplicative structure. Students perform the multiplication in context and use the product to answer subsequent questions.
Lesson 6
Fractions on Number Lines
Students solve a word problem that states, "Landon had 5 boxes of candy. Each box had 8 pieces of candy," and they compute 5×8=40 (then subtract 9). The Basic Skills Review also includes equations using multiplication in context (40×b=360 and a×3=270) so students practice computing products and solving for missing factors. These items require students to treat products as totals arising from groups of equal size.
Lesson 7
Equivalent Fractions
Students solve a word problem in the Basic Skills Review where Lisa has 7 boxes of 10 markers and the answer key shows 7×10=70 (then 70−10=60), which maps a product to total objects in equal groups. Students also encounter multiplication equations such as 50×b=450 and a×7=420 in the review, requiring them to work with products and unknown factors. These items require students to compute and reason with products of whole numbers in contextual and symbolic forms.
Unit 7: Geometry
Lesson 3
What Is a Quadrilateral?
The Basic Skills Review word problem about Deena states: "Deena had 8 bags of jellybeans. Each bag had 10 jellybeans," and the solution shows 8 × 10 = 80, then 80 − 12 = 68, directly representing a total as a product of groups. The rhino enclosure problem uses multiplication to compute area (8 × 8 = 64 sq. ft.), showing product interpretation in a geometric context. The sheet also includes an equation a × 5 = 450, which requires reasoning about a quantity times 5 producing a total.
Lesson 4
Getting To Know Specific Quadrilaterals
Students solve a word problem in the Basic Skills Review where Lonny had 5 bags of cookies with 8 cookies in each bag and compute 5×8=40 before adjusting for cookies given away, which requires interpreting the product as total items in equal groups. Students also encounter a multiplication equation a×8=400 that asks them to reason about a missing factor, reinforcing understanding of multiplication as repeated groups or scaling.
Lesson 6
Dividing Shapes
Students compute areas by multiplying side lengths (e.g., asked to find the area of a 3 by 4 rectangle and told they can multiply the side lengths to get 12 square centimeters). Students solve a contextual multiplication problem about bags of cookies (9 bags × 8 cookies = 72) as shown in the Basic Skills Review answer key. Students also work with unknowns in multiplication (a × 4 = 320) and make shapes with a given number of tiles (10, 12, 15) to partition, which can be used to form and count equal groups.
Lesson 7
Some Geometric Problem Solving
Students use pattern blocks to make a whole hexagon from repeated shapes, for example placing three rhombuses over a hexagon or making a hexagon from six triangles. The activity asks students to count and record how many trapezoids, rhombuses, or triangles make one hexagon and to name those parts as fractions of the whole (e.g., 1 rhombus = 1/3 when hexagon is one whole). The hands-on work requires students to create and compare groups of identical shapes to form a larger shape.
Unit 8: Graphing Data
Lesson 1
Data and Graphing Basics
Students work with tally marks that are shown as groups of five and are asked to represent numbers (the image shows 17 as three groups of five plus two). Students read pictographs that include a key (the flowers pictograph explicitly states one flower image = 10 flowers) and are prompted to consider what each picture represents. Students learn about scaled graphs that count by numbers other than one (e.g., 2, 5, or 10) and decide when to use scaled versus non-scaled graphs.
Lesson 2
Pictographs
Students work with scaled pictographs where each picture represents multiple items (e.g., each book icon equals 10 books on the "Reading a Scaled Pictograph" page and each square equals 5 books on the Library Pictograph). Students are asked to convert totals into numbers of pictures (e.g., 30 apples → show 3 pictures; 65 apples → show 6 1/2 pictures) and to determine what one picture represents (e.g., if 40 books sold, one image represents 10). Students are also asked to create their own pictograph and choose a scale, deciding how many items each picture will represent.
Lesson 3
Bar Graphs
Students solve a word problem about Lisa having 10 bags of cookies with 6 cookies in each bag and compute 10×6=60 before subtracting 24, directly using a product to represent the total number of objects in equal groups. The Basic Skills Review also includes the perimeter problem that uses 6×4=24 to find total fencing and the equation 6×b=420, giving additional context where students work with products of whole numbers.
Lesson 4
Line Plots
Students solve a word problem that states: "Mark had 7 boxes of candy. Each box had 8 pieces of candy," and the solution shows 7×8=56, using multiplication to find the total number of pieces. Another problem uses multiplication for perimeter (8×4=32) when deciding if there is enough fencing. The Basic Skills items require students to compute and apply products in concrete contexts (boxes of candy, sides of a square).
Lesson 5
More Work With Graphing
Students solve a multiplication word problem in Basic Skills Review #25 where they compute 9 × 10 = 90 to find the total number of cookies in 9 bags of 10, then use that product in further reasoning. The "Money in the Bank" activity gives multiplicative relationships ("twice as many pennies as dimes", "half as many quarters as nickels", and "If you multiply the number of half-dollars by 3, it equals the number of quarters") that require students to use and interpret multiplication to find counts. The pictograph task asks students to choose a scale (how much one image will equal) so they represent totals as repeated equal groups on a graph.
Lesson 6
Unit Test
The Unit Test items and pictograph activities require students to interpret a symbol that stands for multiple items (e.g., "If Mark read 35 books in May, how many books does a picture of one book equal? (10)") and to use that value to find totals (e.g., "How many books did Mark read in August? (30)"). The pictograph and bar-graph questions have students count symbols or read scaled values to determine total numbers (e.g., combined counts for days or months). The line-plot and pictograph exercises have students record and interpret repeated measurements (e.g., multiple children growing 1 1/2 inches).
Unit 9: Skills Review
Lesson 3
Reviewing Perimeter and Area
Students are asked to write number sentences using multiplication for regular polygons and to label units, and the perimeter answer key shows perimeters computed with products (e.g., 3 × 8 = 24, 4 × 7 = 28, 6 × 5 = 30, 8 × 4 = 32). In Activity 1 students explain that for a square they can add all sides or multiply because the sides are equal, directly linking multiplication to repeated equal parts. In Activity 2 students draw rectangles on grid paper, compute area by multiplying side lengths (10 × 7 = 70), and make arrays of squares for given areas, reinforcing multiplication as total number of unit squares in rows and columns.
Lesson 4
Reviewing Geometry
In Activity 2 students are asked to draw a rectangle with area 15 square centimeters that has sides 3 and 5, then divide that rectangle into thirds so that each part has five 1-cm squares. Students are asked to show two-thirds and to find another way to divide the same 3-by-5 rectangle into three equal-area parts. Additional fraction tasks (one-fourth of a 16-square area and two-thirds of a 9-square area) require partitioning shapes into equal-size groups of unit squares.