Third Grade - MATH
5: Math
Unit 1: Multiplication and Division I
Lesson 1
Getting Ready to Multiply
Students practice skip counting by 10s with a web activity titled "Practice: Skip Counting by 10s to 300," and multiple skip-counting grids have students identify and color multiples of 10. Students use equal groups to compute totals (for example, the Grapes of Math activity has students group grapes into clusters of 10 to find 5 groups = 50). Students model repeated addition with arrays (e.g., writing 2+2+2+... and 6+6=12) which builds the connection between repeated addition and multiplication.
Lesson 3
Arrays and Equal Groups
Students create and match arrays for multiplication sentences that include factors with 10 (examples: 3×10, 2×10, 4×10) and they practice skip-counting by 10 to find products (Activity 4 and Day 2 activities). Students model equal groups and arrays (Activities 2, 4, 6, and Amanda Bean activities) and write corresponding number sentences such as 4×10 and 3×10. The materials ask students to use counting-by-10s and repeated addition to determine products involving tens.
Lesson 4
Repeated Addition and Number Lines
Students practice modeling multiplication as repeated addition, equal groups, arrays, and number-line jumps (Activity 1, Activity 3, Activity 4). The materials include an explicit example of 3×10 written as 10+10+10 and ask students to represent multiplication sentences on number lines and with repeated addition. Students generate multiplication sentences from domino draws and then model each sentence with arrays, equal groups, repeated addition, and number lines.
Lesson 5
Multiplication and the Abacus
Students use the abacus to represent two-digit numbers (e.g., 18, 30, 57) and to build arrays that represent multiplication sentences (e.g., 10 groups of 4 shown as four columns of 10 for 10×4 = 40). Activities ask students to count by tens and to count beads in columns to find products (explicitly demonstrating 10×6 = 60 and examples such as 7×10 and 8×10 appear in the activity answer keys). Students are prompted to trade beads to make tens and to look for chances to count by 2, 5, and 10 when finding products, which models place-value reasoning and use of properties (e.g., commutativity when showing arrays as rows or columns).
Lesson 6
The Commutative Property of Multiplication
Students create and compare arrays (for example 2×5 and 5×2, 4×7 and 7×4) to demonstrate that switching factors does not change the product. Students write both a multiplication sentence and its switched version in the "Rolling for Products" activity and compute products using counters, an abacus, or a whiteboard. The wrapping-up task asks students to generate multiplication sentences for 20 and explicitly includes 2×10 and 10×2 as examples.
Lesson 11
Multiples of 10
Students repeatedly multiply one-digit numbers by 10: they write and solve problems such as 2×10, 3×10, up to 10×10 on worksheets and the abacus activity. They use place-value language and a heuristic — "when you multiply by 10, you add a 0" — and practice counting by tens and identifying multiples of 10. Activities ask students to create multiplication sentences (e.g., 3×10 and 10×3) and use the commutative property to represent these products.
Lesson 12
Problem Solving With Multiplication
Students practice multiplying one-digit numbers by 10 in multiple activities: the Input/Output tables include a ×10 rule with inputs (e.g., 4, 8, 5, 3) producing outputs (40, 80, 50, 30). Students respond to prompts such as "what number is multiplied by 10 to equal a product of 70?" and complete Multiplication Target circles that include a 10× center. The skills list also names applying properties of operations and using multiples of 10 as part of practice.
Lesson 14
Multiplication and Division Fact Families
Students write and use multiplication and division fact families that include one-digit factors and 10 (for example, the wrapping-up example 7×10=70, 10×7=70, 70÷10=7, 70÷7=10). The student activity sheet explicitly lists multiples for 10 (1×10 through 10×10), and Activity 2 has students make fact-family cards that include families with the factor 10. Students also model grouping with counters (e.g., 20 counters grouped as 4 groups of 5) and apply the commutative property when creating switched multiplication sentences.
Lesson 15
Unit Test
Students write and solve multiplication sentences that involve multiplying by 10 (e.g., 6×10, 7×10, 6×10=60, 7×10=70) and complete word problems that require one-digit times 10 (e.g., 8 people × 10 fingers = 80). The skills list and Interactive Notebook explicitly include 'Multiples of 10' and 'Apply properties of operations as strategies to multiply and divide.' Students also use the multiplication strategies mat (array, equal groups, repeated addition, number line) and practice properties such as the commutative property through fact-family and matching items.
Final Project
Multiples Mini-Posters
Students choose multiples that include 20, 30, and 40 and must represent each multiple in five different ways (arrays, equal groups, repeated addition, number lines, multiplication sentences). Students are asked to apply properties of operations as strategies and to demonstrate the Commutative Property of Multiplication on each poster. The skills list and activities ask students to interpret products, use multiplication strategies, and create multiplication word problems where the multiple is the answer.
Unit 3: Measurement
Lesson 4
Working With Weight
Students are given time to work with multiplication flashcards and multiplication/division fact family cards for factors 2, 3, 4, 5, and 10, so they practice basic one-digit multiplication including multiplying by 10. Students learn and use unit relationships such as 1000 grams = 1 kilogram and compare items to a 1-liter (1 kg) bottle, which involves reasoning about place value when thinking about thousands and units. Students sort and estimate weights (grams vs kilograms) and answer choice questions that require comparing magnitudes (e.g., choosing 600 g vs 10 kg).
Lesson 6
Exploring Volume
Students count and measure cups to find capacities (e.g., determining that 1 pint = 2 cups, 1 quart = 4 cups, 1 gallon = 16 cups) and use those relationships to compute related totals (for example, using 16 tablespoons × 2 = 32 for a pint and ×4 = 64 for a quart). Students are given time to work with multiplication flashcards and multiplication/division fact family cards including factor 10. Students repeatedly record and compare quantities (e.g., counting up to 16 cups for a gallon), which practices basic multiplicative reasoning.
Lesson 7
More Work With Volume
Students repeatedly add 10 milliliters ten times to see that 10 ml + 10 ml + ... (10 times) = 100 ml and draw a mark showing the 100-ml level. They also add 100 milliliters ten times to fill a 1-liter bottle and recognize that 10 groups of 100 = 1000 ml (1 L). The materials prompt practice with multiplication flashcards and fact family cards including the factor 10.
Unit 4: Multiplication and Division II
Lesson 5
Associative Property of Multiplication
Students compute products that include a factor of 10 (Introduction: 2×10 = 20) and solve grouped multiplication problems such as (2×10)×1 = 2×(n×1) where n is identified as 10. Activities and worksheets give repeated practice with associative regrouping (e.g., (0×6)×10, 1×6×3 = 1×(6×3), and several three-factor products). The Skills section and tasks ask students to apply properties of operations and fluently multiply within 100.
Lesson 6
Distributive Property of Multiplication
Students break numbers into tens and ones and compute products using the distributive property (for example, breaking 12 into 10+2 and computing 5×12 as (5×10)+(5×2)). The materials explicitly model and ask students to complete examples such as (4×10)+(4×2) and 5×15 as 5×10+5×5, and students complete worksheets that show (4×10)+(4×2) = 48 and other decompositions. Activities ask students to create arrays, split them, and write equivalent multiplication sentences that produce smaller products to add together.
Lesson 7
Reviewing Properties of Multiplication
The lesson lists the skill "Apply properties of operations as strategies to multiply and divide" and gives multiple worked examples of properties (e.g., 6×4=4×6; (2×5)×4 = 2×(5×4); 6×9 = (6×4)+(6×5)). Students create a foldable and write their own examples for each property, and they sort true/false cards that include statements like 10×1=10, 20×0=0, and 10×0=0×10. Activities require students to identify, generate, and explain examples of commutative, associative, distributive, zero, and identity properties.
Lesson 10
Problem Solving Using Multiple Operations
Students are asked to use multiplication and arrays (Grapes of Math) to solve riddles and to explain their strategies, which involves recognizing arrays like a 5 by 5 and using multiplication facts. In the Chinese Checkerboard activity, students are prompted to circle groups of 10, multiply to find a total for the groups of 10, and add any extras (example shown as 10×12+1=121). The Make a Number activity includes at least one use of 10 in a multiplication expression (10×2) and the materials include a multiplication practice game for additional fact practice.
Lesson 11
Multiplying by Multiples of 10
The Skills section explicitly states multiplying one-digit whole numbers by multiples of 10 in the range 10–90. In Activity 1 students rewrite problems such as 3×40 as 3×4×10, use the associative property ((3×4)×10), and model with ten-rods to count by tens, directly using place-value reasoning. Multiple practice problems, word problems (e.g., 6×30, 7×80, 9×50), and the wrap-up card-and-die activity require students to compute one-digit times a multiple of ten across the 10–90 range.
Lesson 12
Unit Test
The Skills list explicitly includes "Multiply one-digit whole numbers by multiples of 10 in the range 10-90." Students practice problems that match this form (e.g., 6×10, 3×60, 3×90, 50×5, 50×7, 20×8, 10×9, 70×8) in classroom prompts and the unit test. Students complete multiple activities on properties of multiplication (commutative, associative, distributive) including matching sentences to properties and using distributive examples such as 9×8=(9×4)+(9×4).
Final Project
Planning a Picnic
Students are prompted to "use what you know about addition, subtraction, multiplication, and division" and to "use the distributive property of multiplication to break down numbers," which explicitly directs use of properties and place-value strategies. The Skills list includes "Apply properties of operations as strategies to multiply and divide" and "Use multiplication and division within 100 to solve word problems." In the Seating Arrangement activity, students multiply numbers of large picnic tables by their seating capacity (10 people) to check whether arrangements seat 60 people, providing direct practice multiplying one-digit counts by 10.
Unit 5: Area and Perimeter
Lesson 3
Calculating Perimeter
Students solve perimeter problems using multiplication (examples show 4 × 10 = 40 and 4 × 6 = 24) and are instructed to use multiplication for regular polygons (number of sides × side length). The Basic Skills Review explicitly includes the multiplication 6 × 70 = 420. Activities ask students to write number sentences for perimeters and to use repeated addition or multiplication when finding perimeters of shapes.
Lesson 5
Problem Solving With Perimeter
The Basic Skills Review #12 includes the multiplication problem 90 × 7 and the answer key shows 90 × 7 = 630, so students are expected to compute a one-digit number times a multiple of 10. Students are instructed to complete the Basic Skills Review sheet using scratch paper, indicating they will practice arithmetic computations. The answer key explicitly lists the product for that multiplication problem.
Lesson 6
What Is Area?
The Basic Skills Review worksheet includes the problem "80 × 9 =" and the answer key shows 80×9=720, giving students an explicit multiplication problem that matches the standard's form. Several area activities have students build and count arrays (e.g., filling a 4 by 6 rectangle to get 24, rolling dice to make 2 by 3 or 4 by 6 rectangles), which has students multiply rows by columns to find area.
Lesson 7
Calculating Area
Students multiply side lengths to find area and write multiplication sentences (for example, they calculate 8 × 10 = 80 and complete problems such as 3 × 5 = 15, 5 × 6 = 30). Students verify area by tiling and counting then reproduce the result by multiplying two side lengths. Students measure real-world shapes in whole-number units and write the multiplication equations for the areas.
Lesson 8
More Work With Area
Students solve problems in the Basic Skills Review that involve multiplying a multiple of 10 by a one-digit number (e.g., 60 × b = 540 and a × 7 = 420, which requires recognizing 60 × 9 = 540 and 60 × 7 = 420). Students also work with place-value contexts (rounding 3086 to the nearest 10 and 100) that reinforce understanding of tens. These items show students compute with multiples of 10 in numerical problems.
Lesson 10
Problem Solving With Perimeter and Area
Students multiply whole-number side lengths to find areas of rectangles (e.g., the list of rectangles such as 17×1, 15×3, 10×8) and are asked to break larger multiplication into smaller parts using the distributive property (example: 15×3 = (8×3)+(7×3)). Students also compute areas for robot parts and food court stands, requiring multiplication of side lengths and counting squares to find area values (some areas equal multiples of 10, e.g., 80).
Lesson 11
Unit Test
Students are asked to multiply side lengths to find areas (e.g., problems that yield areas: 9 ft × 5 ft = 45 sq ft; 4 ft × 8 ft = 32 sq ft; a rectangle labeled 4 ft and 10 ft with area = 40 sq ft). The review and activities repeatedly prompt students to use multiplication to find area and to compute missing side lengths from given area or perimeter (e.g., area 48 sq ft with one side 6 ft leading to 6 × 8). The student worksheets include multiple calculation problems where students perform one-digit × one- or two-digit multiplications to determine area.
Final Project
Shapesville
Students are asked to multiply side lengths to find areas of rectangles (Skills: "Multiply side lengths to find areas of rectangles with whole-number side lengths") and to measure and draw rectangles (Step 2 practice: 6×6, 4×5, 12×18). In Steps 3–5 students compute missing dimensions from given areas and perimeters (e.g., Building #2 perimeter 40 cm leads to each side = 10 cm; students are asked to explain how they found perimeters and areas for their own designs). Students cut and arrange windows by specified dimensions and check area/perimeter calculations for building components.
Unit 6: Fractions
Lesson 2
Naming Fractions
Students solve Basic Skills Review problems that include multiplication by multiples of ten, for example 10×6=60 in the donut problem, a×30=270 (so a=9), and 4×b=320 (so b=80). The worksheets require students to compute these products or find missing factors involving multiples of 10.
Lesson 3
Fraction Parts
The Basic Skills Review includes multiplication items and algebraic prompts such as "a × 30 = 180" (leading to a = 6) and "4 × b = 120" (implying b = 30). The lesson asks students to work with multiplication flashcards and to make piles of facts they know and need to practice, providing practice with basic multiplication facts. These items show students solving problems that involve a one-digit factor and a multiple of 10 (30).
Lesson 6
Fractions on Number Lines
Students solve problems in the Basic Skills Review that involve multiplication with multiples of ten, for example finding b in 40 × b = 360 (b = 9) and finding a in a × 3 = 270 (a = 90). Students also perform one-digit multiplication in a word problem (5 × 8 = 40) which practices basic multiplication facts. Students complete arithmetic items that implicitly include multiples of ten in equation form.
Lesson 7
Equivalent Fractions
The Basic Skills Review includes the computation 7×10=70 and the equation 50×b=450 (which implies 50×9=450), so students perform multiplication involving a one-digit number and a multiple of 10. The review also contains items like 50×b=450 and a×7=420 that involve understanding multiplication facts and solving for a factor.
Unit 7: Geometry
Lesson 3
What Is a Quadrilateral?
The Basic Skills Review #20 includes a word problem where students compute 8 × 10 = 80 (Deena had 8 bags of 10 jellybeans). The answer key explicitly shows 8(x)10=80, indicating at least one instance of multiplying a one-digit number by a multiple of 10 is practiced.
Lesson 6
Dividing Shapes
The Basic Skills Review (#22) includes the equation a × 4 = 320 with the answer a = 80, which reflects a one-digit number multiplied by a multiple of 10 (4 × 80 = 320). The review also contains multiplication and area problems (e.g., 9 × 8 = 72 and area = 3 × 4 = 12) that involve multiplication facts and using multiplication to find area.
Unit 8: Graphing Data
Lesson 1
Data and Graphing Basics
Students interpret pictographs where a key states that one flower image equals 10 flowers (Activity 2 and Activity 4). Students are asked to reason that if each picture represented one item the graph would be huge and are led to compute totals such as 8 picture symbols representing 80 items. The Scaled or Non-Scaled? page explicitly discusses using scales that count by 10 (alongside 2 and 5) for large data sets.
Lesson 2
Pictographs
Students read and interpret scaled pictographs where a picture represents 10 (e.g., questions asking that one book image represents 10, and that 6 book images represent 60). Students convert counts of picture symbols into total numbers (for example, determining Tuesday = 60 or Monday = 40 from the pictograph). Students create pictographs using a specified scale (choosing what each picture represents) and use keys where each shaded square represents 5 books when making graphs.
Lesson 3
Bar Graphs
Students practice counting by fives and tens when interpreting graph scales (Activity 1 and Activity 3 ask students to determine scales of 5 or 10). The Basic Skills Review includes multiplication with a factor of 10 (10×6=60) and an equation that implies multiplication by a multiple of 10 (6×b=420 leading to b=70). Students also choose and reason about using scales of 5 or 10 when creating bar graphs, which requires working with multiples of 5 and 10.
Lesson 4
Line Plots
The Basic Skills Review includes a problem with 60 × b = 420 (answer b = 7), which requires recognition of a multiplication involving a multiple of 10 (60) and a one-digit factor. The review also contains other multiplication facts (7 × 8 = 56) showing students perform basic multiplication computations.
Lesson 5
More Work With Graphing
Students solve a Basic Skills problem that multiplies 9×10 to find 90 when computing total cookies (9 bags × 10 cookies each). Students also encounter an equation 7×b = 420 that yields b = 60, which reflects multiplication involving a one-digit number and a multiple of 10 (7×60). In the Money in the Bank activity students compute values for coin groups such as 10 dimes = $1.00 and 20 pennies = 20¢, which requires multiplying counts by coin values (including multiples of 10 cents).
Unit 9: Skills Review
Lesson 1
Reviewing Multiplication and Division
Students practice multiplying one-digit numbers by 10 using the laminated input/output activity where they write "x10," draw number cards 1–10, compute the outputs, and explain that multiplying by 10 means adding a zero. Students review and organize multiplication properties (commutative, associative, distributive, identity, zero) by cutting/gluing examples and analyzing example equations such as 8 × 12 = (8 × 2) + (8 × 10). Students also practice basic multiplication facts and fluency through timed games and activities.
Lesson 3
Reviewing Perimeter and Area
Students multiply to find area for a rectangle with sides 10 cm and 7 cm, producing 7 × 10 = 70. Students are asked to write number sentences using multiplication for regular polygons (e.g., 3 × 8 for an equilateral triangle, 4 × 7 for a square). Students also multiply side lengths when finding perimeters of regular shapes and are prompted to explain multiplication strategies for those perimeters.