Students multiply by 10 when exploring the million-dots image (e.g., multiplying 100 by 10 to find 1,000 and scaling to 10,000, etc.). The lesson explicitly lists the skill "Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right," and students build numbers and compare digit values in multiple activities (place value mat, flipbook, Safe Crackers).

Students solve a multiplicative word problem about ticket sales: "Sophie has sold twice as many tickets as Samuel. How many tickets has she sold? (1,048)." The Number Detective clues include multiplicative relations among digits (e.g., "The digit in the millions place is three times the digit in the tens place"), which asks students to use multiplication to determine digits. Several problems require students to compute products or use multiplicative relationships to find unknown quantities.

Students model multiplication with counters, arrays, or drawings in the Introduction when asked to represent 5 × 6 and to explain it as "five groups of six." The Skills list explicitly cites representing verbal statements of multiplicative comparisons as multiplication equations. Students are asked to write multiplication or division sentences for each word problem and solve problems that include a multiplicative comparison (e.g., "she had double the amount of customers").

Students read and solve word problems that use multiplicative-comparison language (e.g., a problem that says a neighbor has "twice as many" or "5 times as many" rose bushes and the answer key identifies this as multiplication). Students are asked to circle key words that indicate which operation to use and to fill out a chart of operation key words for addition, subtraction, multiplication, and division. Students create their own multiplication and division problems to reach a selected challenge number on the "Creating Problems" activity and may have those checked by an adult.

Students set up and solve equations that use multiplication and division (examples: 5 × __ = 10, 16 ÷ __ = 8, 30 ÷ 6 = 5) and write equations with a symbol for an unknown (x+3=10, 28 ÷ y = 4). Students match word problems to equations that use multiplication or division (Renata: 2 × __ = 20; players: __ ÷ 2 = 4) and use a pan-balance model to make both sides equal when solving for unknowns. Students write examples of equations with variables and find the values of the variables during Activity 3 and the wrap-up.

Students convert word problems into equations with a symbol for the unknown (e.g., 3 x 7 = b for "Karen has 3 times as many books as Sal" and n ÷ 3 = 8 for "She gave all of them to 3 friends; each friend received 8"). Students solve multiplication and division word problems (e.g., 6 x 9 = n, 18 ÷ 3 = n) in matching and activity pages. Students identify operation-clue words ("double," "share them equally," "in all") to choose multiplication or division.

Students practice applying multiplication and division operations in multiple activities (Input/Output Tables and What's the Rule?) where they compute outputs using rules like "multiply by 3," "divide by 2," or two-step rules such as "multiply by 2 then add 1." The introduction asks students to distinguish actions ("add 2, multiply by 2") when identifying pattern rules. Think About It problems explicitly ask students to apply rules that include both multiplication and division (e.g., "multiply by 4, then divide by 2").

Students solve word problems that use multiplicative language such as "Susie walked three times as many dogs as Lindy. Lindy walked 5 dogs" and "Lance collected four times as many cans as Sean collected. Sean collected 15 cans" and set up equations like 5 x 3 = n and 4 x 15 = n. Students also solve division comparisons (n ÷ 6 = 8) and complete multiple-choice items where they must pick the correct equation for a word problem (e.g., choosing 4 x 15 = n vs. additive options). Several items require writing and solving equations with a symbol for the unknown (a, b, n), and function-table tasks ask students to identify multiplication rules (multiply by 3 or 4).

The Basic Skills Review includes the word problem "Sally has 5 times as many books as Charles. Charles has 6 books. How many books does Sally have?" with the answer (30), which requires multiplicative comparison. The answer key also shows the equation-based problem "54 ÷ x = 9. What is x? (6)," and the student activity page asks students to solve simple algebraic equations and division remainders.

Students practice grouping by placing tiles into groups of 4 (and 6) to determine multiples, showing concrete grouping to represent multiplication. Students write equations for "groups of" problems (for example, "9 groups of 6" and "4 groups of 5") and draw pictures to show repeated addition as multiplication. Students solve a real-world seating problem (Carly hosting 38 people with tables that seat 6) using drawings or grids and determine the fewest number of tables, applying division and grouping. Students compare multiplication and addition expressions (e.g., 80 × 2 ? 70 + 70) by writing <, >, or =, practicing reasoning about equivalent or different operations.

Students solve explicit multiplication and division word problems such as "Ms. Marcioni bought 7 bags of pasta. Each bag had 100 pieces of pasta. How many pieces did she buy?" and a division problem about 2000 pieces of candy shared into equal bags. The materials repeatedly prompt students to think of multiplication as grouping (e.g., "2 groups of 100") and include pictures of groupings and place-value representations to support solving problems. Practice pages and tables give many multiplication tasks (e.g., 8 x 100, 3 x 1000) and visual worksheets that show groups and tens/hundreds/thousands.

Students solve several real-world multiplication word problems (e.g., Marcus with 30 bags × 20 marbles, Alex selling 4/40/400 tins at $8 each, Jane's tables × seats, pet shelter pounds of food) that require multiplying to find totals. Students complete equations and fill-in-the-blank products (for example 20 × 70 = ___, 50 × 70 = 3500) and use decomposed equations (20 × 40 shown as (2 × 10)(4 × 10) → (2 × 4)(10 × 10)) to show place-value strategies. A visual image and worked examples show decomposition and arrows that represent the multiplication process, supporting students' use of drawings and equations to find products.

Students solve multiple word problems that require multiplicative reasoning, including a hotel with 14 floors and 23 rooms per floor, babysitting $22 per day for 25 days, and the restaurant seating problem that is written as (17 x 6) + (14 x 8). Students draw arrays and base-10 area models to compute products and write addition sentences from partial products (e.g., 200 + 220 + 48 = 468). Students also see an explicit multiplicative-comparison phrasing in Basic Skills ("Kendra has 12 times as many books as Kurt") and work with equations that include an unknown (e.g., 56 ÷ x = 7).

Students solve contextual multiplication word problems (e.g., skyscraper: 56 floors × 24 offices = 1344; 32 teams × 18 players = 576; 37 packages × 48 cookies = 1776). Students use area model drawings (rectangles partitioned into partial-product regions) to represent and compute products, breaking numbers into expanded form and adding partial products. Students also practice equation work (e.g., 63 ÷ x = 7) and generate products from card-created numbers, checking answers with a calculator.

The lesson includes explicit multiplicative word problems students solve, e.g., "Lola has 11 times as many books as Cammie. Cammie has 26 books. How many books does Lola have?" and multi-step context problems (Chef Charles bought 96 boxes of 58 meatballs; 89 balls in 76 shipments). The lesson asks students to illustrate and explain multiplication using equations, rectangular arrays, area models, grids, and expanded form in multiple activities (expanded-form breakdowns and grid-based two-digit multiplication).

Students are asked to choose and teach two multi-digit multiplication strategies from a list that includes arrays and area models, which require drawing and visual representation. The project requires students to create a product (video or poster) that includes words and illustrations and to include at least one real-world word problem using multi-digit multiplication. The evaluation rubric explicitly asks for examples using numbers (e.g., 25 x 32) and at least one word problem involving real-world use of multi-digit multiplication.

The Basic Skills Review includes a word problem where Miguel has 23 times as many stamps as Dana (Dana has 42 stamps) and students compute Miguel's stamps (966), showing practice with a multiplicative comparison. The worksheet also contains several multiplication and unknown-product problems (e.g., 7000 × N = 350,000), which give students practice multiplying and solving for a factor in equations.

The Basic Skills Review includes a word problem that states, "Susan has 30 times as many marbles as Dan. Dan has 38 marbles. How many marbles does Susan have? (1140)," which requires students to use multiplication to solve a multiplicative comparison. The lesson also contains several multiplication and division practice items in the Basic Skills Review that give students practice computing products and quotients relevant to solving multiplicative situations.

Students solve multiplication and division problems in the Basic Skills Review (e.g., 50 x 600, 3200 x 8, division remainder). The review includes a multiplicative comparison word problem: "Sterling has 20 times as many marbles as David. David has 36 marbles. How many marbles does Sterling have?" These items require students to multiply or divide to find answers.

Students draw pictures and write repeated-addition equations to represent multiplication problems (e.g., drawing circles with unit fractions and writing 1/5+1/5+1/5+1/5 = 4/5). Students complete a word problem involving a multiplicative comparison about marbles (the Basic Skills Review includes a problem where one quantity is described as "4 times as many" and students compute the result).

Students solve word problems that require multiplying fractions by whole numbers (e.g., 5 batches × 2/3 cup = 3 1/3 cups) and problems that state multiplicative relationships (e.g., Penny eats 3/4 of Amigo's 12 lb, Sam ate twice as much as Morris who ate 7/8 of a pie). Multiple activities ask students to draw pictures and write equations to show their answers, and Day 2 explicitly prompts students to set up a multiplication sentence (3 × 1/2). Several problem sets require finding totals by multiplying a unit amount by a count (e.g., cheese for 8 pizzas, baking soda for 9 batches).

Students solve multiplication problems that multiply a fraction by a whole number (e.g., 3/4 × 7 for Jason's cookie batches) and complete product practice problems (items 18–22). The test directions ask students to "Draw pictures and write equations to solve the problems," and several word problems require writing equations and computing answers involving fractions and multiplication.

Students solve multiple division word problems that require multiplying or dividing to find equal shares or group sizes (e.g., cookies divided among children, pages per day, people per bus, groups for a maze, money per car wash). Students set up and carry out long division and find quotients and remainders, and they are prompted to check answers using multiplication or a calculator. Students practice placing digits in missing division sentences and use multiplication to verify division results.

Students practice using multiplication and division to convert between units, with explicit rules such as "Going from a LARGE unit to a small unit, MULTIPLY" and "Going from a small unit to a LARGE unit, DIVIDE." Students complete tables and problems that require multiplying (e.g., finding how many centimeters are in 3 meters, converting 3 m to 300 cm) and dividing (e.g., converting 750 cm to 7.5 m, inches to miles). Students match equivalent measures (e.g., 3 yards = 9 feet, 4 feet = 48 inches) which requires multiplicative reasoning.

Students are instructed to "use multiplication and division to convert between units of measurement" and complete numerous conversion exercises (e.g., 25 kilograms = 25,000 grams; 50,000 grams = 50 kilograms). Student pages require converting between ounces/pounds and pounds/tons (matching and fill-in-the-blank items) and include explicit conversion rules: "To convert a large unit to a small unit, multiply" and "To convert a small unit to a large unit, divide." A comparison item asks students to determine which is greater ("Which is greater, 2 tons or 40,000 pounds?"), requiring conversion and numerical comparison.

Students are asked to multiply unit relationships to find equivalents, e.g., the introduction has students draw eight fluid-ounce circles each containing two tablespoons and multiply 8 × 2 to find 16 tablespoons in a cup. The conversion charts and fill-in-the-blank activities require students to use multiplication and division to convert between units (e.g., pints to cups, quarts to gallons, teaspoons to tablespoons). The "Think About It" problems (Marcie vs. Francie; Samuel vs. Marcus) ask students to draw pictures and convert units to decide who drank more, and the metric activity has students convert liters to milliliters and combine amounts (Carlos: 3500 ml + 2 L = 5500 ml).

Students perform many conversion tasks that require multiplication or division (e.g., converting hours to minutes, days to weeks, decades to weeks, minutes to seconds) on the "Converting Time" and "Converting More Time" sheets. Students solve word problems that require multiplicative computation, such as converting 36 minutes to seconds, converting 1 1/2 hours to seconds, and computing pay for hours worked (Sarah paid $11 per hour). Students complete matching and fill-in-the-blank items that require scaling quantities by factors (for example, 96 hours = 4 days and 50 years = 5 decades).

Students calculate area using the formula A = length × width (e.g., the visual example shows A = 6 × 4 = 24). Students practice multiplication in the area exercises (several rectangles require computing area by multiplying dimensions). One perimeter problem asks students to change the width to reach a target perimeter (Mr. Sampson: increase garden perimeter to 66 ft and the answer key states add 4 feet to the width), which requires reasoning about the perimeter equation.

Students find missing side lengths by dividing a square perimeter (16 ÷ 4) and by subtracting known sides from a rectangle's perimeter then dividing to get the other sides. Students divide area by a given width to find a rectangle's length (35 ÷ 5 = 7) and complete application problems (Mr. Harmon and Ms. Scott) that require using multiplication or division with perimeter and area formulas. Diagrams and activity pages present shapes with labeled sides and blanks for unknown measures for students to solve.

Students draw and label rectangles on a grid and compute areas and perimeters for given dimensions. Students solve problems that ask them to fill in missing side lengths by using area (area = length × width) and by using perimeter relationships, which requires division to find an unknown side. The activity pages and example steps instruct students to calculate unknown side lengths using area and to use perimeter values to solve for missing dimensions.

Students convert between units and use multiplication or division to compare measurements (for example, converting 2 miles to 10,560 feet to compare with 9,000 ft and converting hours to minutes). Students complete the "Greater Than, Less Than, or Equal To?" page and the recipe problems, combining and converting amounts (e.g., totaling cups, converting teaspoons to tablespoons, and doubling the lasagna quantities). The lesson asks students which operations they used and why, prompting use of multiplication and division in word-problem contexts.