Students practice finding one-tenth of numbers (e.g., 40,000 ÷ 10 = 4,000 and 1/10 = 0.1) and complete problems that use multiplying or dividing by 10 with whole numbers and decimals. Students consider real-world contexts that use unit fractions, such as choosing 1/10 or 1/100 of a cake and finding 1/10 of 40,000 jellybeans, and they view visuals (cake grids, ten dimes) that illustrate a fraction as division. Students also work problems that move decimal points when multiplying or dividing by 10 and fill in comparisons like "50 is 1/10 of 500."

Students are shown fraction expanded notation where digits are written as products of a whole number and a unit fraction (e.g., (8 × 1/10) = 8/10) and are instructed that (8 × 1/10) is the same as 8/10. Students use decimal and fraction expanded forms (0.82 = (8 × 0.1) + (2 × 0.01) and 0.82 = 8/10 + 2/100) which involve multiplying digits by place-value fractions. Students also work with base-ten grids that visually represent tenths, hundredths, and thousandths, which could support model-based reasoning about fractional parts.

The Skills section explicitly says students will "Use operations on fractions to solve problems involving information presented in line plots." The Holiday Package Line Plot activity asks students to find "the total weight of all the packages that weigh 4 1/4 pounds?", which requires multiplying a mixed number by a whole number (parent key gives 17 pounds). The lesson also has students record and display measurements in quarter-hour and quarter-pound increments, so students work with fractional and mixed-number measurements on line plots.

Students are asked to compute a real-world quantity when they answer: "If Alice decides to make two batches of cookies, how many cups of butter will she need in all?", which requires combining or doubling the mixed-number amount of butter. Students also add and subtract mixed numbers in the walking contest problems (finding who walked farther, how many miles more, and the total miles) and in several practice problems that require writing out each addition or subtraction of mixed numbers. Activity 3 asks students to use the fraction boxes to create addition and subtraction sentences with mixed numbers, reinforcing combining mixed-number quantities.

Students solve multiple real-world problems that require multiplying a whole number and a fraction (e.g., 6 × 1/4 for pies; tacos, apples, smoothies, and walking-distance problems). Students represent problems with repeated addition, pictures/fraction strips, and multiplication equations (tables and activity pages ask for repeated addition, picture, multiplication, and product). Students are instructed to simplify products and convert improper fractions to mixed numbers and to use different strategies to check answers.

Students solve real-world word problems that multiply fractions and whole numbers (e.g., the farmer uses 1/3 of 12 pumpkins; Maria takes 3/4 of 24 cookies; Kiara displays 3/8 of 40 coins) and are asked to write these as multiplication equations. Students use visual fraction models and representations (fraction strips, number lines, arrays, icons, and cut-and-paste activities) to compute products such as 1/2 × 8 = 4, 2/5 of 15 = 6, 1/6 × 30 = 5, and 2/3 × 12 = 8. The unit includes practice matching and quiz items that require using equations and visual reasoning for fraction multiplication (problems like 3/2 × 6, 12/5 × 4, and several word problems).

Students solve a real-world painting problem (finding 3/4 of 1/2) by using fraction strips and area models to show that 3/4 of 1/2 = 3/8. Students practice paper-folding and area-model activities where they fold, shade, unfold, count parts, and write number sentences (for example 2/3 x 1/4 = 2/12 = 1/6). Students use interactive area-model tools and complete word-problem pages (park/garden/cupcakes) where they draw area models, count overlapping shaded parts, and write and simplify the resulting fraction products.

Students use number lines and area models to find products of fractions (for example, finding 3/4 of 1/2 = 3/8) and are guided to draw, mark, and shade number lines and area models. Students solve multiple real-world word problems that require multiplying fractions (hardware store rope, pizza eaten, music club violinists, track painting, brownies, paint/stripes problems). Students learn and practice the multiplication algorithm (multiply numerators and denominators), connect it to visual models, and complete worksheets and quizzes using the algorithm and models.

Students solve real-world word problems that require multiplying fractions in Activity 4 (e.g., band/trumpet, pies, apples, oranges, and dolphins) and are instructed to use fraction multiplication to find answers. Students practice the multiplication algorithm and a cancellation (cross-reduce) trick in Activities 1 and 2 and retake timed quizzes to apply those skills. One problem explicitly asks students to "draw a picture to prove their answer," and Activity 4 references prior work with number lines and area models.

Students convert mixed numbers to improper fractions and use the fraction multiplication procedure (make improper, possibly cancel, multiply numerators and denominators, convert back) in Activities 2 and 3. Students solve real-world word problems that require multiplying fractions and mixed numbers (e.g., the soccer team ate 3/4 of 5 1/2 bags; Joseph runs 3 3/4 laps of a 1/4-mile track). Students also represent multiplication with equations in examples and practice problems (for example, 2 2/3 × 9 9/10 shown as (48/9) × (93/10)).

Students solve multiple real-world word problems that require multiplying fractions and mixed numbers (Activity 4 "Real World Fraction Problems" and the Mindy cupcakes example). The Unit 5 Quiz and practice problems ask students to compute products such as 1 2/3 × 2 3/4 and multi-factor fraction products, showing they practice equations for multiplication. Input/output table activities require students to multiply whole numbers, fractions, and mixed numbers by rules like 2/3, 1 1/2, and 2 1/3, giving repeated practice applying multiplication in contextual formats. Images and prompts encourage students to draw pictures or use number-line/cupcake visuals when solving word problems.

Students construct and count tiled models to find areas with mixed numbers (examples: 5 1/4 x 4 giving 21 sq in; 3 1/2 x 2 1/2 giving 8 3/4 sq ft) and with proper fractions (worksheet problems such as 3/4 in x 5/8 in). Students use expanded-form rectangular decompositions to break mixed-number side lengths into whole and fractional parts and then multiply the parts and sum the partial areas (images and worked examples show 3 + 1/2 by 2 + 1/2 split into 4 smaller rectangles and summed). Students solve multiple real-world word problems (table/tablecloth, garden, wall paint, rug, puppy pen, tabletop) that require computing area by multiplying fractions or mixed numbers and are asked to use either tiling models or the L x W formula to check answers.

Students solve multiple real-world word problems that require multiplying fractions and mixed numbers (e.g., Cliff's fence wire, Mrs. Garcia's coffee, Martin's clay, Emelia's ribbon, and finding the area of rectangles with fractional side lengths). Students are asked to draw pictures or match expressions with visual models (number line, grid, bar model, rectangular area models) to illustrate fraction multiplication (e.g., draw a picture for 5 × 1/2 and 8 × 1/4). Test and review items include computations that multiply fractions and mixed numbers and ask students to simplify and convert to mixed numbers, and some activities explicitly connect fractional side lengths to area calculations.

Students are required to create 20 multiplication problems that include 5 whole-number-by-fraction problems, 5 fraction-by-fraction problems, and 5 problems that include mixed numbers, and then write the product for each problem. Students must draw rectangles with fractional or mixed-number side lengths and write the area for those problems, which asks them to represent products as rectangular area models. Students must compute products and sort problem cards into categories (less than 1, equal to 1, greater than 1 and less than 2, and 2 or greater), and provide an answer key showing the products.

Students complete Basic Skills Review #17, which includes a real-world recipe problem that asks how much milk is needed for 3 1/2 batches when one batch uses 1 1/3 cups (the parent answer key shows converting 1 1/3 and 3 1/2 to improper fractions and multiplying). The review also includes a problem that multiplies the mixed number 4 5/7 by 6, and instructions prompt students to show work and label units. The parent answer key provides the equation-based solution steps for the mixed-number multiplication.

The Basic Skills Review #18 includes real-world problems that require multiplying mixed numbers and fractions: e.g., Brian's peach muffin recipe (1 2/3 × 2 = 3 1/3) and Patty's garden area (6 1/3 × 5 1/2 = 34 5/6). The answer key shows work converting mixed numbers to improper fractions and carrying out multiplication (for example, 19/3 × 11/2 = 209/6). Additional items ask for products of mixed number and whole number (10 1/5 × 6 = 61 1/5), showing students practice equation-based fraction multiplication in real contexts.

Students complete Basic Skills Review #19 problems that include real-world contexts requiring multiplication of fractions and mixed numbers, such as the peach muffin recipe asking 3/4 × 3 1/2 and the yard area problem 7 2/3 × 5 1/2. The answer key shows equation-based computations and final products (e.g., 2 5/8 cups for the muffin problem and 42 1/6 square feet for the yard area). Additional fraction multiplication practice (e.g., 7 3/5 × 8 and 7/3 × 8 1/5) is included on the review page.

Students calculate area for shapes with fractional and mixed-number side lengths (e.g., Problem 1: 3 1/3 ft × 2 1/2 ft; Problem 6: square with sides 4 1/2 yd). The answer key explicitly shows multiplication of mixed numbers and fractions to find area (e.g., 9/2 × 9/2 = 81/4 = 20 1/4 sq yd; 9/4 × 10/3 = 7 1/2 sq ft). Real-world contexts are used for these calculations (a sandbox, a flat package, kitchen countertop, and blueprint design), and students are asked to compute area using the equation Area = length × width.

Students solve a real-world lemonade problem that requires multiplying a fraction by a whole number (1/8 cup per pint for 8 pints = 1 cup). Students compute a multiplication involving a mixed number (find the product of 4 2/3 and 5) on the Basic Skills Review. Students also work a pizza problem that involves partitioning/working with eighths and is solved using fraction multiplication/division (6 pizzas into eighths → 48 pieces).

Students complete Basic Skills Review #24 which includes real-world and computation items that require multiplying fractions and mixed numbers. Examples given and answered in the parent key are: Cassandra's cupcake recipe (1/8 × 15 = 15/8 = 1 7/8 cups), multiplying the mixed number 3 3/5 by 4 (result shown as 14 2/5), and a pizza problem that uses sixths (12 pizzas cut into sixths → 72 pieces). The answer keys show the written multiplication equations and final mixed-number results for these items.

Students solve a real-world fraction multiplication problem in the Basic Skills Review when they calculate sauce needed: 1/3 × 17 = 17/3 and then subtract 4 1/2 to find how much more is required. Students compute the product of a mixed number and a whole number (6 3/4 × 5 = 33 3/4) and simplify the result. Additional items (1/7 × 13 comparison and Tamara's pizza pieces involving eighths) give students practice performing multiplication or equivalent operations with unit fractions and whole numbers.

Students complete input/output tables that require multiplying by fractions and mixed numbers (rules: multiply by 3/4 and multiply by 1 1/2) and are asked to simplify answers and write mixed numbers as needed. Students solve a real-world area problem where they compute the area of a rectangle with width 3 1/2 inches and length twice the width, and the answer key shows the multiplication steps (3 1/2 × 2 = 49/2 = 24 1/2). The provided answer key also shows equation-style work for the table entries and word-problem solutions.