Students are taught that a fraction can be written as a division sentence (for example 1/10 = 1 ÷ 10) and they practice finding one-tenth of numbers through multiple ÷10 problems (e.g., 400,000 ÷ 10 = 40,000 and similar exercises). Students compare one-tenth and one-hundredth of a cake, and they practice moving the decimal point when multiplying or dividing by 10. The activities include numeric practice that shows 1/10 of whole numbers and decimals and explicit exercises interpreting 1/10 as a partition of a quantity.

Students are shown and practice multiplying whole numbers by unit fractions (for example, (8 × 1/10) = 8/10) and writing decimals in fraction expanded notation (e.g., 0.82 = (8 × 0.1) + (2 × 0.01)). The parent plan and activities instruct students to convert digit values to fractional units (such as 3 in 24.673 being 3/1000) and use base-ten grids to represent tenths, hundredths, and thousandths, reinforcing multiplication of digits by unit fractions.

The lesson's Skills section states students will "use operations on fractions to solve problems involving information presented in line plots," and the Holiday Package questions ask students to compute totals (e.g., total weight of all packages that weigh 4 pounds and a parent-keyed question about total weight of packages that weigh 4 1/4 pounds = 17 pounds). Students are asked to create line plots with quarter-hour and quarter-pound hash marks and then answer quantity and total-weight questions that require multiplying a fractional measurement by a count.

Students model and solve problems that multiply a fraction by a whole number using repeated addition and pictures (e.g., six measuring cups each 1/4 cup, cookie and pie examples). Students use fraction strips and are asked to trade and combine strips to produce mixed numbers (e.g., converting 6/4 to 1 1/2). Students practice the algorithm (multiply the numerator by the whole number, keep the denominator) and complete worksheets and word problems (for example, 5 × 2/3 = 10/3 and 5 × 2/3 shown as a worked example).

Students use visual models to find fractions of whole numbers (e.g., number lines dividing 15 into 3 equal parts and showing 1/3 of 15 = 15 ÷ 3). Students use fraction strips and concrete/paste activities to find parts of parts and are asked to write those situations as multiplication problems (examples: 2/5 of 15, 3/4 of 8, 1/6 × 30, 2/3 × 12). The lesson explicitly tells students that multiplying a fraction by a whole number means finding a part of the whole and links 1/3 × 15 to 15/3, showing the a × q ÷ b equivalence.

Students model (3/4) of (1/2) using fraction strips by dividing 1/2 into four 1/8 parts and selecting three to show 3/8. Students fold paper to create area models (for example, 2/3 × 1/4) and count shaded parts to record products like 2/12 (then simplify to 1/6). Unit-fraction area model pages and interactive tools have students draw and interpret overlaps (e.g., 1/3 × 1/2 = 1/6) and match shaded grids to multiplication expressions. Activity 6 returns to the Carlton painting story and asks students to create an area model to show 3/4 × 1/2 = 3/8 and explain their work.

Students use a number line model that directs them to draw 0 and the second factor as endpoints, divide that interval into b equal parts (the first fraction's denominator), and count a parts (the first fraction's numerator) to find the product; the lesson explicitly states, "you read this problem as '3 parts when 1/2 is divided into four parts.'" Students also use area models (brownies) to find a part of a part and are asked to illustrate fraction×fraction problems and to practice whole-number×fraction problems (e.g., 3 × 3/4) and fraction×fraction problems on worksheets. The materials state the algorithm in general (multiply numerators, multiply denominators) and provide many practice problems and visual activities tying the models to the multiplication algorithm.

Students practice multiplying fractions repeatedly: they complete an initial 10-question online quiz, watch a video and complete worksheets that use the multiplication algorithm and cross-canceling trick, and retake a similar timed quiz. Students solve real-world word problems (e.g., fractions of a band playing trumpets, portions of pies and oranges) that require multiplying a fraction by a fraction or a whole number. The materials also prompt students to explain the algorithm (multiply numerators, multiply denominators, then simplify) and to discuss how cancelling before multiplying saves time.

Students are taught to change mixed numbers to improper fractions and then multiply numerators and denominators ( Things to Know; Activity 3 steps: "Make improper fractions", "Multiply numerators", "Multiply denominators"). Students solve multiple practice problems and worked examples that convert mixed numbers to improper fractions and compute products (Activity 2 problems, the worked example 2 2/3 × 9 9/10). Students also apply multiplication of fractions and mixed numbers in contextual word problems (bags of chips, track laps).

Students solve fraction × whole-number problems in real contexts (Mindy gives 2/3 of 24 cupcakes to friends, then 1/2 of the remainder), and they complete input/output tables that require multiplying various inputs by 2/3, 2 1/3, 1 1/2, and 1/4. Students work word problems that involve a fraction of a fraction (e.g., 3/4 of a project with 2/3 of that being colored) and quiz items include fraction×fraction calculations (for example 1/5 × 1/3 and 1/2 × 1/3 × 1/4). The activities ask students to use "of" to decide to multiply and to simplify products, giving repeated practice computing products of fractions and mixed numbers.

Students use the tiling method and rectangular area models to represent products of fractional and mixed-number side lengths (examples: 5 1/4 × 4 shown by tiles; 3 1/2 × 2 1/2 broken into sections). The lesson has an explicit example where a 2 1/3 by 1/2 rectangle is tiled and students combine fractional tiles (1/2 + 1/2 + 1/6 = 1 1/6), and several student activity problems require multiplying proper fractions (e.g., 3/4 × 5/8) and mixed numbers to find areas. The Parent Plan and Skills statements state that students will "represent fraction products as rectangular areas" and "show that the area is the same as would be found by multiplying the side lengths."

Students match fraction multiplication expressions with visual representations (number lines, area/grid models, and bar models) and are prompted to draw pictures to illustrate problems such as 5 × 1/2 and 8 × 1/4. Answer-key images show visual models for fraction×fraction (for example a grid showing 1/3 × 1/2 and rectangles illustrating 4/5 × 2/3) and a strip/area model for examples like 2/3 × 6. Word problems ask students to find "fraction of" quantities (e.g., 6 × 5/6, 3 1/2 × 4/5, and other mixed-number × fraction problems) so students compute and interpret fractions of whole amounts in story contexts.

Students are asked to create and solve 20 multiplication problems that include 5 whole-number-by-fraction problems, 5 fraction-by-fraction problems, 5 mixed-number problems, and 5 rectangular-area problems with at least one fractional side. Students must draw rectangles showing length and width and write the area in the answer column, and the parent-plan skill explicitly names "multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas." Students also must sort problems into product-size categories (less than 1, equal to 1, between 1 and 2, and 2 or greater).

Students complete Basic Skills Review problems that require multiplying mixed numbers and whole numbers (for example, 1 1/3 × 3 1/2 and 4 5/7 × 6). The provided answer key shows students converting mixed numbers to improper fractions and carrying out the multiplication (e.g., 4/3 × 7/2 and 33/7 × 6/1), demonstrating practice with the numeric procedure for fraction × whole-number multiplication.

Students solve several multiplication problems involving fractions and mixed numbers in the Basic Skills Review (e.g., 1 2/3 × 2 = 3 1/3; 6 1/3 × 5 1/2 = 34 5/6; 10 1/5 × 6 = 61 1/5). Students apply fraction multiplication in real-world contexts such as a recipe (doubling ingredients) and finding area of a garden. The parent answer key shows students converting mixed numbers to improper fractions and multiplying numerators and denominators (e.g., 19/3 × 11/2 = 209/6).

Students complete Basic Skills Review #19 items that require multiplying fractions and mixed numbers, including problems like 3/4 × 3 1/2 = 2 5/8 and 7/3 × 8 1/5. Students compute products of mixed numbers and whole numbers (e.g., 7 3/5 × 8 = 60 4/5) and solve a recipe word problem that applies fraction multiplication (Maria's peach muffins).

Students use cut-out sandwiches and tables to partition whole quantities into equal parts (e.g., cutting each sandwich into thirds and sixths) and record results such as 4/3 and 2/3 for sandwiches per person. Students complete charts that show the number of sandwiches (numerator) divided by number of people (denominator) and convert improper fractions to mixed numbers. The cookies activity has students fill a grid of whole-number dividends divided by whole-number divisors, producing fractional and mixed-number quotients and using visual/shaded cells to represent results.

Students compute areas where one or both side lengths are fractions or mixed numbers (e.g., a rectangle with sides 3 1/3 ft and 2 1/4 ft, and a square with side 4 1/2 yd). The answer key shows students multiply converted improper fractions (e.g., 9/4 × 10/3 = 15/2 and 9/2 × 9/2 = 81/4) to find area. Several problems require students to perform fraction-by-fraction multiplication to obtain areas (Calculating Perimeter and Area sheet, sandbox and package problems).

Students complete Basic Skills Review problems that require multiplying fractions by whole numbers and mixed numbers: the answer key shows 1/8 × 8 = 1 (lemonade problem) and 4 2/3 × 5 = 70/3 (product of a mixed number and a whole number). The worksheet problems and answer key show step-by-step numerical computation of these products, and a pizza problem involves partitioning pizzas into eighths (6 ÷ 1/8 = 48) which involves fraction operations.

Students compute products involving a fraction and a whole number in the Basic Skills Review (e.g., 1/3 × 17 = 17/3 = 5 2/3) and multiply a mixed number by a whole number (6 3/4 × 5 = 33 3/4). The review also includes problems that use fraction arithmetic and related operations (e.g., 1/8 ÷ 6 rewritten as 1/8 × 1/6 = 1/48 and comparing 1/7 × 13 to 13/14). These items show students practice calculating products and manipulating fractions and whole numbers numerically.

Students complete input/output tables that require multiplying by 3/4 and by 1 1/2 and dividing by unit and non-unit numbers, and an answer key shows worked numerical products (for example, outputs when multiplying whole numbers by 3/4 and 1 1/2). Students solve context problems that use multiplication with fractions and mixed numbers (finding the area of a rectangle using 3 1/2 × 2, dividing 3/4 among 3 people, and dividing 8 by 1/3). These activities give students practice computing products and quotients involving fractions and mixed numbers.