Students use grid models to shade columns and rows (e.g., 0.3 vertically and 0.5 horizontally) and count overlapping squares to record products such as 0.3 × 0.5 = 0.15, with each square representing one hundredth. Students draw base-10 block diagrams to tile repeated groups of decimal lengths (e.g., 2 × 0.45, 4 × 0.36, 5 × 0.62), exchange hundredths to tenths, and confirm that the tiled area equals the numeric product. Students are asked to compare their area/grid representations with the product found by the numeric algorithm to confirm the two methods match.

Students work with fractional measurements on line plots (quarter hours and quarter pounds) and are prompted to use operations on fractions to answer questions about the data. The student activity asks for the total weight of all packages that weigh 4 1/4 pounds (parent key gives 17 pounds), which requires multiplying the mixed number 4 1/4 by a whole-number count. The Skills section explicitly states students will "Use operations on fractions to solve problems involving information presented in line plots."

Students are introduced to multiplying a fraction by another fraction as "a part of a part" (for example, 1/2 × 1/4 described as half of a fourth). Students lay fraction strips out in a rectangle and are asked to use those strips to find products, and several activities use visual models (number lines, arrays of circles, grouped icons) to represent products like 2/5 of 15, 3/4 of 8, 1/6 × 30, and 2/3 × 12. The lesson includes practice writing multiplication expressions for "fraction of" problems and using visual representations to compute and check products.

Students fold paper and create rectangular grids (e.g., a 3x4 grid) and count shaded small parts to represent products such as 2/3 x 1/4 = 2/12 (simplified to 1/6). The Unit Fractions and Area Models and Making an Area Model pages direct students to divide a rectangle into columns and rows that match the denominators of the two factors, shade numerators in different directions, and interpret the double-shaded small rectangles as the product (for example 1/4 x 3/5 = 3/20). The lesson revisits real-world contexts (the painting problem) and has students use laminated grids or interactive area-model tools to draw tiles and show products such as 3/4 x 1/2 = 3/8.

Students are shown rectangular grid area models (the brownie/pan example with a 3x4 grid) in which 2/3 of the pan and 1/4 of the pan are represented by shaded rows and columns and the overlapping shaded squares equal 2/12. The lesson explicitly asks students to draw and color shapes to show the fraction multiplication algorithm and to connect those visual area representations to the algorithm of multiplying numerators and denominators. The materials prompt students to compare the area model answer (3/8 for 3/4 × 1/2) with the number line model and to use rectangular tilings on several student activity pages to represent fraction products.

Students practice converting mixed numbers to improper fractions and then multiplying numerators and denominators (Activities 1–3 and the step-by-step foldable). Students solve computation problems that multiply mixed numbers and fractions (Activity 2 problems and the "Multiplying Mixed Numbers Practice" sheet). Students apply multiplication of fractions in word problems that multiply fractional quantities (e.g., 5 1/2 × 3/4 for bags of chips and 1/4 × 3 3/4 for laps of a track).

Students are shown multiple tiling models with fractional unit tiles (for example, a 5 1/4 by 4 inch rectangle is partitioned into whole and 1/4-inch strips and counted to get 21 sq in). A mixed-number example (3 1/2 by 2 1/2) is expanded into four subrectangles, areas are found (6 + 1 + 1/2 + 1/4) and summed to 8 3/4, and the result is checked by multiplying the side lengths. Activity 2 presents a 2 1/3 by 1/2 example where students count fractional tiles (1/2 + 1/2 + 1/6) to form wholes and get 1 1/6, and student worksheets include problems requiring fraction×fraction and mixed-number area computations (e.g., 3/4 × 5/8, mixed×mixed).

Students are asked to find the area of rectangles with fractional side lengths (e.g., a rectangle with length 4 1/2 inches and width 2 1/3 inches; a garden 5 3/4 by 3 1/2 feet) and to compute areas in answer keys. Several student pages and answer keys show rectangular area models, grids, and overlapping-region diagrams that represent fraction products (e.g., a grid showing 1/3 × 1/2, rectangular strips showing 2/3 of 6). The activities prompt students to "draw a picture to illustrate" multiplication problems (for example 5 × 1/2, 8 × 1/4), encouraging pictorial/area representations of fraction multiplication.

Students are required to create 5 rectangle problems that show both a length and a width (with at least one side a fraction or mixed number) and then write the area for each rectangle in the provided table. Students are instructed to draw the rectangles for the fractional area problems and to write the product (area) in the answer column. The directions also ask students to use what they know about multiplying fractions as they work and to include at least one fractional area problem in each product-size category.

Students are asked to find the area of a garden with fractional side lengths (6 1/3 ft by 5 1/2 ft) in the Basic Skills Review and the answer key shows the multiplication of mixed numbers (19/3 × 11/2 = 209/6 = 34 5/6). Other items require multiplying mixed numbers or fractions (e.g., 1 2/3 × 2 = 3 1/3; 10 1/5 × 6 = 61 1/5), so students practice multiplying fractions and mixed numbers to produce area or product values.

The Basic Skills Review includes an item asking students to find the area of Mateo's yard given fractional side lengths (7 2/3 ft by 5 1/2 ft) and the answer key shows the multiplication 7 2/3 × 5 1/2 = 42 1/6 square feet. The review also includes explicit fraction multiplication practice (e.g., 7/3 × 8 1/5 and 7 3/5 × 8) so students compute products of fractions and mixed numbers. The area item instructs students to label units, reinforcing that the product represents square units.

Students calculate areas for rectangles and squares with fractional side lengths in multiple problems (e.g., Problem 1: 3 1/3 ft by 2 1/2 ft; sandbox: 4 1/2 yd by 4 1/2 yd). The answer key shows students multiply mixed numbers and fractions to find area (e.g., 9/4 × 10/3 = 7 1/2 sq ft; 9/2 × 9/2 = 81/4 = 20 1/4 sq yd). Quiz and worksheet items require students to compute area for dimensions given as decimals and fractions, so students practice multiplying fractional side lengths to produce area values.

Students complete input/output tables that require multiplying by fractions (e.g., multiply by 3/4 and multiply by 1 1/2) so they practice computing fraction products. Students solve a word problem about a rectangle with width 3 1/2 inches and length twice the width, and they compute area by multiplying 7 × 3 1/2 to get 49/2 (24 1/2). The answer key shows the step-by-step multiplication of the mixed number and whole number to find area.