Students are asked to state and apply the rule that "when you multiply by 10, numbers get greater" and "when you divide by 10, numbers get smaller," and they complete practice problems (e.g., 6 × 10, 54 ÷ 10, 1.2 ÷ 10). Students fill in comparison statements such as "200 is 10 times as much as 20" and "50 is 1/10 of 500," and they answer contextual questions (e.g., choose between 1/10 and 1/100 of a cake, compare 400 jellybeans to 1/10 of 40,000). The activities include place-value reasoning showing a digit represents 10 times as much as the place to its right and 1/10 of the place to its left.

Students use laminated decimal grids to show 0.6 on a tenths grid and 0.06 on a hundredths grid and are asked to notice that 0.6 is much greater than 0.06. Students are shown and write decimal expanded notation such as 0.82 = (8 × 0.1) + (2 × 0.01) and are guided to multiply digits by unit fractions (e.g., 8 × 1/10 = 8/10). The materials state that each decimal place is one tenth the size of the place to its left, emphasizing that moving right scales values by a factor of 1/10.

Students practice multiplying and dividing whole numbers and decimals by powers of 10 (matching problems such as 0.01 × 10 = 0.1, 1,000 ÷ 10 = 100, 10 × 10,000,000 = 100,000,000). Students explain patterns in zeros and decimal placement when multiplying by powers of 10 and complete number-line and exponent-form activities that show repeated multiplication by 10. Parent-plan prompts ask students to state what is ten times a number and what one-thousandth times 10 equals, reinforcing the idea that multiplying by 10 makes numbers larger and dividing by 10 makes them smaller.

Students repeatedly work with multiplying and dividing by powers of 10 and observe that multiplying makes numbers larger and dividing makes numbers smaller (e.g., text: "multiplying makes numbers larger and dividing makes numbers smaller"). Students practice moving digits or the decimal point when multiplying or dividing by powers of 10 (multiple activities ask students to move digits right when multiplying and left when dividing). A comparative task appears in a "Think About It" prompt asking students to decide whether 8.75 × 10^4 is greater than 90,000, which invites comparison of a product to another number.

Students sort expressions that multiply or divide decimals by powers of 10 into 'Greater Than 1' and 'Less Than 1' (Activity 1), using items such as 0.005 × 10^6, 100 × 0.08, and 0.6 ÷ 10. The answer key explicitly groups products by whether they are greater or less than 1, showing expected reasoning about how the other factor (e.g., 0.08 or 10^2) affects the product. The parent prompts require students to explain how digits and the decimal point move when multiplying or dividing by powers of 10, encouraging reasoning about change in size without performing full multiplication.

Students are asked to reason about how products compare to factors in Activity 2: prompts ask, "When you multiply a decimal by a whole number, is the product greater than or less than the decimal?" and "When you multiply two decimal numbers, is the product greater than or less than the two decimal numbers?" The grid activity (Multiplying Tenths Using Grids) visually demonstrates that multiplying two tenths yields a smaller product (e.g., 0.3 × 0.5 = 0.15) without relying on the standard algorithm. Base-10 drawings and the parent notes explicitly prompt students to notice patterns (e.g., comparing 2 × 0.4 and 0.2 × 0.4) and explain why placement of the decimal affects the product.

Students are taught the rule "Going from a large unit to a small unit, MULTIPLY! Going from a small unit to a large unit, DIVIDE!" and are asked to choose M or D for many unit pairs (e.g., Feet to inches: M; Inches to feet: D). Students reason about relative size in examples (e.g., comparing 8 inches vs 8 feet and 96 inches vs 96 feet, and noting there are 12 times more inches than feet) and decide which measurement will be larger without performing full multiplication. Activities ask students to predict how quantities change when converting units (e.g., deciding whether the numeric measure will get bigger or smaller when changing units) and to explain why (foldable, "Which Operation?" and metric stair reasoning).

Students repeatedly convert between units using multiplication and division (for example, the recipe and image showing 4 pints = 4 × 2 = 8 cups and problems like 4 pt 13 c = 21 c). Students solve multi-step conversion word problems that require multiplying by unit conversion factors (e.g., converting liters to milliliters, pounds to ounces, and inches to yards) and the materials include guidance to "review the rules for deciding when to multiply and divide when converting units." Several practice items and answer keys show students applying multiplication as a means of scaling quantities (e.g., 32.5 gal × conversion factors = 260 pt).

Students are asked to decide whether products are greater than, less than, or equal to the whole-number factor in the "Greater Than, Less Than, or Equal To" sheet and the "Scaling Practice" sheet where they circle n <, n =, or n > without solving the multiplication. The "Things to Know" and parent-plan sections state and reinforce that multiplying by a fraction less than 1 yields a smaller product, by 1 yields the same product, and by a fraction greater than 1 yields a larger product. Multiple activities prompt students to compare products to one factor (e.g., word problems about pumpkins, cookies, cookies taken to book club, and the Scaling Practice word problems) and to explain their reasoning using fraction strips, number lines, and visual models.

Students use number lines and area models to represent a fraction of a fraction (for example, 3/4 of 1/2) and identify the resulting part (3/8) from the model. The materials explicitly prompt students to interpret (a/b)·q as a parts of a partition of q and include the statement that multiplying by a proper fraction yields a part of a part, so the product is smaller than the factors. Students are asked to reason qualitatively about which operation (addition, subtraction, multiplication) will give the greatest or smallest result, prompting comparison of sizes without calculation in discussion.

Activity 3 (Always, Sometimes, Never) asks students to decide whether expressions like 1/2 of 1 and 1/2 of 1/2 are greater than, less than, or equal to 1 and to draw general conclusions about multiplying by fractions greater than, less than, and equal to 1. Students complete sample problems on cards and sort statements into "Always/Sometimes/Never," using those examples to justify their placements. The parent/teacher notes and answer key explicitly prompt students to reason that multiplying by a proper fraction yields a smaller product, multiplying by an improper/mixed number (>1) yields a larger product, and multiplying by 1 or 0 yields the same number or 0, respectively.

Students are asked to evaluate statements about products without computing them (circle Always/Sometimes/Never) such as "If you multiply a fraction by a number greater than 1, the answer is greater than 1," "If you multiply a proper fraction by a proper fraction, the product is less than 1," and "If you multiply a fraction by a fraction greater than 1, the answer will be greater than the original fraction." Several activities present rules (e.g., "MULTIPLY BY 1 1/2" and "Multiply by 3/4") with IN/OUT tables that require students to reason about how the second factor changes the size of the result. The answer key gives conceptual explanations (e.g., parts of a whole produce a smaller product, factors greater than 1 produce larger products) that mirror the reasoning students are asked to use.

Students create input/output tables using rules such as "Multiply by 2" and "Multiply by 4" and plot the resulting ordered pairs on the coordinate plane (Patterns on a Coordinate Plane). The gardener/daisy example contrasts growth at 2 inches per day with growth at 1/2 inch per day, putting a factor greater than 1 and a factor less than 1 on the same graph. Students are asked to compare the two data sets and state the relationship (the second set is double the first set).

Students convert division problems to multiplication by creating multiplication problems that correspond to given division expressions (Activity 2 and the Answer Key mapping division to multiplication). Students are prompted to use the term "reciprocal" and to explain multiplication problems when they explain their division work (Parent Plan). Students are asked to decide whether an answer is less than or greater than 1 and to justify that reasoning (prompts: "Is a reasonable answer to this problem less than or greater than 1?" and the Questions to Discuss items about quotients being >1 or <1).

Activity 2 asks students to predict and test what happens to the volume when all dimensions are doubled or tripled and when only one dimension is doubled or tripled. Students complete a table computing volumes for original, doubled, and tripled dimensions (examples: 6×4×3 = 72; doubling one dimension produces 144) and are asked to explain the relationship between dimension adjustments and volume. Parent-plan questions prompt students to reason that doubling one dimension doubles the volume and tripling one dimension triples the volume.

Students are asked to produce a second box with the same height but double the volume (Joey/Travis problems) and to "prove your answer using both a picture and a math sentence," which requires reasoning how changing one dimension (doubling length or width) changes the product (volume). The answer key explicitly states that doubling the length or width will double the volume. Several problems ask students to find missing dimensions given volume (e.g., Lauren's box, base area and height problems), which has students reason about how one factor relates to the product.

Students rank buildings by relative size (Step 2) and choose boxes based on those rankings, thinking about whether a school should be wider or taller than other buildings. Students measure length, width, and height and apply V = l × w × h to calculate volumes (Step 4). Students are prompted to check whether the computed volumes "make sense in terms of the relative sizes of the buildings," which asks them to compare volume results with their prior size judgments.

Students complete input/output tables that require them to multiply numbers by 3/4 and 1 1/2 and to divide by 4 and 1 1/3, so they work with multiplication by factors less than 1 and greater than 1. Students solve word problems that use multiplication as scaling (for example, finding the area when one dimension is twice the other). Students compute actual products and quotients for a variety of fractional and mixed-number factors.