The purpose of this activity is for students to use place value reasoning and properties of operations to relate products of a whole number and a decimal to products of a whole number and either 0.1 or 0.01 (MP7). Students may decide that an equation is false without finding the value of both sides. For example, in the first problem, they may determine that 28 is unreasonable because 0.7 is less than one whole so the answer will be less than 4. When students find the value that makes equations true, they think about place value and the associative property of multiplication.

• Display the equation from the first problem.
• “Is the equation true or false?” (false)
• Display expression:
• “How could we revise this expression to make the equation true?” (Change it to read , , or .)
• Display equation:
• “What can I write in the blank to make the equation true?” (0.7 since that’s 8 groups of 7 tenths or .)

The purpose of this activity is for students to use a diagram to support understanding two different ways to calculate the product of a whole number and a decimal number. The first strategy is one that students saw in the previous lesson. Students used whole number arithmetic to find the number of hundredths in the product and then multiplied that number by 0.01. The second strategy is useful when the decimal has both tenths and hundredths. Using the distributive property, students can find the product of the whole number and the tenths and then the product of the whole number and the hundredths and combine these (MP7). In the next several activities, students will use both of these strategies as they build their understanding of how to find the product of a whole number and a decimal.

• Invite students to share their calculations of the value of using different expressions.
• “How did the expression help to find the value of ?” (I was able to just multiply whole numbers and then notice that the product is that many hundredths.)
• “How did the expression help to find the value of ?” (I multiplied the tenths and then the hundredths. I added them together.)
• “Which strategy do you prefer?” (I like the first strategy because I can just use what I know about whole number products and it will always work.)