The purpose of this activity is for students to find decimal products in a way that makes sense to them. Many approaches are possible including:

• Thinking about the meaning of place value and multiplying by place value.
• Using the hundredths grids.
• Using fractions or a number line.

For the last problem, students may use their understanding of arithmetic, the distributive property, and their work on the first two problems (MP7) or they may make a new calculation. The goal of the Activity Synthesis is to share and connect different strategies for finding the values of the products.

• Invite students to share how they found the value of .
• Display student work or image from the solution.
• “How does the diagram show ?” (There are two groups of 0.7 shaded.)
• “How can you use the diagram to find the value of ?” (I can see that I have or 14 tenths and that’s 1 whole and 4 more tenths.)
• “How is finding the value of the same as finding the value of ? How is it different?” (I could shade part of each of the large squares and then see the total. This time I shaded individual squares rather than rows of squares. In both cases, I can use multiplication to find the product.)

In the previous activity students found products of a whole number and some tenths or hundredths using hundredths grids or a strategy that made sense to them. The goal of this activity is to find these products with a greater focus on place value and the associative property of multiplication (MP7). For example, means 5 groups of 7 hundredths. That means that its value is 35 hundredths or 0.35. This way of thinking about products allows students to use what they know about finding whole number products in order to find products of a whole number and a decimal number (MP8).

• Invite 1–2 students to share their responses and reasoning for the value of .
• “How is multiplying like multiplying ? How is it different?” (When I find the value of , I can still use what I know about . They both have 42 in the product. The unit is different. You have to remember it's 42 hundredths not just 42. The value is smaller for .)