We would like to begin to work with multiplication in the case where the number of groups and the number of objects per group are not whole numbers.
(a)
Give three examples of situations where it makes sense to have a decimal number of groups. For example, think about stories for .
(b)
Give three examples of situations where it makes sense to have a decimal number of objects in each group. For example, think about stories for .
(c)
Give one example of a situation where it does not make sense to have a decimal number for either the number of groups or the number of objects per group. Why is this situation different than the ones you had above?
Write a word problem for which does not involve money. Use our definition of multiplication to explain why it is a problem for that expression.
Draw a picture to help you solve your story in the previous question. How does the picture show what one group looks like? How does the picture show one object? How does the picture show the total number of objects, and what is this total? Explain your thinking in each case.

Using the largest square in the image, find the area of the 3.4-unit by 2.1-unit rectangle without multiplying. Explain your work.
Why is finding the area of the rectangle above related to solving the multiplication problem ? Use our groups-and-objects meaning of multiplication to explain. Where are the groups? What are the objects?
Using the smallest square in the image, find the area of the 3.4-unit by 2.1-unit rectangle without multiplying. Explain your work.
What does the previous question tell us about the relationship between and ? Be sure to use the groups-and-objects meaning of multiplication as well as bundling to explain your thinking.
2025-08-13 00:47:42