# Dog Walker

How many different combinations of people and dogs could walk by?

A dog walker goes by our building every day. They walk different numbers of dogs. Sometimes other people go with them, too. If 14 feet walk by, how many dogs and people could there be? What about 22 feet?

- Think about 14 feet total. How many dogs could there be?
- How many feet do dogs usually have? How many feet do people usually have?

- Is your solution the only solution? How can you be sure?
- If you were to remove a dog from your solution, how many people could you add?
- What other numbers between 14 and 22 would make sense for this problem? What do you notice about the numbers that work?
- Are there any situations when the number of feet would be odd?
- Can you write a problem like this of your own?

In this task, students consider how groups of 2 and 4 might compose a total of 14 or 22. There are multiple possible answers to this problem. As students consider how to break a whole into parts of different sizes, they are thinking about the relationship between equal groups within a whole. This thinking lays a foundation for multiplicative thinking.

Students might choose to begin with a total (14 or 22) and split that total into groups of 2 and 4, or they may choose to use repeated addition to reach the total. Students may also create a representation showing people and dogs, and then count the total of feet and adjust as needed.

Various apps may be used to represent the context of this problem.

- In the Number Frames app, students could count out colored markers to represent the total number of feet (e.g., 14) and then circle groups of 4 and 2 (as shown here).
- In the Number Rack app, students could pull over beads in groups of 2 and 4 until they reach the total using repeated addition (as shown here).
- In the Pattern Shapes app, students could use the shapes to create representations of people and dogs and then count the feet to reach the desired total (e.g., 22), adjusting as needed (as shown here).

As students consider the numbers of people and dogs they might include in their total of 14 or 22, you might ask *How many groups of 2 feet do you need to include? Why? *If students are starting with the total (14 or 22) and breaking it into groups, you might ask *How are you breaking up the total into groups? What size is each group?* If students are solving by adding up to the total (14 or 22), you might ask *How will you know when to stop adding? And how many groups do you have so far? *