Walking the Line Activity

How can we model 3 x 2 using a number line?

Poster Problems - Walking the Line Slide #1

For today, let’s define a “step” as a single step using one foot. Steps can differ in length. We will use the intervals on the number line to represent different sized steps. For example, a step size of 3 will cover 3 units on the number line.

4 x 3 = 12 Let’s see how this is modeled on the number line.

Poster Problems - Walking the Line Slide #2

What happens when we try to model the multiplication for (-4) x 3 on a number line? Let’s use this rule to help with the model. When the number of steps is negative, the walker first faces in the negative direction and walks normally.

Poster Problems - Walking the Line Slide #3

Now, what about modeling 4 x (-3) How is this different from the previous problem? The negative three is telling us how long each step should be. Let’s add this rule. When the step length is negative, we have to step by a negative distance. In other words, we walk backwards.

Poster Problems - Walking the Line Slide #4

How could we model (-4) x (-3) Remember, our established rules say: When the first number is negative, face negative. When the second number is negative, walk backwards.

Poster Problems - Walking the Line Slide #5

X–1+1 –1 Fill in this times table. Use our rules to help you. Poster Problems - Walking the Line Slide #7

Your Turn Complete the Handout. Be sure to show which direction the walking dude is facing.