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Explore how to model multiplication on a number line using different step sizes and directions. Practice with negative numbers and steps of varying lengths. Complete the provided times table and handout to reinforce learning.
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How can we model 3 x 2using a number line? -15 -10 -5 0 5 10 15
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.
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.
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.
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.
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.