To get to understand the number line better, mark out a line on the playground or on the sidewalk outside your house with chalk. At the middle of the line, write 0 (zero). Going one way along the line from zero, write the positive numbers a step apart (1, 2, 3, 4, 5…) and going the other way write the negative numbers (-1, -2, -3, -4, -5). Then one person can call out math problems (addition or subtraction), while the other person acts the problems out by walking along the line. When the actor makes a mistake, you can trade places. Experiment with both positive and negative numbers: try to trick each other. Can you work out a way to mix hopscotch with this game?
You can play a different game with raisins or cookies, or with marbles or small rocks. Have four people each sit down with five cookies. Go around the circle taking turns asking another player for a certain number of cookies. Say how many cookies that person has left. Say how many you have now. If you make a mistake, you have to give the person back a cookie.
More about Commutative operations
More about the number line
Bibliography and further reading about addition:
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