Same Number, Different Tokens

Different-looking token sets can stand for the same number. Find out whether the product changes when the tokens look different.

5 micro-lessons

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Three Ways to Show −2

Three different-looking token sets that all mean −2.

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Another way to see (−4) × 2: add negatives instead of removing positives.

Removing (subtracting) a number is the same as adding its opposite.

So removing 2 positives is the same as adding 2 negatives.

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Placing set (b) four times still gives −8.

Problem. Place set (b), which is 4 negatives and 2 positives, into an empty bag 4 times. What do you get?

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Spot equal token sets and their products.

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Set (c) has 6 negatives and 4 positives. What do 4 copies of set (c) make?

Explain why different-looking sets give the same product.

Explain with zero pairs

Math Talk (Textbook p. 31).

Do we get different answers because the sets for $-2$ look different, or the same answer because they all represent $-2$ ? Explain using zero pairs.
Can $(-4) \times 2$ be found by adding tokens instead of removing them? How?

Use zero pairs in your reason.

Which tokens do you add, and how many times?