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Illustrative Math
Grade 8
Let’s review exponents.
Illustrative Math Unit 8.7, Lesson 1 (printable worksheets)
Exponents make it easy to show repeated multiplication. For example, 2^{6} = 2 · 2 · 2 · 2 · 2 · 2
One advantage to writing 2^{6} is that we can see right away that this is 2 to the sixth power. When this is written out using multiplication, 2 · 2 · 2 · 2 · 2 · 2, we need to count the number of factors. Imagine writing out 2^{100} using multiplication!
Let’s say you start out with one grain of rice and that each day the number of grains of rice you have doubles. So on day one, you have 2 grains, on day two, you have 4 grains, and so on. When we write 2^{25}, we can see from the expression that the rice has doubled 25 times. So this notation is not only convenient, but it also helps us see structure: in this case, we can see right away that it is on the 25th day that the number of grains of rice has doubled! That’s a lot of rice (more than a cubic meter)!
Which expression does not belong? Be prepared to share your reasoning.
Mai and Andre found an old, brass bottle that contained a magical genie. They freed the genie, and it offered them each a magical $1 coin as thanks. The magic coin turned into 2 coins on the first day. The 2 coins turned into 4 coins on the second day. On the third day, the 4 coins magically turned into 8 coins, and this pattern continued for 28 days.
Click on the arrow to see the coins start to magically multiply.
Open Applet
Mai was trying to calculate how many coins she would have and remembered that instead of writing 1 · 2 · 2 · 2 · 2 · 2 · 2 for the number of coins on the 6th day, she could write 2^{6}.
After a while, Jada picks up a coin that seems different than the others. She notices that the next day, only half of the coin is left! On the second day, only 1/4 of the coin is left. On the third day, 1/8 of the coin remains.
Tyler has two parents. Each of his parents also has two parents.
18 generations back because 2^{18} = 262,144
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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