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travis used a ratio table to solve the following problem. read the problem, then identify his strategy by filling in the blank below.
one chocolate bar has 6 squares. how many squares are there in 100 chocolate bars?
| chocolate bars | 1 | 10 | 100 |
|---|
Step1: Analyze the ratio table
The ratio of chocolate bars to squares starts with 1 bar : 6 squares. For 10 bars, since \(1\times10 = 10\) bars, the squares should be \(6\times10=60\) (as seen in the table).
Step2: Extend the ratio for 100 bars
To get from 10 bars to 100 bars, we multiply 10 by 10 (\(10\times10 = 100\)). So we multiply the number of squares for 10 bars (60) by 10: \(60\times10 = 600\). This strategy is using the concept of equivalent ratios (scaling the ratio up by multiplying both parts by the same factor).
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Travis used the strategy of scaling the ratio (multiplying the number of chocolate bars and the corresponding number of squares by the same factor) to solve the problem. The number of squares in 100 chocolate bars is 600, and his strategy involved using a ratio table to scale the ratio of 1 chocolate bar : 6 squares up to 100 chocolate bars by multiplying the number of bars (and thus the number of squares) by 10 twice (or by 100 once, by first scaling from 1 to 10 and then 10 to 100).