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- Draw the table below. Enter the data from the vertical table in Question 2 into the horizontal table.
- Using the table, what is the relationship between the number of cookies Grace gets and the total number of cookies?
- For each data point, write a ratio that shows Grace's share of the total cookies:
- What is the relationship between the numerator and the denominator for each ratio you wrote in Question 11? Look for a pattern.
The ratios you listed in Question 11 are all equivalent to each other. Equivalent ratios are ratios that have the same value. For example, 
and 
are equivalent ratios because they have the same value, even though their numerators and denominators are different from each other. When two ratios are equivalent, their numerators are related to their denominators in the same way. The ratios and are equivalent because the denominators are both four times as big as the numerators.
and are equivalent ratios because they have the same value, even though their numerators and denominators are different from each other. When two ratios are equivalent, their numerators are related to their denominators in the same way. The ratios and are equivalent because the denominators are both four times as big as the numerators.
- What happens to the number of cookies Grace gets as the total number of cookies increases? Does Grace get more cookies, fewer cookies, or the same number of cookies? Explain your reasoning.
- What happens to Grace's share of the cookies? Does the ratio of the total cookies that Grace gets increase, decrease, or stay the same? Explain your reasoning.
“How many cookies would Grandma have to bring for each of us to get 10 cookies?” asked Grace's younger brother, Josh. “We can't use the table because it doesn't go up that high.”