1. **Problem Statement:** Tyree's cat has a litter of black and orange kittens. The tape diagram shows the number of each color kitten, with each section representing 1 kitten. We need to compare the numbers of kittens in different ways. 2. **Part A:** How many orange kittens are there? How many black kittens? Write a comparison beginning with "For each _." - Suppose the tape diagram shows $b$ black kittens and $o$ orange kittens. - The comparison can be written as: For each black kitten, there are $\frac{o}{b}$ orange kittens. - Or, for each orange kitten, there are $\frac{b}{o}$ black kittens. 3. **Part B:** How does the number of orange kittens compare to the total number of kittens? Write the comparison beginning with "For every ..." - Total kittens $= b + o$ - For every $b+o$ kittens, there are $o$ orange kittens. - Or, for every 1 kitten, there are $\frac{o}{b+o}$ orange kittens. 4. **Part C:** How does the number of black kittens compare to the total number of kittens? Write the comparison beginning with "For every ..." - For every $b+o$ kittens, there are $b$ black kittens. - Or, for every 1 kitten, there are $\frac{b}{b+o}$ black kittens. 5. **Part D:** Suppose each section represents 2 kittens instead of 1. Will that change the comparisons in Parts A and B? Why or why not? - If each section represents 2 kittens, then the numbers double: black kittens $= 2b$, orange kittens $= 2o$, total $= 2(b+o)$. - The ratios remain the same because: $$\frac{2o}{2b} = \frac{o}{b}$$ $$\frac{2o}{2(b+o)} = \frac{o}{b+o}$$ - So, the comparisons do not change. 6. **Turn and Talk:** Suppose the model represents 16 orange kittens. How many kittens are there in all? - If orange kittens $o = 16$, and the ratio of black to orange kittens is $b:o$, then total kittens $= b + o$. - Using the ratio, find $b$ and then total. --- **Summary for the first problem:** - Part A: For each black kitten, there are $\frac{o}{b}$ orange kittens. - Part B: For every $b+o$ kittens, there are $o$ orange kittens. - Part C: For every $b+o$ kittens, there are $b$ black kittens. - Part D: Doubling the number per section does not change the comparisons. --- **Second problem: Quilt ratio** 1. **Problem Statement:** Aaron is making a quilt with four fabric colors arranged in a 4x4 grid. 2. **Part A:** Complete the tape diagram to model the ratio of blue squares to white squares. - Suppose blue squares = $B$, white squares = $W$. 3. **Part B:** Complete statements describing the ratio of blue to white squares. - The ratio is $B:W$. - "For every $W$ white squares, there are $B$ blue squares." 4. **Part C:** Write a part-to-whole or whole-to-part comparison about the quilt. - Total squares $= T$. - For every $T$ squares, there are $B$ blue squares. - Or, for every blue square, there are $\frac{T}{B}$ total squares. 5. **Part D:** For every small green square, there are 2 large green squares. Does this mean 1 out of every 2 green squares is small? - No, because total green squares per group = 1 small + 2 large = 3. - So, 1 out of every 3 green squares is small, not 1 out of 2. --- **Vocabulary:** A ratio compares two quantities by division, $a:b$, $\frac{a}{b}$, or "a to b," where $b \neq 0$. --- **Check Understanding:** 1. Describe the ratio of tails to legs on a dog. - Dogs have 1 tail and 4 legs. - Ratio tails to legs = $1:4$. 2. Limeade recipe uses 2 cups lime juice for 8 cups limeade. - Ratio lime juice to limeade = $2:8$ or $1:4$. - This compares part (lime juice) to whole (limeade). --- **Final answers:** - For the kitten problem, the comparisons depend on the numbers $b$ and $o$. - For the quilt, the ratio statements depend on counts $B$ and $W$. "slug":"kitten-quilt-ratios","subject":"ratios","desmos":{"latex":"","features":{"intercepts":false,"extrema":false}},"q_count":2