3.1+Mixing+Juice+0910

W.L. 14/11/09 Math 7B ** The Big Idea  ** Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.

 // What methods are there for comparing things? //
 *  essential Question: **

3.1 Mixing Juice

A. Q: Which recipe will make juice that is the most “orangey”? Explain your answer. A: Mix A will make the most “orangey” juice because if you make all of them into a part to whole relation this is the biggest: Mix A = 2 to 5 > Mix D = 3 to 8 > Mix C = 4 to 12 > Mix B = 1 to 5 or concentrate as percentage of mixture: Mix A = 40% > Mix D = 37.5% > Mix C = 33.33% > Mix B = 20%.

B. Q: Which recipe will make juice that is the least “orangey”? Explain your answer. A: Mix B because Mix B= 1/4 = 0.25 (0.25 cups of concentrate per one cup of water) < Mix C = 4/18 = 0.5 < Mix D = 3/6 = 0.6 < Mix A = 2/3 = 0.66. So Mix B is the least “orangey”.

C. Q: Assume that each camper will get ½ cup of juice. For each recipe, how much concentrate and how much water are needed to make juice for 24 campers? Explain your answer. A: 240*(½) = 120 (for 240 campers you will need 120 cups of juice) Mix A: 0.4 * 120 = 48 cups of concentrate and 0.6 * 120 = 72 cups of water Mix B: 0.2 * 120 = 24 cups of concentrate and 0.8 * 120 = 96 cups of water Mix C: 0.33 * 120 = 40 cups of concentrate and 0.67 * 120 = 80 cups of water Mix D: 0.375 * 120 = 45 cups of concentrate and 0.625 * 120 = 75 cups of water

Follow Up

1. Q: How did you use ratios in solving Problem 3.1? A: I used ratios and then said which on is greater than the other to show my thinking and then used the ratios to make percentages.

2. Q: For each recipe, how much concentrate and how much water is needed to make 1 cup of juice

A: Mix A you need 0.4 concentrate and 0.6 water Mix B you need 0.2 concentrate and 0.8 water Mix C you need 0.33 concentrate and 0.67 water Mix D you need 0.375 concentrate and 0.625 water