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Question: math activity 72 435 math activity 72 averages with columns...

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Math Activity 7.2 435 MATH ACTIVITY 7.2 Averages with Columns of Tiles Virtual Manipulatives Level off columns of color tiles to develop the concept of average (mean). Materials: Color Tiles in the Manipulative Kit or Virtual Manipulatives. When two or more columns of tiles like those below at the left are leveled off so they have the same height but the number of columns does not change, the common height is called the average of the original heights. 1. Use color tiles to build a column of height 9 and another column of height 15. Other than moving one tile at a time, find at least two methods for leveling the tiles so that there are two columns of the same height. www.mhhe.com/bbne a. Using the heights of the columns 9 and 15, and the operations of arithmetic, express each of your leveling-off methods with a number expression. b. Using the results from part a, write two rules for determining the average of two whole numbers x and y, where x is greater than or equal to y c. Express your two rules in part b as algebraic expressions and show these expres sions are equal. 2. Use color tiles to solve each of the following problems. Draw diagrams and explain your reasoning a. The average height of two columns is 10 and the difference of their heights is 3 times the height of the smaller. What are their heights? b. There are a total of 16 tiles in two columns and one of the columns is Ij times the The average of 9 and 5 is 7 height of the other. What is the height of each column? 3. The six columns at the right have been 14- leveled off to represent the average score for one student on six 20-point quizzes. Her average is 14, but to obtain a satisfactory grade, an average of 15 is needed. The teacher gives two options to raise the average: (1) Throw out the lowest quiz score and base the average on the five remaining quiz scores or (2) take a seventh 20-point quiz to raise the average. Which of these options should she choose if the lowest score on the six quizzes was 9 points? Explain your reasoning A. B. Bensett,E. Maier, and L. T. Nelson, Visualiring Number Conceps. Mash and the Minds By.
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