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      In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three- dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

      Rates and Proportions

      Question 1

      Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

      First, we set up our general equation. Because y is directly proportional to x, we have:

      y = cx

      where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

      The next thing we do is plug our values for x and y into the equation so we can solve for c:

      8 =(c)(5)

      Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

      y = 1.6x

      Now, we can plug x = 9 into the equation to find out what y equals:

      y = (1.6)(9)

      y = 14.4

      So, our answer is 14.4

      Question 2

      Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

      This time, our general equation is slightly more complicated because x is squared:

      Like before, we solve for our constant:

      32 = (c)(22)

      32 = (c)(4)

      We get c = 8:

      y= 8x2

      Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

      Question 3

      Y is inversely proportional to x. When x = 2, y = 8. What does y equal when y = 24?

      This time, because y is inversely proportional to x, our general equation is different:

      xy = c

      so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems.

      Solving for the constant, we get:

      (2)(8)= c

      So c = 16 and our equation is now:

      xy = 16

      Solving for y when x = 24 we get y = 16/24 = 2/3

      Question 4

      Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

      As before, we set up our equation:

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