Section C Practice Problems

Problem 1

  1. Complete each table with the first 10 numbers of the pattern.

    1. Pattern 1: Start with 0. Use the rule “Keep adding 5.”

      rectangle partitioned vertically into 10 equal size rectangles

    2. Pattern 2: Start with 0. Use the rule “Keep adding 10.”

      rectangle partitioned vertically into 10 equal size rectangles

  2. What relationships do you notice between the numbers in the 2 patterns?

Show Solution
Solution
    1. 0, 5, 10, 15, 20, 25, 30, 35, 40, 45
    2. 0, 10, 20, 30, 40, 50, 60, 70, 80, 90
  2. Sample response: Each number on the second list is on the first list. Every other number on the first list is on the second list. Each number on the second list is twice the corresponding number on the first list.

Problem 2

  1. Complete each table with the first 10 numbers of the pattern.

    1. Pattern 1: Start with 0. Use the rule “Keep adding 6.”

      rectangle partitioned vertically into 10 equal size rectangles

    2. Pattern 2: Start with 4. Use the rule “Keep adding 6.”

      rectangle partitioned vertically into 10 equal size rectangles

  2. When Pattern 1 has the number 222, what number will be in Pattern 2? Explain or show your reasoning.

Show Solution
Solution
    1. 0, 6, 12, 18, 24, 30, 36, 42, 48, 54
    2. 4, 10, 16, 22, 28, 34, 40, 46, 52, 58
  2. Sample response: 226, because each number on the second list is 4 more than the corresponding number on the first list.

Problem 3

Han and Mai created different patterns using these rules and starting numbers.

Han’s pattern: Start with 0. Use the rule “Keep adding 3.”
Mai’s pattern: Start with 0. Use the rule “Keep adding 10.”

  1. Complete the table with the first 8 numbers in each pattern.

    A B C D E F G H
    Han's rule
    Mai's rule

  2. Locate and label the points on the coordinate grid.

    Coordinate plane. Horizontal axis, Han's pattern, 0 to 25, by 1's. Vertical axis, Mai's pattern, 0 to seventy 5, by 5's. 
    Coordinate plane. Horizontal axis, Han's pattern, 0 to 25, by 1's. Vertical axis, Mai's pattern, 0 to seventy 5, by 5's.

  3. What relationships do you notice between the corresponding terms of these 2 patterns?

Show Solution
Solution
  1. A B C D E F G H
    Han's rule 0 3 6 9 12 15 18 21
    Mai's rule 0 10 20 30 40 50 60 70
  2. Coordinate plane. Horizontal axis, Han's pattern, 0 to 25, by 1's. Vertical axis, Mai's pattern, 0 to seventy 5, by 5's. 
    Coordinate plane. Horizontal axis, Han's pattern, 0 to 25, by 1's. Vertical axis, Mai's pattern, 0 to seventy 5, by 5's. Points plotted at 0 comma 0. 3 comma 10. 6 comma 20. 9 comma 30. 12 comma 40. 15 comma 50. 18 comma 60. 21 comma 70.
  3. Sample responses:
    • The only number in both lists is 0.
    • The numbers in Mai's rule are 3133 \frac{1}{3} times the numbers in Han's rule.
    • The numbers in Han's rule are 103\frac{10}{3} times the numbers in Mai's rule.

Problem 4

The points on the coordinate grid show the results Lin and Tyler got when they each flipped a coin several times.

Coordinate plane. Horizontal axis, number of heads, 0 to 10, by 1's. Vertical axis, number of tails, 0 to 10, by 1's. Lin, 3 comma 5. Tyler, 6 comma 3. 

  1. Who flipped the coin more times, Lin or Tyler? Explain or show your reasoning.
  2. Who got more tails, Lin or Tyler? Explain or show your reasoning.
  3. Flip a coin 7 times and plot the point to represent your results on the coordinate grid. Explain or show your reasoning.
Show Solution
Solution
  1. Tyler. Tyler tossed it 9 times since he got 6 heads and 3 tails. Lin only tossed the coin 8 times since she got 3 heads and 5 tails.
  2. Lin
  3. Sample response: I got 5 heads and 2 tails so I went over 5 for the 5 heads and up 2 for the 2 tails. My point is (5,2)(5,2).

Problem 5

Coordinate plane. Horizontal axis, length in centimeters, 0 to 10, by 1's. Vertical axis, width in centimeters, 0 to 10, by 1's. point at 3 comma 7. 

  1. The point on the coordinate grid represents the length and width of a rectangle. What is the perimeter of the rectangle?
  2. Plot 4 more points to represent 4 different rectangles with the same perimeter as the given rectangle.
  3. What point would represent a square with the same perimeter as the given rectangle?
Show Solution
Solution
  1. 20 cm. Sample response: Twice the length is 6 cm and twice the width is 14 cm.
  2. coordinate plane
  3. (5,5)(5,5). Sample response: It has a perimeter of 20 centimeters. A rectangle with 4 equal sides is a square.

Problem 6

area of base
(square inches)		 height
(inches)

Coordinate plane. Horizontal axis, area of base in square inches, 0 to 3 hundred, by 20's. Vertical axis, height in inches, 0 to 10, by 1's. 

  1. A box is shaped like a rectangular prism. The volume of the box is 240 cubic inches. List some possible values for the area of the base of the box and its height in the table.

  2. Plot the listed base area and height pairs as points on the coordinate.

  3. What do you notice about the plotted points?

  4. Which point do you think represents the most reasonable measurements for the box? Explain your reasoning.

Show Solution
Solution

Sample responses:

  1. area of base (square inches) height (inches)
    240 1
    120 2
    80 3
    60 4
  2. coordinate plane
  3. As the height increases, the area of the base decreases and vice versa. The points do not lie on a line.
  4. I don't think the box should be too high. I think that a base of 60 square inches and a height of 4 inches is the most reasonable.

Problem 7

Andre and Clare create patterns.

  • Andre’s pattern: Start with 2. Use the rule “Keep adding 6.”
  • Clare’s pattern: Start with 1,000. Use the rule “Keep subtracting 7.”
  1. List the first 6 numbers in Andre and Clare's patterns.
  2. Will Andre and Clare ever have the same number in the same spot in their patterns? Explain or show your reasoning.
Show Solution
Solution

  1. Andre: 2, 8, 14, 20, 26, 32

    Clare: 1,000, 993, 986, 979, 972, 965

  2. Sample response: No, the difference between the starting numbers is 998 and the numbers go down by 13 each time. I found 998÷13998 \div 13 and it is 76 with a remainder of 10. So, for the first 77 numbers in their patterns, Andre’s number is less than Clare’s but then after that Clare’s number is less than Andre’s.