Section C: Practice Problems Numerical Patterns

Section Summary

Details

In this section, we generated patterns and recognized relationships between two different patterns.

A

B

C

D

E

F

rule 1: Start at 0. Add 8.

0

8

16

24

32

40

rule 2: Start at 0. Add 2.

0

2

4

6

8

10

Each number in rule 1 is 4 times the value of the corresponding number in rule 2 and each number in rule 2 is  times the value of the corresponding number in rule 1. We also plotted the rules together on a coordinate grid.

Coordinate plane. A, B, C, D, E, F plotted.

We also used the coordinate plane to represent other situations such as the length and width of rectangles with given area or perimeter.

Problem 1 (Lesson 9)

  1. List the first ten numbers starting at 0 and counting by 5s.

  2. List the first ten numbers starting at 0 and counting by 10s.

  3. What patterns do you observe between your two lists of numbers?

Problem 2 (Lesson 10)

  1. List the first ten numbers starting at 0 and counting by 6.

  2. List the first ten numbers starting at 4 and counting by 6.

  3. When the first list has the number 222, what number will be on the second list? Explain or show your reasoning.

Problem 3 (Lesson 11)

The points on the graph, starting in the bottom left and moving up and to the right, represent how Han and Mai counted.

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

  1. How much is Han adding each time in his count? Explain how you know.

  2. How much is Mai adding each time in her count? Explain you know.

  3. Name and locate 3 more points on the graph.

Problem 4 (Lesson 12)

The points on the graph show the results Lin and Tyler got when they tossed a coin.

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 tossed 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. Toss a coin 7 times and plot the point on the graph. Explain or show your reasoning.

Problem 5 (Lesson 13)

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 graph shows the length and width of a rectangle. What is the perimeter of the rectangle?

  2. Plot 4 more points for different rectangles with the same perimeter as the given rectangle.

  3. Which point would represent a square with the same perimeter as the given rectangle?

Problem 6 (Exploration)

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

    area of base (square inches)

    height (inches)

  2. Plot several different possible area and height pairs on the graph.

    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. 

  3. What do you notice about the points on the graph?

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

Problem 7 (Exploration)

  • Andre starts from 2 and counts by 6s.

  • Clare starts at 1,000 and counts back by 7s.

  1. List the first 6 numbers Andre and Clare say.

  2. Do Andre and Clare ever say the same number in the same spot on their lists? Explain or show your reasoning.