# Generating Two Numerical Patterns: 5th Grade Lesson

This 5th grade lesson teaches students how to generate a pattern following a rule and graph ordered pairs on a coordinate grid.

Students will generate two numerical patterns using two given rules and will identify apparent relationships between the corresponding terms. Students will form ordered pairs consisting of corresponding terms from each of the two patterns and graph the ordered pairs on a coordinate plane.

**Lesson Objective:** The lesson is aligned to the Common Core State Standards for Mathematics – 5.OA.3 – Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

**Materials Required:** Calculator, graph paper

## Lesson Procedure:

Generate two numerical patterns, identify relationships between corresponding terms, form ordered pairs from corresponding terms, graph on a coordinate plane.

In the chart below, generate a numerical pattern for each rule shown below.

1. Rule 1: Start at 0. Add 3.

2. Rule 2: Start at 0. Add 6.

Term 1 of the pattern generated from Rule 1 and Term 1 of the pattern generated from Rule 2 is an example of corresponding terms. Term 2 of the pattern generated from Rule 1 and Term 2 of the pattern generated from Rule 2 is another example of corresponding terms.

3. What relationship is there between each of the corresponding terms of the patterns?

Ordered pairs are written as (*x*, *y*) where a point on a coordinate grid is determined by the values of *x *and *y*. The value of *x* denotes the distance the point is from the origin in the horizontal direction and the value of *y* denotes the distance in the vertical direction.

4. Form ordered pairs using the corresponding terms where *x *is the value of the terms in the pattern generated from Rule 1 and *y *is the value of the terms in the pattern generated from Rule 2.

5. Graph the ordered pairs on a coordinate grid.

## Answers

3. Each of the terms in the pattern generated by Rule 2 is 2 times the corresponding term in the pattern generated by Rule 1.

4. (0, 0) (3, 6) (6, 12) (9, 18) (12, 24) (15, 30)

5. Points using the ordered pairs in number 4 should be graphed on a coordinate grid.

## Individual or Group Work

In the chart below, generate a numerical pattern for each rule shown.

1. Rule 3: Start at 0. Add 2.

2. Rule 4: Start at 0. Add 8.

3. What relationship is there between each of the corresponding terms of the patterns?

4. Form ordered pairs using the corresponding terms where *x *is the value of the terms in the pattern generated from Rule 3 and *y *is the value of the terms in the pattern generated from Rule 4.

5. Graph the ordered pairs on a coordinate grid.

**In the chart below, generate a numerical pattern for each rule shown below.**

6. Rule 5: Start at 0. Add 5.

7. Rule 6: Start at 0. Add 7.

8. What relationship is there between each of the corresponding terms of the patterns?

9. Form ordered pairs using the corresponding terms where x is the value of the terms in the pattern generated from Rule 5 and y is the value of the terms in the pattern generated from Rule 64

10. Graph the ordered pairs on a coordinate grid.

## Answers

3. Each of the terms in the pattern generated by Rule 4 is 4 times the corresponding term in the pattern generated by Rule 3.

4. (0, 0) (2, 8) (4, 16) (6, 24) (8, 32) (10, 40)

5. Points using the ordered pairs in number 4 should be graphed on a coordinate grid.

8. Each of the terms in the pattern generated by Rule 6 is 2, 4, 6, 8, and 10 more than the corresponding term in the pattern generated by Rule 5.

9. (0, 0) (5, 7) (10, 14) (15, 21) (20, 28) (25, 35)