# Compare Patterns generated by Addition and Multiplication Rules

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Videos, solutions, worksheets, and examples to help grade 5 students learn how to compare the lines and patterns generated by addition rules and multiplication rules.

### New York State Common Core Math Grade 5, Module 6, Lesson 10

Lesson 10 Concept Development

Problem 1: Compare the lines and patterns generated by addition and subtraction rules.

Problem 2: Compare the lines and patterns generated by multiplication rules. Lesson 10 Problem Set

1. Use the coordinate plane below to complete the following tasks.
a. Line p represents the rule, x and y are equal.
b. Construct a line, d, that is parallel to line p and contains point D.
c. Name 3 coordinates pairs on line d.
d. Identify a rule to describe line d.
e. Construct a line, e, that is parallel to line P and contains point E.
f. Name 3 points on line e.
g. Identify a rule to describe line e.
h. Compare and contrast lines d and e in terms of their relationship to line p.

2. Write a rule for a fourth line that would be parallel to those above and would contain the point (3 1/2, 6)
a. Explain how you know.

3. Use the coordinate plane below to complete the following tasks.
a. Line p represents the rule x and y are equal.
b. Construct a line, v, that contains the origin 0 and point V.
c. Name 3 points on line v.
d. Identify a rule to describe line v.
e. Construct a line, w, that contains the origin and point W.
f. Name 3 points on line w.
g. Identify a rule to describe line w.
h. Compare and contrast lines and in terms of their relationship to line p.
i. What patterns do you see in lines that are generated by multiplication rules?

4. Circle the rules that generate lines that are parallel to each other.

Lesson 10 Homework

1. Use the coordinate plane to complete the following tasks.
a. Line p represents the rule x and y are equal.
b. Construct a line, d, that is parallel to line p and contains point D.
c. Name 3 coordinates pairs on line d.
d. Identify a rule to describe line d.
e. Construct a line, e, that is parallel to line p and contains point E.
f. Name 3 points on line e.
g. Identify a rule to describe line e.
h. Compare and contrast lines d and e in terms of their relationship to line p.

2. Write a rule for a fourth line that would be parallel to those above and that would contain the point (5 1/2, 2). Explain how you know.

3. Use the coordinate plane below to complete the following tasks.
a. Line p represents the rule x and y are equal.
b. Construct a line, v, that contains the origin and point V.
c. Name 3 points on line v.
d. Identify a rule to describe line v.
e. Construct a line, w, that contains the origin and point W.
f. Name 3 points on line w.
g. Identify a rule to describe line w.
h. Compare and contrast lines v and w in terms of their relationship to line p.
i. What patterns do you see in lines that are generated by multiplication rules?

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