*Contributor: Ashley Nail Murphy. Lesson ID: 13891*

Do you like solving riddles? In this lesson, you will study the relationship between groups of numbers and find the rules that tie them all together. It's like solving a riddle!

categories

subject

Math

learning style

Visual

personality style

Lion, Otter, Beaver, Golden Retriever

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

Jace is going shopping for his family. He sees bags of cookies for $2 each! Every bag has 18 cookies inside. He wants to buy 4 bags of cookies.

- How much will that cost him?
- How many cookies will he have?

To help Jace, you need to look at rules and patterns in these numbers.

Look at some other examples first!

Look at the rule for this pattern.

Pattern A: Start at 2 and add 2.

You can use this rule to create a list of terms that can go on forever.

Pattern A: 2, 4, 6, 8, 10 …

Now, look at another pattern and rule.

Pattern B: Start at 6 and add 6.

Like Pattern A, you can use this rule to list terms that can go on forever.

Pattern B: 6, 12, 18, 24, 30 …

Arrange these two lists of terms into a table.

Pattern A |
Pattern B |
||

2 | 6 | ||

4 | 12 | ||

6 | 18 | ||

8 | 24 | ||

10 | 30 | ||

? | ? |

You can easily find the next number in each sequence using the rules for each pattern.

For example, the next term in the Pattern A sequence will be 12. Since you know the rule is to add 2, use 10 + 2 to get 12.

The rule for Pattern B is to add 6, so use 30 + 6 to get 36.

Add these new terms to the table.

Pattern A |
Pattern B |
||

2 | 6 | ||

4 | 12 | ||

6 | 18 | ||

8 | 24 | ||

10 | 30 | ||

12 | 36 |

Say you continue to follow the rule for Pattern A to complete more table rows. Now, you want to find Pattern B’s missing term.

Pattern A |
Pattern B |
||

2 | 6 | ||

4 | 12 | ||

6 | 18 | ||

8 | 24 | ||

10 | 30 | ||

12 | 36 | ||

14 | |||

16 | |||

18 | |||

20 | ? |

You could use Pattern B’s rule and continuously add 6 to each term in the sequence. Or you could figure out the relationship between the numbers in Pattern A and Pattern B.

Each set of corresponding numbers in the table can be rewritten as ordered pairs on a coordinate plane. This can help you figure out the relationship between Pattern A and Pattern B.

(2, 6) (4, 12) (6, 18) (8, 24) (12, 36)

The first value in the ordered pair is multiplied by 3 to get the second value in the ordered pair.

(2, 6) 2 x 3 = 6

Let’s see if this is true for each ordered pair.

(2, 6) 2 x 3 = 6

(4, 12) 4 x 3 = 12

(6, 18) 6 x 3 = 18

(8, 24) 8 x 3 = 24

(12, 36) 12 x 3 = 36

Now, you can write a new rule describing the relationship between Pattern A and Pattern B!

The terms in Pattern B are 3 times the terms of Pattern A

Use this new rule to find the missing term in Pattern B.

If the term in Pattern A is 20, then to find the corresponding term in Pattern B, you need to multiply by 3.

20 x 3 = 60

The missing term in Pattern B is 60.

Pattern A |
Pattern B |
||

2 | 6 | ||

4 | 12 | ||

6 | 18 | ||

8 | 24 | ||

10 | 30 | ||

12 | 36 | ||

14 | |||

16 | |||

18 | |||

20 | 60 |

Using either the rule for Pattern B or the rule for the relationship between Patterns A and B, find the other missing terms.

- Which rule did you use to complete the table?

Look at the table again, but this time think about the rule you didn’t use.

- Do you see how both rules will get you the same answers?

When you are ready to practice on your own, click NEXT to visit the *Got It?* section!