Math 6: number patterns

Unit 2

Number Patterns pg. 10

The first pattern is a shrinking pattern.

The second pattern is an alternating pattern.

The third pattern is an alternating growing pattern.

Explore pg. 10

1, 5, 13, 29, 61 How did you find the pattern rule for the first

pattern? (I subtracted terms and got 4, 8, 16, 32, so I knew

the rule was not multiplying each input number by the same number. I multiplied each term by 2, and got 2, 10, 26, 58,122, …. I noticed that if I then added 3 to each number, I got the pattern)

The pattern rule is: Start at 1. Multiply by 2, then add 3 each time

Explore pg. 10

300, 298, 296, 294, 292 What is the rule for the third pattern?

Pattern Rule: Start at 300. Subtract 2 each time

What type of pattern is this? How do you know?

It is a shrinking pattern; the terms get smaller.

Connect pg. 10

Recursive Pattern: Each term can be found by applying the pattern rule to the previous term.

All above examples are recursive patterns.

Connect pg. 10

Write the 5 terms for a recursive pattern that starts at 7. The Pattern Rule is: Start at 7. Multiply by 2, then add 1

each time.

7x2+1 = 15

15x2+1=31

63x2+1=127

7, 15, 31, 63, 127

Connect pg. 11

We can write a pattern like this:

1, 6, 11, 16, 21

1 = 1x5 -4

6 = 2x5 -4

11 = 3x5-4

16 = 4x5– 4

21 = 5x5 -4

What would the 20th number be?

Connect pg. 11

Take:

1, 6, 11, 16, 21

Find the difference*

-The difference is -5 Pattern rule:

Start at 1. Add 5 each time

Connect pg. 11

1, 6, 11, 16, 21 How do we now extend the pattern? What

number comes next?

How do you know?

Lets try these

6, 13, 34, 97, 286 What do we do first?

FIND THE DIFFERENCE

286 – 97 = 189

97-34 = 63

34 -13 = 21

13 – 6 = 7

What pattern do you see?

What’s the pattern?

6, 13, 34, 97, 286 Each difference is triple the previous difference!

Therefore, this suggests that x3 is part of the pattern rule.

LET’S TRY IT

6 x3 = 18 …. 18 - ? = 13…..5!

13 x 3 = 39…..39 – 5 = 34!!

Continue with all of them!

It matches! Therefore, The pattern rule is: Start at 6 then multiply by 3, then subtract 5.

Homework

PG 12 #1-6