Patterns and Multiplication

Patterns

Math is full of them

Like Multiplication (multiples)

MultiplicationIt’s just really fast addition by jumping

3 6 9 12

4 x 3 =

4 x 3 = 3 + 3 + 3 + 3 = 12

4 5 7 8 10 110 1 2

3 6 9 12

The pattern is called an arithmetic progression

4 5 7 8 10 11

1 three1 x 3

1 2

2 threes2 x 3

3 threes3 x 3

4 threes4 x 3

Each addition of 3 is called a “Multiple” of 33, 6, 9, and 12 are multi ples ( jumps) of 3 starti ng

with 1 three

0

In grade school you learned these progressions by memorizing the multiplication table.

By memorizing these progressions they become very easy to recognize and use in more complicated math patterns like

factoring

12 16 20 24

Starting at 8 you count by 4’s or jump every 4 or add a 4 for each multiple

13 14 15 17 18 19 21 22 239 10 11

What are multiples of 4 starting with two 4’s or 8

8, 12, 16, 20, 24 are all multi ples of 4.That means they fi t in the patt ern of 4’s or

fi t the arithmeti c progression.

8

42 48 54 60

Starting at 36 find 4 multiples of 6Student Practice #1

42, 48, 54, 60 are all multi ples of 6.

36

Click for answer

104 112 120 128

Starting at 12 x 8 or 12 eights, find 4 multiples of 8Student Practice #2

104, 112, 120, 128 are all multi ples of 6and they represent 8x13, 8x14, 8x15, 8x16

96

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80 96 112 128

Starting at 4 x 16, find 4 multiples of 16 and write the multiplication problem each represent.

Student Practice #3 more challenging

80, 96, 112, 128 are all multi ples of 16and they represent 16x5, 16x6, 16x7, 16x8

64

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Stop here unless your students want more of challenge

3.75 4.50 5.25 6.00

Starting at 3 you count by 3/4’s or 0.75 and each jump would be a multiple 0.75

Multiples don’t have to be nice numbers, they can be decimals or fractions.

Generally we don’t call these multi ples because they aren’t nice numbers but they really are multi ples of

0.75

3.00

What other patterns do you notice here? Could you ignore the decimal point and just find multiples of 75 starting at 300

then put the decimal point back in when you’re done?

3.0 3.6 4.2 4.8

Starting at 4 x 0.6 find 4 multiples of 0.6 and the multiplication problems they represent

Student Practice #4 challenging

3.0, 3.6, 4.2, 4.8 are all multi ples of 0.6and they represent 0.6x5, 0.6x6, 0.6x7, 0.6x8

2.4

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