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Published byJeremiah Joyce Modified over 3 years ago

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Everything you need to know about in grade 6 Number Patterns

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Using pattern rules to find outputs

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InputOutput Pattern Rule: x3 -1 (x 3 – 1) 2 5 8

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Usinginput/outputtables to find pattern rules

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InputOutput I notice… This means x2 is important for my patternrule! 1 x 2 = 2 What can I do to get from 2 to 3? Lets see if x2 +1 works with the other inputs and outputs x 2 = = 5 3 x 2 = = 7 4 x 2 = = 9 Yes, I found my pattern rule!

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RecursivePatterns

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We can also find and extend patterns in a series of numbers. For example: 2, 4, 6, 8, 10… Can you tell the pattern rule? + 2 For this pattern we must add 2 to each term in order to find the next term When we apply the pattern rule to the term instead of an input number we call it a recursive pattern

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Recursive patterns can have pattern rules with more than one step For example: 3, 5, 9, 17 Can you tell the pattern rule? Heres a trick: When you cant figure out the pattern rule, compare the differences between terms – 9 = 8, 9 – 5 = 4, 5 – 3 = 2 OR These numbers are all multiples of 2 So… X 2 is important for our pattern rule If I check this, 3 x 2 = 6, but I want to get to 5 so I will then do -1 Now to test my pattern rule x x 2 = 10 – 1 = 9 9 x 2 = 18 – 1 = 17 It works!

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GrowingPatterns

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We can use cubes to create patterns We call the first image Frame 1, the second Frame 2, etc. Frame 1: Frame 2: Frame 3: Frame 4:

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We can put this info. into a table Frame # (Input) # of Cubes (Output) Frame 1: Frame 2: Frame 3: Frame 4: What is the pattern rule? I notice the outputs go up by 2 So… x2 is important 1 x 2 = 2 but I need to get to 1 2 – 1 = 1 Lets test if x2 -1 is the pattern rule 2 x 2 = 4 – 1 = 3 3 x 2 = 6 – 1 = 5 4 x 2 = 8 – 1 = 7 Yes! By putting the info in the drawings into a table, I found the pattern rule.

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Graphingpatterns

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We can take the info. from our input/output table and graph it InputOutputOrdered Pair 11(1, 1) 23(2, 3) 35(3, 5) 47(4, 7) Can you tell how the ordered pair is created? Right! The input is the first number. The output is the second number.

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Input (frame #) Output (# of cubes) Ordered Pair 11(1, 1) 23(2, 3) 35(3, 5) 47(4, 7) Reminder: In an ordered pair, the first number goes on the x-axis (horizontal) and the second number goes on the y-axis (vertical).

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FindingPatterns in Rates

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If I jog an average of 10 km an hour, how much distance will I cover in 3 hours? Lets put this info. in a table HoursDistance Ordered Pair km km 30 km Now I can plot this on a graph (1,10) (2,20) (3,30)

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HoursDistance Ordered Pair km 20 km 30 km (1,10) (2,20) (3,30) Hours KM I can see the path and visualizewhatcomesnext

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If you are given info. in an input/output table, can you graph it? If you are given info. about rates, can you graph it? So… If you answered yes to all five questions… WELL DONE!!! If you are given info. drawn in frames, can you place it in an input/output table? Do you use strategies to find pattern rules? If you are given a graph, can you place the info. in an input/output table?

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Thanks for watching!

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