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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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**Pattern Rule: x3 -1 Input Output 1 2 3 2 5 8 (x 3 – 1) (x 3 – 1)**

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Using input/output tables to find pattern rules

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**x2 is Input Output 1 3 2 5 7 4 9 +1 I notice… +2 This means important**

for my pattern rule! 1 x 2 = 2 What can I do to get from 2 to 3? 2 x 2 = = 5 3 x 2 = = 7 4 x 2 = = 9 +1 Let’s see if x2 +1 works with the other inputs and outputs. Yes, I found my pattern rule!

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Recursive Patterns

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**+ 2 recursive pattern We can also find and extend patterns**

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

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**x2 -1 X 2 Recursive patterns can have pattern rules with**

more than one step OR +2 +4 +8 For example: 3, 5, 9, 17 These numbers are all multiples of 2 So… X 2 is important for our pattern rule Can you tell the pattern rule? Now to test my pattern rule x2 -1 5 x 2 = 10 – 1 = 9 9 x 2 = 18 – 1 = 17 It works! Here’s a trick: When you can’t figure out the pattern rule, compare the differences between terms If I check this, 3 x 2 = 6, but I want to get to 5 so I will then do -1 17 – 9 = 8, 9 – 5 = 4, 5 – 3 = 2

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Growing Patterns

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**We can use cubes to create patterns We call the first image Frame 1,**

the second Frame 2, etc.

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**x2 is important What is the pattern rule? We can put this info.**

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

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Graphing patterns

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**We can take the info. from our input/output table and graph it**

Can you tell how the ordered pair is created? Right! The input is the first number. The output is the second number. Input Output Ordered Pair 1 (1, 1) 2 3 (2, 3) 5 (3, 5) 4 7 (4, 7)

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**on the x-axis (horizontal) and the second number **

Input (frame #) Output (# of cubes) Ordered Pair 1 (1, 1) 2 3 (2, 3) 5 (3, 5) 4 7 (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). 8 7 6 5 4 3 2 1

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Finding Patterns 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? Now I can plot this on a graph Let’s put this info. in a table Hours Distance Ordered Pair 1 10 km (1,10) +10 2 20 km (2,20) +10 3 30 km (3,30)

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**I can see the path and visualize what comes next 1 10 km (1,10) 2**

Hours Distance Ordered Pair 1 10 km (1,10) 2 20 km (2,20) 3 30 km (3,30) I can see the path and visualize what comes next 40 35 30 25 20 15 10 5 KM Hours

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**So… If you are given a graph, can you place the info. in**

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

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