Everything you need to know about in grade 6 Number Patterns

Using pattern rules to find outputs

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

Using input/output tables to find pattern rules

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 = 4 + 1 = 5 3 x 2 = 6 + 1 = 7 4 x 2 = 8 + 1 = 9 +1 Let’s see if x2 +1 works with the other inputs and outputs. Yes, I found my pattern rule!

Recursive Patterns

+ 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

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

Growing Patterns

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

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

Graphing patterns

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)

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 0 1 2 3 4 5 6 7 8

Finding Patterns in Rates

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)

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 0 1 2 3 4 Hours

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!!!

Thanks for watching!