Everything you need to know about in grade 6

1. Everything you need to know about in grade 6 Number Patterns

2. Using pattern rules to find outputs

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

4. Using input/output tables to find pattern rules

5. I notice… +2 +2 +2 This means x2 is 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!

6. Recursive Patterns

7. 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? When we apply the pattern rule to the term instead of an input number we call it a recursive pattern + 2 For this pattern we must add 2 to each term in order to find the next term

8. Recursive patterns can have pattern rules with more than one step OR +4 +2 +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? Here’s a trick: When you can’t figure out the pattern rule, compare the differences between terms Now to test my pattern rule x2 -1 5 x 2 = 10 – 1 = 9 9 x 2 = 18 – 1 = 17 It works! 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

9. Growing Patterns

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

11. 1 x 2 = 2 but I need to get to 1 2 – 1 = 1 Let’s test if x2 -1 is the pattern rule What is the pattern rule? 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 2 x 2 = 4 – 1 = 3 3 x 2 = 6 – 1 = 5 4 x 2 = 8 – 1 = 7 Frame 1: Frame 2: Frame 3: Frame 4: We can put this info. into a table

12. Graphing patterns

13. 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.

14. 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

15. Finding Patterns in Rates

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

17. (1,10) 1 10 km (2,20) 2 20 km (3,30) 30 km 3 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

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

19. Thanks for watching!