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

2. Using
pattern rules
to find
outputs

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

4. Using
input/output
tables
to find
pattern rules

5. 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!

6. Recursive
Patterns

7. + 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

8. 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

9. Growing
Patterns

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

11. 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

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.
Input
Output
Ordered Pair 1
(1, 1) 2 3
(2, 3) 5
(3, 5) 4 7
(4, 7)

14. 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

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?
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)

17. 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

18. 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!!!

19. Thanks for watching!