EverythingEverythingyou need to you need to know aboutknow about

in grade 6in grade 6

NumberNumberPatternPattern

ss

UsingUsingpattern rulespattern rules

to findto findoutputsoutputs

InputInput OutpuOutputt

112233

Pattern Rule:Pattern Rule:x3 -1x3 -1

(x 3 – 1)(x 3 – 1)

(x 3 – 1)(x 3 – 1)

(x 3 – 1)(x 3 – 1)

225588

UsingUsinginput/outputinput/output

tables tables to findto find

pattern rulespattern rules

Input

Output

1 32 53 74 9

I notice…I notice…

+2+2

+2+2

+2+2

This meansThis means

x2x2 is isimportantimportantfor myfor mypatternpatternrule!rule!

1 1 x 2x 2 = 2 = 2What can I do to get from What can I do to get from 2 to 3?2 to 3?

Let’s see if Let’s see if x2 +1 x2 +1 works withworks withthe other inputs and outputs. the other inputs and outputs.

+1+1

2 2 x 2x 2 = 4 = 4 + 1+ 1 = 5 = 5

3 3 x 2x 2 = 6 = 6 + 1+ 1 = 7 = 7

4 4 x 2x 2 = 8 = 8 + 1+ 1 = 9 = 9

Yes, I found my pattern Yes, I found my pattern rule!rule!

RecursiveRecursivePatternsPatterns

We can also We can also find and extend patternsfind and extend patterns in a series of numbers. in a series of numbers.

For example: 2, 4, 6, 8, 10… For example: 2, 4, 6, 8, 10…

Can you tell the pattern rule?Can you tell the pattern rule?

+ 2+ 2For this pattern we must For this pattern we must

add 2 add 2 to each termto each termin order to find the next termin order to find the next term

When we apply the pattern ruleWhen we apply the pattern ruleto the to the termterm instead of instead of

an input numberan input numberwe call it a we call it a

recursive patternrecursive pattern

Recursive patternsRecursive patterns can have pattern rules withcan have pattern rules with

more than one step more than one step

For example: 3, 5, 9, 17 For example: 3, 5, 9, 17

Can you tell the pattern rule?Can you tell the pattern rule? Here’s a trick:Here’s a trick:

When you can’t figure outWhen you can’t figure outthe pattern rule,the pattern rule,

compare the differencescompare the differencesbetween termsbetween terms

+2+2

17 – 9 = 817 – 9 = 8, , 9 – 5 = 49 – 5 = 4, , 5 – 3 = 25 – 3 = 2

OROR+4+4 +8+8

These numbers are allThese numbers are allmultiples of 2multiples of 2

So…So…

X 2X 2is important for ouris important for our

pattern rule pattern rule

If I check this,If I check this,3 3 x 2x 2 = 6, = 6,

but I want to get to 5but I want to get to 5so I will then do so I will then do -1-1

Now to test my pattern ruleNow to test my pattern rule

x2 -1x2 -1

5 x 2 = 10 – 1 = 95 x 2 = 10 – 1 = 99 x 2 = 18 – 1 = 179 x 2 = 18 – 1 = 17

It works!It works!

GrowingGrowingPatternsPatterns

We can use cubes to We can use cubes to create patternscreate patterns

We call the We call the first image Frame 1, first image Frame 1,

the second Frame 2, etc.the second Frame 2, etc.

Frame 1:Frame 1:

Frame 2:Frame 2:

Frame 3:Frame 3:

Frame 4:Frame 4:

We can put this info. We can put this info. into a table into a table

Frame # (Input)

# of Cubes(Output)

1 12 33 54 7

Frame 1:Frame 1:

Frame 2:Frame 2:

Frame 3:Frame 3:

Frame 4:Frame 4:

What is the What is the pattern rule?pattern rule?

I notice the outputs I notice the outputs go up by 2go up by 2

So…So…

x2x2 is important is important

1 1 x 2 x 2 = 2= 2but I need to get to 1but I need to get to 1

2 2 – 1– 1 = 1 = 1

Let’s test if Let’s test if x2 -1x2 -1 is the pattern ruleis the pattern rule

2 2 x 2x 2 = 4 = 4 – 1– 1 = 3 = 33 3 x 2x 2 = 6 = 6 – 1– 1 = 5 = 54 4 x 2x 2 = 8 = 8 – 1– 1 = 7 = 7

Yes!Yes!

By putting the info inBy putting the info inthe drawings intothe drawings intoa table, I founda table, I found

the pattern rule.the pattern rule.

GraphingGraphingpatternspatterns

We can take the info. We can take the info. from our input/output from our input/output

table and graph ittable and graph it

Input Output Ordered Pair

1 1 (1, 1)2 3 (2, 3)3 5 (3, 5)4 7 (4, 7)

Can you tell how Can you tell how the ordered pairthe ordered pair

is created?is created?

Right!Right!

The input is the The input is the first number.first number.

The output is theThe output is thesecond number.second number.

Input

(frame #)

Output

(# of cubes)

Ordered Pair

1 1 (1, 1)2 3 (2, 3)3 5 (3, 5)4 7 (4, 7)

0 1 2 3 4 5 6 7 8

876

54

32

1

Reminder:Reminder:

In an ordered pair, In an ordered pair, the first number goesthe first number goeson the x-axis on the x-axis (horizontal)(horizontal)

and the second numberand the second numbergoes on the y-axis goes on the y-axis (vertical)(vertical)..

FindingFindingPatternsPatternsin Ratesin Rates

If I jog an average of If I jog an average of 10 km an hour,10 km an hour,

how much distance how much distance will I cover in 3 hours?will I cover in 3 hours?

Let’s put this info. Let’s put this info. in a tablein a table

Hours Distance Ordered Pair

112233

10 km10 km+1+100+1+100

20 km20 km30 km30 km

Now I can plot this Now I can plot this on a graphon a graph

(1,10)(1,10)(2,20)(2,20)(3,30)(3,30)

Hours Distance Ordered Pair

112233

10 km10 km20 km20 km30 km30 km

(1,10)(1,10)(2,20)(2,20)(3,30)(3,30)

0 1 2 3 4Hours

403530

2520

1510

5

KM

I can I can see the see the path andpath andvisualize visualize

what what comes comes

nextnext

If you are given info. If you are given info. in an input/output table,in an input/output table,

can you graph it?can you graph it?

If you are given info.If you are given info.about rates, about rates,

can you graph it?can you graph it?

So…So…

If you answered yes toIf you answered yes toall five questions…all five questions…

WELL DONE!!!WELL DONE!!!

If you are given info. If you are given info. drawn in frames,drawn in frames,

can you place it incan you place it inan input/output table?an input/output table?

Do you use strategies Do you use strategies to find pattern rules?to find pattern rules?

If you are given a graph,If you are given a graph,can you place the info. incan you place the info. in

an input/output table?an input/output table?

Thanks for watching!Thanks for watching!