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Algebra Patterning and Graphs

Algebra Patterning and Graphs

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Algebra Patterning and Graphs. Exploring Patterns. e.g. Write the next two numbers in the following patterns and describe the pattern. a) 2, 5, 8, 11, 14,. 17, 20. b) 40, 34, 28, 22, 16,. 10, 4. Add 3. Subtract 6. c) 1, 3, 9, 27, 81,. 243, 729. d) 1, 4, 9, 16, 25,. - PowerPoint PPT Presentation

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Page 1: Algebra Patterning and Graphs

Algebra Patterning and

Graphs

Page 2: Algebra Patterning and Graphs

Exploring Patternse.g. Write the next two numbers in the following patterns and describe the pattern.a) 2, 5, 8, 11, 14, b) 40, 34, 28, 22,

16,c) 1, 3, 9, 27, 81, d) 1, 4, 9, 16, 25,

17, 20 10, 4

243, 729 36, 49

e.g. Draw the next shape in the pattern and add the number below

10631

Add 3 Subtract 6

Multiply by 3

Square Numbers

Page 3: Algebra Patterning and Graphs

Finding a Rule for Linear Patterns- Linear number patterns are sequences of numbers where

the difference between terms is always the same (constant) - Rule generating a linear pattern is: Difference × n ± a constante.g. Write a rule (using n) to describe the following number patterns. n Number

of Squares

(s)

Number of Dots

(d)

1 1 52 4 93 7 134 10 175 13 21

+ 3+ 3+ 3+ 3

+ 4

+ 4

+ 4

+ 4

Rule: s =

Rule: d =3×n 4×n

3×1= 33 = 1- 2

- 2

4×1= 44 = 5+ 1

+ 11. Find the difference between terms and if the same multiply by n

2. Substitute to find constant3. Check if rule works

3×4 – 2

4×4 + 1

Page 4: Algebra Patterning and Graphs

e.g. To make these squares, the amount of matches below are needed.

4 7 10 13These results are shown on the table belowSquares (n)

Matches (M)

1 42 73 10410150

a) Draw the next set of squaresb) Create a rule for the pattern and use it to help fill in the gaps in the table

+ 3

+ 3

M = 3×n

3×1 = 33 = 4+ 1

+ 13×10 + 1

13

3×150 + 1

31451

c) Write the rule in wordsThe number of matches equals three times the number of squares plus one.

3×4 + 1 = 13

Page 5: Algebra Patterning and Graphs

Simple Quadratic Patterns- Quadratic number patterns are sequences of numbers where the difference between terms is not the same - You need to look at the differences of the differences. If it is a ‘2’, then the rule contains ‘n2’e.g. Write a rule for the following pattern

n Term (T)1 42 73 124 195 28

1. Find the difference between terms

+ 5

+ 3+ 7+ 9

2. If difference is not the same, find the difference of the differences!

+ 2+ 2+ 2

Rule: T =

3. If the 2nd difference is a ‘2’, the rule contains n2

n2

4. Substitute to find constant

12 = 11 = 4+ 342 + 3 = 19

5. Check if rule works

+ 3

Page 6: Algebra Patterning and Graphs

Co-ordinates- Are two references used to identify places of interest- The horizontal reference is written first with the vertical second e.g. MapsMathematical Co-ordinates- Are used to describe positions of points

e.g. Plot the following points: A = (1, 3), B = (4, 2), C = (3, -4), D = (-5, 1)

1. Add in axes (if needed)2. Label and number axes x = horizontal, y = vertical

x

y

1234

1 2 3 4 5-3 -2 -1-4-5 -1-2-3-4

3. Plot points using first number as the x co-ordinate and the second the y co-ordinate.4. Label points

AB

C

D

Page 7: Algebra Patterning and Graphs

Co-ordinate Patterns- Involves plotting rules that link the x co-ordinate to the y co-ordinatee.g. Complete the tables below and plot the following rulesa) y = 2x b) y = ½x – 1 c) y = -3x + 2

x y = 2x y = ½x – 1

-2

-1

0

1

2x y = -3x +

2 -2

-1

0

1

2

x-5 -4 -3 -2 -1 1 2 3 4 5

y

-5-4-3-2-1

12345

2 x -1 2 x -2

02

-4

4

-2 ½ x -1 – 1

½ x -2 – 1-1-½

-2

0

-1 ½

-3 x -1 + 2

-3 x -2 + 22-1

8

-4

5

Page 8: Algebra Patterning and Graphs

Scatterplots- Show relationships between two quantities- Has two axes, each showing a different quantity with its own scale

Height (m)

Age (years)

BobJane

Tom

Mary

e.g.

a) Who is the tallest?

b) Who is the same age?c) Who is the oldest?

Tom

Bob and Mary

Jane

Page 9: Algebra Patterning and Graphs

Line Graphs- Show how one quantity changes as another one does

0

20

40

60

80

100

20 40 60 80 100

Sweetcorn boiled then left to cool

Tem

pera

ture

Time (mins)

e.g.a) What is the room

temperature?

b) How long does it take for the sweetcorn to cool down to room temperature?

20ºC

80 – 15 = 65 mins

Page 10: Algebra Patterning and Graphs

e.g. Draw a graph to show how the water level may change in the following situation.- The sink is filled ¾ full of water

- All of the dishes are put into the sink at once- The dishes are washed and removed separately- The water is then drained

Wat

er le

vel i

n si

nk

empty

full

time

Doing the dishes

Page 11: Algebra Patterning and Graphs

Distance/Time Graphs- Are line graphs with time on horizontal and distance on vertical axis.- If the line is horizontal the object is not moving- The steeper the line, the faster the movement

9 am 11 am 1 pm 3 pmtime of day

dist

ance

from

har

bour

(km

)

10

8

6

4

2

0

Distance of yacht from harboure.g.

a) How far out from the harbour did the yacht travel?b) What happened while the graph was horizontal?c) Which part of the journey was quickest?

5 kmThe yacht was stationary

Steepest

The return journey

Page 12: Algebra Patterning and Graphs

Applications- When using graphs to read off values and explain rulese.g. A student lends out his scooter for a fee of $3 and $2 for every km travelled. Complete the table and plot on graph below.Length of

Journey (km)

Charge ($)

12345

0

2

4

6

8

10

12

14

1 2 3 4 5Journey (km)

Cha

rge

($)

Scooter fees

a) What will be the charge for a journey of 2 ½ km?

1 × 2 + 352 × 2 + 37

91113

$8