UNIT 1

^ T «% Number Patterns and \ 1 Pattern Rules

Q u i c k R e v i e w * v

> Here is a number pat tern: 1 ^ JT® ^ ^

. . + 1 + 3 + 5 + 7

^ A pattern rule is:

^ Start at 1. Add 1. Increase the number you add by 2 each t ime.

> Here is another number pat tern: 2 ^ ^ ^ 4 ^ . , . + 2 + 3 + 2 + 3

^ s i A pat tern rule is: Start at 2. Alternately add 2, then add 3.

> Here is another number pat tern: 4 ^ ^ ^ 8 ^ ^ 7 ^ ^ ®

« | . + 4 - 1 + 4 -1 ^ \ A pat tern rule is:

Start at 4. Al ternately add 4, then subtract 1.

Try These

1. Write the next 5 terms in each pat tern.

a) 25 ,29 ,30 ,34 ,35 , , ,

b) 3 ,4 ,6 ,9 ,13 , , , , _

c) 16 ,19 ,17 ,20 ,18 ,

2. Write the first 4 terms of each pat tern,

a) Start at 6. A d d 7 each t ime.

b) Start at 2. Al ternately add 6, then subtract 2.

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P r a c t i c e

Use a calculator w h e n it helps.

1 . Write the next 4 terms in each pat tern. Wri te each pat tern rule.

a) 100,125,120,145,140, , ,

Pattern rule:

b) 85 ,81,90,86,95, , ,

Pattern rule: ^

c) 36,72,144,288,576, , , ,

Pattern rule:

2 . Write the 6 th te rm of each pat tern.

a) Start at 500. Alternately add 50, then subtract 15.

b) Start at 85. Add 7. Increase the number you add by 3 each t ime.

c) Start at 763. Subtract 13 each t ime.

d) Start at 97. Al ternately subtract 9, then add 2.

3 . Start at 999. Wri te the first 7 terms of a pat tern.

Write the pat tern rule.

Pattern:

Pattern rule: i

Stretch Your Thinking

Wri te the first 5 terms of as many d i f ferent patterns as you can that start w i th

the terms 19 ,24 , . . .

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Chapter 1

[ksegsOD ̂ Modelling Patterns

Use m o d e l s to represent , e x t e n d , a n d m a k e

predict ions a b o u t n u m b e r pa t te rns .

You wil l need toothpicks and pennies.

1. Rebecca made a pa t t e rn using too thp icks and

pennies. Then she s tar ted a n u m b e r tab le .

/ \ / -\ /

a) Fill in the shaded cells of Rebecca's number table.

A pattern rule is a description of how a pattern starts and how it continues.

For the pattern 2, 6, 10, 14, the pattern rule is "Start at 2 and add 4 each time."

Number of triangles 1 2 3

Number of toothpicks 3 5

Number of pennies 3

b) Use too thp i cks and pennies t o ex tend Rebecca's

pa t t e rn up t o f o u r t r iang les . Sketch your m o d e l .

c) W h a t is t h e pa t t e rn rule f o r t he n u m b e r o f too thp icks?

W h a t is t h e pa t t e rn ru le f o r t he n u m b e r o f pennies?

d) Predict t h e n u m b e r o f pennies needed f o r f ive t r iang les.

pennies

Make a mode l t o check. Sketch your mode l .

e) Extend t h e pa t te rn f o r up t o seven t r iangles.

Then comp le te t he n u m b e r tab le above.

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Chapter 1

Extending Increasing Patterns

Descr ibe a n d e x t e n d increasing n u m b e r pat terns.

1. W h a t is a p a t t e r n ru le f o r each pa t te rn?

a ) 1 , 3 , 5 , 7 , . . .

Pattern rule:

b) 5, 10, 15, ...

Pattern rule:

c) 12, 22, 32, ...

Pattern rule:

J j i T . i . M M H I i l t M I »

2. Fill in the nex t t h ree numbers in each pa t te rn .

a) 2, 3, 4, , ,

b) 20, 25, 30, . , ,

c) 3, 6, 9, , ,

In an increasing number pattern, each number is greater than the number before. • 10, 11, 12, ... is an

increasing number pattern. The pattern rule is "Start at 10 and add 1 each time."

• 50, 100, 150, 200, ... is an increasing number pattern. The pattern rule is "Start at 50 and add 50 each time."

3. Kate made a tab le t o show t h e ingred ients f o r choco la te macaroons,

a) Extend Kate's pat tern fo r up t o f ive batches. Fill in the table.

Number of batches Butter (mL) Chocolate squares Coconut (mL)

1 100 5 250

2 200 10 500

b) Wr i t e each pa t te rn ru le.

Pattern rule for butter:

Pattern rule for chocolate squares:

Pattern rule for coconut:

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Chapter 1 ^

[kseBSGQ %\ Extending Decreasing Patterns

Descr ibe a n d e x t e n d decreas ing n u m b e r

pa t te rns .

1. W h a t is a p a t t e r n rule f o r each pa t te rn?

a) 10, 8, 6, ...

Pattern rule:

b) 15, 14, 13, ...

Pattern rule:

c) 90, 85, 80, ...

Pattern rule:

2. Fill in t he next th ree numbers in each pa t te rn .

a) 77, 76, 75, , ,

b) 1000, 900, 800, , ,

c) 24, 20, 16 , ,

3. O w e n is pack ing his co l lec t ion o f 150 comic books in to boxes.

10 comics f i t in each box. O w e n created a pa t t e rn t o show

t he n u m b e r o f boxes he needs. His pa t t e rn is 150, 140, 130, ....

a) W h y d o t h e numbers in Owen's pa t t e rn decrease by 10 each t ime?

b) W h a t is Owen 's pa t t e rn rule?

c) H o w many boxes does O w e n need? boxes

4. Jay b o u g h t 47 je l ly beans. Star t ing t h e next day, he ate 5 je l ly beans every

day. H o w many days d id it t ake f o r Jay t o eat all t he je l ly beans?

ll_!flifflBfliflfl__ ? •

In a decreasing number pattern, each number is less than the number before. • 50, 40, 30, ... is a decreasing

number pattern. The pattern rule is "Start at 50 and subtract 10 each time."

• 20, 18, 16, 14, ... is a decreasing number pattern. The pattern rule is "Start at 20 and subtract 2 each time."

Copyright © 2009 by Nelson Education Ltd. Chapter 1: Pat terns in Ma thema t i cs 3

UNIT 1

<fssot»

Using a Variable to Describe a Pattern

Q u i c k R e v i e w

> Look at the pat tern and the table.

1 1 . 1

Figure l . 1 higure2 l

Figure 3 1 Figure 4

Figure 5

Figure Number

Number of Squares

1 4 - 1 + 3

2 5 - 2 + 3

3 6 = 3 + 3

4 7 = 4 + 3

5 A A A A A A A A A A A A

8 = 5 + 3 A A A A A A A A A A A A A A A A

The number of squares is 3 more than the f igure number.

Let the var iable / represent any f igure number :

Number of squares: / + 3

/ + 3 is an expression. It represents the pat tern in the number of

squares.

Try These

1. For the pat tern be low:

a) Complete the table.

Figure 1 Figure 2

Figure 3 Figure 4

Figure

Number

Number of

Squares

A A A A A A A A A A A A A J V A A A A A A A A A A A A A A Figure 5

b) Wri te an expression to represent the pat tern in the numbers of squares.

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Practice

1 . For the pat tern be low:

a) Complete the table.

Figure 1 Figure 2 r . , y Figure 3

F i < 3 u r e 4 F igures

F igu re N u m b e r

N u m b e r o f

Squares

A A A A A A A A A A A / A A A A A A A A A A A A A A A

b) Wri te an expression to represent the pat tern in the number of squares.

c) Find the number of squares in the 10th f igure.

2. For each table, wr i te an expression for the number of dots in any f igure.

a) Figure Number

Number of Dots

1 7

2 8

3 9

4 10

5 A A A A A A A A A A A /

11 A A A A A A A A A A A A A A A

b) f i g u r e Number

Number of Dots

1 2

2 3

3 4

4 5

5 A A A A A A A A A A A /

6 A A A A A A A A A A A A A A A

3. a) Wri te an expression for the number pat tern .

1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , . . .

b) Wri te the next 5 terms in the pat tern.

Stretch Your Thinking

Find the 50th t e rm in each pat tern in quest ion 2 above.

a) b)

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2 Assert*

Using Patterns to Solve Problems

Q u i c k R e v i e w

One box holds 15 books.

> How many books wi l l 2 boxes

hold? 3 boxes? 4 boxes?

Make a table.

Two boxes hold 30 books.

Three boxes hold 45 books.

Four boxes hold 60 books.

> Predict how many books

10 boxes wi l l hold.

Number of Boxes Number of Books

1 15

2 30

3 45

4 A A A A A A A A A A A A A A A A A A A A /

60 A A A A A A A A A A A A A A A A A A A A A

A pat tern rule is:

Mul t ip ly the number of boxes

by 15.

To pred ic t the number o f books 10 boxes wi l l ho ld , mul t ip ly :

10 x 15 = 150 Ten boxes wi l l ho ld 150 books.

Try These

1. One concer t t icket costs $11 .

a) Comple te the table to f ind the cost of

7 t ickets.

b) Wri te a pat tern rule for t he cost.

Number of Tickets Cost ($)

1

2

3

4

c) Predict the cost of 10 t ickets.

d) Extend the pat tern. How many tickets

can you buy w i t h $155?

l A A A A A A A A A A A A A A A A A A A A A A A ' A A A A A A A A A A l

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Practice

1 . Ivo practises the gui tar 25 minutes every day.

a) Make a table t o show how many

minutes Ivo practises in one week.

b) How many minutes does

Ivo practise in 10 days?

c) How many minutes wi l l Ivo

practise in November?

How many hours is that?

d) How many days wi l l it take Ivo to practise a tota l o f 15 hours?

2 . One min ibus holds 18 students.

a) Make a table to show how many

students can ride in 6 minibuses.

b) Wri te a pat tern rule for the

number of students.

c) How many students can

ride in 10 minibuses?

Stretch Your Thinking

Think about the minibuses in quest ion 2 above.

a) How many students can ride in 25 minibuses?

b) How many minibuses are needed for 170 students?

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c h a p t e r 1 Solving Problems Using [kseaoTD Patterns

Identi fy pa t te rns to s o l v e problems.

1. O w e n is coun t i ng his penny co l lec t ion .

He a r ranged t h e pennies in a t r i ang le .

a) W h a t is t h e sum o f t h e t o p and b o t t o m

rows? pennies

b) How can you use a pattern t o count the pennies?

c) How many pennies does Owen have?

You can use patterns to figure out the sum of numbers. How many marbles are there?

5 + 2 = 7

0

4 - 3 7

6 + 1 = 7

The sum of the top and bottom rows is 7. The sum of the second top and bottom rows is 7. The sum of the two middle rows is 7. 7 + 7 + 7 = 21 There are 21 marbles.

2 . W h a t is t h e sum o f t h e numbers in t h e pa t t e rn 2, 4, 6, 8, 10, 12, 14, 16?

Sydney calculates 2 + 1 6 = 1 8 . Use a pa t t e rn t o f in ish Sydney's w o r k .

3. Calculate t h e sum o f t h e numbers in each pa t te rn .

a) 5, 10, 15, 20, 25, 30 b) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Sum: Sum:

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c h a p t e r i Describing Relationships tk3eS£GQ(£) Using Expressions

U s e var iables in e x p r e s s i o n s .

1. B randon is g o i n g t o visit his g randparen ts in

7 days f r o m today. He w r o t e an expression f o r

t h e date he is leav ing: t + 7.

a ) Wha t does the t represent?

b ) Why is the number 7 in the expression?

2 . W r i t e an expression f o r each student 's age. The

f i r s t one is done f o r you .

a ) Jolie is 5 years o lder t h a n her brother .

b + S

A variable is a letter or symbol that represents a number.

An expression is a phrase that uses operations with numbers and variables.

For example, a + 3 is an expression with the variable "a" in it.

The variable a represents any number.

The expression a + 3 means 3 more than a number.

b ) Tyler is 1 year o lder t h a n his sister.

c) Beth is 10 years o lder t h a n her sister.

d ) M a t t h e w is 2 years y o u n g e r t h a n his bro ther .

3. W h a t does each expression mean?

a ) b + 1 c) m - 5

b) p + 3 d) 10 + f

4. Rose has $15 m o r e t h a n Jon.

a ) W r i t e an expression f o r t h e a m o u n t o f m o n e y

Rose has. Use a d d i t i o n .

b) W r i t e an expression f o r t h e a m o u n t o f money

Jon has. Use sub t rac t ion .

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c h a p t e r 1 Describing Number Patterns m&mQ "«n Games

Crea te a n u m b e r pat tern g a m e a n d descr ibe the

pa t te rns .

Shant i , Kate, and Ma teo are p lay ing a 1 2 3 H 5 6 7 8 9 10

n u m b e r pa t t e rn game on a 100 chart . 1 2 3 H 5 7 10

Shant i moves 2 spaces each t u r n . 11 12 13 IH 15 16 17 18 19 20

Kate moves 5 spaces each t u r n . 21 22 23 2H 25 26 27 28 29 30

M a t e o moves 3 spaces each t u r n . 31 32 33 3H 35 36 37 38 39 HO The person w h o passes 100 f irst wins

HI H3 HH HS H% HI HS 19 50 The person w h o passes 100 f irst wins

HI H2 H3 HH HS H% HI HS 19 50 t he game.

HI H2 H3

51 52 53 5H 55 56 51 58 59 60

a) Shanti starts at 10. W h a t n u m b e r 61 62 63 65 66 67 68 69 70

is she on a f te r 3 turns? 62

71 72 73 IH 75 76 77 78 79 80

b) Kate starts at 2. W h a t n u m b e r is 81 82 83 SH 85 86 87 88 89 90 she on a f t e r 3 turns?

91 92 93 3H 95 96 97 98 99 100

c) M a t e o starts at 4. W h a t n u m b e r is

he on a f te r 3 turns?

d) W r i t e a pa t t e rn rule f o r each player.

Shanti's pat tern rule:

Kate's pat tern rule:

Mateo's pat tern rule:

e) Predict w h o w i l l w i n t h e game. Explain your t h i n k i n g .

f) Model the game. W h o wins?

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