Maths Extenders by Teacher Superstore

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Revised edition. Written by David Stephenson. Illustrated by Rod Jefferson. © Ready-Ed Publications - 2007 Originally published by Ready-Ed Publications (1995) P.O. Box 276 Greenwood Western Australia 6024 Email: info@readyed.com.au Website: www.readyed.com.au

COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes. However, this permission is not transferable and applies only to the purchasing individual or institution.

ISBN 1 86397 716 3

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Introduction

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The Maths Extenders book is designed to provide extension and enrichment for upper primary-aged early finishers - to 'extend' their skills in mathematics.

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The book incorporates a range of activities which will extend the abilities of the most mathematically able student. The pages include activities using number patterns, magic squares, number tracks, algebra, number combinations, graphing and so on. In addition, scattered throughout the pages are extra 'Challenges' to further test the children. These are simply shown with a ? and will provide an extra dimension to the student's work. The book is directed towards children in the 10 to 12 age range.

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Contents Extender Tasks 1 ..................................................................... page 4 Extender Tasks 2 ..................................................................... page 5

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Extender Tasks 3 ..................................................................... page 6 Extender Tasks 4 ..................................................................... page 7 Extender Tasks 5 ..................................................................... page 8

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Extender Tasks 6 ..................................................................... page 9

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Extender Tasks 7 .................................................................. page 10 Extender Tasks 8 .................................................................. page 11 Extender Tasks 9 .................................................................. page 12 Extender Tasks 10 ............................................................... page 13 Extender Tasks 11 ............................................................... page 14 Extender Tasks 12 ............................................................... page 15 Extender Tasks 13 ............................................................... page 16

Extender Tasks 14y ............................................................... page 17 © Re ad EdPubl i cat i o ns Extender Tasks 15 ............................................................... page 18 •f orr e v16i e w pur posespage on y• Extender Tasks ............................................................... 19l Extender Tasks 17 ............................................................... page 20 Extender Tasks 18 ............................................................... page 21

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Extender Tasks 19 ............................................................... page 22 Extender Tasks 20 ............................................................... page 23 Extender Tasks 21 ............................................................... page 24

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Extender Tasks 22 ............................................................... page 25

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Extender Tasks 23 ............................................................... page 26 Extender Tasks 24 ............................................................... page 27 Extender Tasks 25 ............................................................... page 28 Extender Tasks 26 ............................................................... page 29 Extender Tasks 27 ............................................................... page 30

Answers ...........................................................................pages 31-36

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Extender Tasks

In the Hen House In a hatchery there are always 500 birds. If there are 110 more hens than roosters ... a.

How many hens and how many roosters would there be? ________ hens

r o e t s Bo r e p ok u S ________ roosters

= 500 altogether.

Now try these. Remember, there is always a total of 500 birds. =

________ hens

________ roosters

210 more hens than roosters

________ hens

________ roosters

96 more hens than roosters

________ hens

________ roosters

14 more hens than roosters

________ hens

________ roosters

332 more hens than roosters

________ hens

________ roosters

1 more hen than roosters

________ hens

________ roosters

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60 more hens than roosters

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Will the final problem work? Why/Why not? __________________________

c. d.

300

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900 67

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= 15

= 2182

= 72

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8 = 480

Which is the largest and by how much? 64 or 46 _________ by __________

? ? ? ? ? 4

Potato chips cost 80c per 100 grams. How much would one tonne cost?

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Use a calculator to help locate the missing signs.

100g

Answer: $________________

Who was Pythagoras? _________________________________________________________ List four facts about him. • ____________________________________ • ______________________________________ • ____________________________________ • ______________________________________ Can you explain his theorem? (Use the back of this page.)

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Extender Tasks

Patterned Response

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a. Place the numbers 1 to 7 so each line is equal.

b. Can you see the pattern? Now repeat using 11 to 17.

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d. Now try 331 to 337.

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c. Now try 21 to 27.

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Now try 21, 22, 23, 24, 25 to equal 46. Explain your results ______________ _______________________________

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Place the numbers 1, 2, 3, 4, 5 so that each large shape (box) adds up to 6. Use each number only once.

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Find the rule then complete the first grid. Create your own pattern in the second grid and challenge a friend to complete. 20

9 2

5 72

2 12

? ? ? ? ? ? ? ?

Who was Archimedes? On the back of this sheet list six facts about him and explain his principle.

Extender Tasks

Drawing Conclusions Draw 4 straight lines to pass through all the nine dots without removing your pencil or tracing back over dots.

. . .

. . . . . . r o e t s . . . Bo r e

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p u Mystery Numbers S

. . .

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Arrange the digits 1 to 9 to make this sum correct. Can you find other solutions that work?

ReadyEdPubl i cat i ons Golfing © Luck

•f orr evi ew pur posesonl y•

A skilled golfer hits either 160m, 90m, 40m, or 5m every shot. He always hits straight and if the distance is correct the ball goes in the hole. What distances should he hit to get the lowest scores?

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DISTANCE 295 180 370 125 305 275 145 515 70

HITS TAKEN *

SCORE

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HOLE 1 2 3 4 5 6 7 8 9

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*Show the hits taken, e.g. 205 = 160, 40, 5m = Score 3. *Note: Often you might get a lower score by hitting past the hole then hitting back.

? ? ? ? 6

Golomb was a famous mathematician. Why was he famous? ________________________________________ ___________________________________________________________ ___________________________________________________________

Extender Tasks

Tempting Triangles

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Trade Off

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Place the numbers 1 to 6 in the first triangles so that each side is equal. Find three more different solutions.

Think Quick!

Lemonade is $1.20 per litre. © ReadyEdPubl i c at i on s60 1.5 litre How much would bottles cost? •f orr evi ew pur posesonl y • Answer:

A farmer sold 47 animals and was paid $595.00. If cows were $20.00 each, sheep $10.00 each and chickens $5.00, how many of each did he sell? =

______________

______ sheep @ $10.00 =

______________

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______ chickens @ $5.00 =

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Sale Total:

Calculations

______________ $595.00

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Re-arrange the numbers and signs to make the boxes equal.

7 +

6 =

x 72

$_________

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______ cows @ $20.00

2 2

? ? ? ? ? ? ? ? ?

Draw the following triangles. Equilateral:

Scalene:

Isosceles:

Extender Tasks

Maths Challenges Challenge a friend and see who wins, best of three games. •Place 21 counters in a pile. •Take it in turns to remove between 1 to 6 counters (you can't pass). •The winner is the player who picks up the last counter. GAME SCORE Me

r o e t s Bo r e p ok u S What is the pattern?

Opponents

_______________________________

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_______________________________

Magic Squares

Complete the first magic square so each column and row adds up to the same total.

6 24

Solve This

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Think Quick!

Use 6 matchsticks to create 4 equilateral triangles, i.e. all sides the same length. Hint: You may have to think at a higher level to solve this.

Icecream costs $3.90 for a 1.5 litre carton. How much is that per litre?

Answer: $_________

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Draw your solution here. 8

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Find some different solutions for these.

? ? ? ? ?

How long have you lived? I am ... ............. years old

............. weeks old

............. hours old

............ months old

............. days old

............ minutes old

Extender Tasks

Sign Of The Times A sign writer charges the following rates to paint letters. A = $1.00 F = $6.00 K = $11.00 P = $16.00 U = $21.00 Z = $26.00

B = $2.00 G = $7.00 L = $12.00 Q = $17.00 V = $22.00

C = $3.00 H = $8.00 M = $13.00 R = $18.00 W = $23.00

D = $4.00 I = $9.00 N = $14.00 S = $19.00 X = $24.00

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E = $5.00 J = $10.00 O = $15.00 T = $20.00 Y = $25.00

What would the following signs have cost?

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For Rent

Zoological Gardens

$________

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Stop

$________

Create signs costing the following values.

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$18.00

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$12.00

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$38.00

Find 20 words costing less than $20.00

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_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

_________________ $ ____

________________ $ ____

$72.00

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Think Quick! Paint costs $2.20 per 50mls. How much would it cost for a 2.5 L tin?

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Answer: $_________

? ? ? ? ?

Which is smallest and by how much?

53 or 35 ____________________________ ____________________________

Extender Tasks

Number Systems

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Our base 10 number system is derived from the Hindu-Arabic number system. For example using the number 3 293:

10s

Units

0 0 9

0 0 0 3

0 2

= 3 293

oo k

The headings a computer uses would be:

2 x 2 x 2 x 2 (16s)

{

2 x 2 x 2 (8s)

2 x 2 (4s)

2 x 2 x 2 x 2 (16s)

2 x 2 x 2 (8s)

2 x 2 (4s)

(shows base)

Units

} }

= 11012

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So 21 in base 2 could be written as:

10 x 10 (100s)

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Other bases can also be used, e.g. computers use base 2. For example using the number 13:

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10 x 10 x 10 (1,000)

Units

= 101012

Why do computers use base 2? _____________________________________________________ Make up your own chart and convert these to base 2. a. 7

b. 26 = __________ 9 = __________ © Rea dyEdPubc.l i cat i ons __________ e. 31 = __________ f. 22 = __________ •f orr e vi ew pur po ses__________ onl y• __________ h. 32 = __________ i. 35 =

__________

d. 12 = g. 18 =

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Converting Back Convert these base 2 numbers back to base 10.

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What is the highest number in any column in base 2? _________________________________

a. 1012

__________________

b. 11112 __________

} o c . e } r o st r

d. 10012

__________________

e. 11012 __________

f. 101012 __________

For example:

16s

Units

1102 =

16s

10112 =

? ? ? ? 10

c. 10102

= (4 + 2) = 610

= (8 + 2+1) = 1110

__________

Use base 2 to show the ages of your family and friends. Me ________________

Mum ______________

Dad ___________________

Teacher ____________

___________________

_______________________

Extender Tasks

Patterns Complete these patterns. a)

12,

18,

_____ _____ _____ _____ 5,

_____ _____ _____ _____ _____

r o e t s B r e ooQuick! Time's Up Think p u k S _____ _____ _____ _____

START

TIME TAKEN

1.00 pm

74 mins

5.41 am

310 mins

59 mins

END TIME

If a T.V. commercial costs $26 a second, what would a series of ten 30 second commercials cost?

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Complete this time chart.

Answer: $_________

12.02 pm

How much change from a $10 000 budget? $_______

9.27 P am u © ReadyEd bl i cat i ons 200 mins 1.19 am • f orr evi ew p ur po?sesonl y• 4.27 am 6.58 am

11.58 am

6.30 am

400 mins 206 mins

2.06 pm

340 mins

10.54 am

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12.01 pm

Ordering

11.59 am

? ? ? ? ? ?

On the back of this page draw these shapes:

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A pentagon

A trapezium

A dodecagon

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Four students lined up for class. List all the different orders in which they could stand.

_____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________

Kylie

Tim

Carol

David

Extender Tasks

Squaring up Find the pattern and complete these squares.

12 6

27 18

r o e t s Bo r e p ok These add upu Discount S 15

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Using the digits 0, 1, 2, 3, 4, 5 complete these sums. 14 20 + 35 69

41 25 + 03 69

A video shop offers 25% off all games. Can you work out their new prices?

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e.g.

'Street Fighter' was $122.00 Now:$_________

'NBA Jam' was $139.00

+ +dP © R e a d y E ubl i cat i on s _________ 87 87 87 •f orr evi ew pur poseso nl y• 'Mario Bros' was

Now:$

$98.00

Now:$_________

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What is a 24 hour clock? ________________________________

Where is it used? _______________________________________ Complete this chart using the 24 hour clock.

2400

11.49 pm

8.11 am

e. 12

24 HOUR TIME

3.27 pm

Now:$_________

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Research Time

OUR TIME

'Sonic' was $112.00

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1321

? ? ? ? ? ? ? ? ? ?

How many seconds in a week?

_________________

Extender Tasks

Pathways

How Fast?

Ross is a very exacting paper boy. He has worked out a different path for every day of his week's delivery round.

If a cyclist can ride 100m in 50 seconds, how long would these journeys take if he goes at the same rate?

600m __________

2400m __________

1260m __________

5km

12.6km __________

100km __________

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__________

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Key Information 1. He starts and finishes at the Depot. 2. Available paths are all shown as lines on the diagram. 3. He visits everyone once only. 4. He uses each path or combination of paths only once a day.

Find the rule

Depot

______

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Show in order the paths he could have taken.

Monday

Tuesday

Depot________________ Depot

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Depot ________________ Depot

Symbols

Fill in the missing digits.

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Wednesday Depot ________________ Depot Thursday

Depot ________________ Depot

Friday

Depot ________________ Depot

Saturday

Depot ________________ Depot

Sunday

Depot ________________ Depot

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) =

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4 12 © ReadyEdPubl i c a t i o ns 7 18 3 5 5 e o ______ •f orr evi ew pur pos s n l y•

Euclid was famous because... _________________________________________________ 13

Extender Tasks

Pathways

That's Logical

S) and moving in Commencing at start (S any direction upwards, sideways, downwards or diagonally, one box at a time, create the highest total possible in 5 moves.

1. A family had 11 pets made up of birds and cats. If there were 36 legs altogether, how many of each were there?

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__________________________________

2. It now shows 10. After 4 more it will show 2. What is it? __________________________________

3. Two coins add up to 25c. One is not a five cent coin. What are the two coins?

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__________________________________ 4. If three girls eat 3 cakes in 3 minutes, how long does it take 1 girl to eat a cake?

__________________________________

© ReadyEdCostly Publ i cat i ons Cat •Highest total possible is: If r a cat eatss 1/3 can o of n food a day and •f orr evi ew pu p o e s l y • each can costs $1.17, how much would Mark your pathway on the grid.

it cost to feed...

•Now try for the lowest total: a. 1 cat for 1 week? b. 1 cat for 12 days?

_______________

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Mark your pathway on the grid. Use a different coloured pencil.

_______________

te Missing . Digits o c . che e r o t r s super c. 2 cats for 20 days? d. 5 cats for June?

_______________ _______________

Use the digits 1 to 9 so that the puzzle totals 27 vertically and horizontally.

Research and draw an... •acute angle •obtuse angle •right angle 14

Extender Tasks

Match This 1. Arrange 12 matches as shown.

5. Arrange 9 matches into 3 triangles as below. Move 3 matches to make 5 triangles. Draw your solution.

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a)Move 3 matches to make 3 squares. b)Move 4 matches to make 3 squares.

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2. How can you arrange 3 matches to equal 6 without breaking them? Draw your solution.

6. You have 8 matches. Remove 3 and still have 8 left. Draw your solution.

7.u Arrange 24 into 9 squares. © ReadyEdP bl i cmatches at i o ns •f orr evi ew pur posesonl y•

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4. Arrange 15 matches into 5 squares as below.

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3. Arrange 5 matches to make 2 triangles. Draw your solution.

Remove 8 matches leaving 2 squares. Draw your solution. 8. Without breaking them can you turn 9 matches into 10? Draw your solution.

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Remove 3 matches to leave 3 squares. Draw your solution.

How many matches? If each match weighs 1 gram how many matches would weigh... 37 grams________

1293 grams________

1.2 kg________

5 kg________ 15

Extender Tasks

Cross Puzzle 1

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1. ________________________________

6. ________________________________

7. ________________________________ 8. ________________________________

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Make up another set of clues that will also fit these answers.

Across

9. ________________________________

11. _______________________________

Across

14. _______________________________

1. 6. 7. 8. 9. 11. 14. 16. 17. 18. 19.

16. _______________________________

/2 a million - 3 (6 x 6) - 7 68 more than 3/4 of 1000 73 + 61 1 /2 of 96 7 /8 of 11000 (20 x 18) + (15 x 18) 12 x 8 Double 31 10 years before the Sydney Olympics Triple 17 1

18.u _______________________________ © ReadyEdP bl i cat i ons 19. _______________________________ •f orr evi ew puDown r posesonl y•

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1. ________________________________ 2. ________________________________

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Down 1. 2. 3. 4. 5. 10. 11. 12. 13. 15.

17. _______________________________

3. ________________________________ 4. ________________________________

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4 dozen (9/10 of 1000) + 20 1 /2 dozen less than 1000 3 x 26 Sum of 3 internal angles of a triangle = 0 730 + 136 (11 x 8) + 11 39 less than 700 19 more than (170 x 3) 54 - 300

5. ________________________________

10. _______________________________ 11. _______________________________ 12. _______________________________ 13. _______________________________ 15. _______________________________

Extender Tasks

Create - A - Puzzle The answers have been filled in for you. Create the clues that fit and make this puzzle correct.

Teac he r 1

Across

7 6

___________________

= 397

___________________

= 926

___________________

= 373

___________________

= 12

___________________

= 73

10. ___________________

= 64

11. ___________________

= 69371

Down

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r o e t s 6 Bo r e p o u k 3 7 S 9

1. u ___________________ © ReadyEdP bl i cat i ons= 3031 ___________________ 9 •f orr evi ew pu2.r p osesonl y=• ___________________

= 793

___________________

= 9673

___________________

=72

___________________

= 747

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. te o chart ? Complete. c Think Quick! this che e ? r o r st supe ?r Answer: _________

10. ___________________

How many triangles can you find?

? ? ? ? ? ?

= 63

Milli =

___________________

Kilo =

___________________

Centi =

___________________

Hecto =

___________________

Extender Tasks

Darting Here and There 51 is a common dart game using 3 darts. Can you complete the following score card to make 51? (Remember all numbers,1 - 20, have double or triple scores.) e.g. 16 + 19 + 16 = 51 or 12 + 11 + 28 (Double 14) = 51. Complete these 3 dart combinations. You must use all 3 shots and each combination must be different.

r o e t s Bo r e p ok u S 17 + .......... + .......... = 51

11 + .......... + ........... = 51

15 + .......... + .......... = 51

13 + .......... + ........... = 51

18 + .......... + .......... = 51

14 + .......... + ........... = 51

16 + .......... + .......... = 51

9 + ............ + ........... = 51

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Teac he r

20 + 13 + ................. = 51

What number would you aim for to score 51 with one dart? ________________________

Dart Board

How many games?

Use a dart board to copy in the numbers on to the board below. • Add the opposite numbers. • Is there a pattern? • Could you create a pattern by rearranging the numbers?

Using 2, 3 or more numbers link the numbers that total 89.

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9 82

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Colour 10 link ups. You can use a number more than once.

o c . che e r o t r s super Match Ups

In a round robin competition there are 10 dart players. How many games of darts would you need to play for every one to play everyone else once? ___________________________________ How many more games would be needed if there were 14 players? ___________________________________

Extender Tasks

An ''Interesting'' Problem A couple wants to purchase a Mazda worth $35 600. The following purchase plans were available to them.

Plan A

E.g.

r o e t s Bo r e p ok u S (a) Car price (b)Interest @ 12% (c)x 5 years

= $ 35 600 = $ 4 272 = $ 21 360

Total Payout (a) + (b) = $ 56 960 ÷60)= $ 949.33 Payment per month (÷

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Teac he r

Borrow the money from their bank at 12% p.a. interest over 5 years. How much would they pay back in total? ______________________________________ How much per month would this be? ______________________________________

Plan B

Use a finance company and pay $780 per month over 6 years.

Plan C© Re adyEdPubl i cat i ons

•f orr evi ew pur posesonl y•

Use a mortgage broker whose rates are set at 10% p.a. for the first 2 years, then 14% for the next 3 years (calculate as for Plan A).

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Plan _________________ at ___________________

2. Which will be the cheapest option overall?

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Plan _________________ at ___________________

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1. Which will be the cheapest option monthly?

o c . c e r Riches Galore h er o t s super

3. How much cheaper is it than the dearest option? ___________________________________________

If you saved 35c a day and 55c each day of the weekend. how much would you have saved this year in ... •January:

________________________

Why might each year's savings be different?

•February:

________________________

______________________________________

•March:

________________________

•December: ________________________

______________________________________ ______________________________________ 19

Extender Tasks

Most Economical Compare the following vehicles. In city traffic a Ford Focus runs on premium fuel @ 75 cents per litre. It travels 18 kilometres on each litre.

A Ford Falcon runs on regular unleaded fuel @ 56 cents per litre. It travels only 12 kilometres on each litre.

r o e t s Bo r e p ok u S

Which car would be cheaper to run in city traffic and by how much?

Cheaper by

$4.17 _____________

$4.67 _____________

_____________

Over 250 km

_____________

Over 500 km

_____________

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Ford Falcon

Over 100 km

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Ford Focus

In country driving a Ford Focus travels at 20 km per litre whereas a Falcon travels at 16 km per litre. Which car would be cheaper on the following country trips and by how much?

_____________

Over 500 km

_____________

List 5 things that would alter a car's fuel consumption.

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Car Survey

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_____________

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? ? ? ? ? ? ? ?

Over 250 km

o c . che e r o t r s super

• _______________________________ • _______________________________ • _______________________________ • _______________________________ • _______________________________

What percentage of vehicles in the school car park are Hyundai's, Fords, Toyotas or Holdens?

____________________________________ ____________________________________ ____________________________________ ____________________________________

Extender Tasks

What's Missing? Use your calculator to fill in the missing signs.

600

1000

115 = 268

200

r o e t s Bo r e p ok u S = 10

= 726

= 3000

Arrange these in order from smallest to largest and then add them. a.

167 - 90,

34,

9 x 8,

(1/2 100 + 1/4 100),

23.6 x 3

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____________________________________________________ = total ___________

.67 of 100,

(3 x 3 x 10),

16.3 x 5.8,

94 - 53

____________________________________________________ = total ___________

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On The Average

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____________________________________________________ = total ___________

A cricketer's average is calculated by adding all the runs he makes in each game divided by the number of games. Calulate these averages.

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Barry Basher

o c . che e r o t r s super 62, 0, 53, 0, 39, 0, 86, 0

____________________________

69, 32, 12, 6

____________________________

23, 21, 18, 26, 43, 29, 35, 32

____________________________

Harry Hooker

39, 3, 4, 7, 29, 112, 6, 50

____________________________

Tim Tipper

0, 6, 12, 24, 48, 96

____________________________

Dave Driver Kevin Correct

Who, on average, is the best batsman? ____________________________________________ Which two would you select for the next game? Why? _____________________________ ________________________________________________________________________________ 21

Extender Tasks

Equal All-round Re-arrange the signs and numbers in each circle to make the circles equal in value.

6 x 3

100

r o e t s Bo r e p ok u S =

Using + and - arrange the numbers from each circle into number sentences of equal value. 2

8 2

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Teac he r

= ©R eadyEd= Publ i cat i ons Arrange the numbers and signs from each circle into number • f o rr eequals vi e wsame ptotals. ur posesonl y• sentences so each sentence the 2

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+ 3

x x

16 4

36 10

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. te o c Pose - A - Problem . che e r o t r s super =

Make up a similar problem to share with your class.

Made up by: =

___________________

Tried by: ___________________

Extender Tasks

Leap Frog In the video game 'Lenny The Frog' each coloured frog is able to jump set distances. Your task is to 'jump' each frog to safety by making sure it lands in the pond in the least number of jumps possible. HINT: Often it is quicker to jump past the pond and return.

r o e t s B r e oo Game 1 p u k S Distance it can jump

Safety Pond 10m from each frog.

(Show how many jumps each frog must take.)

e.g. Pink Frog

210 cm and 80 cm

Red Frog

110 cm and 5 cm

Blue Frog

35 cm and 10 cm

Green Frog

28 cm and 12 cm

Black Frog

240 cm and 30 cm

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Teac he r

Frog

= (4 x 210 cm) + 80 + 80 cm = 6 jumps

jumps

©R e aand dy EdP bl i cat i on 505 cm 5 cm = u = sjumps •f orr evi ew pur posesonl y•

Yellow Frog

Finish

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Game 2

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Start

o c . che e r o t r s super

Now try again with a 35 m target. Red Frog

110 cm and 5 cm

jumps

Blue Frog

35 cm and 10 cm

jumps

Green Frog

28 cm and 12 cm

jumps

Black Frog

240 cm and 70 cm

jumps

Yellow Frog

505 cm and 5 cm

jumps

Extender Tasks

Mixed Labels A pet store attendant collected $929 for the day's sales. List five different combinations of what could have been sold for that day, e.g. 12 dogs, 8 coats, 1 lead = $929.

r o e t s Bo r e p ok u S Cat coats $12

Canaries $22

Cat Food $7

Leads $5

Fed Up

1. ____________________________________________

If a dog eats 3/4 of a can of food a day, how many cans would be eaten in July?

2. ____________________________________________

____________________________ © ReadyEdPub l i cat i ons If each can costs $1.52, what would it cost to feed him in ____________________________________________ •f orr evi ew pur po sesonl y• December?

3. ____________________________________________

____________________________

5. ____________________________________________

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Crack this Code Use the 'code chart' below to decipher the message. 24,

26, 24, 16

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___ ___ ___ ___ M=

Q = 10

___ ___ ___ ___

24, 12, 23,

o c . che e r o t r s super

___ ___ ___ ___ ___ A=

19, 18, 8

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Cute Dogs $69

Extender Tasks

Graphs Complete the graph below using the student information. Student A has already been plotted on the graph for you. Include your own details and plot these on the graph. 70

60 55

Teac he r

r o e t s Bo r e p ok u S

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W E I G H T (kgs)

45 40

35 30

1000

1050 1100 1150 1200 1250 1300 1350 1400

1450 1500 1550 1600

HEIGHT (cm) © ReadyEd Publ i cat i ons Student Information Questions •Height f or r ev i ew pur posesonl y• (cm) Weight (kgs) Using the information shown on the 36

B. Luke

1320

C. Ross

1480

D. Carol

1360

E. Tim

1520

F. David

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1490

G. Cameron

1330

H. Kate

1310

I. John

1530

J. Yourself

..........

graph complete the following questions: 1. Who is the tallest? ______________________

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1060

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A. Andrew

2. Who is the lightest? _____________________ 3. Rank them shortest to tallest by their letters.

o c . che e r o t r s super 52 45 37 62

..........

______________________________________

4. Rank them heaviest to lightest by their letters. ______________________________________

5. Who are you closest to...

in height? _____________________________ in weight? ____________________________ on the graph? _________________________

Choose 3 people and on the back of this sheet draw their shape. 25

Extender Tasks

Drawing Triangles

r o e t s Bo r e p ok u S

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Draw 8 triangles together. What is the least number of lines needed?

Triangle Patterns Follow the pattern and draw in the diagram.

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___ triangles together creates ___.

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4 triangles together creates 5.

___ triangles together creates ___.

. te o c Complete these patterns . che e r o t r s super Can you find them?

a. 1, 3, 6, 10 ...

Why are these called triangular numbers?

Can you find them?

____________________________________ ____________________________________

Use the back of this sheet to draw an array for each number. b. What would the first four square numbers be? ____________________________________ Use the back of this sheet to draw an array for each square number.

Extender Tasks

Meaty Combinations Eric the butcher's assistant forgot which label went with which item. Can you fill out this customer report and decide who bought what? e.g. Customer spent $15.50 and bought 2 kgs of item 2.

Val ue

e Valu

1. Customer 1 spent $6.40 and bought 2 kgs of item________

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Teac he r

Spe cia l

Ir tee o m3B t s r Item 2 $ m e o 3 e . t 20 k I p $5. ok 4 g g g u 75 k k 5 0 2 . kg 5 S $7 . 2 $

1 m e t I

ue Val

2. Customer 2 spent $12.15 and bought 2 kgs of item_______ and 1kg of item_______

3. Customer 3 spent $8.90 and bought 1 kg of item_______ and 2 kgs of item________

4. . 5. Customer 5 spent $20.90 and bought 2 kgs of item________ and 2 kgs of item________

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7. Customer 7 spent $12.50 and bought 5 kgs of item_______

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6. Customer 6 spent $26.85 and bought 3 kgs of item________ and 3 kgs of item________

8. Customer 8 spent $33.25 and bought 3 kgs of item________ and 2 kgs of item________

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o c . che e r o t r s super

9. Customer 9 spent $11.45 and bought 1 kg of item________ and 1 kg of item_______ and 1 kg of item________ 10. Customer 10 spent $22.80 and bought 4 kgs of item_______ and 4 kgs of item________ 11. What was the butcher's total sales for the day? ________ 12. How much meat did he sell in total?_________

Day's Profit If the butcher's meat cost $96.00 and Eric's wages were $27.00, how much profit did he make for the day?

Extender Tasks

Saving Up - No Way Luke was a paper boy with a very sweet tooth. Every time he earned $12.00 he would buy lollies. He was paid 3c a paper and delivered 50 papers a day.

r o e t s Bo r e p ok u S

How many days before he had earned $12.00? ____________________________________

Luke's buying chart.

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Gobstoppers 50c

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Luke has three favourite sweets. How much will Luke spend on lollies each time and how much change will he receive from $12.00?

Squirts 1c

Liquorice Sticks 6c

Change from $12

1. 15 gobstoppers

$ _________

$ __________

2. 10 gobstoppers and 3 liquorice sticks

$ _________

$ __________

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Cost

3. 27 liquorice sticks and 150 squirts

$ _________

$ __________

4. 12 gobstoppers and 7 liquorice sticks

$ _________

$ __________

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o c . che e r o t r s super

5. 6 gobstoppers and 9 liquorice sticks and 123 squirts

$ _________

$ __________

6. 110 liquorice sticks and 269 squirts

$ _________

$ __________

What combinations of lollies could he buy so that he'd spent every cent?

________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________

Extender Tasks

Can Can Recycling aluminium cans is a good idea for the environment and a good way to earn money. a. List 10 places that would be good collection points for cans.

b. If you collected 12 cans a day, how many would you have in a year?

r o e t s Bo r e p ok u S

___________________________________

• ____________________________________ • ____________________________________

c. What would you get for your collection if you were paid 3c for each can?

• ____________________________________

___________________________________

• ____________________________________

d. How much a week is this?

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Teac he r

• ____________________________________

___________________________________

• ____________________________________

e. If the price increased by 25% how much more would the cans bring?

• ____________________________________ • ____________________________________ • ____________________________________

___________________________________ f. If each can was crushed to 6 cm high, how high could they be stacked?

___________________________________

•f orr evi ew pur p oaluminium seso nl ykilo. •About Scrap is 95c per how many empty cans equal 1 kg?

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There is an easy way of totalling consecutive numbers. Can you find it? e.g. 1 + 2 = 3, 1 + 2 + 3 = 6, 1 + 2 + 3 + 4 = 10, 1 + 2 + 3 + 4 + 5 = 15 Can you see the pattern? Try these: Hint: What's the mid point and is it odd or even?

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a.1 + 2 + 3 + 4 + 5 + 6 =

o c . che e r o t r s super _______

b.1 + 2 + 3 + 4 + 5 + 6 +7 =

_______

c.1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 =

_______

Now try: d.1 to 17 =

______________________

e. 1 to 20 =

______________________

f. 1 to 50 =

______________________

g.1 to 100 =

______________________

Answer: _________

? ? ? ? ?

Now that you know the rule, impress your friends by adding large amounts of consecutive numbers. e.g. 1 - 1000 = 500,500

Extender Tasks

Solve This A grisly murder has been committed at a country guesthouse. Your job is to solve the murder using all the information given.

Kitchen

r o e t s Bo r e p ok u S

The guesthouse has 4 rooms. There were 4 guests and 4 potential weapons were found.

Dining Room

Lounge

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The following information is known to be true. 1. Mr Adams was in the same room as the baseball bat. 2. The arsenic was in the dining room. 3. Ms Ball was in the lounge. 4. Mr Doust wasn't in a room next to Mrs Cook. 5. The hunting knife wasn't in the dining room. 6. Mr Doust wasn't in the dining room. 7. The murder took place in the room next door to where the pistol was. 8. Mr Adams was in a room next to Mrs Cook. 9. The victim was not killed by a blow to the head. 10. The pistol was in one of the men's rooms.

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Hall

Arsenic

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Pistol Arsenic Hunting Baseball Knife Bat

Mr Adams Ms Ball

Mrs Cook Mr Doust

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o c . che e r o t r s super

The murderer was

________________________________

The room was

________________________________

The weapon was

________________________________

Answers

Extender Tasks 1 - Page 4

Extender Tasks 3 - Page 6

In The Hen House

Drawing Conclusions

a. b. c. d. e. f. g.

. . .

305 Hens 195 Roosters 280 220 355 145 298 202 257 243 416 84 500 is even. Even and odd (1 more) = even.

. . .

r o e t Mystery Numbers s B r e oo Calculations p u k S

Teac he r

Golfing Luck

Largest: 46 by 2800

Think Quick $8000

Extender Tasks 2 - Page 5 3

331

337

335

20 36 24 10 72 100

4 6 12 5 6 5

5 6 2 2 12 20

3 1 6

332

Trade Off

o c . che e r o t r s supThink er Quick Answers will vary e.g. 22 cows @ $20 6 sheep @ $10 19 chicken @ $5

b. 20 being added 3 times to central box.

Patterns

334

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2 4

Tempting Triangles

333 336

15 d.

Square Up 5 1

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Score 4 Score 2 Score 4 Score 3 Score 5 Score 4 Score 5 Score 5 Score 2

m . u

7 c.

160, 90, 40, 5 90, 90 160, 160, 90, - 40 90, 40, - 5 160, 160, -5, -5, -5 160, 160, - 40, - 5 90, 40, 5, 5, 5 160, 160, 160, 40, - 5 160, - 90

Patterned Response 6

Hole 1 Hole 2 Hole 3 Hole 4 Hole 5 Hole 6 Hole 7 Hole 8 Hole 9

738 216 954

638 154 792

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a. 900 - 300 ÷ 40 = 15 b. 67 x 33 - 29 = 2182 ÷12 x 12 = 72 c. 72÷ d. 30 - 15 + 45 x 8 = 480

187 362 549

467 352 819

$ 440 $ 60 $ 95 $ 595

$108.00 9 12 14 7 18 25

Calculations 20

20÷4 = 5 4+5=9

5 + 7 x 3 = 72÷12 x 6 = 2 x 2 x 9

=36

Answers

Extender Tasks 5 - Page 8

Extender Tasks 7 - Page 10

Maths Challenges

Number Systems

Person who goes second will win if they always add up to multiples of 7.

7 = 1112

26 = 110102

9 = 10012

12 = 11002

31 = 111112

22 = 101102

Magic Squares

r o e t s Bo Converting Back r e p ok u S Extender Tasks 8 - Page 11 18 = 100102

27 12

19 12

21 24

Solve This

Think Quick

a. = 5 d. = 9

b.= 15 e. = 13

Patterns a) b) c)

c. =10 f. = 21

24, 48, 96, 192 (doubling) 7, 11, 9, 13, 11 (alternative numbers + 2) 38, 78, 158, 318 (double + 2)

Times Up 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

35 = 1000112

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23 12

32 = 1000002

2.14 pm 10.51 am 11.03 am 177 mins 9.59 pm 151 mins 6.38 pm 10.40 am 5.14 am 1438 mins

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STOP = $70 FOR RENT = $96 SAVE = $47 ZOOLOGICAL GARDENS = $183

Answers will vary e.g. $12 = bee, $18 = can, $38 = sand, $72 = school

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Think Quick

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T.V. Commercial - $7 800 Change $2 200

Ordering -

o c . che e r o t r s Sign of the Times super 24 ways

????

Under $20 e.g. fee, me, can...

Pentagon

Lettering - $110.00

?????

Trapezium

Smallest - 53 by 118 Dodecagon (12 sides)

Answers

Extender Tasks 9 - Page 12 Find the Rule Squaring Up

(+2 x 2) 5 14; 6 16; 9 22; 12 28

Symbols 26 +15 41

24 x6 144

27 11) 231

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14 50 23 87

51 34 02 87

10 24 53 87

53 41 02 96

25 31 40 96

03 42 51 96

Pathways 31 36 19 17 40 31 9

18 24 31 29 19 17 18

9 14 42 30 22 26 11

24 21 16 2 27 33 12 9 57 29 32 18 S 51 64 25 48 55 12 27 22 16 13 23 9 12 16 19

Page 14

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r o e t s Bo r e p ok u Extender Tasks 11 These Add UpS 15

Highest total 234 Lowest total 68

That's Logical © ReadyEdP ubl i cat i ons a. 1527 b. 12.00 a.m 1. 7 cats 4 birds c. 2349 • d. f 811 e. 1.21 pm 2. Hour hand on a clock o r r e v i e w p u r p o s e s onl y• Discount 3. 20c and 5c (N.B. one is not a five cent coin) Research Time

4. 3 minutes

????

Missing Digits

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604,800 seconds in a week

Extender Tasks 10 - Page 13

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Pathways Depot Depot Depot Depot Depot Depot Depot

1 3 7 9 6 8

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$91.50, $104.25 $73.50, $84.00

o c . Angles che e r o t r s super

1, 2, 3, 4, 5, 6, Depot - Monday 2, 3, 4, 5, 6, 1 Depot - Tuesday 5, 6, 1, 2, 3, 4 Depot - Wednesday 6, 1, 2, 3, 4, 5 Depot - Thursday 5, 4, 3, 2, 1, 6 Depot - Friday 4, 3, 2, 1, 6, 5 Depot - Saturday 6, 5, 4, 3, 2, 1 Depot - Sunday

How Fast

Costly Cat a. $2.73

Acute

b. $4.68

Obtuse

c. $15.60 d. $58.50

Right

•600 m=5 mins; •2400 m=20 mins; •1260 m=10 min 30 sec (10.5mins) •5 km=41 mins 40 secs (41.66 mins); •12.6 km=105 mins; •100 km=833 mins 20 secs (833.33 mins)

Answers

Extender Tasks 12 - Page 15 Extender Tasks 15 - Page 18 Match This

Darting Here and There

Any non repetitive combination that equals 51 e.g. 20 + 13 + 18 = 51 11 + 20 + 20 = 51... 1 shot = Triple 17

2. V1

r o e t s B r e Match Ups o p ok u S Extender Tasks 16 How Many Games? -45. 82.

6. V111

8. TEN

An Interesting Problem

How Many Matches?

Plan A $56 960, $949.33 per month, Plan B $56 160, $780 per month, Plan C $57 672, $961.20 per month

b. 1293

c. 1200

d. 5000

Extender Tasks 13 - Page 16

Cross Puzzle 1

8 8

9 16

Answers will vary each year depending on how many weekends in each month (i.e. when the month starts).

*Leap year

Extender Tasks 17 - Page 20 Most Economical

8 15

City

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1. Cheapest monthly Plan B by $181.20 2. Cheapest overall Plan B by $1 512

Country

100km 250km 500 km 100km 250km 500km

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a. 37

Page 19

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Teac he r

Many answers will fit - e.g. 27 + 52 + 20

Ford Focus by 48c Ford Focus by $1.25 Ford Focus by $2.50 Ford Falcon by 25c Ford Falcon by 62.5c Ford Falcon by $1.25

o c . che What's Missingr e o r st super

Extender Tasks 14 - Page 17 Extender Tasks 18 - Page 21 Create A Puzzle

Any question that fits the answers given.

Think Quick How many triangles? - 14

a. 56 + 97 + 115 = 268 b. 600 - 200÷ 40 =10 c. 8 x 9 x 10 + 6 = 726 d. 1000÷2 x 6 = 3000

Smallest To Largest a. 23.6 x 3, 9 x 8, (1/2 100 + 1/4 100), 167 - 90, 34, total = 375.8 b. 94 - 53, 67 of 100 (7 x 12), 3 x 3 x 10, 16.3 x 5.8, total = 376.54 c. Triple 29, (11 x 9) + 22, 1/8 of 1000, a gross, total = 477

Answers

On the Average

Extender Tasks 22 - Page 25

Barry 30 Kevin 28.37 Tim 31

Questions

Dave 29.75 Harry 31.25 Best average Harry: 31.25

Selector Barry bound to get a score. Tim getting better by two fold.

1. Tallest - John 2. Lightest - Andrew 3. Shortest to Tallest - Andrew, Kate, Luke, Cameron, Carol, Ross, David, Tim, John: A, H, B, G, D, E, F, E, I. 4. Heaviest to Lightest - Tim, John, Ross, David, Carol, Cameron, Luke, Kate, Andrew: E, I, C, F, D, G, B, H, A. 5. Answers will vary.

Teac he r

Answers will vary e.g. (3 x 6) + 6 = 8 x 6÷2; 100 - 27 - 28 - 21 = 24 21 + 21 - 21 x 2 = 2 x 3 x 4 + 18 = 36 + 16 - 10 = 42

16 lines

Extender Tasks 20 - Page 23 Leap Frog Game 1

Complete these patterns

Red (9 x 110) + 5 + 5 = 11 jumps Blue (35 x 28) + 10 + 10 = 37 jumps Green (34 x 28) + (4 x 12) = 38 jumps Black (4 x 240) + (2 x 30 )= 6 jumps Yellow (2 x 505) - (2 x 5) = 4 jumps

•

• • •

Page 26

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r o e t s Bo r e p ok 23 Equal All-roundu Extender Tasks S Drawing Triangles Extender Tasks 19 - Page 22

• • • • • • 6 • • • • • • • • •

• • • • • • • • • • 10 • • • • • • • • • • • • • • • • 16

Extender Tasks 21 - Page 24

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Extender Tasks 24 - Page 27 Meaty Combinations

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Red (32 x 110) - 4 x 5 = 36 jumps Blue (100 x 35) = 100 jumps Green (125 x 28) = 125 jumps Black (14 x 240) + (2 x 70) = 16 jumps Yellow (7 x 505) - (7 x 5) = 14 jumps

1. 2 kgs of item 3 2. 2 kgs of item 3 and 1 kg of item 4 3. 1 kg of item 1 and 2 kgs of item 3 4. 3 kgs of item 4 and 1 kg of item 1 5. 2 kgs of item 2 and 2 kgs of item 3 6. 3 kgs of item 3 and 3 kgs of item 4 7. 5 kgs of item 1 8. 3 kgs of item 2 and 2 kgs of item 4 9. 1 kg of item 1 and 1 kg of item 3 and 1 kg of item 4 10.4 kgs of item 1 and 4 kgs of item 3 11.Total sales: $174.95. 12.Total kgs 43 kg.

o c . Crack This Code c e her r o t s s r u e p Fed Up Mixed Labels Answers will vary.

Means ''crack this code''.

23 1/4 cans, $35.34

Day's Profit Profit $51.95.

Answers

Extender Tasks 25 - Page 28 Saving Up-No Way 8 days

Luke's Buying Chart Cost $7.50 $5.18 $3.12 $6.42 $4.77 $9.29

r o e t s Bo r e p ok u S Change $4.50 $6.82 $8.88 $5.58 $7.23 $2.71

Answers will vary, e.g. 24 gobstoppers, 1000 squirts, 23 gobstoppers and 50 squirts.

Extender Tasks 26 - Page 29 Can Can

b. 4380 cans e. $32.85 more

c. $131.40 f. 262.8 metres

d. $2.52

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Teac he r

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

c. 1275

d. 5050

(Rule is midpoint x last digit, e.g. 1, 2, 3, 4–5, 6, 7, 8 = midpoint 4.5 x 8 = 36.) Note: The midpoint is bewtween 4 and 5, i.e. 4.5

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Extender Tasks 27 - Page 30 Solve This

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Murderer: Ms Ball Room: Lounge Weapon: Hunting knife

m . u

a. 153

o c . che e r o t r s super