Everyday Maths: Book 2 - Ages 9-11

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For Ages 8 - 10 r o e t s Bo r e p ok u S

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Everyday Maths Book 2

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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Mathematics problems set in a real world . te context. o c . c e her r o st super

Written by Jane Bourke. Illustrated by Rod Jefferson. © Ready-Ed Publications - 1997 Published by Ready-Ed Publications P.O. Box 276 Greenwood WA 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 168 8


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Contents 4

Division and Combinations of Money Garage Sale

7

Timetable reading; time intervals Time Out Mary’s Many Movements Train Travel

8 9 10

Problem Solving: Number problems, written computation Fence Frenzy Newspaper Round

11 12

Measuring Circumference Wheel Problems

13

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Problem Solving: Guess and check Farmer Frank’s Fruit Brainteasers 1 Brainteasers 2

Problem Solving: Make a list; restate the problem Scarecrow! Sorting Sneakers Maths Comprehension: Using a graph Holiday Heat Weight Watching 1 Weight Watching 2

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Teachers’ Notes and Problem Solving Strategies

14 15 16

17 18

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Calculating areas and perimeters Amazing Areas 1 Amazing Areas 2

24 25

Problem Solving: Act it out Parcel Pile-Up

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Problem Solving: Construct a table School Sports Classroom Chaos Story Time Brainteasers 5 Brainteasers 6

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Problem Solving: Working backwards Brainteasers 3 Brainteasers 4

26

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Problem Solving: Relationships between units of time Calendar Calculations Calculating Distances Frequent Flyer

27 28 29 30 31

32

33

Problem Solving: Draw a picture Fruit Salad Parent Night Brainteasers 7 Brainteasers 8

34 35 36 37

Answers

38 - 40

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Teachers’ Notes The idea of Problem Solving activities often conjures up images of numbers and objects that have no direct meaning for students other than teaching the basic problem solving strategies. The activities in this book are designed to present real life problems in a realistic context so as to provide children with situations in which every day problem solving and comprehension skills are required. The activities are based around recurring characters who find themselves exposed to a range of problems that need to be solved; the sorts of problems that students may one day encounter.

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Problem Solving Strategies

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Most pages include a challenge activity, usually an extension of the main problem, which will further consolidate comprehension skills. Included throughout the book are brainteaser pages which focus on a particular problem solving strategy, highlighted at the foot of the page. These brainteasers can be photocopied and individually glued on to card so as to create a set. Students might like to think up their own brainteasers to add to the set.

There are many strategies for solving every day maths problems. Some of the main problem solving strategies have been explained below. In some cases examples of problems are given where the particular strategy can be applied. Guess and check: Probably the first strategy children might try and definitely the easiest. By making a guess and checking their answer children have a point of reference on which to base all other guesses.

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An example: I am thinking of two consecutive numbers that when multiplied give 182. A guess might be to try 14 x 15 which would give 210. Obviously the next guess would try lower numbers. 14 Total

210

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15

Act it out: Students quite often need to visualise the problem, especially where people or objects are concerned. Counters, coins and students can be used to help solve the problem.

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Some examples: There are 48 players in the darts championships. Each player stays in the competition until they lose a game. How many games must be played to find the club champion? A caterpillar crawls up the tree 2 m every day. Every night it slips back 50 cm. The tree trunk is 10.5 m tall. How long will it take for the caterpillar to reach the top of the trunk? Make a model: When problems cannot be acted out, the next best thing is to make a model using cubes, matches and so on. Make a drawing, diagram or graph: Graphs and diagrams are particularly useful for trying different combinations or clarifying information. An example: Jack has a rectangular field that has an area of 360 m. What are the possible dimensions of the rectangle? Page 4

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Look for a pattern: This strategy can be used in many number and space activities to help simplify the problem. Number patterns: It takes three matches to make a triangle, 5 matches to make 2 triangles. How many matches are needed to make 3 triangles? Spatial Patterns: How many squares are there on a checker board? Construct a table: By organising data in a more meaningful way children can better see relationships, patterns and possibly missing information. This strategy is best used where different information is given about each person or object in the problem. A table can include all the information and eliminate irrelevant information.

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Swimming

Tim

Jess Kelly Max

Tennis

Netball

Hockey

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An example: Tim, Jess, Max, Jane, Tannie and Kelly each play sport over the weekend. They all play a different sport. Match the person to their sport based on the following: Tim doesn’t like swimming but enjoys cricket. Jess likes tennis more than swimming. Kelly enjoys netball. Max won’t play hockey. Jane doesn’t like cricket or diving. Tannie plays the sport that Max doesn’t like.

Cricket

Diving

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Jane

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The solution can then be found through the process of elimination.

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Tannie

Make a list: All possibilities can be listed when using this strategy and again the process of elimination can be used.

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An example: You have three T-shirts: red, blue and yellow; and four pairs of jeans: green, black, navy and light blue. How many different combinations can you wear? Restate the problem: This is best used to make sure students fully comprehend the problem and know what they need to do to find the solution. An example: At the supermarket Sarah bought some groceries. All the things she bought were the same price and she bought as many things as the total number of pence she was charged for each item. If her bill was $6.25 how many things did she buy? This could then be rephrased as: How many things can be bought with $6.25 where they all cost the same amount? Ready-Ed Publications

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Solve a simpler problem: By exploring a simpler problem, an apparently difficult task can be made easier. Students can look for a pattern and then transfer this pattern to the larger problem. An example: There are 20 people at a meeting. Everyone shakes hands with each person once. How many handshakes take place? This could be tried with a group of five and then children can look for a pattern.

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Account for all possibilities: This strategy can be used in addition to some of the strategies already mentioned such as making a list.

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An example: Emily is playing Monopoly and wants to buy Park Lane at a cost of $400. She has four $100 notes, ten $50 notes, seventeen $20 notes, eight $10 notes, fifteen $5 notes and six $1 notes. How many different combinations of $400 can she hand over to the banker?

Use logical reasoning: This strategy involves students using what they already know to solve a problem. A solution can be reached when logical reasoning is used to draw conclusions about mathematics. Strategies involve using models, known facts, properties and relationships to explain thinking.

An example: Ann, Brendan, Cathy and Daryl all play an instrument in the school band. They play the tuba, violin, flute and harp. Ann plays the harp and Brendan does not play the violin. If Cathy plays the tuba, what does Daryl play?

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Work backwards: This strategy works best when a problem is stated so that the final outcome is clear. In such a case the condition that existed earlier needs to be determined.

Flight departure Delay of one hour and fifteen minutes Arrived two hours early

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10.30 10.30 less 1.15 = 9.15 9.15 - 2.00 = 7.15 pm

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An example: Michael arrived at the airport and noticed that he had to wait two hours for his flight. A delay of one hour and fifteen minutes was announced. Michael’s flight eventually departed at 10.30 pm. At what time did Michael actually arrive at the airport?

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Tips for Students (Make a wall chart of these points.)

Make sure you understand the problem. Have a go even if you just play around with the problem. Try a variety of strategies. Learn from your mistakes. Keep a record of your working out for the bigger problems so that you can refer back if needed. Check your answers.

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Garage Sale

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Crazy Charlie’s Mum was tired of Charlie’s old toys and bikes lying around the shed and warned that Charlie better do something fast or she would throw out everything at the rubbish dump. Crazy Charlie knew that although he didn’t really want any of his old toys, he would be able to get some money for them. He labelled each object with a price and had quite a few customers attend the sale. Use the information to help answer the questions below.

© ReadyEdPubl i cat i ons and some old books. If she spent $9.00 altogether, how many books did she •f orr evi ew pur posesonl y•

1. Counting Carrie spent her pocket money on the Batman and Robin costumes

buy? .......................................................................................................................

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2. Mary Measure spent a total of $5. If she only bought two items, what did she buy?

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............................................................................................................................... 3. Spacy Sam spent all of his $20 on the old bike, a book on horses and some

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lucky dips. How many lucky dips did he end up with? ............................................... 4. Arty Ash bought the rollerskates and managed to get the swing for half price. How much change did he get from $20? .................................................................. 5. Neil Number didn’t buy any lucky dips or old books but managed to spend

$27.50. What did he buy? ....................................................................................... 6. Crazy Charlie’s cousin bought the left-over items. How much did he spend and what did he buy? .....................................................................................................

Challenge: How much money did Crazy Charlie end up with? ................................................ Ready-Ed Publications

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Time Out Mary Measure is always running late for school. She knows that school starts at 8.45 am but never seems to get there before 9.00 am. Last week Mary Measure was late every single day. On Monday she arrived at 9.01 am, Tuesday at 9.03 am, Wednesday at 9.00 am, Thursday at 9.10 am and Friday at 9.06 am. 1. How late was Mary Measure on:

Monday: ....................................................

Tuesday: ...............................................

Wednesday: ..............................................

Thursday: ..............................................

Friday: ......................................................

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2. What is the total number of minutes that Mary missed at school that week? ...............

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3. What is the average number of minutes that she was late each day? ........................

Mary Measure had a note sent home to her mother. It was decided that Mary would make an extra special effort to arrive on time each day. Mary was ready and waiting for class at these times of the following week: Monday 8.30 am

Tuesday 8.24 am

Wednesday 8.35 am

Thursday 8.31 am

Friday 8.25 am

© ReadyEdPubl i cat i ons • f or r ev ewbecause pur posesonl y• Mary’s favourite subject isi maths she

4. What is the total number of minutes that Mary had to spare? ...............................

6.

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usually gets to measure something. Maths is at a different time each day. After school has started at 8.45 am, how long does Mary wait each day before the class starts maths?

Daily Maths Timetable Monday 9.30 am

Tuesday 10.00 am

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Thursday 1.00 pm

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5. On average, how early did Mary arrive at school that week? ................................

Friday 11.15 am

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Mon: ................. Tues:................. Wed: ................ Thurs: ............... Fri: .................

Challenge

Find out exactly how long you are in class at school each day. To do this you will have to subtract the times that you spend at break and lunch. How much time do you spend in class?.................................................................... How much time does your class spend on maths, sport and art? ........................ Exactly how many minutes does it take for you to travel to school? ......................

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Mary’s Many Movements Mary Measure keeps very busy after school. Tuesday

Wednesday

Thursday

Friday

4.00

Violin

Swimming

Softball

Piano

Walking the dog

4.30

Violin

Homework

Softball

Free

5.00

Free

Free

Piano

Computer

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Monday

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Homework Free

Homework

Piano

Homework

Walking the Gymnastics dog

6.30

Dinner

Dinner

Dinner

Dinner

Use Mary’s weekly timetable above to answer these:

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5.30

Dinner

© ReadyEdPubl i cat i ons 2. On what activity does Mary spend the most time? .................................................. •f orr evi ew pur posesonl y• 3. How much time does Mary spend playing the piano? ............................................. 1. How long does Mary play the violin for? ..................................

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Challenge: What Day Is It? Match each day with a sentence below:

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4. How many minutes are spent per week completing homework? ............................

On this day Mary has only two activities: ...............................................................

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Today Mary has an activity, which is not homework, that she also has on Friday: ............................................................................................................................... This day Mary doesn’t play any musical instrument: ............................................. At 5.30 on this day Mary has an activity that she also has on Wednesdays and Thursdays: ............................................................................................................. Mary has softball on this day: ................................................................................

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Train Travel Crazy Charlie is off to visit the water slides with Spacy Sam, Mary Measure, Neil Number and Counting Carrie. The Wild Water World playground is in Curve Cove and they will need to catch a train there and back. Use the timetable below to answer the questions.

Weekdays to Curve Cove

Weekdays from Curve Cove

Power

Circular

Curve Cove

Curve Cove

Circular

Power

Silver

0800 hrs 0830 0900 0730 0745 0800 0830 1100 1130 1200 1230 1300

0803 0833 0903 0733 0748 0803 0833 1103 1133 1203 1233 1303

0809 0839 0909 0739 0754 0809 0839 1109 1139 1209 1239 1309

0815 0845 0915 0745 0800 0815 0845 1115 1145 1215 1245 1315

1600 hrs 1630 1700 1730 1745 1800 1830 1900 1930 2000 2030 2100

1606 1636 1706 1736 1751 1806 1836 1906 1936 2006 2036 2106

1612 1642 1712 1742 1757 1812 1842 1912 1942 2012 2042 2112

1615 1645 1715 1745 1800 1815 1845 1915 1945 2015 2045 2115

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1. Crazy Charlie catches the train from Silver Station.

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Silver

© ReadyEdPubl i cat i ons How many trains run before 11.00 am (1100 hrs)? ................................................... •f orr evi ew pur posesonl y• Neil Number lives right near Circular Station. If he catches the same train as Crazy

How long will his train trip there and back be? ......................................................

2. 3.

Charlie, how long will Charlie have already been on the train for?

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............................................................................................................................... 4. Spacy Sam thinks it would be fantastic if they could spend at least nine hours at Wild Water World. He must be back at Silver Station to meet his mum at 6.15 pm (1815 hrs). What trains can they catch in the morning if they want to spend this much time there?

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...............................................................................................................................

5. Altogether, how many trains run in the afternoon and evening? ............................ 6. Mary Measure’s mum had car trouble when she went to drop Mary at Power Station. Mary missed the 9.30 am (0930 hrs) train from Silver Station. If she caught the very next train when would she arrive at Curve Cove? ...............................................................................................................................

Challenge -

Who was there the longest?

Crazy Charlie caught the 8.00 am train and arrived back at Silver Station at 5.45 pm. Mary Measure caught the 9.45 am train and returned on the 6.00 pm train from Curve Cove. Spacy Sam arrived at Curve Cove at 8.45 am and was back at Silver Station by 6.15 pm. How much time did each child spend at the water slides? Page 10

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Fence Frenzy 1. Spacy Sam is painting the wooden fence around the school. He has bought six tins of paint from Roy G. Biv’s Paint Shop and spent exactly $200. What tins did he buy? .............................................................................................

Roy G Biv’s Paints

Outrageous Orange

$28.00

Yucky Yellow

$36.00

Great Green

$43.00

Bluish Blue

$51.00

Interesting Indigo

$29.00

Vivacious Violet

$35.00

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$25.00

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Racy Red

2. Spacy Sam decided he only wanted to use four colours when painting the

© ReadyEdPubl i cat i ons many red posts will there be if Sam uses equal amounts of each colour? ............ •f orr evi ew pur posesonl y• Sam’s brother, Ben the builder, is building a path around the fence. He will be fence.There are 392 posts in the fence. If one of the colours is Racy Red how

3.

using 7 different colours of brick. Each brick is the same width as one fence

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post so he will lay 392 rows of bricks. If each row is four bricks wide, how many

bricks will he need altogether? ..............................................................................

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4. If he is using equal amounts of each colour of brick, how many times will he use

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each colour? .......................................................................................................... 5. Ben can lay 60 bricks in 30 minutes. How long will it take him to complete the path? ...................................................................................................................... 6. Spacy Sam knows he can paint 4 posts in 10 minutes. If he keeps up at this rate, how long will he take to complete the fence? ................................................

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Newspaper Round Counting Carrie has got a new job delivering the local newspaper. She delivers a paper to all the houses on her street. The first house is number 1 and the last house on the street is number 209. Carrie’s favourite number is 9. 1. How many number 9’s will Carrie see on the letterboxes as she delivers the

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paper? .................................................................................................................... 2. Counting Carrie is given 9c for each paper that she delivers. How much money

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will Carrie make for each paper round? ...................................................................

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3. Calculate the amount of money Carrie would earn if she made the following amounts of paper rounds:

a. Four rounds in a week: ................................................................................ b. One paper round every week for 16 weeks: ................................................

4. Carrie wants to save up for a new bike. She has seen a bike she likes for $199.00 and has decided to save every cent from her paper round so she can buy it as soon as possible.

© ReadyEdPubl i cat i ons a. How many paper rounds will she have to complete before having enough • f orr evi ew pur posesonl y• money to purchase the bike? ...................................................................... b. How much change will she have? ...............................................................

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c. How many weeks will pass before Carrie has enough money for the bike if she completes a paper round every Tuesday and Thursday? .....................

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Challenge:

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As she did her round Counting Carrie noticed that houses with letterboxes by the front gate have three different types of letterbox. She has counted twice as many brick letter boxes as tin letterboxes and has counted 104 cylindrical letter holders. How many letterboxes are brick and how many are made from tin? ............................ Hint: Remember how many letterboxes there are! Page 12

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Wheel Problems Neil Number and Crazy Charlie were raking the leaves in the back garden and decided to use the wheelbarrow to move them into a pile. The wheelbarrow was very old and made a loud clank every time the wheel turned once. Neil counted 18 clanks from the pile of raked leaves to the compost heap. 1. He made a total of 5 trips to the heap and back. How many times did the

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wheelbarrow make a noise? ..................................................................................

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2. Crazy Charlie thought he’d jog around the block with the wheelbarrow and count the clanks. He counted 235 clanks. Neil Number thought it might be interesting to see the difference in the number of clanks if Crazy Charlie walked with the wheelbarrow instead. Crazy Charlie jogs three times as fast as he walks. How many clanks would the wheelbarrow make if he walked using the same route?

...............................................................................................................................

3. The boys found Mr Number’s trundle wheel in the shed and measured out ten metres. They then wheeled the wheelbarrow along the exact distance and counted 20 clanks. They measured the following distances as well. Can you work out the number of clanks they should expect to hear for each distance? a.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 200 m .............................................. b. 400 m ..................................................

e. 179 m ..............................................

f. 425 m ..................................................

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Challenge: Wheeling Past

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d. 78 m ....................................................

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c. 59 m ................................................

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Neil Number was waiting for Crazy Charlie at the bus stop. While he waited he counted the wheels on all the cars and buses that went past. He counted 44 wheels and noted that there were more buses than cars. If buses have six wheels, work out how many cars went past and how many buses went past. Use this table to help you find the answer: Number of Cars Number of Buses Total Wheels:

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Farmer Frank’s Fruit 1. Neil Number, Spacy Sam and Crazy Charlie visited the farm one weekend. Farmer Frank allowed them to pick some fruit to take home. They decided to pick peaches with Neil picking the most. Sam picked ten less than Neil and Charlie picked six more than Sam. If Charlie picked twelve peaches how many did Neil and Sam pick?

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Neil: ..................................................... Sam: .............................................................

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2. Farmer Frank sells fruit from his orchard every Sunday at the markets. He sells apples at 30c and pears at 70c. One day Neil Number spends $7.20 on a bag of fruit containing apples and pears. He has twelve pieces of fruit altogether.

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a. How many apples did he buy?...............................................................................

b. How many pears did he buy? ................................................................................ Use the table to help you: Number of Apples Number of Pears

© ReadyEdPubl i cat i ons Spacy Sam bought 7r oranges and 5 plums forr ap total ofs $4.50. How much does • f o r e v i e w p u o e s o n l y • Farmer Frank sell his oranges for? Hint: The plums are less than 50c each.

Total:

3.

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Cost of plums: Total cost:

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Cost of oranges:

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Challenge: Which fruit? Farmer Frank has two new orchards. One has 20 orange trees and produces 70 oranges a day. He sells the oranges for 50c each. The other orchard has fifteen plum trees which produce 90 plums a day. He sells the plums at 40c each. Which orchard makes more money? Page 14

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Brainteasers 1 A. Mary Measure, Spacy Sam and Neil Number were at the swimming pool. Mary Measure’s and Neil Number’s laps added up to 30, Neil Number and Spacy Sam did 17 laps altogether and Spacy Sam’s and Mary Measure’s laps added up to 25. How many laps did each person swim?

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Show your working out here:

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B. Mary Measure, Spacy Sam and Neil Number decided to practise their diving while at the pool. Spacy Sam and Neil did 25 dives altogether. Mary did 7 dives less than Spacy Sam. Neil did twice as many dives as Mary. How many dives did each person do?

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*Problem Solving Strategy: Guess and Check

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Brainteasers 2

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C. After their day at the pool, Mary, Neil and Sam went home for afternoon tea. Altogether Mary and Neil ate 15 strawberries, Neil and Sam ate 20 strawberries and Mary and Sam ate 19 strawberries. How many strawberries did each child eat? Show your working out here:

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D. Crazy Charlie had a strange dream. He dreamt he was on Mars and was seeing strange creatures. There were two types of creatures, Quadroids with four legs and Trizoids with three legs. Altogether Crazy Charlie counted 31 legs and noticed that the number of Quadroids was one less than the number of Trizoids. How many were there of each?

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*Problem Solving Strategy: Guess and Check Page 16

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Scarecrow! Spacy Sam was tired of the crows eating all his newly planted seeds and decided to take some action. He went to the local second-hand shop and saw quite a selection of clothes which he thought would look good on a scarecrow. Spacy Sam could only afford to spend $2.40 on clothing. hat

50c coat $1.00

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skirt 60c

shoes 50c

T-shirt 25c

jeans $1.00

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shirt 45c

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tie 40c

1. On the scarecrows below draw six different combinations Spacy Sam could use that would cost $2.40 or less. Tick the scarecrow outfit he should buy.

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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Sam also needs to buy some more seeds. Circle the bargain bin below which represents the best value.

Buy 4 for $1 and get 1 free!

Get 2 packs for the price of 1!

Get 4 packs for the price of 3!

Pack of 50 seeds

Pack of 40 seeds = 35c

Pack of 60 seeds = 50c

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Sorting Sneakers Neil Number, Crazy Charlie, Mary Measure, Counting Carrie and Spacy Sam were playing football at the playing field. They had all taken their shoes off and left them by the side. The gardener had moved all the shoes into a pile so he could mow the lawn and the shoes were all mixed up. They were all different sizes although no one could remember what their actual size was. Mine are larger The sizes were 4, 6, 7, 8, and 9.

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Use the clues above to decide who owns which pair. 1. Write the sizes for each person: Neil Number ......................................... Crazy Charlie ........................................ Mary Measure .......................................

Sam’s are smaller than mine.

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Mine are an even number.

than Neil’s.

Mine are the largest of all.

Mine are the smallest ones.

© ReadyEdPubl i cat i ons Spacy Sam............................................ •f orr evi ew pur posesonl y• Counting Carrie .....................................

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2. The students’ football team did so well throughout the season that the coach bought everyone in the team four new pairs of sports shoes. Each child now has a blue pair, a red pair, a black pair and a white pair. The coach has said that since these are their team colours, they can mix up the colours anyway they like. Colour all the possible combinations of shoe colours that each child could wear.

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Holiday Heat During school holidays Mary Measure visited Sunshine Cove with her family. She loves nothing more than measuring things and decided to record the temperatures of each day so that she can measure some of the differences. Using her mercury thermometer she recorded the following temperatures for the ten days of her holiday:

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29° C 27° C 31° C 33° C

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Day 1 Day 2 Day 3 Day 4

Day 5 Day 6 Day 7

35° C 38° C 36° C

Day 8 Day 9 Day 10

26° C 28° C 27° C

Use Mary’s chart to answer these :

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1. Which day had the highest temperature? .............................................................. 2. Between which two consecutive days was the greatest change in temperature?

...............................................................................................................................

3. What two days had the same temperature and what was this temperature?

© ReadyEdPubl i cat i ons What was the range in temperature over Mary’s holiday? ..................................... •f orr evi ew pur posesonl y• What temperature would fall in the middle of this range?......................................

...............................................................................................................................

4. 5.

6. Did any day have this middle temperature as a maximum? ..................................

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7. Look at the temperatures on Mary’s chart. How many times over her holiday

did the temperature decrease from the previous day? ..........................................

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8. How many times did the temperature increase from the previous day? ................

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9. What was the average temperature over Mary Measure’s holiday? ...................... 10. By what degree does the average temperature differ from the middle

temperature? .........................................................................................................

Challenge: How hot? Using your atlas or an encyclopedia, locate a place on the following continents that has a similar average to Sunshine Cove: Asia, Europe, South America.

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Weight Watching 1 Nora Number and Myrtle Measure noticed that over the years they had been putting on more weight. They decided to join Weight Watchers and recorded their weight loss over the first two months. Kg Kg Nora Myrtle 90

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Weeks

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1. What did the two women weigh when they first joined Weight Watchers? ...............................................................................................................................

2. How much did each woman lose over the eight weeks?

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3. Which woman lost the most weight during Weeks one and two?

............................................................................................................................... 4. Which week did not result in any weight loss at all?

............................................................................................................................... 5. What was the average weekly weight loss for Nora and Myrtle? ............................................................................................................................... 6. How much heavier than Nora was Myrtle after Week 8? ........................................

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Weight Watching 2 Record Myrtle’s weekly weight loss on the graph below: Week

Kilos

Week

Kilos

Week

Kilos

Week

Kilos

75

Week 13

74

Week 17

72

Week 21

66

Week 10

74

Week 14

72

Week 18

70

Week 22

64

Week 11

73

Week 15

71

Week 19

68

Week 23

63

Week 12

73

Week 16

73

Week 20

67

Week 24

62

Kg

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Week 9

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15 16 17 Weeks

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24

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Challenge: Considering Nora put on weight while she was on her diet (Weeks 12 and 16), what was her overall weekly average weight loss from Weeks 9 - 24? Ready-Ed Publications

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Brainteasers 3 E. Counting Carrie counted all the different animals when she visited the zoo. She counted twice as many tigers as cheetahs. The number of leopards was three less than the number of tigers. There were five times as many zebras as leopards. Carrie counted 25 zebras. How many animals did she see altogether at the zoo?

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Show your working out here:

© ReadyEdPubl i cat i ons •f o rr evi e ur p ofirst se sheospent nl y • Neil Number went shopping inw threep shops. In the shop a quarter

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of his money. He spent a third of the remaining money in the second shop. He left the last shop with $6 which was half of what he had when he entered the third shop. How much money did Neil Number take on his shopping trip?

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*Problem Solving Strategy: Working Backwards Page 22

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Brainteasers 4 G. Crazy Charlie was standing on the roof of a skyscraper. He dropped a bouncing ball onto the footpath below. Each time it touched the ground, it bounced back half as high, with the first bounce being half as high as the skyscraper. If its fourth bounce was 5 metres high, what height did Charlie drop it from?

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Show your working out here:

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H. Each day Mary Measure saves 5 cents more than she did the day before. On Saturday, 25 July, Mary had saved 30 cents. How many cents did she save on Wednesday, 22 July? Show your working out here:

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*Problem Solving Strategy: Working Backwards

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Amazing Areas 1 Neil Number, Crazy Charlie and Mary Measure take turns in having each other over after school. Mary suggests they work out who has the biggest back garden. Look at the areas below and calculate the play area in squares for each garden. (i.e. don’t include the shed area in Neil’s garden.) Charlie’s Garden

Mary’s Garden

Neil’s Garden

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Shed

© Rea dy EdPubl i ca i ons Area - ............................... Area -t .............................. If each square one square metre, measure perimeter for n each back garden: •represents f orr ev i ew p ur pthe os eso l y • 2. Perimeter - ..................

Perimeter - .....................

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3. Crazy Charlie’s Dad is planning on adding a patio to the back of his house using the garden. It will measure 3 metres by 4 metres. How much actual garden space will be left when it is finished?

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1. Area - .........................

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4. Mr Number is going to knock down the old shed in the corner of his garden. What will the new area and perimeter of the garden be once the shed is gone? ............................................................................................................................... ............................................................................................................................... Page 24

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Amazing Areas 2

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Spacy Sam’s garden has the largest area of all. It has one side that is 10 metres long, two sides that are both 5 metres each and the perimeter is 34 metres. Draw Spacy Sam’s garden on the grid below:

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Challenge:

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What is the longest perimeter a shape with an area of 36 square metres can have? Hint: Use the gridlines below and compare your answers with others.

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Parcel Pile-Up Neil Number has a new after school delivery job. He delivers parcels for Mr Hammer at the Hardware Store. He has a large pile of packages that need to be dropped off this afternoon, however, he can only fit a certain number in his bike basket at a time in these combinations: 3 square parcels 2 square parcels and a rectangular parcel 4 circular parcels. 2 rectangular parcels and 2 circular parcels

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1. What is the least amount of trips Neil can do the delivery in for the following days:

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Tuesday 7 squares 6 circles 4 rectangles

Wednesday 2 squares 3 circles 3 rectangles

Thursday 4 squares 5 circles 2 rectangles

Monday: ........................................................... Tuesday: ...........................................................

Friday 1 square 7 circles 6 rectangles

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Monday 5 squares 3 circles 4 rectangles

© ReadyEdPubl i cat i ons Friday: .............................................................. •f orr evi ew pur posesonl y• Wednesday: .....................................................

Thursday: .........................................................

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50c

75c

60c

How much will Neil Number receive for each day’s work?

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2. Costs per delivery are as shown below:

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Tuesday: ...............................................

Wednesday: .........................................

Thursday: .............................................

Friday: ..................................................

Challenge: Mr Hammer has given Neil Number the choice of being paid either per parcel or per trip he makes. He is offering $1.80 per trip. Based on the deliveries that Neil did this week, should he accept Mr Hammer’s offer? Page 26

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School Sports 1. On the first day of school at Digit Primary, Carrie counted 388 students. At the assembly the children were evenly divided into four school sport teams: Red, Green, Gold and Blue. How many students were placed in each team? ...............................................................................................................................

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2. During Term One, 24 new students were enrolled at the school. How many students would there have been in each team at the end of the term? ...............................................................................................................................

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3. In Term Two, 6 children left and 2 arrived. These students were placed evenly into the teams. a. What was the total school enrolment at this time? ............................................

b. How many children were in each team? ............................................................

4. In Term Three, 28 children left when another school opened nearby. Of the students, 14 were in Blue team, 6 were in Red and the rest were in Green. How many students were in each team now?

© ReadyEdGreen: Pub l i cat i ons .................................................. Gold:......................................................... Blue: ..................................................... •f orr evi ew pu r p osesonl y•

Red: ..........................................................

5. Counting Carrie is sure that there is a way that the teams can be made even by moving a few students around. How can this be done?

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Carrie wants to know if her team, Gold, will do well in the Athletic Sports. Apparently last year, the Sports were very exciting because a team that had not won for at least ten years came first. Work out the order of the teams last year from the clues given below? Spacy Sam: “Red won the year before last and Green the year before that!” Crazy Charlie: “I couldn’t believe my team, Blue, came second.” Neil Number: “It was strange that the team that won two years ago came last the very next year!”

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Classroom Chaos 1. Someone has messed up all the furniture in Crazy Charlie’s classroom. Crazy Charlie knows that there were some four-legged chairs as well as some three-legged stools but he is not sure how many of each. He has counted all the legs and has found that there are 40 altogether. He knows there are at least 5 stools.

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How many of each seat are in the classroom? ...................................................... ...............................................................................................................................

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I know I did a drawing of a person.

I hate weaving and sculpting but I like Carrie’s painting.

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2. Someone else has removed the names from the artwork at the back of the room. Crazy Charlie has no idea who did the art but some of the students have been able to help: I think Ash’s rug looks great! I like the jewellery someone made for Mary.

I made mine for someone else.

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Use the grid below to match the art with the right person: Painting

Neil Mary

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Drawing

Sculpture

Mobile

Weaving

Jewellery

Carrie Sam Ash Charlie Page 28

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Story Time Counting Carrie loves to read. Some people say she likes reading more than counting as she is most often found in a corner with her head in a book. She reads a large variety of books. 1. Work out how many books of each kind she has read in the past month using the clues below:

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Use the table to help you: Mystery Stories Comics

Science

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Carrie read 7 more mystery books than comics. The number of comics she read was 3 more than the number of fairytales. Carrie read 6 times as many mystery stories as non-fiction stories. She read 1 more science book than the total number of fairytales. Half of the total number of books Carrie read were mystery stories. Carrie read a total of 17 mystery and comic books.

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© ReadyEdPubl i cat i ons Non-fiction •f orr evi ew pur posesonl y• Total number of books Fairytales

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2. In the library the books have been placed in order by rows. Use the clues below to write the correct title on each aisle. The Non-fiction books are between the Classics and the Fairytales. The Adventure books are on the end next to the Reference row. The Mystery books are between the Fairytales and the Reference books. The Classics are in Row 1.

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Classics

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Brainteasers 5

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I. Neil Number’s double decker school bus can carry 90 students. It starts out empty, then one child gets on at the first stop, two at the second stop, three at the third stop and so on. After how many stops will the bus be full?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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J. At Farmer Frank’s fruit shop Crazy Charlie noticed that every time three customers came into the shop another customer would leave. The first time there was only one other customer besides Charlie and he left when three new customers came in. The second time one of the first three customers left when another three customers arrived. At the moment there are 13 customers including Charlie in the shop. How many groups of three had entered Farmer Frank’s shop?

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*Problem Solving Strategy: Make a Table Page 30

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Brainteasers 6

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K. Mary Measure has taken up jogging. Each day she jogs 200 m further than she did the day before. On her tenth day she jogged four kilometres. What distance did she jog on the first day?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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L. Spacy Sam had a birthday party and invited 30 friends. The first two guests arrived at 4.00 pm. The next two guests arrived at 4.05 pm and the third pair of guests arrived at 4.10 pm. The guests continued to arrive in pairs every five minutes. What time was it when all the guests had arrived?

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*Problem Solving Strategy: Make a Table

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Calendar Calculations

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Mary Measure likes to mark important dates off on her calendar. She always marks off her birthday, 28 September, and the birthdays of her family members. Mrs Measure’s birthday is on 11 August and Mr Measure’s is on 24 December. Her older brother Mike’s is on 28 December and her little sister Marcy’s is on 21 June. Other important dates Mary marks off include Christmas Day, New Year’s Day, Anzac Day, the first day of each season, the middle day of the year and the shortest and longest days of the year.

© ReadyEdPubl i cat i ons Mark Mary’s dates onr for her calendar too work outs theo following: •f or e vand i euse wthep ur p se nl y•

1. How many days from Mary’s birthday until Christmas? .............................................

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Year’s Day? ............................................................................................................ 3. True or False: Mike’s birthday is closer to Mary’s birthday than Marcy’s

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birthday................................................................................................................... 4. What will the date be three weeks and four days after Mary’s mother’s birthday? ............................................................................................................................... 5. What date will it be exactly seven weeks before Anzac Day? .................................... 6. Next year Mary’s birthday will fall on a ..................................................................... Every member of Mary’s family has a small party on their birthday. Between what two birthdays will Mary have to wait the longest for a party? ...............................................................................................................................

Challenge: Find out on what date the shortest and longest days of the year fall. Page 32

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Frequent Flyer

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2120 km

643 km 707 km

2227 km

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Spacy Sam’s older brother, Sebastian, is a very busy businessman. He often flies all around Australia and New Zealand attending conferences and meetings. Spacy Sam has kept a record of all Sebastian’s flights over the last month. Use the distances below to answer Spacy Sam’s questions.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 2643 km

618 km

1040 km

325 km

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Flights Taken by Sebastian in Month of September 2 Sydney to Brisbane 20 Perth to Adelaide 5 Brisbane to Hobart 22 Adelaide to Melbourne via Sydney 23 Melbourne to Auckland 10 Hobart to Melbourne 26 Auckland to Wellington 15 Melbourne to Sydney 30 Wellington to Sydney 18 Sydney to Perth

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1. How far did Sebastian fly between 1 and 6 September? ........................................... 2. On what day did Sebastian travel more than 3200 km? ............................................. 3. What was the total distance covered between 20 and 24 September? ............................................................................................................ 4. How far did Sebastian travel altogether? ................................................................... 5. What was the average distance travelled each day for the month of September? ............................................................................................................................... Ready-Ed Publications

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Fruit Salad 1. Mrs Number decided to make a fantastic fruit salad with fruit from Farmer Frank’s orchard. She had 5 oranges, 4 pears, 20 strawberries, 6 apples, 5 bananas, and 20 cherries. She cut each orange into eight pieces and then each piece in half. She cut each pear into quarters and then each quarter in half. She cut each strawberry in half. She cut each apple into quarters and then each quarter into four. She sliced each banana into ten slices. She removed the pit from the cherries by cutting them in two.

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How many pieces of fruit were in Mrs Number’s fruit salad? ...................................... 2. You are making Mrs Number a Giant Fruit Sundae to thank her for the salad. You want to use at least 30 pieces of fruit without wastage, and using the same types of cuts as Mrs Number used. Name six different fruits you could use, and describe how you would cut each fruit. 1. ....................................................................

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• .................................................................... ....................................................................

2. ....................................................................

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5. ....................................................................

.................................................................... 6. ....................................................................

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Parent Night Mary Measure, Spacy Sam, Counting Carrie, Neil Number, Arty Ash and Crazy Charlie were each given parts in the school play. Since they were all in the same play their parents decided they should all work together to help make costumes and props. Crazy Charlie’s parents suggested that everyone visit their house for a meeting to decide how they would help with the preparations. On Tuesday night the parents of each child went to Crazy Charlie’s house. There were a total of 12 parents. The six fathers all shook hands with each other.

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1. How many handshakes took place?

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........................................................

2. Mrs Measure bought some bags of sweets for the children to eat while the adults were having their meeting. There are five bags each containing 48 mixed sweets. Mary Measure is in charge of sharing them equally among the six children. How many sweets should each child receive?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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3. Mrs Number brought a cake tin filled with 12 banana muffins and 12 blueberry muffins. It was dark where the cake tin was and Mrs Number could not tell what sort of muffins she was removing. What was the least amount of muffins she needed to take out to make sure she had at least one banana muffin and one blueberry muffin?

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........................................................

Challenge: Cutting the Cake Crazy Charlie’s mum made a cake for her guests to have with coffee. Of all the guests, eight people wanted a piece. She had already cut the cake into four pieces. How could she cut the cake into eight even pieces using just one cut? Ready-Ed Publications

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Brainteasers 7 M. Crazy Charlie has made a lemonade tower using his mum’s champagne glasses. He used 10 glasses and had four levels. His mum has said they can try and make a giant lemonade tower with eight levels. How many champagne glasses will they need?

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Show your working out here:

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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N. Spacy Sam’s family has driven past 10 signposts while driving in a car rally. Each signpost is placed 25 kilometres apart and the first signpost is 10 kilometres after the starting line. What is the total distance they had travelled when they passed the tenth signpost?

Show your working out here:

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*Problem Solving Strategy: Draw a Picture Page 36

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Brainteasers 8 O. Neil Number went shopping in the shopping centre and noticed that the computer shop was between the shoe shop and the bookshop. The bookshop was between the computer shop and the sports shop, and the first shop was the shoe shop. What is the order of the shops?

P.

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Show your working out here:

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Mary Measure is weighing fruit at Farmer Frank’s shop using balance scales.

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She has found that one apple weighs the same as two plums, one plum weighs the same as three strawberries and one strawberry has the same weight as two cherries. How many cherries will Mary need to balance one apple?

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*Problem Solving Strategy: Draw a picture

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Answers Sheet 1 - Garage Sale 1. 2 books, 2. Old tennis racquet and a lucky dip, 3. 3 lucky dips, 4. $6, 5. Old tricycle and the baseball bat; or skates, swing and baseball bat, 6. 6 lucky dips and 7 old books = $16.50. Challenge: $92.00. Sheet 2 - Time Out 1. 16 min., 18 min., 15 min., 25 min., 21 min. 2. 95 min. 3. 19 min. 4. 80 min. 5. 16 min. 6. 45 min., 1 hr 15 min., 1 hr, 4 hr 15 min., 2 hr 30 min.

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Sheet 3 - Mary’s Many Movements 1. 1 hour, 2. Homework, 3. 2 hours, 4. 180 minutes.

Challenge: Monday, Thursday, Friday, Tuesday, Wednesday.

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Sheet 4 - Train Travel 1. 30 minutes, 2. 7, 3. 9 minutes, 4. 8.00 am and 8.30 am, 5. 15, 6. 10.00 am.

Challenge: Charlie - 9 hours and 15 min., Mary - 8 hours, Sam - 9 hours and 15 min.

Sheet 6 - Newspaper Round 1. She will see 41 number nines, 2. $18.81, 3.a) $75.24, b) $300.96, 4.a) Carrie will need to make 11 paper rounds to save $206.91, b) She will have $7.91 left over, c) 6 weeks. Challenge: Brick - 70, Tin - 35.

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Sheet 5 - Fence Frenzy 1. 2 tins of Racy Red, 1 tin of Outrageous Orange, 1 Yucky Yellow and 2 Great Green. 2. 98 posts, 3. 1568 bricks, 4. 224 times, 5. 13 hours and 4 minutes, 6. 16 hours and 20 minutes.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Sheet 7 - Wheel Problems 1. 180 times, 2. It would still clank 235 times as the distance has not changed. 3. a) 400, b) 800, c) 118, d) 156, e) 358, f) 850. Challenge: 2 cars and 6 buses.

Challenge: The plum orchard - it makes $36. Orange orchard makes $35.

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Sheet 9 - Brainteasers 1 A. Mary - 19 laps, Sam - 6 laps, Neil - 11 laps. B. Mary - 6, Sam - 13, Neil - 12. Sheet 10 - Brainteasers 2 C. Mary - 7, Sam - 12, Neil - 8. D. 4 Quadroids and 5 Trizoids.

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Sheet 8 - Farmer Frank’s Fruit 1. Neil -16, Sam - 6, 2. a) 3 apples, b) 9 pears, 3. An orange costs 50c and a plum costs 20c.

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Sheet 11 - Scarecrow! 1. Answers will vary. 2. A. If you spend a dollar you will get 250 seeds. B. If you spend $1.05 you will get 240 seeds C. If you spend $1.50 you will get 240 seeds. The best value is the first bargain bin.

Sheet 12 - Sorting Sneakers 1. 6, 8, 9, 4, 7, 2. There are sixteen combinations.

Sheet 13 - Holiday Heat 1. Day 6, 2. Days 7 and 8, 3. Days 2 and 10, 27° C, 4. There is a 12° range between 26° and 38°, 5. 32° C, 6. No, 7. Four times, 8. Five times, 9. Challenge: 31° C. 1 °. Challenge: Answers will vary. Sheet 14 - Weight Watching 1 1. Nora - 68 kg, Myrtle - 85 kg, 2. Nora - 8 kg, Myrtle - 10 kg, 3. Myrtle, 4. Week three, 5. Nora - 1 kg, Myrtle - 1.25 kg, 6. 15 kg.

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Sheet 15 - Weight Watching 2 Challenge: The total weight loss over the four month period was 16 kilos as Myrtle put on weight twice which had to be taken off again. Divided by 16, the average weekly loss is 1 kg. Sheet 16 - Brainteasers 3 E. 42 - 8 tigers, 4 cheetahs, 5 leopards, 25 zebras.

F. $24.

Sheet 17 - Brainteasers 4 G. 80 metres. H. 15 pence.

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Sheet 18 - Amazing Areas 1 1. Charlie - 25 squares, Mary - 30 squares, Neil - 27 squares, 2. Charlie - 20 metres, Mary - 28 metres, Neil - 28 metres, 3. 13 square metres, 4. Area - 33 square metres, Perimeter - 28 metres. Sheet 19 - Amazing Areas 2 Answers will vary.

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Sheet 20 - Parcel Pile-Up 1. Mon - 4, Tues - 5, Wed - 3, Thur - 4, Friday - 5. 2. Mon - $7.30, Tues - $10.10, Wed - $5.05, Thur - $6.50, Friday - $9.20.

Challenge: Neil would make $37.80 for the week if he was paid $1.80 per trip. By parcel he makes a total of $38.15. He will make 35c more if he is paid by the parcel, therefore he should not accept the offer. Sheet 21 - School Sports 1. 97, 2.103, 3. a. 408, b. 102, 4. Red: 96, Green: 94, Gold: 102, Blue: 88, 5. One solution: Place one of the students from Red into Green and then put 7 students from Gold into Blue. The teams now have 95 students each. Challenge: Gold, Blue, Green, Red.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Sheet 22 - Classroom Chaos 1. 8 stools and 4 chairs 2. Neil, drawing; Carrie, painting; Ash, weaving; Charlie, jewellery; Mary, mobile; Sam, sculpture. Sheet 23 - Story Time Mystery - 12, Comics - 5, Science - 3, Fairytales - 2, Non-fiction - 2; Total number of books = 24. 2. 1 - Classics, 2 - Non-fiction, 3 - Fairytales, 4 - Mystery, 5 - Reference, 6 - Adventure.

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Sheet 25 - Brainteasers 6 K. 2.2 km. L. 5.10 pm.

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Sheet 24 - Brainteasers 5 I. 13. J. 5.

Sheet 26 - Calendar Calculations 1. 88, 2. 35 weeks and 6 days, 3. True, 4. 5 September, 5. 7 March, 6. Monday; Mark’s and Marcy’s.

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Sheet 27 - Frequent Flyer 1. 2544 km, 2. 18 September, 3. 5406 km, 4. 15 111 km, 5. 503.7 km. Sheet 28 - Fruit Salad 1. 318 pieces, 2. Answers will vary.

Sheet 29 - Parent Night 1. Fifteen handshakes took place. 2. 40 lollies. 3. She needs to remove at least 13 muffins as the first twelve she pulls out could all be banana. If there are only 12 banana muffins, the 13th muffin must be blueberry. Challenge: The cake is cut into quarters already so all she need to do is cut it once horizontally through the middle to make two layers of four pieces. Sheet 30 - Brainteasers 7 M. 36. N. 235 km. Sheet 31 - Brainteasers 8 O. Shoe, Computer, Book and Sports shops.

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