Solving Maths Problems for Years 3-4 by Teacher Superstore

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Contents Teachers’ Notes

4 5 6 7-8 9-11 12 13 14

Section Two: Sam’s Birthday v8.1 Curriculum Focus Support & Extension Questions A Maths Story: Sam’s Birthday Activity 1 - Party Plan 1 Activity 2 - Party Plan 2 Activity 3 - Age Problems

15 16 17-18 19-21 22 23 24

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Section Three: At the Zoo v8.1 Curriculum Focus Support & Extension Questions A Maths Story: At the Zoo Activity 1 - Zoo Enclosures Activity 2 - Shopping Questions Activity 3 - Zoo Timetables

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Section One: Movie Mayhem v8.1 Curriculum Focus Support & Extension Questions A Maths Story: Movie Mayhem Activity 1 - Movie Timetables Activity 2 - Candy Bar 1 Activity 3 - Candy Bar 2

25 26 27-28 29-31 32 33 34

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Section Four: The Check-Up v8.1 Curriculum Focus Support & Extension Questions A Maths Story: The Check-Up Activity 1 - Measuring Liquids 1 Activity 2 - Measuring Liquids 2 Activity 3 - An Apple A Day

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Section Five: Go Crushers! v8.1 Curriculum Focus Support & Extension Questions A Maths Story: Go Crushers! Activity 1 - Basketball Scores Activity 2 - Sharing Pizzas Activity 3 - Fun With Heights Section Six: The Sleepover v8.1 Curriculum Focus Support & Extension Questions A Maths Story: The Sleepover Activity 1 - Game Scores Activity 2 - Code Breaker Activity 3 - Sleep Times

45 46 47-48 49-51 52 53 54 55 56 57-58

59-61 62 63 64

Teachers’ Notes This book contains a series of open-ended maths problems based on fun and engaging stories. The problems are placed into real life everyday contexts in which the students are likely to find themselves. It’s important for students to know that open-ended maths problems have more than one answer and that students often need to add to the information to be able to solve them. For example, if the problem is: ‘If I have 30 tablets, how many days will it take me to finish them all?’, students need to decide how many tablets the patient is required to take each day to work out how many days it would take to finish the course. They could work out answers for 1 a day, 2 a day, 3 a day, etc.

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A benefit of using open-ended problems is that all students in one class, each with their range of experiences and mathematical knowledge and skills, can be working on the same problem. This is because these problems can be solved using a variety of strategies which means students can tackle them at their own level.

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You will notice that the problems based on the stories have accompanying support and extension questions. This allows for further differentiation. If there are students who seem to be struggling with the main problem (this will often happen when you are first introducing these kinds of problems) it is a good idea to have a support question on hand for them to attempt first. In my experience usually once students have worked through the support question they are then ready to move on to the main question. The extension questions are there for the students who solve the main problems quickly to challenge them further.

Reflection time is important when implementing these lessons, not just at the end of a lesson, but also during it. It is important to stop at regular intervals and share how students are tackling the problems. This allows students to share successes and to learn about a range of different strategies. It also helps those students who may be struggling or are using a strategy that isn’t working for them.

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The questions that you pose during these lessons are also important. These questions can help students delve deeper or think more critically. For example: What would happen if…? Can you do it a different way? How do you know….? Have you found all the answers? How could you make this problem more challenging/easier? (This question encourages them to take responsibility for their own learning.) Prove it! Convince me! Can you show me/explain to me how you got your answer? Can you find a pattern?

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All questions and activities are linked to the v8.1 Australian Curriculum. As Problem Solving is one of the proficiency strands, it is important that students are able to use all mathematical concepts that they have learnt in a problem solving situation. This book will also help to address Reasoning as students are required to show and explain their thinking and working out. Understanding may also be shown as students need to have some understanding of mathematical concepts taught to be able to apply the knowledge to solve a problem.

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or eBo st r e p ok u Section One: S

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Movie Mayhem

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Teacher notes

Movie mayhem

v8.1 curriculum FOCUS

Number and Algebra

Measurement and Geometry

Statistics and Probability

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

Year 3:

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Year 4:

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Investigate equivalent fractions used in contexts (ACMNA077) Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080) Explore and describe number patterns resulting from performing multiplication (ACMNA081) Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

Convert between units of time (ACMMG085) Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

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Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059) Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060

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Discussion (before):

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When was the last time you went to the movies? What did you see? How often do you go to the movies? Can you remember the first movie that you ever saw at the cinema? How long do movies usually go for? How much does it cost to go to the movies? Can you get discounts? How much does it cost for a whole family to go to the movies? What do you like to eat at the movies? 6

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Discussion (after):

Design a ticket that you would get when you go to the movies. What information needs to be on it? What maths is involved? How much money would a cinema take in a day? Think about how much a movie ticket is; how many people might see each movie and how many movies might cinemas play in a day? How many different ways can you make $7.85? How much change would you get from a $10 note? How many different ways can you make that change? (See answers on page 8.) My friend gave the last movie he saw 7/10 – what does this mean? Think of the last movie that you saw - what would you rate it? What does this rating mean to you?

Teacher notes

Movie mayhem

Support & Extension Questions

1. What time might the movie start and finish? Support: If the movie starts on the hour, draw what the start and finish times might be on an analogue clock. Extension: The movie doesn’t start on the hour. Can you draw the start and finish times on an analogue and digital clock?

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2. What might Jane’s money be made up of and what might Zain’s money be made up of? Support: If Jane and Zain both have $2.85 in coins, what might their money look like? Extension: What is the maximum and minimum amount of notes and coin they could have? 3. How much money might Zain have? Support: All three notes are the same. Half of the coins are gold. Draw what this might look like. Extension: What is the most Zain can have? What’s the least? If all his notes are different and he has doubles of coins, how much might Zain have?

© ReadyEdPubl i cat i ons 4. What might the original ticket price be and how much will Zain save? •f orr evi ew pur posesonl y• Support: If Zain saves $1, what might the original ticket price have been?

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What if he saves $2? Or $3? Extension: What if Zain had got 3/5 off the price of his ticket? 5. How much might Zain’s ticket cost and how much change might Zain receive? Support: If Zain paid with a $5 note and all the coins were the same, what might his change have been? What would have been the cost of the ticket? Extension: How many different answers can you find? What is the most that the ticket could have cost and what is the least that it could have cost?

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o c . cdealebe and what might be the cost e r 6. How much might theh of the items separately? o t r s s r u Support: If the three items costp $4,e how much might each of the three items cost? Extension: Zain just wants popcorn and a drink. Jane said she would have the ice-cream from the deal. How much should Jane pay to Zain?

7. How many seats might be in each cinema? Support: There are 8 rows of seats. Can you draw what this might look like and work out how many seats there are altogether? Extension: If the other cinema has two more rows of seats, how many seats altogether? How many more seats are there than in the first cinema? 7

Teacher notes

Movie mayhem

Support & Extension Questions

8. How many slices of pizza might be left on the tray and how many slices of pizza do you think the original pizza was made up of? Support: If there are 2 pieces of pizza left, how many might there have been in the original pizza? What might this look like? Extension: What if there is 2/5 left?

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9. How many squares might be in the block of chocolate and do you think it will be possible to share the block of chocolate out evenly? How many squares will the children each receive? Support: If the children all receive 6 squares of chocolate, what might the block of chocolate look like? Extension: Imagine that the children can’t share the block of chocolate out evenly. What might the block of chocolate look like? How many squares will be left over? 10. Do you think this is possible (going to the toilet and back in 45 seconds)? What things are possible to do in 45 seconds? Support: Think of two tasks that you think you could complete in 45 seconds. Test this by asking someone to time you while you complete these tasks. Extension: How many times can you write your name in 45 seconds? Estimate, and then time yourself to see how accurate your estimate is. With this information, can you work out how many times you could write your name in a minute? Or five minutes?

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Answers

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Discussion (after) Page 6

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How many different ways can you make $7.85?

E.g. 3 x $2, 1 x $1, 50c, 20c, 10c, 5c or 1 x $2, 4 x $1, 2 x 50c, 4 x 20c, 1 x 5c How much change would you get from a $10 note?

$2.15

How many different ways can you make that change?

1 x $2, 1 x 10c, 1 x 5c or 1 x $1, 1 x 50c, 3 x 20x, 1 x 5c

Activity Pages Candy Bar 2 Page 14 E.g. 2x $5 notes, 2 x $2, 2 x 50c, 1 x 10c = $15.10 or 1 x $10, 1 x $5, 3 x 50, 1 x 20c, 1 x 5c = $16.75

section one: movie mayhem

A maths STORY Movie mayhem

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We had finally convinced our parents that we were old enough to go to the movies on our own. So Liam, Jane and I are going to see Space Hero. Jane’s parents are going to pick us up as soon as the movie finishes. The movie goes for 1 hour and 48 minutes.

Read the story Movie Mayhem and solve the problems along the way.

1. What time might the movie start and finish?

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In the car on the way to the movies, Jane got out her money and counted it. It looked like she had way more money than me but as she counted it, I realised that we had exactly the same amount.

2. What might Jane’s money be made up of and what might Zain’s money be made up of?

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Mum had given me some money but not as much as I wanted, so I had taken a little bit extra out of my moneybox. I had three notes and eight coins.

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o c . che e r o r st super Finally we were parent-free! We headed straight to the queue to buy our tickets. I was lucky. Mum had given me a coupon which meant that I could get 1/3 off the price of my ticket.

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1/3 off the mo ticket price

4. What might the original ticket price be and how much will Zain save?

section one: movie mayhem

The lady gave me my ticket and I handed her the money. I paid with a ten dollar note and the lady handed me my change which was made up of three coins.

5. How much might Zain’s ticket cost and how much change might Zain receive?

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6. How much might the deal be and what might be the cost of the items separately?

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Once we had our tickets, we headed straight for the candy bar. While lining up we were trying to work out how much we would save if we bought the deal which included a popcorn, ice-cream and a drink rather than buying each item separately. We worked out that we would be saving $2.75.

candy deal

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SAVE $2.75

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Loaded with food from the candy bar, we headed into the cinema. We were in the smaller of the two cinemas. Each cinema had the same amount of seats in each row but next door had 3 more rows of seats. 7. How many seats might be in each cinema?

section one: movie mayhem

The advertisements were just starting, and on the screen was an advertisement for the local pizza place. There was a picture of a pizza tray with only a quarter of the pizza left. It looked delicious!

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9. How many squares might be in the block of chocolate and do you think it will be possible to share the block of chocolate out evenly? How many squares will the children each receive?

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I had bought a block of chocolate that we could share. Jane was sure that we wouldn’t be able to share it out evenly, but Liam was sure that we would.

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8. How many slices of pizza might be left on the tray and how many slices of pizza do you think the original pizza was made up of?

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10. Do you think this is possible? What things are possible to do in 45 seconds?

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“I can make it there and back in 45 seconds?”

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needed to go to the toilet. He was sure that he could make it there and back in 45 seconds.

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“How was As we all hopped into the movie?” Jane’s dad’s car the first

“10 out of 10?”

thing he asked was, “How was the movie?” We all gave it a very enthusiastic 10/10!

section one: movie mayhem

Activity 1 - Movie Timetables Create a movie timetable for one day. Things to consider: there is only one theatre and the cinema is open from 10am until 8pm. See how many movies you can fit into the day. Remember to allow time for cleaning between each session.

Start Time

Duration

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Movie

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Many cinemas have multiple theatres. On a separate sheet of paper, create a different timetable for a cinema with more than one theatre. Some of the movies that are showing might be the same as the ones that you have listed above. Give people a few different session times to choose from. 12

section one: movie mayhem

Activity 2 - Candy Bar 1

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Think about your favourite things to eat at the movies. In the space below draw your own cinema candy bar! What items will you sell? How much are you going to sell them for? Will you have any special deals? What will the savings be on these deals?

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. te oelse to answer. c Write at least three questions about your candy bar for someone . che Eg. How much would it cost if I bought an ice-cream andr ae small popcorn? o t r s super Question 1:_ ______________________________________________________

__________________________________________________________________

Question 2:_ ______________________________________________________

__________________________________________________________________

Question 3:_ ______________________________________________________

__________________________________________________________________ 13

section one: movie mayhem

Activity 3 - Candy Bar 2 There are many ways to make any amount of money. Zain has 2 notes and 5 coins in his wallet. How much money might he have? Draw two different amounts and find their totals, then work out the difference between the two amounts. Repeat this process twice, using different amounts.

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Amount 1

Situation 1 Situation 2

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Draw 

Situation 3

Difference

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Draw 

???? ? ? ?

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Imagine that all Zain’s notes and coins are different. What is the most money that Zain could have?

$_______________

What is the least amount of money that Zain could have? $_______________ 14

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or eBo st r e p ok u S Section Two:

Sam’s Birthday

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Teacher notes

Sam’s Birthday

v8.1 curriculum FOCUS

Number and Algebra

Measurement and Geometry

Year 3:

Year 4:

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

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Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Investigate equivalent fractions used in contexts (ACMNA077) Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) Explore and describe number patterns resulting from performing multiplication (ACMNA081) Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

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Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060)

Convert between units of time (ACMMG085)

Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086) Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)

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Discussion (before):

Discussion (after):

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In your class, who has already had their birthday this year? Who still has to have a birthday? Express this as fractions. Did you have a party or other celebration for your birthday? Have you ever helped plan a party?

What are the costs involved in having a party? Whose was the last party you went to? Did you R.S.V.P. for the party? Why is this important? What do you have to do to prepare for a party? What Maths is involved? 16

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How many years, months, weeks, days old are you? Can you work out how many months, weeks or days (or minutes or seconds) until your next birthday? If I have 48 lollies how many people can I share them with evenly? (See answers on page 18.) Create a timetable or list of jobs that would need to be done leading up to a party. What would need to be done the month before, the week before and the day before?

Teacher notes

Sam’s Birthday

Support & Extension Questions

1. Can you help Sam work out how many months, weeks and days old he is? Support: How many months are there in a year? How many months old would Sam be if he was 9 years old? What strategies do you have for working this out? Extension: Can you work out how many seconds old Sam is? Can you work this out for your own age?

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2. If the lollies are shared out amongst the bags evenly and there are 5 left over, how many lollies might there be altogether? Support: If there are only 6 lolly bags, how many lollies might be in each bag? What about if there are 8 lolly bags? Extension: Is there a pattern to help you work this out? 3. If there are 60 chocolates, how many chocolates might each person receive? Support: What if there are 12 people? How many would each person receive? How do you know this? Extension: How many different ways can Sam share the chocolates evenly? How many different ways could Sam share the chocolates if he ate one?

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4. How many people might Sam have invited to his party? Support: If the number of people invited to Sam’s party can be divided to make 6 equal groups of 5, can they also be divided to make equal groups of 3? Does this work for other equal groups of 5 people? Extension: What if the party guests need to be divided into equal groups of 4?

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5. Can you work out how many friends from Sam’s basketball team and how many of his classmates were invited to his party? Support: What if half the party were from Sam’s class? How many might this be? Extension: What if another 2/6 were other friends from Sam’s school but not in his class?

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o c . che e r o r st s r u 6. What time might the party start and finish? e p Support: What if the party starts exactly on the half hour?

Extension: The start time makes a pattern on the digital clock. What time might it be and what time would it finish?

7. Can you help Sam write out a timetable for his party? Don’t forget the cake! Support: How many different activities do you need to include in the timetable? If the party runs for 2.5 hours in total, how long does each activity in the timetable need to go for? Extension: What might need to be done before and after the party? Can you create a timetable for the whole day? 17

Teacher notes

Sam’s Birthday

Support & Extension Questions

8. How many different skirt/top outfit combinations can Lily make? Support: If there are 6 tops, how many outfits combinations could there be? Can you draw what this might look like? Extension: If Lily adds 3 different pairs of shoes, how many outfit combinations are possible now?

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9. What might be the time on the clock? Support: What o’clock times make a right angle? Use a clock to help you. Extension: How many different times make a right angle? 10. How could Sam arrange the cupcakes on the platter? Support: If there are exactly 30 cupcakes, how many different ways could Sam arrange them? Extension: How many cupcakes are there in each container? How many cupcakes are there altogether? How many ways could they be arranged?

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If I have 48 lollies how many people can I share them with evenly? 2 people = 24 each, 3 people = 16 each, 4 people = 12 each, 6 people = 8 each, 8 people = 6 each, 12 people = 4 each, 16 people = 3 each, 24 people = 2 each Activity Pages Party Plan Page 22

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Venue

bowling alley cinema play Centre home skating rink farm park

Age Problems Page 24 9 years old

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$15 $13.50 $17.95 $7 (food, drink and jumping castle) $11 $8.80 $5 (food and drink only)

How Many People Sam Can Invite 8 8 6 17 10 13 24

section two: sam’s birthday

A maths story: sam’s birthday

Read the story Sam’s Birthday and solve the problems along the way.

“Happy Birthday!” Mum, Dad and Lily were standing over me. I didn’t know what time it was but still, I couldn’t help but smile. “Happy Birthday Sam!” yelled Lily again. “Nine years old today. I can’t believe it,” said Mum. “Or 76 months,” said Dad. That didn’t sound right….

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1. Can you help Sam work out how many months, weeks or days old he is?

2. If the lollies are shared out amongst the bags evenly and there are 5 left over, how many lollies might there be altogether?

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While Mum made me a birthday breakfast of pancakes with ice cream, Dad started putting together the lolly bags ready for my party. Each one was going to contain a water pistol and a tub of slime - and of course lollies! Lots of lollies!

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Mum served me my pancakes, “Here you go birthday boy!” As I sat enjoying my pancakes I watched Dad adding the chocolates to the lolly bags and I started wondering if we were going to have enough chocolates. I was trying to work out how many chocolates were in each bag.

3. If there are 60 chocolates, how many chocolates might each person receive?

section two: sam’s birthday

Leading up to my birthday, Mum and I had argued a lot about how many people I could invite. Eventually we both compromised. At least the amount of people that we agreed on could be evenly divided into groups of 3 and 5 which would work out perfectly for the party games.

4. How many people might Sam have invited to his party?

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5. Can you work out how many friends from Sam’s basketball team and how many of his classmates were invited to his party?

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Writing the guest list was tricky. I wanted to invite my whole grade and all my friends from basketball, the neighbours and everyone I knew! But there was no way Mum was going to let me have that many people at the party. Out of all the people who I invited to my party, a 1/3 were from my class and a 1/6 were my basketball friends.

Dear Friend,

You are invited to

Sam’s Birthday Party

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6. What time might the party start and finish?

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Mum and I had also argued about the length of the party. Mum wanted the party to go for just 2 hours but I wanted it to go for 3 hours. Eventually we compromised, and decided the party would go for 2.5 hours.

o c . che e r o There were quite a few games thatr I really wanted to playt at my party. I had trouble s su r p2.5e working out how many games I could fit into hours. Mum suggested that I write out a timetable for the party to make sure that I had time to do everything that I wanted to do. 7. Can you help Sam write out a timetable for the party? Don’t forget the cake!

section two: sam’s birthday

Lily was busy choosing her outfit for the party. I already had my outfit picked out (one that I got for my birthday), but Lily had what looked like her whole wardrobe out on her bed! When I walked past I could see that she had laid out 6 different skirts and a heap of tops.

8. How many different skirt/top outfit combinations could Lily make?

“What to wear?”

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9. What might be the time on the clock?

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We didn’t have long left until the first guests would be arriving and the party would be underway. I think I was almost ready. I looked up at the clock to check exactly how long I had left and noticed the hands on the clock were at a right angle.

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10. How could Sam arrange the cupcakes on the platter?

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check with Mum and Dad to see if there was anything left that I could help with. “Could you get the cupcakes that we made yesterday and lay them out on that platter please sweetie?” asked Mum. I grabbed the giant, rectangular platter and the two containers of cupcakes and got to work. I hadn’t counted how many cupcakes there were exactly but I could see that there were more than 30 and less than 50 cupcakes.

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Ding dong! That will probably be my first guest! I wonder who it is?

section two: sam’s birthday

Activity 1 - Party Plan 1 Parties can be quite expensive. Leading up to Sam’s party, he argued with his Mum and Dad about how many people he could invite to his party. His Mum said she would not spend more than $120 on the party. Using the information below, can you work out how many people Sam could invite to his party at each venue?

bowling alley cinema

$13.50

play centre

$17.95

skating rink

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home

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Venue

or eBoHow Many People t s r e Cost Per Person p ok Sam Can Invite u S $15

o c . che e r o t r s s r u e p Which venue would you choose and why?

park

$5 (food and drink only)

_________________________________________________________________ _________________________________________________________________ Research: Research another place for Sam to host his birthday party. What are the costs involved? How many people can Sam invite if he has his party at this venue? Show your working out and answer on the back of this sheet. 22

section two: sam’s birthday

Activity 2 - Party Plan 2 After Sam selected a venue for his party, there was still many other things for him left to organise. Make a list of some of the things that you think Sam needs to organise for his party (for example, the cake, decorations, lolly bags). Research how much each will cost and then work out the total cost of the party.

or eBo st r e p ok u S Cost

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Item

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o c . che e r o r st suabove r pe Sam might not be able to have all the items included in his party. Pick Total Cost:

three that you think he may want and work out the total cost of the three.

_________________________________________________________________ _________________________________________________________________ Add this to the cost of a venue from the previous page to work out the subtotal. _________________________________________________________________

section two: sam’s birthday

Activity 3 - Age Problems Use the information below to work out how old Sam is. (You can use a calculator.) Show your working out.

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If Sam has taken 78,840,009 breaths in his life so far, how old might he be?

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Can you work out, based on your own age, how many times you have blinked in your life? (Again you can use a calculator.) Remember to show your working out.

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At the Zoo

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or eBo st r e p ok u S Section Three:

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Teacher notes

At the Zoo

v8.1 curriculum FOCUS Measurement and Geometry

Number and Algebra Year 3:

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

or eBo st r e p ok u S

Year 4:

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080) Explore and describe number patterns resulting from performing multiplication (ACMNA081) Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

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Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059) Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060)

Convert between units of time (ACMMG085) Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

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Discussion (before):

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Discussion (after):

Have you ever been to a zoo? Where was it and how long did it take to get there?

My sister said she could count 68 feet? How many zebras and how many kangaroos might there be? (See answers page 28.)

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What are some of the animals you might see at the zoo? How long would it take to see them all? How much does it cost to go to the zoo?

What other places have you visited that have an entry fee? Where have you visited and how much was the entry fee? How many people do you think visit a zoo each day? How many people do you think would visit a zoo in one year? Do you take lunch, snacks and drinks when you go to the zoo or buy them there? Why? 26

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If I buy an item from the kiosk and I get five coins in change, what might I have bought and how much change might I have received? Find out the cost for you and your family to go to the zoo for a day. Can you work out what it would cost for your class to go to the zoo? Using a map of a zoo, find a path from one of your favourite animals to another. Write a set of directions for someone to follow.

Teacher notes

At the Zoo

Support & Extension Questions

1. If it costs the family $48 to enter the zoo, what might the cost be for each ticket? Support: It turns out that the zoo has a special offer on. It is only $20 for the whole family to enter the zoo. How much might each ticket be now? Extension: Each ticket is a different price. How much might each ticket be? 2. How many emus and kangaroos might be behind the fence? Support: If there are 24 animals, how many might there be of each animal? Extension: There are 12 wombats in the enclosure next door. How many legs are visible now? How many toes are visible?

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3. Can you work out how many butterflies and how many birds landed on the zoo keeper? Support: If there are 20 birds and butterflies altogether, how many birds and how many butterflies are there? How many wings are there altogether? Extension: How many different combinations could there be of birds and butterflies? 4. What could Spencer and Lucy buy with their $10? How much change would they each receive? Support: Select one to two items and draw the coins needed to pay for them. Extension: How much money would you need to buy one of everything?

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5. What time might the show start and finish? Support: Each show starts on the hour or the half hour. Can you find a pattern? Extension: The penguin show starts 18 minutes later and runs for 47 minutes. What time might it start and finish?

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6. Can you work out the different combinations of flavours Lucy and Spencer can make? Support: Spencer’s favourite flavours are vanilla, chocolate and strawberry. How many combinations can he make with these flavours? Extension: Once you have worked out all of the combinations for 10 flavours, can you work out the combinations for 20 different flavours more easily? 7. How long do you think it will take Spencer to get to the front of the queue? Support: If each person takes thirty seconds and there are 4 toilets, how long will it take? Extension: How long will it take if each person takes a different length of time and the difference between the longest and the shortest time is 2 and a half minutes? 27

Teacher notes

At the Zoo

Support & Extension Questions

8. How many elephants and rhinos might there be? Support: If there are 30 animals altogether, how many elephants and how many rhinos are there? Extension: There are even more elephants and rhinos in the next enclosure. How many altogether are there now?

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9. If each mummy turtle has the same number of babies, how many mums and how many babies are there? Support: If there are 24 turtles altogether and 4 mums, how many babies do they each have? Extension: How will you know when you have found every possible answer? What if there are 60 turtles?

10. Spencer and his family have been at the zoo for 7 ¾ hours. What time might they have arrived and what time might they have left? Support: If they arrived on the hour and had lunch exactly 2.5 hours later, what time might they have arrived and what time might they have stopped for lunch? Extension: Can you make a timetable of the day? What might it look like?

Answers

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Discussion (after) Page 26 My sister said she could count 68 feet? How many zebras and how many kangaroos might there be? E.g. 16 zebras and 2 kangaroos, 15 zebras and 4 kangaroos, 10 zebras and 14 kangaroos

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Activity Pages Zoo Enclosures Page 32 E.g. 10 square enclosures and 12 triangular enclosures, 7 square enclosures and 16 triangular enclosures Shopping Questions Page 33 •What is the total cost of the sandwich and the ice-cream? •What is the price of two packets of chips? •What is the cost of a pie, chips and icy-pole? •What is the cost of a sandwich and a fruit salad? •How much change would I get from $5 if I bought a chocolate bar? •How much change would I get from $20 if I bought a fruit salad?

section three: at the zoo

A maths story: at the zoo

Read the story At the Zoo and solve the problems along the way.

We arrived at the zoo just as it was opening. I could see that Dad was trying to work out the entry fee as he took his wallet out.

Admission Admission 1 Adult Admission 1 Adult Admission 1 Adult 1 Adult

Zoo Zoo Zoo Zoo

“Spencer, let’s go!” Dad and Lucy were already in the car and Mum was shooing me out the door. After weeks of rain, the sun was shining and we were finally heading out for our day at the zoo.

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Dad finished paying and turned to Lucy and I and asked, “Where would you two like to go first?” We looked at the map and decided to head left and see the kangaroos and emus first. As we approached their enclosure Dad told me that he could see thirty-six feet under the fence.

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1. If it costs the family $48 to enter the zoo, what might the cost be for each ticket?

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2. How many emus and kangaroos might be behind the fence?

o c . ch e Next stop was the butterfly enclosure. “Look r e o at this one Spencer!” said Lucy excitedly. r st super The butterflies were Lucy’s favourite. As we walked through the entrance we could see a zoo keeper doing a talk and as he spoke a bunch of butterflies, and even some little birds, landed on him. I could count fortytwo wings!

3. Can you work out how many butterflies and how many birds landed on the zoo keeper?

section three: at the zoo

“I’m hungry!” I announced about halfway round the zoo. “Must be lunchtime!” said Mum. We went straight to the café. Dad gave us $10 each to spend. There were quite a few things to choose from.

4. What could Spencer and Lucy buy with their $10? How much change would they each receive?

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5. What time might the show start and finish?

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After lunch we decided to go and see a show. We had a look at the timetable and there was a ‘Birds of Prey’ show starting in just ten minutes. It only went for twenty minutes.

© ReadyEdPubl i cat i ons After the show, Lucy said she was still Can you work many different ortor e i ew u6. r p o se sout ohow nl y • hungry! So• we f headed thev kiosk for p combinations of flavours Lucy and

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Once we had finished our ice creams we checked the map to figure out which animals we hadn’t seen yet. All of a sudden I really needed to go to the toilet. Dad and I found the nearest toilet block quickly but there were fifteen people in the queue already! 30

Spencer can make?

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an ice-cream. They had a huge ice cream selection. They had more than ten different flavours - and you could order up to three scoops!

7. How long do you think it will take Spencer to get to the front of the queue?

section three: at the zoo

Mum and Lucy were waiting impatiently when we finally got out. We headed off in the direction of the elephants and rhinos. These were some of my favourite animals at the zoo. They were just so huge - and I really liked their tusks and horns. Between all the elephants and rhinos I could count 36 horns and tusks.

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We did it! We saw almost every animal in the zoo! On the way out we just had to pop into the reptile enclosure. There was one tank with some big turtles and heaps of baby turtles! They were so small. “Oh it’s mummies and their babies!” cried Lucy. There were fortyeight turtles altogether.

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Elephants & Rhinos

8. How many elephants and rhinos might there be?

9. If each mummy turtle has the same number of babies, how many mums and how many babies are there?

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Home time! I was exhausted but it had been so much fun. And I was pretty happy with my zoo animals book that I bought at the gift shop on the way out.

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10. Spencer and his family have been at the zoo for 7 3/4 hours. What time might they have arrived and what time might they have left?

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What a great day! But now I have to go home and do my Maths homework. Ugh! Could you think of anything worse? 31

section three: at the zoo

Activity 1 - Zoo Enclosures The zoo is made up of lots of different enclosures for the many different animals. At the zoo the enclosures are in the shapes of squares or triangles. If there are 76 sides altogether, how many enclosures might there be of each shape? Find two different answers and show your working out for each.

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Solution 1:

adyEdPubl i cat i ons Solution 2:© Re

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Extension: What if there were hexagon shaped enclosures as well? What if there were 90 sides altogether? Show your working out.

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section three: at the zoo

Activity 2 - Shopping Questions Spencer and Lucy have so many things to choose from at the zoo’s kiosk. Have a look at all the different items that they can purchase and then see if you can solve the problems.

Zoo Kiosk

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hot chips $3.75

pie $4.10

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or eBo st r e p ok u ice-cream $4.40 S icy pole $3.50 chocolate bar $1.95 fruit salad $6.80 drum stick $3.80

ReadyEdP ubl i cat i o s sushi© $3.40 sandwich $4.50 rolln $4.85

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What might the questions be, if the answers are:

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1. _____________________________________________________

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$8.90

2. _____________________________________________________

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$6.80

3. _____________________________________________________

$11.35

5. _____________________________________________________

$3.05

6. _____________________________________________________

$13.20

$11.30

Extension: Write your own question and then give the answer to a friend to see if they can work out what the question is. 33

section three: at the zoo

Activity 3 - Zoo Timetable There are many things that you can see and do each day at the zoo. Create a timetable of shows and activities that you can do when visiting a zoo to help people plan their day.

Time

Activity

or eBo st r e p ok u S Feeding the wombats (15 mins)

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E.g. 2.30pm

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o c . che e r o r st supe r Answer these questions based on your timetable.

1. Would a visitor have time to do and see everything in one day? ___________________________________________________________ 2. How long would it take a person to do and see everything on the timetable? ___________________________________________________________ 3. Pick four activities from the timetable that you would like to do. On a separate piece of paper, create your own timetable for your day at the zoo spanning the time that you arrive until the time that you leave. 34

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or eBo st r e p o u k Section Four: S

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The Check-Up

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Teacher notes

The check-up

v8.1 curriculum FOCUS

Number and Algebra

Measurement and Geometry

Statistics and Probability

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

Interpret and compare data displays (ACMSP070)

Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

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Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

Year 4:

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084) Convert between units of time (ACMMG085)

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Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096)

Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

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Discussion (before):

Discussion (after):

When was the last time that you went to the medical centre? Do you ever go to the medical centre for a check-up? What is a check-up? What kinds of things does the doctor check? What does the doctor do to make you feel better? Do you know your height?

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Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

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Explore and describe number patterns resulting from performing multiplication (ACMNA081)

How tall were you when you were born?

What might your height have been each year from birth until now?

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How much taller do you think you will grow? Make a list of places where you might see numbers in palindromes (time, money, etc.).

Give some examples of numbers that are palindromes. Work out the sum of all the ages of the people in your family. Give the answer to someone as a problem to solve. Can they work out the individual ages? Create a doctor’s schedule. What might his/her daily timetable look like?

Teacher notes

The check-up

Support & Extension Questions

1. How long might it take Louise to finish her course of tablets? Support: If there are 24 tablets altogether, how long will it take Louise to finish the course? Extension: How many tablets would Louise have taken in total in a week? What about in a fortnight? A month?

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2. What time might it be? Support: If both hands are pointing to the number 9, what time is it? Use a clock to help you. Extension: Are both hands on a clock ever together but not pointing to a number? If so, what time could it be? 3. How many patients do you think the doctor can see in one day? Support: If each patient takes 15 minutes, how many could the doctor see in 2 hours? Extension: The last 10 patients each took 1.5 minutes longer than the person before them. How long did the 10 patients take altogether?

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Extension: Can you convert all your measurements to millimetres? Can you convert them to anything else? 5. How much might Louise weigh? Support: What if the numbers were in a twos pattern? Extension: How many different patterns can you find?

. te o c 6. How many steps do you think you would take in a day? . chesteps do you think you wouldr e Support: How many take while walking from o t r s su r your classroom to the front of your school? pe Extension: Now can you work out how many steps you would take in a week? What about in a month?

7. How many letters might be on the chart altogether? Support: How many letters would there be, if there was one letter in the top row and there were 6 rows? Extension: What if each line had 2 more letters than the line before it? What about 3 more letters?

Teacher notes

The check-up

Support & Extension Questions

8. What might the numbers be? Support: Which numbers look the same backwards? Make as many 4 digit number combinations using these numbers as you can. Extension: How many different numbers can you use? How many combinations can you make?

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9. What might the graph have looked like? Support: What might it have looked like if the doctor had recorded 5 different measurements? Extension: Can you show what it might have looked like on three different kinds of graphs?

10. How old might each member of the family be? Support: If Louise’s Mum and Dad’s ages add up to 63, what might Louise and her sister’s ages be? Extension: If each person’s age is different, can you work out how old they all might be in years and months exactly?

Activity Pages Measuring Liquids Page 42 E.g. 250 ml cup = 12 cups, 200 ml = 15 cups, 100 ml = 30 cups

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Measuring Liquids 2 Page 43

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Instructions

How many pills should you take over the period of a month? (Show working out.)

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1 pill on the first day, 2 on the second day and 165 3 the next day. Repeat.

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3 a day and 1 every second night.

105

2 in the morning, 3 at lunchtime and 2 at night every second day.

105

3 every second day and 2 every third day.

1 a day and 4 every third day.

section four: the check-up

A maths story: The check-up

Read the story The Check-Up and solve the problems along the way.

I really like my doctor. He always gives me a jellybean before I leave. Even though I am only going for a check-up today, I am hoping that he will still give me a jellybean. The last time I went to see the doctor was in winter when I got the flu. The doctor gave me tablets to make me better faster. I had to take three tablets a day - two in the morning and one at night.

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1. How long might it take Louise to finish her course of tablets?

Three tablets a day

Two tablets in the morning

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MEDICINE

Instructions for Louise:

One tablet at night.

Thankfully I am not sick this time. I am just going for my yearly check-up. We waited in the waiting room for a while. I looked up to check the time and noticed that both hands on the clock were pointing to the same number.

2. What time might it be?

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I wondered how much longer it would be until it was our turn. I looked around at all the people in the waiting room and thought at this rate, the doctor would be here until midnight!

Waiting Room

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3. How many patients do you think the doctor can see in one day?

“How much longer?”

section four: the check-up

The lady behind the desk finally called my name. “You can go through now,” she said, smiling. “Hi Louise,” said Dr. Thomas. “You look much better than you did the last time that I saw you.” The first thing he wanted to do was check how much I’d grown. I stood against the wall while he used the measuring tape to check my height. “Wow Louise! You have grown 7.5 centimetres since your last check up!” he said.

or eBo st r e p ok u S 5. How much might Louise weigh?

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Next the doctor checked my weight. The doctor’s scales were digital, not like the ones that we have at home. I noticed that when I hopped on them, the numbers that came up on the scales were in a pattern.

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4. What was Louise’s height before, and what is it now?

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6. How many steps do you think you would take in a day?

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Louise?” I told him I was, but at school my friends and I are starting to play soccer. Dr. Thomas thought it was great that I was getting a lot of exercise. I guess I did get a lot of exercise. I wondered how many steps I would take in a day.

o c . che e r o r st sup e Dr. Thomas wanted to check my eyes next. I had tor cover one eye and then read the letters off the chart on the wall. Each line had one more letter than the one before it. 7. How many letters might be on the chart altogether?

section four: the check-up

While Dr. Thomas made notes on his computer I glanced in the mirror next to the eye chart. I could see the end of the doctor’s phone number from a sign behind me. I noticed that the number didn’t look any different with or without the mirror.

8. What might the number be?

or eBo st r e p ok u S “I have grown

9. What might the graph have looked like?

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Before we left, he handed me a graph of my height. It showed my growth since I was born. It seemed that there was a period of time, when I didn’t grow at all and then a period of time when I grew heaps!

heaps.”

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On the way home in the car Dad studied the graph. “You know you are quite tall for your age Louise,” he said. I wondered how tall I was supposed to be for my age. I thought about the ages and heights of everyone in my family. I didn’t know everyone’s heights but I did know that when you add all four of our ages together you get 88.

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10. How old might each member of the family be?

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“Well done!” said Dad. “Next week it’s the dentist!” Oh great. I popped my jellybean in my mouth. My dentist does not give me jellybeans. But maybe she’ll give me a sticker….

section four: the check-up

Activity 1 - Measuring Liquids 1 My doctor asked me to drink 3 litres of liquid that he gave to me the day before my appointment. How many cups will it take until I have drunk it all?

Cup Size

r oe.g. e 12B cups st r e oo p k Su

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e.g. 250 ml

How Many Cups?

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Choose a container and a cup that don’t have any measurements on them. Estimate how many cups it will take to fill the container. Then measure to find out the actual amount.

Estimate:

_ ______________________

Actual amount:

_ ______________________

section four: the check-up

Activity 2 - Measuring Liquids 2 Sometimes when we are unwell we have to take medication to get better. Can you work out how many pills you would have to take in a month using the information below? Instructions

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3 a day and 1 every second night.

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1 pill on the first day, 2 on the second day and 3 the next day. Repeat.

How many pills should you take over the period of a month? (Show working out.)

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2 in the morning, 3 at lunchtime and 2 at night every second day.

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1 a day and 4 every third day.

Create a pattern similar to the one above, and see if a friend can solve it. 43

section four: the check-up

Activity 3 - An Apple A Day An apple a day keeps the doctor away! Do you know how long the peel of one apple might be? How could you work this out? Using a piece of paper, see if you can come up with an estimate.

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Draw or describe how you arrived at your estimate.

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Your estimate:____________________________________________________

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o c . che e r o t r Explain why you think your estimate isp going tos be the closest. su er

Find a partner and record his/her estimate:____________________________ What’s the difference between your estimates?_________________________

_______________________________________________________________ _______________________________________________________________ Try and peel an apple in one so you end up with one big long peel (your teacher might do this for the whole class). How long is it?_ __________________________________________________ How close is your estimate? _ _______________________________________ 44

Go Crushers!

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or eBo st r e p ok u Section Five: S

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Teacher notes

GO crushers!

v8.1 curriculum FOCUS

Number and Algebra

Measurement and Geometry

Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

or eBo st r e p ok u S

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)

Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060)

Year 4:

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

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Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080) Explore and describe number patterns resulting from performing multiplication (ACMNA081)

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Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

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Discussion (before):

Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

o c . che e r o r st super

Do you or anyone who you know play basketball? Have you ever been to a basketball game? What was the score of the last game that you went to/played? Have you been to a stadium to watch a basketball game? Have you been to a stadium of any kind to watch any sport? How are the seats in a stadium arranged? Do you have a sports jersey? What team is it for? Do you have a number on the back?

Discussion (after):

Convert between units of time (ACMMG085)

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Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

Make a record of all the sports jersey numbers that your classmates have. Select two of the numbers and use them to make a pattern. John has 6 different jerseys all with different numbers on and when added together they make 150. What might the numbers be? (See answers on page 48.) The difference between the highest and lowest numbers on the jerseys is 37. What might the two numbers be? What might the other numbers be? Halfway through a basketball game, the scores actually match the time on the clock. What could this look like? (See answers on page 48.) Is there a chance that the score could be double the time? What would this look like? (See answers on page 48.)

Teacher notes

GO crushers!

Support & Extension Questions

1. Can you help Miranda work out how many seats there might be in the whole stadium? Support: If there are 48 seats in one section, how might they be arranged? Can you draw this? Extension: What is the least amount of seats there could be? What is the greatest amount of seats there could be?

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2. How many points might the Crushers have scored in each half? Support: If they scored 30 points in the first-half, how many might they have scored in the second-half? Extension: How many 1 point shots and how many 3 point shots might have been scored? 3. What might the pattern look like? Support: What if the numbers were increasing by 5s? Extension: What if it was a pattern using 2 different operations, e.g. + 5 – 2?

4. Can you figure out what the numbers might be? Support: If there are only 2 people, and their numbers add together to make 40, what might their two numbers be? Extension: If there are 6 people and they all have different numbers, how many different solutions can you find?

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5. How tall might each player be? Support: The difference between the two players’ heights is 9 centimetres. What might each of their heights be? Extension: The average height of the players in the other team is 1.54 centimetres. What might their individual heights be?

o c . 6. How many points might they each have scored? che e might each of the r o Support: If one player r scored 7 points, how many points st super others have scored? Extension: If 2 players scored the same amount, what might the third player have scored? Can you find the answers? Is there a pattern? 7. Miranda has $50. What can she buy and how much change will she get? Support: Miranda buys a poster for $9.85. Draw the money she might have paid with. Extension: Miranda has brought some of her own money from home. She now has $100. She buys three items. How might she have spent her money and how much money might she have left? 47

Teacher notes

GO crushers!

Support & Extension Questions

8. How many people do you think they can feed with 24 pizzas? Support: If 6 people score 2 pizzas, how many slices might they each get? Extension: What is the maximum and minimum amount of people that can be fed with 24 pizzas? Explain your answer.

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9. What might the scoreboard look like? Support: Did you find a pattern? What if the difference is 29 points? Extension: If the Rockets are on 36 points, what are the Crushers on?

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Answers

Discussion (after) Page 46 John has 6 different jerseys all with different numbers on and when added together they make 150. What might the numbers be? E.g. 20, 30, 28, 22, 18, 32 or 1, 33, 36, 45, 15, 20 Halfway through a basketball game, the scores actually match the time on the clock. What could this look like? E.g. Crushers – 12 Rockets – 20 Time: 12:20 Is there a chance that the score could be double the time? What would this look like? Crushers – 20 Rockets – 46 Time: 10: 23

Sharing Pizzas Page 53

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10. What might be the time on the clock? Support: How many different times could be made if the pattern increases by 2s or 5s? Extension: How many different times could there be? Have you included 24 hour times?

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Activity Pages Basketball Scores Page 52 Crushers 34 27 52 4 or 54 24 or 62 48 66 59 107 or 35 179 or 67

How many How many slices of pizza people each? to feed? 4 3/4 of a pizza each (3/12 slices or 6/24 slices) 6 2/3 of a pizza each ( 2/12 slices or 4/24 slices) 10 1/2 pizza each – 1/10 slices or 3/30 slices) 4 1 and a half pizzas each (3/12 slices or 6/24 slices) 12 2/3 of a pizza each (2/24 slices or 4/48 slices) 15 2/3 of a pizza each (2/30 slices or 4/60 slices) 50 2/5 of a pizza each (2/100 slices or 4/200 slices)

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How many pizzas?

Rockets 17 41 or 13 18 29 43 23/73 38 32 or 86 71 123

10 20

Difference 17 14 34 25 19 25 28 27 36 56

section five: go crushers!

A maths story: go crushers! We were on our way to see the Coledale Crushers pump the Randwell Rockets. Mum was taking my best friend Jack and I to watch our local basketball team - the Crushers!

1. Can you help Miranda work out how many seats there might be in the whole stadium?

There are more than 50 but less than 100 seats in each section.

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As we walked in, we scanned the aisles for our seats. It wasn’t a huge stadium yet there seemed to be a lot of seats packed in. They were in four sections (two on each side of the court) and each one was in a perfect array. I was trying to work out how many seats were in each section. I estimated that there were more than 50 but less than 100 seats.

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Read the story Go Crushers! and solve the problems along the way.

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As the game was just about to start I thought back to the last Crushers game. It had been a slow start but a dramatic finish. They finished on 64 points!

The whistle blew and the Crushers had the ball! They were off to a great start! Within 10 minutes they were 8 points ahead and the Rockets called a time out. While the Crushers were huddled together I noticed that the people sitting in the front row across the court were all wearing team jerseys and their numbers made a pattern.

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3. What might the pattern look like?

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4. Can you figure out what the numbers might be?

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The game started again 5. How tall might each player be? and the Rockets came back looking like they meant business! Within 30 seconds they scored. The player that shot for goal looked like she could almost reach the ring while standing! She was easily the tallest player out there! I remember reading that the average height of the Crushers team was 1.76m.

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6. How many points might they each have scored?

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Mum had said that I could buy something from the merchandise stand. Even though we were starving we headed there first before everything sold out. I couldn’t decide what to buy.

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By half-time we were up by just 2 points! During that half, 22 of the points had been scored by just 3 of the players.

7. Miranda has $50. What can she buy and how much change will she get?

1.76 metres

The teams were still huddled together. Now I was looking at the people in the front row on our side. When I added the numbers on their jumpers together it made exactly 200!

section five: go crushers!

8. How many people do you think they can feed with 24 pizzas?

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We got back to our seats just as the whistle went for the start of the second-half. The game was so close and everyone was on the edge of their seats. Half-way through the secondhalf another time out was called, this time by the Crushers. The Crushers were now down by 14 points!

9. What might the scoreboard look like?

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Once we had purchased our merchandise we joined the line for the canteen. There was a long line and I wondered how much food would be left by the time we got to the front of the queue. I was reading the board trying to decide what to buy when I overheard a conversation from the kitchen. “I don’t think we have enough pizza!” “How many pizzas do we have left?” “24.” 24 sounded like a lot of pizzas to me! I wondered how big they were and how many slices they were cut into.

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Goals

Points

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10. What might be the time on the clock?

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The players were still huddled. I was fidgeting in my seat waiting for the game to start again! I looked up at the scoreboard to check how long was left and noticed the time was making a pattern.

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Goals

o c . che e r o st Down to the last 5 minutes and it r was back to ae 2 point difference. s r u p As I watched the clock continue to count down, the Crushers ran the length of the court for another goal. They scored a second quickly and easily. Scores were even! One minute to go. The ball went out. It was a Crusher’s throw in. Thirty second to go. Two players passed the ball back and forth struggling to find a space to get through. Ten seconds to go. One player saw her move, took off down the court and scored! The stadium went crazy! Another heart-stopper! Our next game would be against the Jamestown Jets who are currently unbeaten! What do you think our chances are of winning that game?

“Go Crushers!”

section five: go crushers!

Activity 1 - Basketball Scores Take a look at the basketball scores in the table below. Can you complete the table and work out the difference between the scores?

Crushers

Rockets

Difference

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18 29

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Play some ‘basketball’ games with a partner. Each person rolls a 20 sided dice. Record each person’s score and work out the difference between the two. 52

section five: go crushers!

Activity 2 - Sharing Pizzas How many slices of pizza can you eat? How many pizzas do you think you need to feed a group of people? From the information below can you work out how many slices of pizza each person will receive? Show your working out.

How many pizzas?

How many slices of pizza each?

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How many people to feed?

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section five: go crushers!

Activity 3 - Fun With Heights There are many different Maths problems that you can create to do with height. 1. Measure your height. How tall are you?

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2. How tall is the average basketball player?

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or eBo st r e p ok u S from the shortest to the tallest (your teacher could time In class, line up in order you to see how long this takes).

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3. What is the difference between this height and your height? ___________________________

4. What is the difference in centimetres between the shortest person and the tallest person in your class? ___________________________ 5. Where is your place in this line?

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6. Who is stood right in the middle of this line? ___________________________

7. How tall is she/he? 8.

and the height of the tallest person in your class? ___________________________

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9. What is the difference between your height and the height of the shortest person in your class? ___________________________

. tmeasurements for the shortest person and the tallest o person in 10. Find out the e c . the world. che e r o r st s shortest: r ___________________________ upe

tallest:

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11. What is the difference between these two heights?

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12. How much taller are you than the world’s shortest person?

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13. How much shorter are you than the world’s tallest person?

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or eBo st r e p ok u Section Six: S

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The Sleepover

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Teacher notes

the sleepover

v8.1 curriculum FOCUS

Number and Algebra

Measurement and Geometry

Year 3:

Year 4:

Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

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Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) Explore and describe number patterns resulting from performing multiplication (ACMNA081) Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

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Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060)

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)

Compare objects using familiar metric units of area and volume (ACMMG290)

Who has been to a sleepover or had people over for a sleepover at their house?

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Pair up and work out how many days between you and your partner’s birthdays. How did you work this out? Can you work out how many days there are between your birthday and the birthday of someone in your family? I have 4 pizzas, can I share them evenly between 5 people? 6 people? 8 people? How? (See answers on page 58.) If I only had 5 hours sleep, how long would it take me to catch up on the sleep I’ve missed? If August starts on a Wednesday, what day of the week would the 19th be? If September 13th is a Thursday what day of the week does September start on? Is there a pattern? (See answers on page 58.) Create your own question for a friend to try and answer.

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Was this sleepover with friends or was it with family? Why did you have a sleepover? Was it for a birthday? What kinds of things do you do at a sleepover? Where does everyone sleep? What are some things you need to organise for a sleepover? What Maths is involved in organising a sleepover?

Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

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Discussion (before):

Convert between units of time (ACMMG085)

Teacher notes

the sleepover

Support & Extension Questions

1. How many movies might this be? You will need to think about how long each movie might run for. Support: If there are 6 movies, how long might each run for? Extension: Each movie runs for a different length of time. The difference between the longest movie and the shortest movie is 56 minutes. How long might each movie run for?

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2. How many pizzas do you think will be needed to feed everyone? How many slices will each person receive? Support: If they had 2 pizzas, how many pieces would they each receive? What about with 4 pizzas? Extension: If there were 6 pizzas how many different ways could they cut them and how many slices would they each get? What fraction of the pizza might that be? 3. What might Tim and Liam’s scores be? Support: If Liam’s score is 8, what is Tim’s score? What if Liam’s score is 14? Extension: What if Tim quadruples Liam’s score?

4. What might these towers look like? Support: Draw what the towers might look like if there are 6 towers and each tower has 2 more blocks than the one before it. Extension: How many blocks do you think have been used altogether?

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5. How many combinations will Jake and Noah have to try to crack the code? Support: If the next number is a 2, how many different numbers could there be to try? Extension: How many different numbers are there? What if Jake and Noah don’t know the first number? How many different combinations are there then?

o c . 6. When might Liamc and Noah’s birthdays be? e h r e o Support: If Liam’s birthday is on March 12th, what date do you think Noah’s t r s s r u e p birthday will be on?

Extension: Is there a pattern? Would the pattern be the same for each month? Explain. 7. How many sleeping bags could fit in the spare room? Support: Can they fit 5 in there? Draw some different ways that they might be able to arrange them. Extension: What are the measurements of a sleeping bag? What is the maximum amount of sleeping bags that they could fit in the room, and how many different ways could they arrange these? 57

Teacher notes

the sleepover

Support & Extension Questions

8. How many different combinations of ice cream, toppings and lollies could the children make? Support: How many different combinations could they make with just 4 flavours of ice cream and 3 different toppings? Extension: How many different combinations could they make if there were 3 bowls of lollies? What about 4 or 5 bowls? Is there a pattern?

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9. How many hours sleep might each child have had? Support: If Noah and Jake had 7 hours sleep between them, how much sleep might the rest of the children have had? Extension: Can you work out exactly how many hours and minutes sleep the children all had?

10. How many pancakes might need to be in the stack and how tall would it be? Support: Draw what the stack would look like if the children each had three pancakes. Extension: If the children all had a different amount of pancakes. How many pancakes were in the stack? Give three possibilities.

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Scoring Patterns

Points Earned

5 points a minute

After 10 mins: 50

After 35 min: 175 After 1 hour: 300 1 point the first minute, 2 the second, 3 the third etc…. up to 10 points in the tenth minute. Then the pattern repeats.

After 10 mins: 55

10 points the first minute, minus 8 points the second minute then add 4 points the next minute. Repeat the pattern.

After 10 mins: 28

After 35 min: 180

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If August starts on a Wednesday, what day of the week would the 19th be? If September 13th is a Thursday what day of the week does September start on? Is there a pattern? The 19th would be a Sunday. If September the 13th was a Thursday then the 1st of September would be a Saturday.

Activity Pages Game Scores Page 62

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Discussion (after) Page 56 I have 4 pizzas, can I share them evenly between 5 people? 6 people? 8 people? How? 5 people might each get 8 equal sized pieces each, 6 people might get 2 large slices each, 8 people might get ½ a pizza each.

After 1 hour: 330 After 35 min: 66

After 1 hour: 120

Code Breaker Page 63 If you can solve this you are a clever code breaker! A = C, B = D, C = E, etc… (2 letters on) Sleep Times Page 64 Fell Asleep

Woke Up

10.30pm 10.10pm 9.35pm 11.20am 11.27am 11.23pm 12.15am

6.55am 5.50am 4.50am 6.15am 6.45am 5.17am 7.04am

Time Asleep How Much More Sleep Needed? 8 hrs 25 mins None 7 hrs 40 mins 20 mins 7 hrs 15 mins 45 mins 6 hrs 55 mins 1hr 5 mins 7 hrs 18 mins 42 mins 5 hrs 45 mins 2 hr 6 mins 6 hrs 49 mins 1 hr 11 mins

section six: the sleepover

A maths story: The Sleepover

Read the story The Sleepover and solve the problems along the way.

“Hi Jake!” Noah was the first to arrive. Liam’s Mum was dropping the others off in about an hour. I had asked Mum and Dad ages ago if I could have my friends over for a sleepover and they agreed as long as we had it on the school holidays. The five of us were going to have so much fun!

“Hi Jake!”

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As soon as the others arrived we went through the movies that I had hired earlier and started planning a movie marathon. We had about 7 hours of movies to watch!

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1. How many movies might this be? You will need to think about how long each movie might run for.

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2. How many pizzas do you think are needed to feed everyone? How many slices will each person receive?

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ordered enough because we were all starving!

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There was going to be about a 45 3. What might Tim and Liam’s scores be? minute wait for the pizzas, so we headed into the spare room to play video games while we waited. Liam and Tim started playing first. Half way through their game, Tim had already tripled Liam’s score. 59

section six: the sleepover

While Tim and Liam continued to battle it out, Kane was playing around in a pile of Lego. He had created a series of towers. Not only was there a coloured pattern in the towers but the heights of the towers were in a pattern too.

4. What might these towers look like?

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While waiting for our turn, Noah and I found my sister’s diary down the side of the couch. It had one of those locks on it where you had to work out the four digit passcode. I had tried watching when she put it in, and I knew that it started with a four.

Before we cracked the code, it was our turn at the game. And before we finished our turn on the pizzas arrived! While scoffing the pizza we started talking about Liam’s birthday which was only two weeks away. We were going bowling for his birthday. Noah was trying to work out how long it was until his birthday. I knew that there is exactly 40 days between Liam and Noah’s birthdays.

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5. How many combinations will Jake and Noah have to try to crack the code?

6. When might Liam and Noah’s birthdays be?

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o c . che e r o We set up our sleeping bags r st super in the spare room to get ready for our movie marathon. Mum had been reluctant to let me have four friends stay over at one time because she didn’t think that 5 sleeping bags would fit in the spare room. The room was about 3 x 3 metres. I thought that was plenty of room!

7. How many sleeping bags could fit in the spare room?

section six: the sleepover

8. How many different combinations of ice cream, toppings and lollies could the children make?

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Before we got too comfy Mum came in to tell us dessert was ready! She had set up an ‘ice cream bar’ for us. It looked amazing! There were four different flavours of ice cream, three different flavoured toppings and a bunch of bowls with different lollies inside to put on top to decorate.

Liam was the first to fall asleep. He didn’t even make it through the first movie! Noah and I were the last ones up. In the morning we figured out that between the five of us we had slept for a total of 27 hours.

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Dad cooked up stacks of mouthwatering pancakes for breakfast. Again, we were all starving! I wondered how tall the stack would be if it had enough pancakes to feed all of us?

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9. How many hours sleep might each child have had?

o c . che e r o r st super 10. How many pancakes might need to be in the stack and how tall would it be?

“I bet that I can eat my height in pancakes before my Mum gets here!” exclaimed Liam. Well, he had about 40 minutes until his Mum was due to arrive. Do you think he can do it? 61

section six: the sleepover

Activity 1 - Game Scores Jake plays the same video game three times. Each time he plays, he applies a different scoring system. Look at the three scoring systems below. Which scoring system will award Jake with the most number of points?

Scoring Systems

Points Earned

After 10 minutes: o eBo t s r r e p o u After 35 minutes: k S After 1 hour:

Jake is awarded 1 point in the first minute, 2 points in the second minute, 3 points in the third minute, etc…. up to 10 points in the tenth minute. This pattern is repeated.

After 10 minutes:

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Jake is awarded 5 points a minute.

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Jake is awarded 10 points in the first minute, minus 8 points in the second minute, add 4 points the next minute. Repeat the pattern.

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After 10 minutes:

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After 1 hour:

o c . che After 1 hour: r e o r st super After 35 minutes:

Can you work out from the information above, how many points Jake will have after 1 hour and 45 minutes if applying each scoring system? Scoring system 1:__________________________________________________ Scoring system 2:__________________________________________________ Scoring system 3:__________________________________________________ 62

section six: the sleepover

Activity 2 - Code Breaker Can you crack the code?

Crack The Code Kh

aqs

engxgt

eqfg

uqnxg

vjku

aqs

dtgcmgt

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _! A =

ctg

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__ ___

r o e t s r e _ _ _p _ _ _ _ _ _ _ _ _B _o _o _ ___ k Su

ecp

H =

O =

E =

L =

S =

F =

M =

N =

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Can you create your own code? Can anyone crack your code?

section six: the sleepover

Activity 3 - Sleep Times The experts say you need to have 8 to 9 hours sleep a night otherwise you will be tired and lethargic during the day. Can you complete the table below and then work out how much more sleep you need to avoid being tired and lethargic during the day? Fell Asleep

10.10pm

5.50am

9.35pm

7 hrs 15 mins

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r o e t s Bo How Much More r e Woke Up Time Asleep p okSleep Needed? u 8 hrs 25 mins S

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6 hrs 55 mins

5.17am 6 hrs 49 mins

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6.15am

o c . che go to sleep?_ _________________________ e r 1. What time do you normally o t r s s r u e p 2. What time do you normally wake up?_____________________________ 3. How much sleep do you get a night?_ ____________________________ 4. How much sleep do you get in a week?_ __________________________ 5. How much sleep do you get in a month?__________________________

On the back of this sheet, draw the digital and analogue times for your answers to questions 1 and 2.