Solving Maths Problems for Years 5-6

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Title: Solving Maths Problems For Years 5 - 6 © 2016 Ready-Ed Publications Printed in Australia Author: Anita Green Illustrator: Alison Mutton

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Contents Teachers’ Notes Section One: School Camp v8.1 Curriculum Focus Support & Extension Questions A Maths Story - School Camp Activity 1 - Milkbar Buddies Activity 2 - Shopping Questions Activity 3 - Camp Timetable

Section Three: Moving Day v8.1 Curriculum Focus Support & Extension Questions A Maths Story - Moving Day Activity 1 - Box Creations Activity 2 - Bedroom Designs Activity 3 - Fraction Blocks

5 6 7-8 9-11 12 13 14 15 16 17-18 19-21 22 23 24

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Section Two: Athletics Carnival v8.1 Curriculum Focus Support & Extension Questions A Maths Story - Athletics Carnival Activity 1 - Long Jump Results Activity 2 - Long Jump Problems Activity 3 - Paper Planes

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Section Four: Footy Fever v8.1 Curriculum Focus Support & Extension Questions A Maths Story - Footy Fever Activity 1 - Footy Numbers Activity 2 - Footy Sale Activity 3 - Shopping Problem

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Section Five: Fun At The Beach v8.1 Curriculum Focus Support & Extension Questions A Maths Story - Fun At The Beach Activity 1 - Food Stall Activity 2 - Temperature Data Activity 3 - Bargain Shopping

Section Six: The Case Of The Missing Bear v8.1 Curriculum Focus Support & Extension Questions A Maths Story - The Case Of The Missing Bear Activity 1 - Veggie Patch Design Activity 2 - Veggie Fractions Activity 3 - Area And Perimeter

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

59-61 62 63 64

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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.

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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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School Camp

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

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Teacher notes

School Camp

v8.1 curriculum focus

Camp bus

Number and Algebra

Measurement and Geometry

Year 5: Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

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Solve problems involving multiplication of large numbers by oneor two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

Solve problems involving division by a one digit number, including those that result in a remainder(ACMNA101)

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Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Compare 12- and 24-hour time systems and convert between them (ACMMG110)

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Compare, order and represent decimals (ACMNA105) Create simple financial plans (ACMNA106)

Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division (ACMNA121) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

Year 6:

© ReadyEdPubl i cat i ons Connect decimal representations to the metric system (ACMMG135) •f orr evi ew pur pos esonl y• Convert between common metric

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

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Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

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Discussion (before):

Interpret and use timetables (ACMMG139)

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Have you ever been on a school camp? How long was it for?

How many have you been on?

Where have you been to?

What activities did you do while you were there?

What are the best things about school camps?

What are the worst things about school camps?

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units of length, mass and capacity (ACMMG136)

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Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

Discussion (after):

How many ways could you arrange 145 people into equal groups? (See answers on page 8.)

How might the beds be arranged at a school camp? How many rooms would there be and how many beds would there be in each room?

How many minutes is 1000 seconds?

How many seconds are in one day?

(See answers on page 8.)

What might the ratio be of girls to boys at a camp? How many does this mean there are of each gender?

Teacher notes

School Camp

Camp bus

Support & Extension Questions

1. How many buses will be needed and how many students will be on each bus?

Support: If there are 6 buses how many students will be on each bus?

Extension: What is the most and least amount of buses you think will be needed? Would every bus be full? How many students would be needed to fill all of the buses?

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2. It is 345 kilometres to camp. How long do you think it might take to get there?

Support: If they are travelling on average 80 kilometres per hour?

Extension: How fast would they need to go to get there in 3 and a half hours? Could they do it quicker?

3. How many different outfit combinations could Sam make with the shorts and t-shirts?

Support: What if he has 8 t-shirts?

Extension: What if he had 1/4 as many t-shirts to shorts? Or 3/4?

4. How many different outfit combinations can he make now?

Support: Can you draw a picture to help you?

Extension: What if there are 4 pairs of shoes? Or 6? Or 8?

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5. What might the temperature be for each day?

Support: What if the highest temperature is 28 degrees and the lowest is 21 degrees?

Extension: What if there is a range of 12 degrees?

6. Is it even possible for the students to be placed into 9 equal groups? What equal groups can they make?

Support: How many students will be in each group and how many will be left over?

Extension: If the students get into 6, 7 or 8 groups, how many students will be in each group? Can you see a pattern?

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7. Sam didn’t go right to the top but he did climb 1.45 metres higher than Jack.

How high might Sam and Jack have climbed?

Support: If Jack climbed 3.85 metres, how high did Sam climb?

Extension: How far away might Jack and Sam have been from the top?

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Teacher notes

School Camp

Camp bus

Support & Extension Questions

8. How long might it have taken Sam and Jack to complete the obstacle course?

Support: If Sam finishes the obstacle course in 5 minutes and 6 seconds what might Jack’s finishing time be?

Extension: Create an obstacle course in your school yard. Estimate how long it will take you to complete it and then try it. How close were you to your estimate?

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9. How many tables would be needed for 125 students plus teachers? How might these be arranged? Can you draw what the hall might have looked like?

Support: If there were 8 tables set up, then how many students will be sat at each table?

Extension: Is there any way that you can set the tables up so that all of the tables are full? If you do have one table not filled, how many more students would you need to fill this table? How many students would that be altogether?

10. If each cordial container holds 4 litres, what might the ratio of cordial to water be in each container? What do you think would be the perfect ratio?

Support: If the parts (cordial to water) are each 200ml what might the ratio be?

Extension: What is the perfect ratio? How much cordial and water is this?

Can you use this ratio to work out how much cordial and water is needed in 1 litre? What about in 1 cup?

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11. What might Liam, Sam and Jack’s scores have been and what might these cards have looked like?

Support: If Sam’s score was 67 and he had 9 cards what might the cards look like?

Extension: What is the highest score Sam could possibly have? What’s the lowest? What is the difference between the two scores? What if every card was different?

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Answers Discussion (after) Page 6 How many ways could you arrange 145 people into equal groups?

E.g. 2 groups – 70 in each; 4 groups 35 in each; 7 groups – 20 in each.

How many minutes is 100 seconds? How many seconds are in one day?

16 minutes, 86,400 seconds

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section 1: School Camp

A maths STORY school camp

Read the story School Camp and solve the problems along the way.

“Ok, Mum, you can go now!”

“Sam, I’m not leaving until you get on that bus,” Mum said firmly.

We added my bags to the luggage pile and I went and stood with the other 125 excited campers.

Camp bus

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1. How many buses will be needed and how many students will be on each bus?

Finally the luggage was packed onto the buses and it was time to leave. “Bye Mum!” I yelled as I ran to get on the bus with my friends. I sat by the window facing Mum just as she had asked. I swear she was probably still standing there waving when we were half way to camp.

2. It is 345 kilometres to camp. How long do you think it might take to get there?

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When we arrived we had to quickly find our cabins and unpack. Mum had done most of my packing. This hadn’t been a good idea. She had packed me less than half as many t-shirts as shorts!

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© ReadyEdPubl i cat i ons 345kms •f orr evi ew pur posesonl y• School Camp

3. How many different outfit combinations can Sam make with the shorts and t-shirts?

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I dug deeper and found just three pairs of shoes.

4. How many different outfit combinations can he now make?

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section 1: School Camp

After unpacking we congregated in the courtyard. Outside there was a blue sky! The average temperature for the next five days at camp, according to the forecast, was going to be 25 degrees.

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You will be placed into 9 equal groups.

The teachers announced that we were going to be doing our first two activities that afternoon. I was really hoping that I would get to do the Giant Swing! The teachers explained to us that we would be placed into 9 equal groups.

6. Is it even possible for the students to be split into 9 equal groups? What equal groups could be made?

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5. What might the temperature be for each day?

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© ReadyE7. dSam Pdidn’t ubgol i c a t i o ns right to the top, but he did climb 1.45 metres higher than Jack. How •f orr evi ew phigh ur poSam se sJack on l y • might and have climbed?

Dan and I were in the same cabin and we were in the same activity group! Our first activity was….. the Giant Swing! I was determined to reach the top!

o c . che e r o Our first activity on the second dayr st super was the obstacle course. I was tired from a lack of sleep the night before.

I don’t know how many times I tripped over things during the obstacle course. It seemed to take forever! Jack ended up finishing the course 132 seconds quicker than me.

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8. How long might it have taken Sam and Jack to complete the obstacle course?

section 1: School Camp

Lunch time! My group were on lunch duty. This meant that we had to set up all the tables in the lunch hall.

9. How many tables would be needed for 125 students plus teachers? How might these be arranged? Can you draw what the hall might have looked like?

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10. If each cordial container holds 4 litres, what might the ratio of cordial to water be in each container? What do you think would be the perfect ratio?

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The next lunch duty task was to make up containers of cordial by diluting the cordial with water. When I got there two containers of cordial had already been made up. One was really light in colour so I could tell that it was too weak. The other looked darker and when I tasted it, it was way too strong!

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11. What might Liam, Sam and Jack’s scores have been and what might their cards have looked like?

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On the last night we were given some free time. My cabin all sat around a table playing a game of Uno. Liam won the first game! Jack and I still had a handful of cards.

We counted up O our scores and the NUNO U difference between our scores was 37 points.

As the bus pulled up out the front of the school I saw mum standing there and wondered what the chances were that she had been standing there since I left!

I missed you so much!

“I missed you so much!” cried Mum. I had only been gone for 56 hours! I think?! Camp was so much fun but I definitely needed to catch up on some sleep!

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section 1: School Camp

Activity 1 - Milkbar Buddies

Camp bus

Next door to the camp was a milk bar that was owned by 4 friends. They each put in some money to buy the business together: Friend 1: 25% Friend 2: 30% Friend 3: 10%

or eBo t s r e How much do you think the milkbar cost? Estimate the cost and then work out p o how much each personu borrow.

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Friend 4: 15%

Friend 1

Friend 2

Friend 3

Friend 4

Loan

Eg. 20,000

5,000

6,000

2,000

3,000

4,000

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Cost Of Milkbar

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section 1: School Camp

Camp bus

Activity 2 - Shopping Questions

The students were allowed to visit the milkbar once while at camp and buy one item each. They discovered that 4 people worked at the milkbar: Person 1 – does the book keeping Person 2 – works behind the counter Person 3 – stacks the shelves

or eBo t s r e If the milkbar makes a profit each week of $620 how mucho do you think each p ushould receive as a wage? Show yourk person who works there working out below S and explain your answer.

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Person 4 – does all the orders and deliveries

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Extension: Work out how much each person should be getting paid per hour.

How much do you think they should be getting paid per hour for the jobs that they do?

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section 1: School Camp

Activity 3 - Camp Timetable

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A lot of organising goes into planning a camp. There needs to be a very structured timetable so that everyone knows what they need to do and where they need to be. Using the table below create a timetable for a first day at camp. What might it look like? What activities might happen on the first day?

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Note: Record all your times in 24 hour time.

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Extension: Continue your timetable and plan what the rest of the week would look like at camp!

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

Athletics Carnival

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Teacher notes

athletics carnival

v8.1 curriculum focus

Number and Algebra

Measurement and Geometry

Year 5: Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

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Solve problems involving multiplication of large numbers by oneor two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

Solve problems involving division by a one digit number, including those that result in a remainder(ACMNA101) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Recognise that the place value system can be extended beyond hundredths (ACMNA104) Compare, order and represent decimals (ACMNA105)

Year 6:

Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)

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Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

Connect decimal representations to the metric system (ACMMG135)

© ReadyEdPubl i cat i on s metric Convert between common units of length, mass and capacity (ACMMG136) •f orr evi ew pur pos esonl y•

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128) Multiply and divide decimals by powers of 10 (ACMNA130)

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Discussion (after):

Discussion (before):

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Does your school hold an annual athletics carnival?

Time how long it takes everyone in your class to run the 100 metres. Record the results and order them.

How else could you present this information?

Do you compete in a team at the school athletics carnival?

Imagine that your friend ran the 100 metres in 15.12 seconds and you ran it in 15.2 seconds. Your friend thinks her time is the quickest but you think your time is faster. Who is right? Can you explain why either you or your friend was incorrect and got confused?

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What events are held at an athletics carnival?

What is your favourite event at the school athletics carnival?

What is a PB? Do you have a PB? In what event?

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Interpret and use timetables (ACMMG139)

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Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

I asked Jack a question about the athletics day and his answer was 1.23 metres. What might my question have been? (See answers on page 18.)

If there are 5 people in a race, how many different combinations are there for finishing? Can you draw something to explain your thinking? (See answers on page 18.)

Teacher notes

athletics carnival

Support & Extension Questions

1. How many different combinations could there be for the order in which the students finish?

Support: What if there were just 4 people in the race? What if there were 5?

Extension: How many different combinations for 6, 7 or 8 people? Can you find a pattern?

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2. What might the students’ exact times have been?

Support: What if all the students’ exact times were to one decimal place?

What if they were to two decimal places?

Extension: Imagine that the times were so close that they were all between 13.4 and 13.5 seconds. What might the times be?

3. What might Ollie’s and the winner’s jumps have measured?

Support: If all Ollie’s jumps added together total 4 metres and 11 centimetres, what might each individual jump be? What is the difference between the best and worst jump?

Extension: What might the total of all three of Ollie’s jumps be? What might be the difference between his best and worst jump?

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4. Can you draw what you think Ollie’s map might look like?

Support: Make a path on your map to get from one event to another.

Describe your path to someone to see if he/she can follow it.

Extension: Write out a set of directions for someone to get from one place to another.

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5. What might Ollie’s timetable look like?

Support: Create a timetable which runs from 9am until 3pm. Include Ollie’s 8 events and two breaks to eat.

Extension: Create a full timetable of Ollie’s day in 24 hour time, from when he got up until he goes to bed.

6. What do you think the ratio of cordial to water might have been? What should the ratio be?

Support: If the ratio was 1:4 and there was 1 litre of cordial, how much cordial and how much water do you think has been used?

Extension: Could you test this out on a smaller scale? Chose three different ratios and test each out.

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Teacher notes

Support & Extension Questions

athletics carnival

7. What might the new record be?

Support: What is the new record? What was the old record? Can you do anything in 1/10 of a second?

Extension: What would it look like if it was one hundredth of a second? Or what if it was one thousandth of a second?

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8. What might the exact height be of each of Ollie’s jumps?

Support: What if two of the jumps were exactly 1.46 metres?

Extension: What if the difference between the best and worst jumps was 65 centimetres?

9. What might the winner’s distance have been?

Support: Can you explain why this a prime number?

Extension: How many prime numbers are there between 1 – 100?

10. How many students might be waiting at the high jump station?

Support: If there were 140 people, how many of them are at the high jump station?

Extension: What if there were 3/4 at the high jump station? Or 3/8?

Answers

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Discussion (after) Page 16 I asked Jack a question about the athletics day and his answer was 1.23m. What might my question have been?

E.g. Measurement for his high jump or long jump, difference between his worst and best jumps, how many metres in front the winner was?

If there are 10 people in a race how many different combinations are there for finishing?

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Activity Pages Long Jump Problems Page 23 What would the total length of Henry’s jumps be?

What is the difference between the shortest and longest jumps?

What is the greatest difference between one person’s jumps?

What is the total of everyone’s first jumps?

What is the total of Abbey’s jumps?

What is the difference between Nathan’s two jumps?

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section 2: Athletics Carnival

A maths STORY athletics carnival

Read the story Athletics Carnival and solve the problems along the way.

“On your marks, get set, GO!” My first race of the day and it was a 100 metre sprint. As we raced down the straight I heard someone shout my name, “Go, Ollie!” The runners were all so close. I could have reached out and touched the people running beside me.

Anybody could win this one.

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1. How many different combinations could there be for the order in which the students finish?

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I came a close second! The winner was a kid who I recognised from a year above me. The result was so close though. Our finishing times were all between 13 and 14 seconds.

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2. What might the students’ exact times have been?

o c . chThe ejumps. My first jump My next event was long jump. teachers record the best of r three e o r st su was 1.34 metres but my next two jumps were both better than this. I came second again. r e p The difference between mine and the winner’s jump was 12 centimetres.

3. What might Ollie and the winner’s jumps have measured?

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section 2: Athletics Carnival

I wasn’t sure when or where my next event was so I pulled out my timetable and map. The map was a bird’s eye view of our school oval.

It used a co-ordinate system and a key. It had seven areas marked out for the different events as well as the canteen.

4. Can you draw what you think Ollie’s map might look like?

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5. What might Ollie’s timetable look like?

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According to my timetable I had a bit of a break until my next event. I grabbed some food out of my bag and headed over to where I could see Charlotte and Sarah already sitting. I needed to keep up my energy. I still had 6 more events to go! Luckily I had a couple more breaks throughout the day.

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6. What do you think the ratio of cordial to water might have been? What should the ratio be?

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My next event was shot put. I had a little time until it started so I walked over to the drinks stand to grab a cup of cordial.

As I drank it I thought it tasted and looked more like water! I wondered how much cordial they had put in. At home I make my cordial pretty strong!

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As I was drinking, an announcement was made through the loud speakers. Someone had broken the school record for the 800 metres! It had been beaten by 1/10 of a second!

7. What might the new record be?

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The school record has been broken for the 800 metres!

section 2: Athletics Carnival

At the high jump station, they were between groups so a couple of people were doing some warm up jumps.

I headed over and joined the queue. I got about 5 good jumps in and jumped an average of 1.21metres.

8. What might the exact height be of each of Ollie’s jumps?

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9. What might the winner’s distance have been?

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Shot put had never been my best event. I was pretty happy with my throws but the winner threw a lot further than me! I can’t remember her exact distance but I know it was a prime number.

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sitting in groups around the oval. There were still some students who were finishing off their last events. About a quarter of them were lining up at the high jump station. They must have been running a little behind.

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High Jump Station

10. How many students might be waiting at the high jump station?

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© ReadyEdPubl i cat i ons f oover. rr e vi ew were pur posesonl y• The day was• nearly Most students

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I ended up with three ribbons by the end of the day. Back in the classroom I found that 3/4 of our class got at least one ribbon and 1/5 got a first! I thought that was pretty impressive. I couldn’t wait to go home and show my family the ribbons.

1 2 3 s n r t d d

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section 2: Athletics Carnival

Activity 1 - Long Jump Results Allow everyone in your class to have two turns each at long jump. Record measurements for every jump.

1. Think about how you can display the results. Make sure that you consider how to show students’ first and second jumps.

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2. Do a rough copy of your graph below.

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3. On a separate piece of paper complete your good copy.

4. What are two questions someone might have about your graph? ______________________________________________________________ _________________________________________________________________ ______________________________________________________________ _________________________________________________________________ 22

section 2: Athletics Carnival

Activity 2 - Long Jump Problems Below are the long jump results for a group of students.

Name

Jump 1

Jump 2

Jacob

3.35m

3.4m

Ava

Henry

Sophie

2.7m

Abbey

3.3m

Nathan

3.86m

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Teac he r

Liam

3.08m 3.2m r o e t s B r e oo p 3.5m 3.79m u k S 2.9m 3.21m

2.65.m 3.48m 4m

© ReadyEdPubl i cat i ons What might the questions bew if the are...?

•f or r evi e panswers ur po sesonl y•

3.

4.

5.

6.

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2.

6.11m

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1.

1.3m

o c . che 22.69m e r o r st super 14cm 29cm

6.78m

Extension: Create a maths problem of your own from the results above and give someone else the answer to see if he/she can work out the question.

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section 2: Athletics Carnival

Activity 3 - Paper Planes When you are given three jumps at long jump or high jump you often get better with each jump as you are likely to try new strategies, such as measuring out your run up, lifting your knees higher, etc.

Make a paper aeroplane and throw it three times. Record the distance that the plane travels in centimetres for each throw. Can you convert each distance into metres and millimetres?

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Teac he r

or eBo st r e p okDistance in Distance in u Distance in metres centimetresS millimetres

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

Do you think that you can get your plane to fly further? Make some adjustments to the plane and/or your throwing technique. Throw it three more times.

What adjustments did you make?

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_____________________________________________________________________ Record the distance that the plane travels in centimetres for each throw. Can you convert each distance into metres and millimetres?

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centimetres

o in Distance c . millimetres che e r o r st super Distance in metres

Did your plane go any further this time? Why or why not? _____________________________________________________________________ _____________________________________________________________________ 24

Teac he r

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

Moving Day

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Teacher notes

moving day

v8.1 curriculum focus

Number and Algebra

Measurement and Geometry

Year 5: Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) Solve problems involving multiplication of large numbers by oneor two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

or eBo st r e p ok u S

Solve problems involving division by a one digit number, including those that result in a remainder(ACMNA101)

Recognise that the place value system can be extended beyond hundredths (ACMNA104)

Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111) Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)

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Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

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Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

Compare, order and represent decimals (ACMNA105)

Year 6:

Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

Connect decimal representations to the metric system (ACMMG135)

Convert between common © ReadyEdPubl i cat i on s metric units of length, mass and capacity (ACMMG136) • f o r r e v i e w p u r p o s esonl y• Interpret and use timetables Add and subtract decimals, with and without digital technologies, Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

Multiply and divide decimals by powers of 10 (ACMNA130)

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Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

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Discussion (before):

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Have you ever had to move house? Why did you move?

How far away was your new house from your old house?

Why do you think people move house?

Have you ever helped somebody to move house?

If you were to move house, how many boxes do you think that you’d need to pack up your belongings in your bedroom?

Do you know the average house price in your state or territory?

How do real estate agents work out what houses are worth?

26

(ACMMG139)

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and use estimation and rounding to check the reasonableness of answers (ACMNA128)

Discussion (after):

If your parents bought a house for $250,000, how much would they need to sell it for to make a 50% profit? A 20% profit? An 85% profit?

(See answers on page 28.)

If Toni needs to drive 284 kilometres, how fast would she be driving if it took her 6 hours to get there? What about 4 hours? Or 2 hours? (See answers on page 28.)

Can you create a net for a box with a volume of 30cm3?

Draw a bird’s eye view of your bedroom. Make sure that it is to scale.

Teacher notes

Support & Extension Questions

moving day

1. What might be the volume of each of the boxes?

Support: What if the length was 50cm and the width was 60cm?

Extension: If the length was half the width but double the height?

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Teac he r

2. If all the boxes are the same size can you work out how many could fit into the moving truck?

Support: If the inside of the moving truck is 30m3?

Extension: Create a table to show your working out. Make a column for the box size and one to record how many of that size box will fit in the truck.

3. How many short boxes does Austen need to pack his 400 cards?

Support: If Austen has 5 boxes how many cards will go in each box?

Extension: What if the last box isn’t full? How many boxes are there and how many more trading cards would be needed to fill the last box?

4. What size might each of the rooms be in Austen’s new house? Can you draw what this might look like?

Support: If each of the three bedrooms is 12m2 what might the size of the other rooms be?

Extension: What if every room is a different size? What if it is two storey?

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5. What might the ratio of blue to red blocks be? How many of each colour might there be?

Support: What if the ratio is 1:4? How many of each colour might there be now?

Extension: Pick a ratio. Can you find a pattern for the amount of blocks?

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o c . ch e 6. What does this mean and how much yard space will the family have in their new r e o home? t r s s r u e p Support: If the yard space is 300m , what size will the new yard be?

2

Extension: Can you write out how you worked it out? Can you use your working out to teach someone else how to do it?

7. How much might they have sold it for and how much profit did they make?

Support: If they bought the house for $200,000, how much did they sell it for, and how much money did they make?

Extension: What if they made only a 30% profit? What if they got 120% profit?

27

Teacher notes

Support & Extension Questions

moving day

8. If the family drive an average of 70 kms per hour to get to their new house, how long might the drive take?

Support: If it takes 3.5 hours, how fast are they going?

Extension: How would the time to get there change if they were driving at 85 kilometres an hour?

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Teac he r

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9. If Austen has 8 boxes to put his cars inside, how many cars can he pack in each box?

Support: If Austen fits 15 cars in each box, how many boxes might he need and how many cars is that altogether?

Extension: If the last box isn’t full, how many cars does he have altogether and how many are in the last box?

10. Can you draw what the piece might look like?

Support: Can you draw what it might look like if it has 2 lines of symmetry?

Extension: Can you describe your design to someone else to draw?

Draw another symmetrical design for someone to finish. Draw half, and get a friend to complete it and make it symmetrical.

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Answers

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Discussion (after) Page 26 If your parents bought a house for $250,000 how much would they need to sell it for to make a 50% profit? A 20$ profit? A 80% profit?

50% profit - $375,000 20% profit - $300,000 85% - $462,500 If Toni needs to drive 284 kilometres, how fast would she be driving if it took her 6 hours to get there? What about 4 hours? Or 2 hours?

6 hours = 44kms per hour, 4 hours = 71kms per hour, 2 hours = 142kms per hour

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Activity Pages Box Creations Page 32 E.g. 5 x 3 x 4, 10 x 2 x 3, 2 x 5 x 6 Fraction Blocks Page 34 E.g. 30 = 10 red (1/3) 15 blue (1/2) 5 other (1/6) or 20 = 4 red (1/5) 12 blue (3/5) 4 other (1/5)

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section 3: Moving Day

A maths STORY moving day

Read the story Moving Day and solve the problems along the way.

“Here you go Austen,” Mum said as she piled a heap of boxes into my room. “This should be enough for the rest of your stuff.” I hoped that she was right. I took a look at the boxes. They were all the same lengths and widths but they were different heights.

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Mum had given me a heap of short boxes. I knew that she had given Lily heaps too and that yesterday Dad was packing all his stuff out of the garage into the short boxes. I wondered how many of these short boxes they could fit into the back of the moving truck.

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1. What might be the volume of each of the boxes?

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

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2. If all the boxes are the same size can you work out how many could fit into the moving truck?

o c . e I had no idea where to c h r e o start. I grabbed some r st super short boxes to pack

3. How many short boxes does Austen need to pack his 400 cards?

all my trading cards in them. I had been collecting these cards for a long time and I now had 400 cards.

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section 3: Moving Day

4. What size might each of the rooms be in Austen’s new house? Can you draw what this might look like?

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I was going to have so much more room for all my stuff. My mum is always complaining about how messy my room is but that’s just because I have nowhere to put anything. I began packing up my Lego.

Mum had sorted my Lego into colours in small zip-lock bags. I don’t really know why, but I noticed that I had a significantly small number of red pieces compared to blue pieces.

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Teac he r

After I had packed all the cards away so they were safe, I grabbed one of the taller boxes and started piling in things from under my bed. I thought about our new house as I packed. It was nearly twice the size of this house. Our new house is 262sqm.

5. What might be the ratio of blue to red Lego blocks? How many of each colour might there be?

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I looked out my window into our very empty backyard. I remember hearing Dad tell our neighbours that when we move our yard space will increase by 150%.

Our yard space will increase by 150%.

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6. What does this mean and how much yard space will the family have in their new home?

section 3: Moving Day

Mum and Dad have lived in our house since before I was born. They were very excited when the house was finally sold as they had sold it for quite a bit more than they had paid for it all those years ago. Mum said that they had sold it for 75% more than they bought it for.

FOR SALE

7. How much might they have sold it for and how much profit did they make?

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Teac he r

8. If the family drive an average of 70kms per hour to get to their new house, how long might the drive take?

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We had lunch before we left. We would be having dinner tonight in our brand new house. I wondered how long it would take us to get to our new house. I wasn’t exactly sure yet how far our new house was from our old house.

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9. If Austen has 8 boxes to put his cars inside, how many cars can he pack in each box?

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After lunch, I really needed to get packing.

Next I got out my car collection. Boy did I have a lot of cars!

o c . che e r o r st super

When I had finished packing I walked out the front of the house. I found Dad packing some last minute things from the garage. He had an ornamental piece that used to be stuck to the front of our house. I had always loved the design of it. It had four lines of symmetry.

10. Can you draw what the piece might look like?

I looked back at our new house as we drove away. As sad as I was to be leaving our old house I was excited to be going to our new house. After all, my new room was huge! And we had a pool! I started thinking about how I could set up my new room.

I started imagining a design for the perfect bedroom…

I am so excited!

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section 3: Moving Day

Activity 1 - Box Creations You have been asked to design a box for a small toy. All you know is that the volume of the box needs to be 60cm3.

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Teac he r

Draw your design below.

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Draw what the net would look like for your box.

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Extension: Using a coloured piece of paper draw the net to scale and see if you can create it! How can you prove it is 60cm3?

32

section 3: Moving Day

Activity 2 - Bedroom Designs It can be fun to move house and set out a new room, especially if your new room is bigger than your old room! If you could design your perfect bedroom what would it look like? How big would it be? What would you want in it?

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Using the space below, design your ultimate bedroom! Remember to record all the measurements.

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Get some feedback from a friend. What is your friend’s favourite thing about your room? What suggestions do they have for you?

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section 3: Moving Day

Activity 3 - Fraction Blocks Austen had a lot of Lego that he needed to pack before moving. Using the table below can you decide how many blocks he had to pack and what fraction of the blocks might have been red or blue?

Note: You can use materials to help you.

or eBo st r e p ok u S 6 red – 1/4 12 blue – 1/2 6 other – 1/4

Eg. 24

How many other coloured blocks are there?

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How many blocks How many blocks How many blocks altogether? are red? are blue?

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Section Four: Footy Fever

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35

Teacher notes

footy fever

v8.1 curriculum focus

Number and Algebra

Measurement and Geometry

Statistics and Probability

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Year 5: Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

Solve problems involving division by a one digit number, including those that result in a remainder(ACMNA101)

Teac he r

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Compare, order and represent decimals (ACMNA105)

Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112)

Year 6:

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123) Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

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or eBo st r e p ok u S

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

Connect decimal representations to the metric system (ACMMG135)

Describe probabilities using fractions, decimals and percentages (ACMSP144)

Convert between common metric units of length, mass and capacity (ACMMG136)

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

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

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

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Discussion (before):

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Which team do you barrack for?

Why do you follow this team?

Do you watch the footy (AFL) on T.V? Have you ever been to a game?

Who is your favourite player?

Do you have a footy (AFL) jumper? Does it have a number on it?

36

Discussion (after):

Connect volume and capacity and their units of measurement (ACMMG138)

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

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Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

If one team’s score at the end of the game is 137 points, how many points might they have scored each quarter? Come up with 5 different possibilities. How many goals and points is this for each quarter? (See answers on page 38.)

o c . che e r o r st super

Players can have more or less chance of kicking a goal depending on the angle that they are kicking from. Choose an angle and predict your chance of kicking a goal on that angle. Test it out and see if you are right. Does the distance from the goal make a difference?

What do you think is the maximum capacity of your classroom? How would you work this out?

Play a pretend game of footy (AFL) with a friend. Take it in turns to roll the dice. You get two turns for each quarter, one for the goals and one for the points. Do this for all four quarters and then add up your points to work out who won!

How could you adapt this game to make it easier/harder?

Teacher notes

Support & Extension Questions

footy fever

1. If the difference between the shortest player and the tallest player is 37.25 centimetres, what might be the height of each player?

Support: What if one of the players is 179.83 centimetres?

Extension: What is the tallest height a player could possibly be? What is the shortest? Use this information to help you.

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2. What might be the age of each player?

Support: If the average age of 5 players is 29, how old might each player be?

Extension: How do the ages change depending on the number of players?

3. What might be the numbers on the 6 players’ jerseys?

Support: If one of the numbers is 27, what might the other numbers be?

Extension: What if one of the numbers was 1? What if the difference between the highest and lowest numbers was 35?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 4. What might each team’s score be and how many goals and points does this

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equate to for each team?

Support: If one team’s score is 37 points, how many goals and points might this be? What would the other team’s score be?

Extension: Choose one of your scores for each team and come up with as many goal/point combinations as you can.

o c . che e r o r st super

5. What might be the stadium’s maximum capacity and how many people might be at the game?

Support: What if the stadium holds 50,000 people?

Extension: What if the stadium is only 4/9 full?

6. What might the scoreboard look like for each team?

Support: If both scores at half-time are 65, what might each team’s goals and points look like?

Extension: Come up with three different scores. Then come up with four different combinations of goals and points for each score.

37

Teacher notes

Support & Extension Questions

footy fever

7. What might the original price be and how much will Tayla pay?

Support: If Tayla pays $6 for a hat and $3 for a scarf, what are the original prices of the hat and scarf?

Extension: Tayla buys a hat, a top and a scarf for $24. How much might each item be and what might the original prices of each item be? How much did she save?

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8. If 3/8s of the burgers on the tray are chicken burgers and 1/4 are cheese burgers, how many are there of each burger?

Support: If there are 48 burgers, how many are there of each?

Extension: What amounts can you find that can be equally divided into eighths and quarters?

9. What does this mean and how have the statisticians worked this out?

Support: Can you draw a picture to explain where the player might be kicking from? Where do you think he would have the greatest chance/least chance of scoring and why?

Extension: Where might the player be standing? What do you think your chance is of kicking a goal from there? Could you test it out and find out your percentage?

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

Answers

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10. Can you work out what the chances are of Tayla getting her footy tips all correct?

Support: What if there are just 6 games?

Extension: What is the chance of Tayla getting her footy tips all incorrect? What percentage is she most likely to get incorrect?

o c . che e r o r st super

Discussion (after) Page 36 If one team’s score at the end of the game is 137 points, how many points might they have scored each quarter? How many goals and points is that for each quarter?

E.g. Q1 – 27 (4 goals, 3 points), Q2 – 34 (5 goals, 3 points), Q3 – 39 (5 goals, 5 points), Q4 – 37 (6 goals, 1 point) Activity Pages Shopping Problem Page 44 Hat = $13, Tops = $18

38

section 4: Footy Fever

A maths STORY footy fever

Read the story Footy Fever and solve the problems along the way.

“Come on, Tigers!” The cheers could already be heard around the ground and the game hadn’t even began. At last, the players started to run out on to the field and the chants and cheers got louder. It was exciting to know that the game would start soon. I noticed as the players huddled around the coach on the field that there was a big difference between the tallest and the shortest players.

Teac he r

1. If the difference between the shortest player and the tallest player is 37.25 centimetres, what might be the height of each player?

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© ReadyEdPubl i cat i ons I also remember 2. e What might theu age of each player?

• f orr vi e wbep r p os esonl y• reading that the

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average age of all AFL players is 29.

o c . che e r The players took their positions o r st super on the ground. There were six players standing close to where we were sitting. One of them was my favourite player!

As I read the numbers on the players’ tops I realised that if I added them all together, it totalled 127.

3. What might be the numbers on the six players’ jerseys?

39

section 4: Footy Fever

The game was soon underway and I was sat on the edge of my seat watching as the lead changed several times. By quarter-time the Tigers were up by 26 points.

4. What might each team’s score be and how many goals and points does this equate to for each team?

scoreboard Tigers Goals

Points

magpies score

Goals

Points

score

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5. What might be the stadium’s maximum capacity and how many people might be at the game?

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As the second quarter got started Dad was trying to work out how many people were at the game. The stadium could hold a lot of people and it was only about two-thirds full.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• When the siren went at

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6. What might the scoreboard look like for each team?

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half-time, the scores were even! It was going to be a very interesting secondhalf. Even though the team’s had the same scores, they had each scored a different amount of goals and points.

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o c . che e r o r st sthe per I had brought some money with me to u match, as Dad said I could buy something from the merchandise stand. It was a good day to make a purchase, as they had a big sale on.

They had 25% of all hats, 50% of all tops and 75% off all beanies and scarves.

25% o

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40

75% o

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7. What might the original prices be and how much will Tayla pay?

section 4: Footy Fever

I decided to purchase a hat and a scarf. I chucked them on as it was getting a little chilly.

Then we headed to grab some lunch before the third-quarter started. I was so hungry and I really wanted a burger. They had a full tray of burgers. There were plain beef burgers, cheese burgers and chicken burgers. cheese

Teac he r

beef

8. If 3/8s of the burgers on the tray are chicken burgers and 1/4 of the burgers are cheese burgers how many are there of each burger?

chicken

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Dad bought me a cheese burger and a drink and we rushed back to our seats just as the third-quarter was starting. In less than a minute a player was lined up ready to kick a goal. As he got ready, the scoreboard flashed up his stats and it said that he had 60% chance of kicking it through the goals.

9. What does this mean and how have the statisticians worked this out?

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The player scored the goal! As the players ran back to the centre, scores from another game that was playing today were displayed on the board. The team I had picked was down by 33 points. I was behind in my footy tips so I need to get them all right this week!

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

10. Can you work out what the chances are of Tayla getting her footy tips all correct?

o c . che e r o r st super

Even though it had been a draw at half-time, our team ended up winning by 56 points! A thrashing! On the way home Dad and I were discussing the highlights of the game. I could still picture the final scoreboard in my head. Can you imagine what that scoreboard might have looked like? I can’t wait for next week’s game!

scoreboard Tigers Goals

Points

magpies score

Goals

Points

score

41

section 4: Footy Fever

Activity 1 - Footy Numbers Many people own footy (AFL) jumpers and often people get their favourite player’s number printed on the back of their jumpers. Some people who play footy for a team might have their own special number on their jumpers.

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Teac he r

Find out from the students in your class who has a footy (AFL) jumper and what number they have on it. Record all the numbers in the box below.

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1. What maths problems can you create from these numbers? For example, what is the total, if all the numbers are added together? Write down two maths problems for a friend to solve.

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2. Can you find two numbers that when added together make another number from the box? __________________________________________________________________ 3. Pick four numbers from the box and add them together. Give the total to a friend and see if they can work out which four numbers you added together. Get a friend to do the same for you. How quickly can you work out the answer? a. _____ + _____ + _____ + _____ = _____ 42

section 4: Footy Fever

Activity 2 - Footy Sale

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In the story Footy Fever, Tayla visits the merchandise stand and buys a hat and a scarf. Draw what you think the merchandise stand might look like.

Don’t forget to include original and sale prices for the items.

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1. What two items would you buy from the merchandise stand and how much would you save?

Item 1: ____________________________________________________________

Item 2: ____________________________________________________________

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2. If you were to buy one of everything from the merchandise stand what would it cost?

3. What would it have cost before the sale?

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4. How much are you saving?

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5. What is the difference between the cheapest and the most expensive items?

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section 4: Footy Fever

Activity 3 - Shopping Problem My friend Holly and I bought some items from the merchandise store the last time that we were at a match. I can’t remember how much each item cost, but I do know that I bought two hats and one top for $44 and Holly bought one hat and three tops for $67.

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How much might the hats and tops have cost individually? Show your working out below.

Tayla:

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Holly:

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1. If the hats are being sold for 1/3 off the original price, what is the original price?

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o c . __________________________________________________________________ che e r o r st s 3. What would Holly and Tayla have paid before the sale? up er 2. If the tops are 25% off, what is the original price?

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4. How much did they save?

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5. Create your own shopping problem like this one. Give it to somebody else to solve.

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

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Fun At The Beach

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Teacher notes

fun at the beach

v8.1 curriculum focus

Number and Algebra

Measurement and Geometry

Year 5: Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

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Year 6:

Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122) Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123) Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124) Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127) Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128) Year 6 - Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

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Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Solve problems involving division by a one digit number, including those that result in a remainder(ACMNA101) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Create simple financial plans (ACMNA106) Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107) Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)

Connect decimal representations to the metric system (ACMMG135)

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Do you like the beach?

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Which beaches have you visited?

Do you know which beach is closest to your house?

What do you like to do at the beach?

Who do you go to the beach with?

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Connect volume and capacity and their units of measurement (ACMMG138)

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Convert between common metric units of length, mass and capacity (ACMMG136)

Discussion (after):

How many steps do you take in one day? How could you work this out?

In the story Ivy has a collection of shells. Can you draw a collection of buttons and colour 3/8 purple and 1/3 green?

Did you solve the number plate problem on page 51? All the digits on both plates added to make 16! What is the secret to solving these: 258 and 369, 324 and 831?

(See answers on page 48.)

Can you create your own number plate problem for someone else to solve?

Ivy has made some beaded jewellery and is going to start selling it. To be able to make a 75% profit on each item, how much would she have to sell each item for? What might the cost be of making each item? (See answers on page 48.)

Teacher notes

fun at the beach

Support & Extension Questions

1. What might the temperature be and what might the temperature of the water be? What is the difference between the two?

Support: What if the difference between the two is 17 degrees?

Extension: Can you find out what the average temperature difference is between the air and the water at the beach normally?

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2. If the sandcastle is a metre high what might be the height of each individual bucket?

Support: What if there are 5 buckets and they are all the same size?

What if there are 6 buckets?

Extension: What if the average of the buckets’ heights is 22cm? What if each bucket is measured to the nearest millimetre?

3. Can you work out how many drops of water are in Ivy’s bucket?

Support: How many drops of water are in one cup? How could you find out?

Extension: Can you explain what you would do to work it out? Estimate and then test it out.

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4. If the difference between the two team’s scores is a triangular number how far ahead might the winning team be?

Support: If 6 is a triangular number (1 + 2 + 3) what other triangular numbers do you know?

Extension: How many triangular numbers can you find? Which one do you think it is if they are winning by a mile?

. tedo you think a whale might weigh? Can you estimate o how many 5. How much c . of you would weigh the same as a whale? c e h r Support: If you weigh 37.8 kilograms cant you work out what ten times er o s su15p er your weight is? What about times your weight?

Extension: Come up with a rough estimate and then do some research to see if you can find the average weight of a whale and then try and work it out more accurately.

6. I knew the perimeter of the blanket was 7 metres. What might the area of it be?

Support: What if the area is 32 metres and one side is 2 metres?

Extension: Find three possibilities for the perimeter and record the area for each.

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Teacher notes

Support & Extension Questions

fun at the beach

7. How far might the family have walked and how many steps might they have taken?

Support: If they had only walked 200 metres, how many steps would they have taken? How might you work this out?

Extension: How far do you think you could walk in half an hour? How many steps would you need to take to walk this far? How could you work this out?

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8. If it cost the man $200 to set up his van beside the beach for the day, how many ice-creams would he need to sell to make a profit?

Support: What if he sold the ice-creams for $2? What if they were $1.50?

Extension: If he sells 85 ice-creams a day, how much would he need to sell them for to make a profit?

9. 1/8 of Ivy’s collection looked like snail shells. How many snail shells might she have?

Support: What if there were 40 shells altogether? Or what if you knew oneeighth was 7 shells?

Extension: What if 2/7 were coned shaped?

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Answers

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10. How many friends could Ivy share her shells with? How many shells would each friend receive?

Support: What if Ivy has 60 shells? How many different ways can the shells be shared? What if each friend receives 8 shells? How many friends are there and how many shells are there?

Extension: What if Ivy has over 200 shells?

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Discussion (after) Page 46 Did you solve the number plate problem on page 51? All the digits on both plates added to 16! What is the secret to solving these: 258 and 369, 324 and 831?

One number more. When all multiplied together will equal the same.

Ivy has made some beaded jewellery and is going to start selling it. To be able to make a 75% profit on each item, how much would she have to sell each item for? What might the cost be of making each item?

E.g. Cost to make $1 – sell for $1.75, cost $8 – sell for $14, cost $5 – sell $8.75

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section 5: Fun at the Beach

A maths STORY fun at the beach

Read the story Fun At The Beach and solve the problems along the way.

It was the warmest day of summer so far. I had been asking Mum and Dad if we could spend a day at the beach for what seemed like forever! When we arrived, Mum thought that the water would be much cooler.

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Ivy was busy making a sandcastle. It actually looked really good. She had used different sized buckets and was stacking them on top of each other to make one really tall sandcastle. The castle was at least a metre high!

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1. What might the temperature be and what might the temperature of the water be? What is the difference between the two?

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2. If the sandcastle is a metre high what might be the height of each individual bucket?

o c . che e r o t r s s r u e p Ivy walked down to the water to fill her bucket. I think she wanted to make a moat around her castle. “Do you think there is about a million drops of water in here?” she asked me pointing to her bucket. How did I know? Was that even possible to work out?

?

3. Can you work out how many drops of water are in Ivy’s bucket?

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section 5: Fun at the Beach

A bit further up the beach there was a group of people playing beach volleyball. They looked like they were having so much fun. I overheard them talking about the scores. One team were winning by a mile!

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5. How much do you think a whale might weigh? Can you estimate how many of you would weigh the same as a whale?

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Off in the distance I could see a boat. We all guessed what the people on the boat might be doing. Mum thought that they were having a nice lunch, Dad thought they were going whale watching and I said that maybe they were fishing. I hope Dad was wrong. I didn’t want to see any giant whales out there!

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4. If the difference between the two teams’ scores is a triangular number, how far ahead might the winning team be?

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6. I knew the perimeter of the blanket was 7 metres. What might the area of it be?

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After lunch, Dad, Ivy and I decided to go for a walk along the beach. We walked for about half an hour up the beach, and when we turned around we couldn’t even see our original spot anymore. So we turned around and began to head back.

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Mum asked me if I could lay out the picnic blanket while she got everything out ready for lunch. She had packed ham, chicken, rolls, fruit and more. My mouth was watering just looking at it all. Luckily, the picnic blanket was big enough to fit it all on.

7. How far might the family have walked and how many steps might they have taken?

section 5: Fun at the Beach

When we got back to Mum she suggested that it was time for ice-creams. We walked over to a van set up at the back of the car park. I ordered a double chocolate mint cone while Dad was asking the man about his van, “How much does it cost you to set up here for the day?” he asked.

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While I was finishing my icecream, Ivy had started to collect shells. Her collection was growing quite large and contained some awesome looking shells.

9. 1/8 of Ivy’s collection of shells looked like snail shells. How many snail shells might she have?

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8. If it costs the man $200 to set up his van beside the beach for the day, how many ice-creams would he need to sell to make a profit?

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Ivy started scooping up all her shells and piling them into one of her bigger buckets, “I want to take these home and share them with all my friends,” she explained.

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10. How many friends could Ivy share her shells with? How many shells would each friend receive?

As we piled all our stuff in to the car to head home, Ivy pointed to the number plate on the car next to us. “Hey that’s like ours!” she exclaimed.

Our number plate was 196 and their number plate was 727. They weren’t the same? I wonder what she meant. Do you know?

727

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section 5: Fun at the Beach

Activity 1 - Food Stall You have been given the opportunity to run a food stall at the local market. Use the space below to plan your food stall. Include:

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- what item(s) you are going to sell; - what your expenses will be; - how much you plan on selling your item for; - whether there will be any special deals; - an estimate of what you expect to sell in a day; - how much profit you expect to make.

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1. What is the least amount that you could sell your item for and still make a profit?

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2. Do you think it would be better to sell your item for lesse and sell more of your c h r item, or increase the price e but not sell as much? t Explain your answer. o r s s r u pe __________________________________________________________________

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3. What strategies could you use to maximise your profit?

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section 5: Fun at the Beach

Activity 2 - Temperature Data Record the lowest and highest temperatures for each day in one week.

Day Of The Week

Lowest Temperature

Highest Temperature

Monday Tuesday Wednesday Thursday

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Friday

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Saturday Sunday

1. What is the average temperature for the week?_ __________________________ 2. What is the range in temperature for the week?___________________________

© ReadyEdPubl i cat i ons •f or r evi e wp ur pose on l y • one Next, record the forecasted (high) temperature fors each day during

3. On a coloured piece of paper, graph the results above. How can you graph the data so that you can see both the lowest and highest temperatures?

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Day Of The Week Monday Tuesday Wednesday Thursday

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Forecasted Temperature

Actual Temperature

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week. Then record the actual (high) temperatures for each day during a week.

Record the differences between the two sets of temperatures.

Difference between the temperatures

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Friday Saturday Sunday 1. What is the greatest difference between the two sets of temperatures?________ 2. Graph your results on the back of this sheet. How can you graph these results so that it is clear for others to read?

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section 5: Fun at the Beach

Activity 3 - Bargain Shopping On the way back from the beach, Ivy and her family stop at a shop. Ivy spots a sign on the window as they walk in. Every item is on sale! What will Ivy buy and how much money will she save?

Specials

Items For Sale Green bike - $120 Red bike - $80 Blue bike - $100

Bikes – 25% off r o e t s B r e oo – 10% off Scooters p Sports k equip. – 50% off Su Basketball -

$33

Netball - $29

Soccer ball - $27.50

White scooter - $ 75

Bubble machine - $46

Gold scooter - $95

Coloured bubbles - $18

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Bubble rocket - $30

Bubble toys – 15% off

Complete the table, using the information above.

Total price (original)

Total price (after discounts)

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Black scooter - $ 60

Total amount saved

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Items

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or eBo st r e p ok u SSection Six:

The Case Of The Bear ©Missing ReadyEdPub l i cat i ons

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Teacher notes

the case of the missing bear

v8.1 curriculum focus

Number and Algebra

Measurement and Geometry

Year 5:

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Compare 12- and 24-hour time systems and convert between them (ACMMG110) Use a grid reference system to describe locations.

Describe routes using landmarks and directional language (ACMMG113)

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Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122) Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123) Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127) Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128) Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

. te Discussion (before):

Connect decimal representations to the metric system (ACMMG135) Convert between common metric units of length, mass and capacity (ACMMG136)

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Have you ever lost something?

Did you end up finding it?

How did you feel when you realised it was lost?

What did you do to try and find it? Did anyone help you?

What do you think the police do to help people find things?

What should you do if you find something that you think someone else may have lost?

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Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

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Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

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Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098) Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Compare, order and represent decimals (ACMNA105) Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107) Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)

Discussion (after):

I know my mum’s passcode for her phone. I know when I multiply all the digits together it makes 50. What might the digits be? How many different answers can you find? (See answers on page 58.)

What is the average height of the students in your class?

How could you find this out?

Imagine that you have been asked to retrace your steps over the last 24 hours. How accurately could you do this? Write out everything you have done in the last 24 hours.

Using a map could you find a 3 kilometre area around your school? Where would it start from? Where does it go to? What streets does it include? How long would it take you to walk around the perimetre of this 3 kilometre area?

Teacher notes

the case of the missing bear

Support & Extension Questions

1. Buddy has been missing for 74 hours. What time might it be now and what time was it the last time that he was seen?

Support: If the time is 11am on Saturday, what time was it, the last time that Buddy was seen?

Extension: Can you work out how many minutes Buddy has been missing?

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2. Buddy’s age is a prime number. How old might Buddy be?

Support: How many prime numbers can you find? Which one do you think is Buddy’s age and why?

Extension: Can you explain to someone else what a prime number is?

Which do you think is Buddy’s age and why?

3. How much tape might Harley need to tape off the area?

Support: If one side of Violet’s bedroom is 3 metres, what might the area of the bedroom be?

Extension: What if one side was 2.4 metres?

© ReadyEdPubl i cat i ons 4. What ber the size of w Harley and Violet’s and what might •might f or ev i e p ur pohouse ses o nl y •be the

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size of their backyard?

Support: Can you work out the sizes if the total land size is 1000m2?

Extension: If the house is 238m2, what size might each room be?

5. How long might each of the two hallways be?

Support: If one hallway is 7.83 metres, how long might the other hallway be?

Extension: If the difference between the two hallways is 23 centimetres, how long might each of them be?

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Support: What if one of the numbers is 1 and the rest are even numbers?

Extension: How many different answers can you find?

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Teacher notes

the case of the missing bear

Support & Extension Questions

7. If the average of all their heights is 1.65 metres, what might their individual heights be?

Support: If there are 4 people and 2 are actually the same height, what are the individual heights?

Extension: What if the range of their heights is 35 centimetres?

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8. Can you draw what each shed might look like?

Support: Using your drawings, can you explain to someone how one is 1/4 bigger than the other?

Extension: Can you work it out mathematically? For example if the first shed is 6 metres x 8 metres x 2 metres, what will the measurements of the other shed be?

9. If Harley is going to search an area of 3 kilometres, how many people do you think he will need to help him and how long will it take us to search this area?

Support: How big is your school? How long do you think it would take you to search it? Hide an object in an area in your school and see how long it takes a group to find it.

Extension: Create a map of the 3 kilometre area that Harley intends to search. Using this map make a plan for the search party.

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Answers

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10. What might the area of the veggie patch be?

Support: What if one side of the veggie patch is 6 metres?

Extension: How many different areas might there be? How will you know when you have all the possible answers?

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Discussion (after) Page 56 I know my mum’s passcode for her phone. I know when I multiply all the digits together it makes 50. What might the digits be? How many different answers can you find?

E.g. 2451, 5222, 5181 Activity Pages Veggie Patch Design Page 62 E.g. 2m x 12m, 8m x 3m, 6m x 4m Veggie Fractions Page 63 1/4 carrots = 10, 1/5 tomato = 8, 3/8 lettuce = 15 other (7/40) = 7 58

section 6: The Case Of The Missing Bear

A maths STORY - The case of the missing bear

Read the story The Case Of The Missing Bear and solve the problems along the way.

“Ok. When was the last time you saw him?” My little sister Violet had come to me in tears because she had lost her bear, Buddy. It was her favourite toy and she’d had it for as long as I could remember. She told me when the last time that she saw him was and I jotted the information down in my notebook.

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“Can you tell me how old Buddy is?” I asked.

“Umm… well he has just had his birthday,” Violet said, after thinking for a while. I watched as Violet sat trying to work out Buddy’s age.

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1. Buddy has been missing for 74 hours. What time might it be now and what time was it the last time that he was seen?

Can you tell me how old Buddy is?

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I took some more details about Buddy and then I investigated the crime scene (Violet’s bedroom) and decided to tape off the area. I knew that the area of Violet’s room was 12m2.

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3. How much tape might Harley need to seal off the area?

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4. What might be the size of Harley and Violet’s house and what might be the size of their backyard?

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section 6: The Case Of The Missing Bear

In order to create an accurate map of the crime scene I measured the distance down each of the main hallways in our house. When I added the two lengths together I got a total of 13.74 metres.

5. How long might each of the two hallways be?

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6. What might the four digits be?

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I knew that Violet had a secret box in her room where she kept things that she didn’t want anyone to see (mainly me)! “I am going to need the code to that box,” I told Violet.

“No way!” she exclaimed.

“I need to be thorough in my investigation if we are going to find Buddy.”

Violet very reluctantly told me her 4 digit code. When I multiplied the four digits together I found that they equalled 80.

© ReadyEdPubl i cat i ons •f o rr vi e w pu po”s sViolet on l yme •the most “I am also going to need ae recent photograph ofr Buddy, Ie said. found

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7. If the average of all their heights (Mum, Dad, and the neighbours) is 1.65 metres what might their individual heights be?

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The house next door had two sheds. I had always thought this was suspicious.

Why would anyone need two sheds? I pictured one shed full of long lost toys from all over the neighbourhood! The second one was 1/4 bigger than the other.

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recent photograph she had. It was time to interview the suspects. I started with Mum and then Dad. My neighbours were out the front too so I asked them about whether they had seen Buddy. While interviewing them I noted down each of their heights.

8. Can you draw what each shed might look like?

section 6: The Case Of The Missing Bear

Violet had made her way out into the front yard to find me and see how my investigation was going. “Have you found Buddy yet?” she asked sadly.

“No,” I replied. “But don’t worry, we will find him.” I asked Violet to retrace her steps from the last few days. Violet only recalled being at home and school and at the shops with Mum. This gave me a 3 kilometre radius from our house.

“But don’t worry, we will find him.”

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While thinking about getting together my search party our dog Scooby ran through the side gate and ran around our legs in the hope of us taking him for a walk. While he was jumping about crazily I noticed that his nose and paws were very dirty. I recalled seeing small patches of dirt on Violet’s carpet and bed. I thought about this as I dragged Scooby back into the backyard. I looked at the veggie patch. It was fenced off with thatched fencing to stop Scooby getting in to it.

Dad and I had used 28 metres of fencing to go the whole way around it.

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9. If Harley is going to search an area of 3 kilometres, how many people do you think he will need to help him, and how long will it take him to search this area?

10. What might the area of the veggie patch be?

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The thatched fencing was still intact so he hadn’t got in there. I noticed a series of holes that he had dug around the trees and the garden around the backyard. And then it clicked. “VIOLET!” I yelled. She came running into the backyard. “What?” she asked.

“Has Scooby been in your room lately?” I asked. She looked confused. Then she noticed the dirt on Scooby’s paws and the holes in the backyard and she realised what I was thinking.

We madly started digging through the areas where we could see Scooby had been. I was on the third hole when… “AHA!” I pulled Buddy out of the hole. Violet came rushing over and grabbed Buddy from me and hugged him tightly, dirt and all. “Thank you, thank you, thank you Harley!” said Violet repeatedly. She turned to Scooby. “Naughty Scooby!” she scolded. Scooby sat there excited, waiting for her to hide Buddy again as if this had all been a game!

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section 6: The Case Of The Missing Bear

Activity 1 - Veggie Patch Design

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Use the space below to design some veggie patches that are 24m2. How many different designs can you come up with? What is the perimeter of each one? Can you work out what the largest and smallest possible perimeters you could have for a veggie patch with an area of 24m2?

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Extension: Can you create a veggie patch with an area of 24m2 that is an irregular shape? What is the perimeter of this veggie patch?

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section 6: The Case Of The Missing Bear

Activity 2 - Veggie Fractions Often when we plant vegetables we plant them in arrays (a systematic arrangement of the same object - usually in rows and columns). Can you plant 40 vegetables in an array below?

Make sure that there are:

An array of lettuces

1/4 of carrots

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1/5 of tomatoes

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3/8 of lettuces

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What fraction is this? _________

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How many spaces are left? ________

Now design your own veggie patch. How many veggies will you plant?

How will they be arranged? What fraction of your veggie patch is each vegetable?

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section 6: The Case Of The Missing Bear

Activity 3 - Area And Perimeter Did you work out how much tape Harley needed to tape off Violet’s bedroom on page 59 in the story The Case Of The Missing Bear? Imagine that you have 70 metres of tape. What sized area could you tape off with that much tape?

Area

Perimeter

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Shape

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Extension: Could you tape off an irregular shape?

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