# What’s new in Maths Matters Resources?

## MATHS SESSION – MENTAL WARM-UPS – Measurement “What do I know?”

Real-life maths is all around us. But often your students sit on mathematical information without fully thinking about it. These activities grew out of an analysis of NAPLAN data over 10 years ago. We discovered that across Australia students looked at information with a one track mind. For example, 2 cakes cost $1.50 – they read it at face value. Yes, two cakes cost $1.50. They didn’t follow through with any other implication. For example, 4 cakes cost $3, 20 cakes cost $15, 1 cake costs 75 cents. If they were half price the original cost for 2 cakes was $3, and so on.

These 5 Measurement Mental Warm-ups “What do I know?” cover Length, Area, Mass, Volume & Capacity and Time – with 10 suggestions for each sub-strand. They are included in the Grades 3/4 section but will apply across a wider range of students.

In just one minute can your students brainstorm with a partner everything they can think of that has a mathematical link to what is shown. Don’t just limit yourself to the sub-strand either, try to create as many mathematical connections as you can, by discussing and sharing ideas as a whole class.

We want students who can think for themselves without us breathing down their necks all the time. We need independent thinkers who can stand on their own two feet and see mathematics all around them. We need students who go out into the adult world thinking mathematically.

## NUMBER & ALGEBRA – FRACTIONS – Pizza Slices Challenge 3456

Yesterday Duffy and I had lunch at our local cafe and were surprised to see that our pizza had been cut in quite an unusual way. Here it is as Pizza Slices Challenge for your low block Grades 3 and 4 students, or for Grades 5 and 6 to tackle as well.

We have left it as quite an open challenge so that your students can solve it using a variety of strategies. It would be best if they worked with a partner so that they can discuss and explain their thinking. But we know you prefer to see at least one sample solution, so we have included that also in quite a lot of details as the concepts are not always easy to understand instantly.

Keep on the lookout for other real-life maths problems. They are all around you!

## MATHS PHOTOGRAPHS – MULTIPLICATION – 4 bread & butter puddings

Food seems to be a recurring theme this week! How delicious – 4 bread and butter puddings straight out of the oven from Cafe M at Tamarama. What an effective way to focus on groups of 4 as part of your multiplication & division activities.

Use the photo as a Mental Maths Warm-up by challenging your students to count by 4s for as far as they can. Link to money by giving these puddings a price e.g. 4 for $16 so some students can count by 16s as they count off groups of 4 puddings. Link to division by talking about larger groups e.g. The cafe baked 48 muffins for a party and sold them for $144. How much will 4 cost?

## MASS/VOLUME ACTIVITIES – ANZAC Biscuits Recipe 3/4

Cooking is a wonderful way to involve your students in real-life mathematics. Proportional reasoning, estimating, doubling or halving a recipe, so much to think about.

Here is a recipe for some delicious ANZAC Biscuits – the recipe makes 18 biscuits. We’ve included a 12-step recipe guide for those students who need to follow the instructions in an easier to read format. Plus we’ve included step-by-step photographs so your students can see what to expect along the way.

Yum, yum, what are you waiting for!

## GEOMETRY – POSITION PHOTOGRAPHS – iphone compass points

What a brilliant use of new technology. If you have access to a mobile phone you now have access to a built in compass. Or if not, you can easily download one. These 4 photographs show what North, South, East and West look like on a mobile phone compass.

Using your mobile phone, you can go on a daily direction walk with your students. Find where due north is in your school playground. Repeat for each of the other main compass points. What about NW and NE? There are 8 compass points waiting for your attention. At the end of the week check your students understanding of the 8 compass points by calling out a direction and asking them to stand exactly where they estimate this to be with their hands pointing to the direction. Check with your iphone. Award a certificate to those students who feel totally comfortable with how to orient themselves around the school.

## MATHS PHOTOGRAPHS – Creatures – 4 fish

Here are 4 funny ceramic fish to inspire your students to explore sea creature maths – use them for counting, addition and subtraction, multiplication and division. So many mathematical uses.

See how we have used these to make Fish Patterns for Early Stage 1 students, 11 pages of Patterns and Algebra activities. Create your own patterns using all the individual fish. Or use a Fish Pattern card to copy and continue a pattern. Talk about it with your partner – what fish comes first? second? third? How do you know what the pattern looks like? How will you continue it? What fish doesn’t belong in this pattern?

You can also use the Pattern Shape cards with the individual cut out fish and students who are ready for a bigger challenge. What fish might each shape represent? Can you find a match to the Fish Pattern cards? Why do you think there is or os not a match?

Of course your students can also create their own fish pattern and shape pattern cards for other pairs or small groups of students to use.

## MATHS PHOTOGRAPHS – Creatures – 3 Aussies

Everyone loves Australian animals. Here are 3 more we have added to our collection – a Brushtail Possum, an Echidna and a Sea Eagle. Use them as part of your daily Mental Maths Warm-ups. Give your students one minute to brainstorm with a partner all the maths facts they already know. About how long or tall might these creatures be? How heavy? How long might they live for? How many babies do they have at one time? Where in Australia might you find them? They can then research individual facts at home to present to the class the next day.

The Sea Eagle, for example, is the second largest raptor in Australia. Males have a mass up to 3.7 kg, and a wingspan up to 2 metres long. Females can be even larger. They live along the coast of Australia, but are also found in China, India, SE Asia, Indonesia and New Guinea. Their nests are sometimes found 30 m off the ground. And they usually move about 50 km away from where they were born. There may be about 100 000 Sea Eagles living in the world. It is also featured on the Singapore $10 000 note and is the emblem for the Manly-Warringah Sea Eagles football team.

## GEOMETRY – POSITION PHOTOGRAPHS – Distance Sign Hawks Nest

Public signs are an efficient way to communicate distances that matter. If you are on a bush walk, there is a big difference between a 2 km walk and a 20 km walk. Or between something that takes 10 minutes and something that takes 1 hour. You can use this community distance sign from Hawks Nest NSW to get you started on a whole discussion about measuring distances at your school.

Your students can make their own school distance sign. First talk about all the important areas in your school e.g. The Principal’s Office, the canteen, the toilet block, the front gate, the sports field, the after school care room. Where should you begin your measuring? e.g. from the front entrance gate? The office? How will you check the time taken to go from the start to the finish? (e.g. walk at a normal pace with a stopwatch?) Divide the class into smaller groups and ask each group to select one area. What equipment will they need? (e.g. trundle wheels, tape measures, stopwatches or clocks) How will they check their accuracy? (e.g. measure to and from their area then back again). Once you have all the measurements ask the groups to swap information and check another group’s distances and times. Once everyone is convinced that the distances and times are accurate then discuss what sort of signage to create.

Some students may even like to follow this up at home by making a distance and time information sign about areas around or near where they live.

## MEASUREMENT – TIME ACTIVITIES – Mix and Match Time Grades 3/4

Here is a simple way to practise saying the time in different ways using a wrist watch or an analogue clock. Mix and Match Time Challenge is for 2 or more students.

To start, notice the difference between the shape, size and colour of the hour and minute hands. To read the time correctly you need to see these differences quickly. Focus next on the angles the hands make. Is the hour hand before at or after a number? What does this mean? e.g. If the hour hand is just before a number such as 1 then it is not yet 1 o’clock. Look at the minute hand. Where is it in relation to the 12? If it is just after the twelve? Then that next hour has only just begun. Is it closer to the 6? If so it is almost half past the hour. Has it gone past the 6?

You can also use the large examples of the watch and red analogue clock face Read the Time Flashcards. These are great for Mental maths Warm-ups. Hold up one card at random then brainstorm all the things you know based n this clockface. e.g. 10:15 – one hour later will be 11:15, half an hour before was 9:45, 1 minute later will be 10:16, 2 hours before was 8:15. Encourage your students to create as many time follow-ups as they can, based on this initial time shown on the flashcard.

Later students can practise reading the time using watches and clocks without numbers. It is really only the position of the hands that matter on an analogue clock. Look at our Numberless Clockfaces, also in Time Activities for grades 3/4.

## MATHS PHOTOGRAPHS – MULTIPLICATION & DIVISION – Maria and 30 eggs

Real-life maths is all around us – we just need to keep our eyes open. This photograph of Maria and 30 eggs was taken at our local cafe, The Spanish Deli, this morning. I couldn’t resist sharing this one with you all. Multiplication and division in action. These eggs had just been delivered in a 5 x 6 array. How many is that altogether? How do you know? e.g. 10 x 6 = 60 and half that is 30. 5, 10, 15, 20, 25, 30 if you count by 5s. What if Maria had 2 trays delivered? How many eggs would that be? 10 trays like this? If Maria orders 100 trays like this in a month how many eggs might that be in one day? If she uses 3 eggs in every omelette how many omelettes can she make from 1 tray? 2 trays? 10 trays?

We can go on forever thinking of possible maths questions to solve. But that’s what you need to do with your students – encourage them to create their own questions. They can consider costs per tray and per egg, cost of a hamburger with an egg, cost of an omelette with 3 eggs.

How can you use this photograph today in your classroom?

## MEASUREMENT ACTIVITIES – TIME – Which one takes longer? F12

Young students need to practise comparing and discussing different time events. Here’s something to add to your activities for the younger students at your school, Which one takes longer?. With a partner, take a time event card each and talk about what this would look like in your daily life. Time events are not fixed, so of course painting a wall may be a very small job and just involve touching p a few areas in under 10 minutes. Or it could be more involved and take quite a long time. Talk about which event might take longer and why. Or could each of the two events take exactly the same amount of time? There are some language cards to place in between the two time event cards so you can create a time “story” together.

## MATHS GRAPHICS – PEOPLE – Jumping Girl

Duffy is going crazy drawing a whole new set of people graphics for you to use with all your maths activities. This jumping girl is only the start. Keep checking Graphics: People over the next few weeks while we add a few at a time.

Use this graphic as a stimulus for class discussions.

- How high can you jump?
- What’s the highest anyone in the world can jump from a standing start?
- Do taller people jump higher than shorter people?

In Data you can list all the things that make your students want to jump for joy. Then put them into a list according to the most popular to the least popular suggestion. How might you graph what you discover? What are three data comments you can make about this list?

## PLACE VALUE ACTIVITIES – Grades 3/4 – Mystery 4-digit numbers

It’s always a challenge for your students once you move off the straight and narrow path. These 2 activities, Mystery 4-digit numbers, are designed to keep your students thinking. All they need to do is to discover which three 4-digit numbers fit all the given rules. Quite easy if they have their thinking caps on. Plus we include a detailed explanation of one way to work out the matching answers for those students who need more support. Once they get the idea perhaps they can think of other similar challenges themselves.

What if you discover three completely different mystery odd numbers which all have digits that add to 12? (e.g. 1551, 3333 and 5115)

Or three odd numbers where all the digits add to 10? (e.g. 1441, 3223 and 5005)

## 2D SHAPES PHOTOGRAPHS – Bali geometric ceromonial decorations

Just back from a delightful 2 week holiday to Ubud, Bali. The ceremonial decorations there are almost overwhelming in both their beauty and their construction. Most are made from strips of palm leaves, a few staples and “toothpicks”.

You can try to create some of your own using coloured paper squares. Most are rotation patterns, made from repeating a cut out palm leaf shape. Let your students’ imaginations run wild.

The Balinese also use these decorations as part of their ceremonial dances. You can find these photographs in 2D Shapes Photographs and also 3D Objects Photographs.

## NUMBER & ALGEBRA – Multiplication & Division Photographs – 9 Happy Children

Remembering your groups of 9 maths facts is not an easy task. Ideally by the end of Grade 4 students should have quick recall for all their multiplication and division facts to 10 x 10. This group of 9 happy children is one way to help them focus on adding groups of 9, looking for a pattern and locking them into their memory bank. There is also a Groups of 9 Happy Children Poster to help you with your Mental Warm-ups.

## NUMBER & ALGEBRA – PLACE VALUE PHOTOGRAPHS – Door 77

I know, I know. Yet another place value number in a real life setting. I just can’t resist them. This one was found on the streets of Morpeth, near Newcastle. Where can your students see numbers around them? What’s the largest number in their street? Is it odd or even? If 2 people live in each house from 1 – 77, how many people is that? What if there are 4 people in each house? 10 people? Could 100 people live in a house like this one? Why? Why not? What number is 100 more than 77? 1000 more? Is there a street in your suburb that has 1000 numbers? Why? Why not? What is the number of the house 3 up from this one on this side of the street? (79, 81, 83) Is there an easy way to work this out?

I am sure there are oodles more place value questions you can ask your students, using this photograph as the stimulus.

## NUMBER & ALGEBRA – Fractions & Decimals – Rhino Decimal Counts 5/6/7

Decimals seem to always be one of those difficult concepts for your Stage 3 students to get their heads around. Here is a variety of Decimal resources to help.

*Decimal Number Cards*so your students can create random numbers to compare and manipulate.*Decimal Number Lines*in 4 different forms for your students to visualise proportional reasoning with decimals. Where will their number appear on each number line? Is it smaller than, the same as or larger than half way between two given numbers?*Rhino 1-place Decimal Counts*cards for pairs of students to practise counting by simple 1-place decimals as far as they can in just one minute. Keep practising until each student is confident they can count aloud without any finger manipulation or pen and paper scatchings.*Rhino 2-place Decimal Counts*for pairs of students to practise counting by simple 2-place decmals.*Rhino Maths Facts*cards to use in any way you like. But they will be a good companion to the counting cards to help make some of the counting numbers come to life. Which rhinos live for 0.35 centuries? Which rhinos grow to a mass of about 0.9 tonnes? Or have a horn that grows to 0.95 m?

## STATISTICS & PROBABILITY – DATA PHOTOGRAPHS – Jellybeans

Everything you need for a brilliant discussion on the different jellybean colours you can discover in one packet. Twenty-one beautiful colour jellybean photographs for those maths sessions where you are not able to use real jellybeans. And using photographs is more hygenic!

Think about how many jellybeans mights be in the whole pack? What estimation strategies work best for you? Which colour appears to be the most common? The least common? Which colour jellybean do you like to eat the most? I love black jellybeans but they are always amongst the least plentiful colours.

What might a jellybean graph look like? How can you transfer a graph made from jellybeans to a workbook page? e.g. Will you draw in all the jellybeans? Use a colour code and dots or squares? Will you use any grid paper? What scale will you use/ How will you label your grid? What title will you give it?

Do all packets of jellybeans have the same numbers and colour combinations? How can you find out? e.g. Every class could investigate the contents of one packet of jellybeans. You can collect all the data you can from your class to share and compare at a whole school assembly.

What questions can you ask each other about your jellybean discoveries? Why doesn’t the maker of the jellybeans put in equal colour numbers? When were jellybeans invented? Where? Who invented them? Why were they invented? Why might they be a bean shape and not a sphere or a cube shape?

## MEASUREMENT – LENGTH PHOTOGRAPHS – Mt Banks 1049 m

A bush walk is a great way to see the countryside. And the Mt Banks walk in the Blue Mountains National park is a popular one, especially with families as it is not too arduous. Mt Banks was named after the famous colonial botanist Sir Joseph Banks. It stands about 100 km west of Sydney. It has an elevation of 1049 m and the walk to the top is about 4.8 km. It has a unique basalt cap for the top third. The lower two thirds section is made from Sydney sandstone.

There’s plenty of maths facts here to get your Stage 3 students started for a series of Length sessions. How high does a hill have to be before we call it a mountain? Which NSW mountains are taller than Mt Banks? Shorter? The same height? Which NSW mountain is the tallest? By how much more? How long would it take to walk to the top and back if it is a fairly easy walk? Lots of statistics as well as length measurements to consider.

And thanks to my bush-walking sister Lee for contributing this photo to our website.

## MATHS GRAPHICS – Numbers and Symbols – Animal Numbers

We have just uploaded Duffy’s latest Animal Numbers 0 – 9, a spectacular assortment (including one bird …) to delight and inspire your Early Stage 1 and Stage 1 students. Use them as headers on an activity card or as a stimulus for a discussion about where you will find this number in real-life.

Each animal is based on the matching digit in Comic Sans font. What a clever boy he is!

By the way, did you know that an “animal” includes mammals, birds, fish, reptiles and amphibians? Perhaps later Duffy will try to construct some sea-creature numbers too?