# What’s new in Maths Matters Resources?

## NUMBER & ALGEBRA – PLACE VALUE – Hooray for Wombat

Our Maths Matters Creative Director, John Duffield, has just published his first iBook. It’s called *Hooray for Wombat.*

What a wonderful way to investigate the numbers 1 – 9 and then 10 – 90 using the delightful animal characters Duffy created originally for our website’s Place Value Graphics.

We look forward to many more books to come. Congratulations Duffy!

## CHANCE GRAPHICS – Paper, rock, scissors

Paper/rock/scissors is a game of chance between two people. On a signal you each make one of 3 shapes with your hand – rock (a closed fist), paper ( a flat hand) or scissors (a fist with two fingers making a V). The outcomes are that you make the same shape or a different shape. If the shapes are different then paper covers rock (paper wins), rock crushes scissors (rock wins) and scissors cut paper (scissors wins).

This game began in China and Japan and is a simple way to select who goes first, for example, in another game. It is like flipping a coin, throwing a die or drawing a straw from a pile. It is a selection method.

There is even an official website for discussing the rules if this game.

## STATISTICS & PROBABILITY – Chance Graphics

Duffy has just created a sweet set of children to help you talk about Chance with your students. What’s the chance of having a boy or a girl? Twins? Triplets? Quadruplets?

Your chance for having a boy is about 50% and 50% for having a girl. But many of you will know families that are all boys or all girls. Having all boys or all girls is almost always due to simple chance. Scientists have actually researched this topic and find that boys are 52% more likely than girls, so you really have a very slight increased chance of having a boy.

Did you know that Nigerian women enjoy the highest rate of twin pregnancies in the world? About 1 in 22 Nigerian women have twins. In 2013 there were 4475 sets of twins born in Australia, out of a total of 298 984 births. This represented about 15 in 1000 births. And of these 15 sets of twins, about 30% are identical. So fewer than 5 in 1000 births in Australia are identical twins.

In 2015, there were 84 sets of triplets born in Australia, out of a total of 305 377 births. That’s a 26 in 100 000 chance of having triplets. And there has been a 400 percent increase in the rate of triplet births over the last 20 years. To create identical triplets, the original fertilised egg splits and then one of the cells splits again. Identical triplets occur in about one in a million pregnancies, a rare event indeed.

Did you know that the odds of conceiving quadruplets is predicted to be one in 729 000? To create identical quadruplets, one fertilised egg needs to split into 4 separate embryos. Phew.

## MEASUREMENT – VOLUME & CAPACITY – Stage 1 Estimating fifths

Regular practice estimating volumes will help your students develop effective proportional reasoning. We use this skill when we think about multiplication and division. We also use this skill when we think about fractions. I am working on a whole set of these activities but this is the first in the STAGE 1 set. It will help your students think about fifths. It will help them understand how to mentally divide a length into 5 equal parts. Later sets will focus on dividing a given volume into halves, thirds, quarters and tenths.

The theme of FILL IT TO THE TOP (fifths) is orange juice. Even though you are just discussing a picture card, encourage your students to imagine it is a container of real orange juice. You want to share this juice equally between 5 people.

Develop a simple language routine to discuss the fraction parts. If this is one fifth, how many more fifths do you need to fill this container to the top? If this is two fifths, how many more fifths do you need to fill this container to the top? If this is three fifths, how many more fifths do you need to fill this container to the top? If this is four fifths, how many more fifths do you need to fill this container to the top?

Remember to talk about the full container as five fifths or one whole container full.

This activity is also part of our STAGE 1 Mental Warm-ups.

## MEASUREMENT – VOLUME & CAPACITY – Stage 2 Volume Mental Warm-up

For some reason Volume and Capacity is one of the mist difficult sub-strands in Primary Mathematics to both teach and learn. Too many Year 3 students are not able to answer Stage 1 questions in National or International Assessments.

- Yes it is a language problem.
- Yes it is a lack of whole class resources problem.
- Yes it is a messy water problem.
- Yes there may be more important strands or sub-strands to focus on.

But … that doesn’t mean we ignore Volume and Capacity. There are still important concepts for students to take with them into adult life. The ability to estimate amounts in a given container, to think about litres and millilitres, for example.

We have just uploaded How much water is that? for your Stage 2 students. It involves using real containers and water to establish the Volume concepts in real life. You then switch to 2D representations to help students internalise their experiences using the following 4 cards:

Your goal is for your students to use proportional reasoning to estimate how many cups of water they need to fill each container. It sounds simple, but only 52% of year 3 students in the Year 3 2016 NAPLAN Numeracy Paper were able to do this successfully.

This activity is also part of our STAGE 2 Mental Warm-ups.

## MATHS PHOTOGRAPHS – 2D PATTERNS – Ikat Textiles

Ikat textiles are amongst the most beautiful geometric patterns in the world. And they are so complicated to design and create that it is a wonder that they exist at all. I have just uploaded lots of textile photographs, including about 10 ikat ones. “Ikat” means “to tie” or “to bind”.

Ikat is a resist dyeing technique where you dye the warp yarn before you weave it. Different bundles are tightly bound then dipped in the dye. These might be unbound and then rebound in a different way before being dipped in a different colour dye. All the bindings are removed at the end of the dye process then the yarn is used to weave the cloth. The weft yarns are dyed in a solid colour. Once you set up the warp yarn you can see the pattern before you start the weft design weaving. Once woven of course some of the yarn is not in exactly the right position so you get a slightly blurred effect. Famous ikat textile villages can be found in Kalimantan, Sulawesi and Sumatra. The tribal groups are Dayak, Toraja and Batak.

You can also create weft ikats. This time the weft threads are bound and dyed but it is much more difficult to weave as the design only shows once it is actually woven!

And you can even get double ikats. These textiles are created by first binding and dyeing patterns into both the warp and the weft yarn. Utterly astounding! Very few places still create these complex patterns. You can see them in Tengenan in Bali and Puttapaka and Bhoodan Villages in India.

You can find ikats also in Central and South America, Central Asia and Japan. In the 19th century, Bukhara and Samarkand in Uzbekistan were famous centres for silk ikats.

## NUMBER & ALGEBRA – MONEY PHOTOGRAPHS – Afternoon Tea

What a delicious way to think about adding or subtracting, multiplying or dividing money with 2-place decimals. Here are 4 shots from the beautiful Hopetoun Tearooms in Melbourne.

My favourites were the raspberry tarts! If they cost $6.75 each, how much for 10? What change would you get from $100? If you bought two tarts and shared them between 4 people, how much would each person pay? If you want to buy the raspberry tarts for a party and give everyone half a tart each, how many will you need to buy if you expect 10 people at your party? How much will this cost? How much change from $50? From $100?

I am sure you and your class will be able to create many more money stories like these ones. Perhaps you could even think about how you might cook some tarts together, just like these ones?

## MATHS PHOTOGRAPHS – CREATURES – Tropical coral and fish

Did you know what the water temperature has to be for tropical fish to survive comfortably? It is 25 – 27 degrees centigrade. Imagine how global warming will affect our sea creatures.

Here are 6 new photographs of tropical fish to inspire your next maths discussion with your students. How many different tropical fish can you find in Australia? What do they eat? How long do they live? What are key facts you need to know to keep them in a tank in your home? How many eggs do they lay at one time? What are their predators? Where can you find them along the Australian coast. How many might you find in a school of fish? How far might they travel in a day?

## NUMBER & ALGEBRA – PLACE VALUE to 100 PHOTOGRAPHS – Floor numbers

I love seeing numbers in real life. But it gets difficult to see quite large numbers doesn’t it. We have just included 4 new photographs of floor numbers in high rise buildings (Floor 27, 28, 29 and 80). The larger of these numbers is a little blurred but it is Floor 80 in the Empire State Building in New York. It was taken by our gym buddy, Costa, on a recent trip to New York. Imagine all the class discussions that relate to floor levels. For example, the Empire State Building has 102 floors. But is this the most in the world? It is 381 m tall or 443 m from the ground to the tip at the very top. What does that tell us about the height of each floor? It was built way back in 1932 so imagine all the buildings that must be even taller than this today.

Currently the Burj Khalifa in Dubai is the world’s tallest skyscraper with a height of 828 m. It was built in 2010 and has 163 floors. The Empire State Building is now only the 34th tallest building in the world. But in 2020, the Jeddah Tower in Saudi Arabia will become the world’s tallest building. It will be 1008 m tall. That’s more than a kilometre!!!!! And it will have 167 floors at a crazy cost of about $1.5 billion. It was originally planned to be 1.6 km tall – that’s one mile in the old measures. It was designed by the architect Adrian Smith, who also designed the Burj Khalifa.

## HISTORY of MATHEMATICS – Medieval and Renaissance PHOTOGRAPHS – Money Stainglass Windows

What a different way to study the history of money. This set of Money Stainglass Windows photographs shows how money was made and distributed in the Middle Ages. They were taken in the Palazzo Massimo alle Terme (National Roman Museum). Each stain glass picture can be the basis of a fascinating discussion with your students. What do you think the people are doing? Why? How many people might be involved? How might we do this today? What did money look like in the Middle Ages? Why do we have money? What might we do if we did not invent money as a system?

## GEOMETRY – 2D Patterns PHOTOGRAPHS – Tribal textile patterns

What a beautiful way to investigate patterns and design. People have been creating magnificent geometric patterns for 1000s of years. Wandering nomads weave camel and sheep hair to produce rugs, and those closer to big towns spin silk and weave intricate designs – clothes, decorations for the house, cloths for rituals. Here are plenty of examples of tribal textiles to start a conversation with your students.

Are the designs symmetrical? How many different colours are used? Are the designs simple or complex? Who might create such a textile? How long might it take them to weave or embroider?

Follow up in your own classroom by decorating some placemats or decorated cloths. Try creating some simple weaving frames and weave coloured wool.

## MEASUREMENT – TIME PHOTOGRAPHS – iphones, wristwatches and digital clocks

It’s always a good idea to discuss time concepts daily – whether you teach Kinder or Year 6. Digital time is everywhere and most of the latest gadgets only show digital examples of time passing.We just uploaded 6 new photographs to help with your class discussions.

Elect one student to be your weekly time monitor. As a class, decide on a list of times for your focus this week. Ask the time monitor to let everyone know when this time is approaching e.g. afternoon for Kinders, 1:30 pm for Year 1, a quarter to 11 for Year 2 and so on. We also have a great range of quick daily mental warmups for time. I love the Numberless Clockface cards. Try them today with your class. We include teacher instructions to get you started.

## NUMBER & ALGEBRA – PLACE VALUE GRAPHICS – Skateboard digits

To start the year off we have just uploaded a brand new set of 1 – 9, 10 – 90, 100 – 900 and 1000 – 9000. They are all based on Duffy’s new set of Skateboard Robots. Heavens knows where he gets all his crazy ideas from but they look brilliant and should be a great way to focus on Place Value and Whole Number concepts in Term 1.

How many different ways can you talk about 3000?

e.g. 1 more than 2999, 1 fewer than 3001, 3000 ones, 300 tens or 30 hundreds. It is a multiple of 2, 5 and 10. It is also a multiple of 3 and 6. It is also a multiple of 4 and 8. But it is NOT a multiple of 9, 11 or 12. Half of it is 1500, Double 3000 is 6000. Ten times more would be 30 000. 3000 mL of orange juice is the same as 3 litres. 3000 m is the same as 3 km. 3000 square metres is the same as 3 tenths of a hectare.

What else will your students think of? Use a 1 minute time limit and challenge them to discuss their ideas with a partner.

Create a class book to share at the next school assembly.

Create a financial plan to raise $3000 over the year for your favourite school charity. e.g. We have 40 weeks so that’s $75 per week or $15 per day. What can we do to earn that much money?

## NUMBER GRAPHICS – NUMBERS & SYMBOLS – Robot Skateboarder Digits 0 – 9

Wow, Duffy has really gone crazy. He has created this delightful set of robots that are all skateboard fanatics. They look like they are in a frantic skateboard race with their bodies forming the digits 0 – 9.

Use them in a wide variety of classroom activities. Make 3, 4, 5, 6-digit numbers to discuss as part of your daily Maths Mental Warmups. Add them to an activity card.

e.g. Did you know that 4840 is the number of square yards in an acre? This is an old imperial measurement from the time of the British. In Australia we now measure area in hectares, as part of the SI measurement system. An acre is now 0.405 hectares.

## NUMBER & ALGEBRA – FRACTIONS & DECIMALS – If this is one unit (Stage 3 Fraction Cards)

Fractions are a nightmare for students. I am not sure why this is, as underneath it all fractions are just another way to look at objects, by breaking them into smaller parts. The complication comes when we don’t visualise the link between objects and numbers. Fraction numbers without any link to objects in the primary school can be disastrous. To help your students visualise equal parts of shapes, we have created this activity called, “If this is one unit, then what is that?”

We think it will best suit Stage 3 students, but try it with Stage 2 as well. All you need to do is imagine inside your head how a smaller 2D shape can be combined to create a larger 2D shape.

For example, look at this yellow square, if this is one unit, then how does this unit shape relate to the blue trapezium? Can you mentally visualise how the yellow square will fit onto the blue shape? If so, what part is left? What part of another yellow square does this represent?

Can you see that it is a whole yellow square plus half of another one? So this blue shape is 1 and a half times the area of the yellow square.

What about this green trapezium. How many yellow squares could fit onto the same shape?

Can you see that it is the same as two yellow squares? One yellow square fits in the middle. The other yellow square could split in two and fit to cover the ends.

This activity contains plenty of discussions like this one to help your students imagine multiples of areas, multiples of fraction units.

We have also added the graphics separately for you to use any way you wish. See Fraction & Decimal GRAPHICS.

Please note that we have included suggested solutions to each of our Fraction Questions.

## MULTIPLICATION & DIVISION – PHOTOGRAPHS – 30-legged creature

Arghh! This creature was crawling along our car port ceiling when I took this photograph of a 30-legged creature. We counted … and think we see 15 pairs of legs. What a different way to discuss multiples of 2 with your Stage 1 students. What if there were 2 creatures like this – how many pairs altogether? How many legs is that? How do you know? How many legs on 5 creatures? 10 creatures? 100 creatures? What is an easy way to help you count by 30s? e.g think of your groups of 3 tables facts and add a zero? Quickly add on mentally by 30 each time?

## GEOMETRY – 3D PHOTOGRAPHS – Cylindrical crab hole

We are surrounded by 3D objects. Even creatures can create them. This photograph of a crab hole was taken yesterday at Bennett’s Beach, Hawks Nest. The beach was covered with these 3D spaces, built by industrious sand crabs, almost perfect cylinders.

These crabs are quite elusive and spend most of their time hidden underground. Did you know that a sand crab, unlike other crabs, can only move backwards? They have no claws on their front pair of legs. They feed in the wash zone where the tidal waves go up and down the shoreline. Sand crab tails also have the largest number of sensory neurons so they are often used in lab studies. And female sand crabs can lay up to 45 000 eggs at a time, even though most eggs do not survive..

## NUMBER & ALGEBRA – PLACE VALUE from 100 PHOTOGRAPHS – 108, 8300 & 8765

It is always a good time to discuss Place Value with your students. Place Value is one of the biggest ideas in Primary Mathematics. Thanks to the use of Hindu-Arabic numerals and the creation of zero, your students can explore the power of Base 10 in all its beauty.

We just added 3 more number shots to our Place Value from 100 Photographs:

What will your students talk about?

e.g. 8300: What does each digit represent? What does this number look like in Base 10 blocks? How many i the 1s place, 10s place, 100s place, 1000s place? What is the total number of 1s, 10s, 100s, 1000s in this number? What is this number rounded to the nearest 10, 100, 1000 or 10 000? What if I took 1000 away? 5000 away? 8000 away? How many more to make 10 000? 20 000? What could you buy with this if it was money? If you were a shop owner, how many $100 skateboards could you buy with this amount?

If these are centimetres, how many netres is that? How many kilometres? If these are square metres, how many hectares is that? If these were millilitres, how many litres is that? If these were kilograms, how many tonnes is that? If these are seconds, about how many minutes is that? About how many hours?

## MEASUREMENT – VOLUME & CAPACITY – Photographs – Teapots

Teapots galore. These four teapots are from my personal collection of over 300 teapots.

A fun way to talk about volume with primary students. How many cups does each one hold? If you filled it up 4 times how many cups of tea can you serve? Which teapots hold more, the same or less tea? What’s the smallest teapot in the world look like? What does the largest teapot in the world look like? If one teapot holds 5 cups how many times will you need to fill it to serve 2 cups of tea to 6 people?

I’m sure you and your students will create many more teapot problems to solve.

## MATHS GRAPHICS – Numbers & Symbols – Water Digits 0-9

Duffy has just uploaded this beautiful set of 0 – 9 Water Digits. We used them to create our latest set of Sea Creatures 1 – 10 Posters. Use them with Early Stage 1 students as a stimulus for drawing and counting their own sea creatures 1 – 10. Or create 2-digit to 6-digit numbers on your smartboard with older students, as part of your daily mental warm-ups. Challenge everyone to create matching facts about water e.g. 495 – 495 L is almost 500 L of water or half a tonne, 495 mL is almost half a litre of water, 505 L more would make a tonne.