# What’s new in Maths Matters Resources?

## 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.

## MATHS GRAPHICS – Creatures – Sea Creatures

Duffy is creating a delightful set of sea creatures for you. There will be at least 10 and when he is finished we will create a set of Sea Creatures 1 – 10 Counting Posters. Remember to use our resources in a variety of ways, not just for maths. They may be the stimulus for a set of stories or poems. They may be part of a Science unit on the effects of humans on the sea.

Each illustration can be used for online research too. What are all the maths facts your students can discover about each creature?

e.g. Sea turtles:

- Australia has some of the largest marine turtle nesting areas in the Indo-Pacific region.
- Australia has the only nesting populations of the flatback turtle.
- Raine Island, in the northern Great Barrier Reef, is home to the world’s largest green turtle rookery, with an annual nesting population of 30 000 female turtles.
- Marine turtles have lived in the oceans for over 100 million years.
- Adult Green Turtles have a shell length of about 1 m and their average mass is about 130 kg.
- Green Turtle hatchlings are only 5 cm long with a mass of 25 g.
- Green Turtles lay about 115 eggs per clutch, and produce about five clutches per season.

## MATHS GRAPHICS – Counting – Wild Animal 1-10 Posters

Ten leaping cheetahs – just one of our new Wild Animal Counting 1 – 10 Posters. Young students need plenty of variety to develop flexible number concepts. Apart from the obvious counting of all the creatures on each poster, challenge your students to visualise adding and subtracting creatures too. What if three more cheetahs joined these ones – how many cheetahs will there be? What if 10 more joined? What if 3 cheetahs were too tired and stopped to take a rest?

Encourage your students to create these “What if?” stories for each other.

## WHOLE SCHOOL PLANNING – Maths Improvement Plans – Term 1 – Number Resources Checklists

We’ve had many requests for us to create Number Resources Checklists and have just uploaded one for each Stage. We tried to link each item in the list to any existing resources we supply, but could only link it to the general page, not the specifc item. At least this shows you which page to look at. As you can see, there are plenty of items that we think are essential for effective mathematics teaching. Resources to use as large flash cards for whole class discussion, for example. Perhaps you can make at least one set and share it with another class.

We are constantly creating more resources so these checklists will be updated at the end of each term. If you can see any items you think are still missing, please write to us and we will do our best to create what you need. Our aim is to provide all the essential resources that will make your teaching life a breeze. We want you to love teaching mathematics and see it as a highlight of your day. And of course we want your students to have the resources they need so that they love maths too and understand how it fits into daily problem solving in their own lives.

## MATHS GRAPHICS – COUNTING – Multiples of 100 Alien Eyes

Stage 1 students will love counting multiples of 100 when it is all about Alien Eyes. We need to provide our students with a wide variety of Base 10 models to help them develop a flexible image of how our Place Value system works. This set of 100 – 900 posters is just one resource we provide. In Place Value Graphics there are also single aliens with one eye, single aliens with 10 eyes and then a spaceship full of 10 aliens who each have 10 eyes.

## MATHS GRAPHICS – COUNTING – Multiplication & Division Arrays

These colourful new Multiplication & Division Arrays will help you talk about number facts and number patterns with your students. For example, 10 groups of 4 triangles are the same number as 4 groups of 10 triangles. It’s also the same as two groups of 2 x 10 triangles. Or the same as two groups of 4 x 5 triangles. What more can your students discover?

## MATHS GRAPHICS – Fractions & Decimals – Decimal Number Expanders and Decimal Place Value Charts

We have been revising our Graphics section and just added heaps of new resources to help you with Fractions and Decimals. We have Decimal Number Expanders ( so your students can create their own decimal number and describe them to a partner), Decimal Place Value Charts (so your students can create random decimal numbers using either a spinner of digit cards, then describe and compare these with a partner), Fraction Posters (e.g. thirds of a cake, fifths of a beaker of liquid) (so your students can more easily visualise what different amounts look like). Plus we improved our Fraction Cake graphics so that your students can “see” the missing parts of the whole cake. Again, this should help them more easily visualise what each fractional part looks like.

## MATHS GRAPHICS – Place Value – Spinners

Even though they might not work as effectively as a plastic commercial spinner, have a go at making your own Place Value Spinners with your students. All you need is a photocopier, A4 Cardboard sheets, scissors and a split pin. We have created a variety of colours and a range of values from 0, 1, 2 … 9, 0; 10, 20 … 90; 0, 100, 200 …900 and 0, 1000, 2000 … 9000. Plenty to keep your students happy creating random numbers for their activities. What are you waiting for?

## COUNTING GRAPHICS – Multiples of 10 to 90 Sheep Posters

Counting by 10s is one of the essential early counting skills. Practise counting by 10s with your Early Stage 1 (Kinder/Reception/Prep) students daily. You can stand up and jump as you count. Or clap your hands and then your heads as you count by 10s. Anything to get them moving rhythmically whilst they count. These Multiples of 10 – 90 Counting Posters will help you consolidate this oral counting with representations of groups of 10. Stop at one multiple and check that students can say the multiple before or the multiple after that number. Or ask them to count by 10s while you clap your hands. When you stop they whisper the number they are at to a friend.

## LENGTH PHOTOGRAPHS – 14 new resources

We’ve been focussing on our length resources this week. Duffy is drawing 4 sports people (coming soon) and I’ve just uploaded 15 new Length Photographs. Many of these are items you use to measure both informal and formal length. Use them as part of your introductory discussion to a length unit. Many people are unfamiliar with the formal equipment. What can you use this item for? What has it got to do with length? Where do you start and finish your measurement? e.g. this photo shows a Diameter Gauge. Notice the measurments are smaller at the lower pointy end and larger at the wider section. This makes sense when you put this object into the top of an open container, such as a jar. It is one way to measure the inside diameter. Always encourage our students to estimate the diameter first, before they start to measure.

## MATHS GRAPHICS – CREATURES – Alpaca and friends

Duffy has been hard at work creating 4 new farm animals for me to use on my new Algebra Animal Antics Level 1 Stage 3 activities. I just flick my fingers and demand a creature, then voila, they suddenly appear ready for all of us to use. He is SOOOO clever! Duffy’s favourite is the alpaca (he knows I love these in real-life too). My favourite is the duck. Which new creature do you like best?

We have also created a set of cute 1-10 Farm Animal Counting posters. You can find these all together in F/1/2 Counting Activities or separately in Counting Graphics.

## NUMBER & ALGEBRA – Patterns & Algebra – Algebra Animal Antics S3

What a lot of animals. We’ve tried to help your students understand algebra concepts by substituting animals rather than just a geometric symbol to represent numbers in a number sentence.

Algebra Animal Antics Level 2 is for your medium block students in Stage 3 (Grades 5/6/7). We’re calling these 2 dot or Level 2, for want of a better description. Each set has 4 cards that create the clues for one number puzzle. There are 4 sets like this to enable each group to practise this idea 4 times before they attempt to create some of their own. Once you (or your students) have photocopied each set and cut out the cards, you’re ready to go. Everything is there to help you, including sample solutions for those students who need the scaffold.

Bev is working on similar P&A cards for 1 dot Level 1 (high block students) and 3 dot Level 3 (low block students) right now. They should be ready some time soon.

## MATHS GRAPHICS – 2D Shapes – Stars

Stars galore – and on the same night as the Oscars are announced in America!!

Lucy creates all our special technical designs and these stars are no exception. Beautiful bright colours and points from three to ten.

Use them to create patterns, discuss angle size and length measurements. And remember that these can fold to create magical multi-sided 3D pyramids.

## MATHS GRAPHICS – SPECIAL OCCASIONS – Birthday Party

A birthday party is a good excuse for a maths discussion and further exploration. How many people do you want to invite? What do you need to say on the party invitation? What time should people arrive? How long will they stay? What do you need to provide for your guests? What is your budget? When do you need to get everything ready? Who will help you? We’ve just uploaded 3 new illustrations for our Birthday Party theme in Special Occasions.

How can your students use these as a stimulus for their mathematical thinking?

## NUMBER – Place Value Graphics – Winner

Imagine you won the lottery. What extra good deeds could you do? You can use this latest “Winner” Maths Graphic from Duffy as part of a daily Mental Warm-up, as a focus for counting by 100s or as a stimulus for a lesson about Money.

Did you know that:

- There are over 170 different currencies in the world today.
- More Monopoly money than real money is printed each year in the USA – a Monopoly game has $15140.
- Our word “cent” comes from the Latin word “centum” – a hundred, a hundredth part.
- Cattle were the first form of money and the Latin word “caput” (head of cattle) eventually became our word “capital” in reference to money.
- The word “money” evolved from the old Roman goddess Juno Moneta. Roman coins were made in her temple.
- “Bankrupt” evolved from the medieval Italian “banca rotta” (broken bench). Moneylenders worked at a bench and when they ran out of money the bench was broken.
- “Pygg” was a type of clay in medieval England. It was used to make jars to store money. Today we have “piggy banks”.
- Hungary printed the highest denomination banknote in 1946. It was worth 100 quintillion pengoes. That’s 1 000 000 000 000 000 000 (18 zeroes).
- Obsolete bronze 1 and 2 cent Australian coins were melted down to create the Sydney 2000 Olympics medals.
- Australia was the first country to produce plastic polymer bank botes that are almost impossible to counterfeit.
- Fake $50 Australian notes can be discovered by scratching the clear window with a coin. If the star comes off your $50 banknote is a fake.

I wonder what mathematical discoveries and explorations you and your students will make using this graphic?