# What’s new in Maths Matters Resources?

## GEOMETRY – 2D Shapes Photographs – Crazy Tesselated Path

Tesselations are not always regular. Sometimes they are quite messy – like this Crazy Tesselated Path you see here. At first glance it looks like a random fitting of individual tiles but if you look very closely you will see a pattern. Can your students spot it easily? Look at the individual tiles. How many straight sides do they have? Why are they all so different? Why not just use a few tile shapes? Crazy paving uses a wide variety of shapes because of all the spaces created by trying to fit together non-symmetrical, irregular shapes. You need a new shape to exactly fit the spaces created.

One follow-up activity is to create your own crazy tile path with a pencil and paper. You may like to start drawing on a 1 cm grid.

## NUMBER & ALGEBRA – Counting Photographs – 30 floor building

We’re always adding new photographs to the website. Plenty to keep you going – but we just can’t resist getting out the camera when we see something interesting for you. Here is another angle for a Sydney building site with floors 1-30 visible. Will it go higher? What if the builders add 3 more floors? 10 more floors? What floor will you be on if you are working 10 floors lower than the 17th floor? If you have to add special light fittings to all the even number floors, which floors will they be?

## NUMBER & ALGEBRA – FRACTION ACTIVITIES – Grades 1/2 Counting Apple Quarters POSTER

Yay – more food. And its healthy for you too.

Fractions come to life by counting real apple quarters. But if you don’t have access to real apples then here’s a Counting Apple Quarters Poster to help you. Use it as part of your daily Maths Mental Warm-ups.

Select a student to point to each apple quarter on the poster while the rest of the class count aloud either together or one-by-one. “One quarter, two quarters, three quarters, four quarters …” Encourage your students to improvise by saying equivalent names too. e.g. “two quarters or one half”. Or keep counting by quarters then at random call out STOP. Whoever is next at counting has to say how many whole apples and how many extra quarters. e.g. “17 quarters: that’s 4 whole apples and one extra quarter.”

Talk about effective strategies to help you visualise combined quarters quickly. Can you think in groups of 4 when you look at this poster?

## MULTIPLICATION & DIVISION ACTIVITIES – ACARA Content Codes

ACARA Codes from the Australian National Curriculum have been added to all our Multiplication and Division activities. Just type the ACARA Code into our Search facility to instantly find a matching activity for your next Maths Session. What are you waiting for?

## NUMBER & ALGEBRA – MULTIPLICATION ACTIVITIES – Spend Your Money (Grades 567)

Your students enjoy activities with money as it makes sense to them. Studies show that students often succeed at mental money calculations more than just pen and paper ones. Spend your Money provides a variety of real-life money applications for your Stage 3 students to practice mental calculations with multiplication or pen and paper algorisms. Imagine they are a buyer for a company where they need to purchase up to 10, multiples of 10, 100 or even 1000 products at a time.

There are 4 cards at each level (High Block : 1- digit, Medium Block : 2-digits, Low Block : 3- or 4-digits) to help you plan for at least 3 groups. So there are at least 4 combinations of starting costs e.g. Football Socks $14, Sunflower Plant $23, Concert Ticket $56 or Skateboard $87. Then there are 10 Buy Cards for students, which tell them to multiply by a number from 1 to 9 at random – plenty here to keep 3 small groups working within a Maths Session.

Plus they can create further cards of their own using shopping catalogues. The possibilities are endless.

## NUMBER & ALGEBRA – COUNTING ACTIVITIES – Counting Tigers 3s Poster

Although the National Curriculum and State Mathematics Syllabus content does not continue the emphasis on counting into Stage 2 and 3, counting is a vital skill for all students. Counting helps you internalise the number system. It helps you form visual images of how the number system operates. it helps prepare you mentally for adding and subtracting, multiplying and dividing.

Here at Maths Matters Resources we provide a wide range of counting resources that continue into Stage 2 and 3. For example, this Counting Tigers 3s POSTER for your Stage 2 students will help students think in multiples of 3. Start by memorising just a few multiples e.g. 3, 6, 9, 12. As this becomes automatic, introduce a few more multiples e.g. 3, 6, 9, 12, 15, 18, 21. Eventually your students will memorise all multiples up to 27 tigers altogether. Try starting at 27 and counting backwards by 3s.

Record the multiples in counting order. Who can see a pattern in these numbers? How might this pattern help you memorise the counting sequence? For example, add the digits in the multiples 3, 6, 9, 12 becomes 1+2 = 3, 15 becomes 1 + 5 = 6, 18 becomes 1 + 8 = 9. Does this pattern continue for ever? How will you find out?

## NUMBER & ALGEBRA – COUNTING ACTIVITIES – How many farm animals? F12

Subitising is the process of recognising the exact number of objects in a small group without the need to count them one by one. “Subito” is an Italian word for “right now”. This ability to see “chunks” or groups at once helps you count more easily. We are all familiar with domino dot patterns, for example. It helps us separate and combine numbers quickly. This is useful when adding, subtracting, multiplying and dividing.

How many farm animals? is a great way for young students to try to subitise without a specific pattern. Each card contains a set of farm animals from 0 – 9 animals. The animals are scattered unevenly across the page. You can start by showing each card to your students and asking them how many animals they see. Gradually build up your speed until you flash each card for a fraction of a second. If they are still able to recognise the correct number of animals, ask them to explain what strategy they used to do this.

## GRAPHICS – MEASUREMENT – Tamarama Tide Chart

A fabulous new Tamarama Tides table packed with opportunities for mathematical investigations in your Measurement – Time maths sessions. Use this table with the 5 Tamarama tide photographs. What’s the time difference between low and high tide? Is it always this difference in time? What’s the difference in height between low and high tide? Is it always this difference? Do all beaches have the same difference in tides? Why? Why not? How will you find out? If you collect online data about tides at Tamarama Beach for one week, is there any pattern?

## NUMBER & ALGEBRA – MONEY PHOTOGRAPHS – French Pastry $3.50

I must have a thing about food mustn’t I! These delicious French pastries are $3.50 each. A great start for a daily mental warm-up with Stage 2 or 3 students.

What if you bought 10 – how much will that cost? What if you share with a friend – how much should you each pay? What if you share one pastry between 3 friends? If you are the baker and you decide to sell 10 pastries for $30, is that a better decision than selling 10 separate pastries at $3.50 each? Why do you think this? If each pastry costs you $1.25 to make, how much profit is that per pastry? If you plan to give each person at a party half a pastry each, how many will you buy if you expect 18 guests? How much will this cost you?

Hmmm … how else might you use this maths photograph in your next maths session?

## GRAPHICS – ADDITION & SUBTRACTION – Tins of baked beans

Yes yes … food again! But just imagine what you and your students can do with these baked beans.

We’ve created groups of 1 – 10 tins so there’s plenty of potential for addition and subtraction, multiplication and division. All your number facts from 1 + 1 to 10 + 10 can be explored, described, discussed, manipulated. And because they are in groups you can repeat them to create equal groups for developing concepts in multiplication from 1 x 1 up to 10 x 10.

There are even possibilities for counting, measurement and decimals … each tin has a mass of 220 g so Stage 3 students can select a group and calculate how many grams altogether. Is that more or less than 1 kg? How would you write that as a decimal number? Or link to money and give each tin a value e.g. $2.90. Estimate the cost of a random group of tins then find a way to check your estimate. e.g. 7 tins is about 7 x $3 so that’s close to $21 to buy 7 tins.

## GRAPHICS – ADDITION & SUBTRACTION – Gingerbread Counters

Just what you need after the festive season … more food!

Click here to see 5 delightful gingerbread counter graphics for exploring your addition and subtraction number facts to 5, and later to 10. Integrate them with the traditional story about the Gingerbread boy. Or use them on your smartboard as addition and subtraction combinations in your daily mental warm-ups. Or as equal groups of 1, 2, 3, 4 or 5 for early multiplication and division discussions.

And remember, we already have a lovely set of individual gingerbread counters as cards to cut out in our F/1/2 Counting Activities.

## GEOMETRY – 3D PHOTOGRAPHS – Richard Moffatt’s Metal Spheres

South Coast sculptor, Richard Moffatt, created the gigantic 5 metre diameter sphere which stands beside the Monaro Highway as a gateway sculpture for the Snowy River Shire. He used slightly curved metal beams left from the construction of Blue Cow Ski Tube in the 1980s. It has a mass of 7 tonnes. This sculpture is so large that it had to be cut into 5 pieces, taken by truck to the site, then reassembled and welded on the spot.

A smaller version of this sculpture, and many more, are scattered across the garden at Wild Brumby, Jindabyne. Richard loves to use recycled industrial metal which creates a beautiful earthy texture. We have just uploaded 7 of Richard Moffatt’s magnificent spheres photographs as an inspiration for your students. Look carefully and you will see how Richard creates a curved surface using straight lines and ones with a slight bend in them. One of his spheres is made entirely from the heads of old metal shovels, another is made from old brake discs.

How might your students create their own spheres from found materials? How will they create the curved surface? Could they cover a balloon, for example, then pop it when their sculpture is complete?

## NUMBER & ALGEBRA – Counting Photographs – How many sheep?

How cute. Twenty-one sheep all facing to the right – a lovely sculptural wall piece found on a cafe wall in Cooma. Use this with your Early Stage 1 (Kinder) students as an estimation activity.

How many sheep are there? What’s your estimate? Look at the photograph for only a few seconds before hiding it. Can you explain to a partner why you think your estimate is an effective one? What made you think of this number? How can you check? e.g. Count out a group of 5 then estimate how many more groups like that there could be? Use a pointer and touch each sheep as the class counts aloud? Can you count backwards? Once you know how many sheep there are (21), start at that number and try counting back by 1s? Can you count back by odd numbers ie count back by 2s?

Try some addition and subtraction questions too. If there were 4 more sheep, how many would that be altogether? If you had 21 sheep and 10 were taken to another paddock, how many sheep would that leave?

## NUMBER & ALGEBRA – PLACE VALUE PHOTOGRAPHS – 2015

At Maths Matters Resources we realise that everyone lives in different places all over Australia (and of course the world …) but we could not resist this lovely way to represent our new year 2015. Use this as a stimulus for a Number discussion about 4-digit numbers. Is it odd or even? How do you know? Why are you sure about this? What will be the date in 100 years from now? 100 years ago? You can keep a special 2015 year book and record special events of interest to your class throughout the year then present your favourite items at an end-of-year assembly using this photograph as your visual stimulus. If you add all the digits what number do you get?

If you rearrange the digits what’s the largest number you create? The second largest number? Is this a multiple of 5? How do you know? Is it a multiple of 10? How do you know? Is it a multiple of 3? What does this number look like on an abacus? On a number line? With Base 10 blocks? If you have this much money to spend on a holiday with a family of 4, where will you go? How long will you stay? What might some of your costs be?

## GEOMETRY – 3D SYMMETRY Photographs – Emperor Gum Moth

Oh my goodness. The beauty of our large Emperor Gum Moths, found in Australia and parts of New Zealand. This photograph is a close-up of a male Emperor Gum Moth from Hawks Nest NSW. Males have these feathery antennae. Their scientific name is Opodiphthera eucalypti as the caterpillars spin their cocoons mainly on gum trees. It can take up to a year or even up to five years for the adult moth to hatch from the cocoon and then it lives for only a few weeks. The wing span is up to 150 mm. Their wings have 4 “eyes in a symmetrical pattern. And look at the beautifully symmetrical antennae.

You can see another huge moth in the Maths Matters Resources Length Photographs (this is the giant Atlas Moth with a 25 cm wingspan).

## MEASUREMENT – TIME PHOTOGRAPHS – Tamarama tide chart and high/low tides

We uploaded 5 shots like this one from beautiful Tamarama Beach in Sydney as a wonderful basis for exploring tides as part of your Maths Session. They can integrate 12 and 24 hour concepts in the Time substrand with height in the Length substrand.

These photographs were taken on 8 and 9 January 2015. Low tide was just 0.4 m at 5:32 pm on 8 January. The next day high tide was at 11:36 am and it was 1.7 m. Can you spot the tide changes when you compare the low and high tide photographs looking to the north or to the south? Tamarama Beach has a bit of a dip down to the sea so the tide is perhaps not as obvious as at other beaches.

If your students live near a beach they can take their own photographs for a mathematical discussion. What cause the tide? Why is it sometimes high and sometimes low? When do the highest tides occur in the year? Why? When are the lowest tides Why? What is the greatest difference between high and low tide in one place in the world?

## NUMBER – PLACE VALUE PHOTOGRAPHS – Painted Rectangular Prism 1929

Local councils regularly attempt to brighten up the sidewalks by encouraging artists to decorate street telecommunication boxes. Here is one painted by local artist Stephen Evans at Bondi. He has imagined the box as an old Bondi Tram, Number 1929. At Maths Matters Resources we love to discover this sort of object to share with you in your classroom.

For primary students there are plenty of mathematical things to talk about. There are the 3 numbers – 1929, 1953 and 131 700 – so you can explore plenty of Place Value number concepts together. What’s 1000 more or less? What’s 10 times more or less? What’s the smallest number you make if you rearrange the digits in each number?

For Measurement and Geometry you can estimate the height, width and depth of the real box, based on ones you have seen in the street. You can estimate the area of each face of this rectangular prism, or the volume.Then there are questions of scale. How has Stephen worked out how large or small to paint his “tram”. You can ask everyone to bring in an empty grocery box from home. What object could this represent in real-life? How might you paint the outside surface? What proportions will you use? Why?

For Data you can ask your class to look out for these boxes in their own streets and suburbs. Keep a tally of how many they see that are painted or plain. Collect all the data and put it together as a class graph.

## NUMBER & ALGEBRA – MULTIPLICATION PHOTOGRAPHS – 50 x piles of 4 tomatoes

This photograph was taken at one of the markets in Yangon, Myanmar. Beautiful fresh tomatoes carefully placed into a lovely 4s pattern. Great for estimating a large quantity at a glance then finding a way to check your guess. Counting by 4s is so much faster than counting by 1s.

How much might these cost? How many do you need to make a nice salad for 4 people? Or to make a tomato sauce for some pasta for 4 people? What’s the largest size tomato ever grown? What’s the smallest? How long does it take a tomato to grow? How tall does a tomato plant get?

In Myanmar along Inle Lake tomato plants grow on floating islands tended by farmers in wooden canoes. Which other countries are famous for growing tomatoes? Can they grow anywhere?

How will you integrate this photograph into your daily maths activity today?

## NUMBER & MEASUREMENT – Multiplication and Position Activities (29 pages) – Grades 5/6/7

Phew. What a mammoth task. We have just uploaded a gigantic 29 pages of resources all based on an imaginary Little Town Shopping Centre. Plenty here for a whole unit of work for pairs of students, small groups, even the whole class. Develop Position Stage 3 skills and understandings by reading maps and directories, locating shops using co-ordinates, length measures and points of the compass. Practise and improve Multiplication & Division skills by calculating shop rentals for a year or a week and see the difference if you rent in the country, up at the mountains, by the seaside or in a big city. Calculate the cost of new floor coverings for your shop using 4 different materials. Which one will better suit your budget? See plenty of large numbers in action plus decimals and money too.

## MEASUREMENT – VOLUME & CAPACITY PHOTOGRAPHS – 130 mL milk

How much does a 6 month old baby drink in one day? One week? Here is baby Alex’s drink bottle. It contains 130 mL of milk. He has this 4 times a day. This bottle has the capacity to hold 240 mL but his mum only fills it to the 130 mL mark. Use real life Volume and Capacity photographs to remind your students how maths is all around us. Australia is slipping behind many countries in student ability to do well at everyday maths problems. So this is a great way to keep your students thinking and problem solving. What other activties can they create related to this 130 mL milk bottle?