# What’s new in Maths Matters Resources?

## 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 of tomatoes 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?

## MEASUREMENT – GRAPHICS – Time – December/January Calendar

Yes it’s that time of year again. Only four more weeks until Christmas and the New Year and then a nice holiday break. Here’s Duffy’s festive planner to help motivate your students with their calendar skills for December 2014 and January 2015.

What is the date exactly 2 weeks before Christmas? If my family has booked a holiday on the South Coast for 3 weeks starting on Monday 21 December, what date do we go back home? If I look after a friend’s dog every Saturday for \$5 an hour for 3 hours, how many hours do I work in December and January? How much money will I earn? My grandma will be 65 three weeks after Christmas Day, so what is the date of her birthday? Encourage your students to record their own calendar question related to this double calendar and calculate the answer, then put these into a special box and draw out one idea a day to discuss together.

## MEASUREMENT – VOLUME & CAPACITY – Photographs – Litres

What does one litre look like? You need to bombard your Year 2 – 6 students with this constantly so they develop an effective visual representation in all shapes and forms. Here are – milk and juice. Ask everyone to collect their own litre containers and bring them in to school. Fill them with water outside in the playground and then watch as students pour their litre of water into a wide variety of other shapes. Ask them to estimate where the level may go up to, think about what a half or quarter of a litre might look like, 100 mL, 200 mL and so on. Give an award at assembly to students who can estimate a litre to within a 10% accuracy level.

## MATHS GRAPHICS – CREATURES – Koala

Here is Duffy’s latest illustration, a gorgeous koala called Luis – the alpha male in the population at Hawks Nest NSW. Australian animals can be an effective focus for real-life maths activities. Koalas are not actually a bear – they are a marsupial so they raise their babies in a pouch. One joey is born each year and its about  2 cm long. It stays in the mother’s pouch for about 6 months. The adults eat about 500 g of eucalypt leaves each night but they can only absorb about 25% of this food as it is very tough to eat. They sleep for 18 – 20 hours each day so that they can digest all the toxins from the gum leaves. Although there are over 600 types of eucalyptus, koalas can eat only about 50 different types of eucalyptus leaves, including swamp mahogany (eucalyptus robusta). About 80% of koala habitat has disappeared in Australia and the estimate is that there are between 40 000 to 80 000 koalas left. Koalas live for 14-16 years in the wild. Koala fossils have been dated to 20 million years ago. Did you know that koalas also have very similar fingerprints to humans?

## NUMBER & ALGEBRA – FRACTIONS Activities – Comparing Halves 567

Playing around with models of equivalent fractions can help your students visualise equal areas. These models can also be useful for developing proportional reasoning skills. Comparing Halves challenges your students to find different ways to create a half from quarters and also from eighths. In this activity, Lee wants to create a flower garden with equal areas of red and yellow flowers so your students manipulate equivalent fractions while trying to work out a solution. This is a useful way to revise flexible thinking with your Stage 3 students.

## MATHS GRAPHICS – Measurement – November Calendar

Wow – the year is flying past and it is almost November! Here is a cheerful rainbow version calendar to use anywhere from Foundation through to Grades 6 or even 7. What are some key events happening with your class in November? In the school? In your town or city? Your country? Daily calendar questions are a useful way to reinforce days, months and seasons. What was the day and date 4 days before the 1st of November? What will be the day and date 3 days after 30 November? Two weeks after 13 November will be …?

## NUMBER & ALGEBRA – FRACTIONS/DECIMALS – Sliced Bread Mental Warm-up Stage 3

Any of our maths graphics can be used for a Mental Warm-up. This bread graphic is a lovely way to start your Maths Session. So where’s the maths in a loaf of bread I hear you ask? What a great question for your Stage 3 students! Your students need to be able to think and breathe mathematics on their own, without us always asking the questions for them. Challenge your students to create at least one new mathematical idea each day. Use the graphic on your electronic whiteboard or photocopy and laminate for regular use. Lots of suggested challenges to start them off if necessary. The sign of success is when you can sit back and let them do all the mathematical thinking.

## MATHS GRAPHICS – MEASURMENT – 500 g Peas

Peas, glorious peas. Here is Duffy’s latest graphic – 500 g Peas.

• Did you know that peas have been around since at least 4800 BC (Egypt)? How long ago is this? How many different ways can you work it out?
• The average mass of just one pea is between 0.1 and 0.36 g. How can your students verify this information? What different strategies can they suggest?
• This graphic shows a 500 g bag of frozen peas.How much might they cost? Is it cheaper to buy a 1 kg pack? Are baby peas more or less expensive than normal size peas? How many peas might be in a 500 g pack? What’s a quick way to estimate this?
• 95% of peas are sold frozen. Why would this be? What are the advantages? Disadvantages?
• Each year a town in Suffolk, UK, celebrates a Pea Festival. What would your students create as a festival event?

## NUMBER & ALGEBRA – PATTERNS & ALGEBRA – Pick my flower pattern F12

Your Early Stage 1 and Stage 1 students need plenty of practice creating and discussing patterns. Pick my flower pattern contains teacher instructions, 4 sets of flower cards, plus 2 sets of dot pattern cards, to help improve pattern skills using real-life objects. And they can also try recording their patterns or creating a new pattern card for another team to follow. Younger students can use the cards for sorting too and explain the basis for their sort.

## NUMBER & ALGEBRA – MONEY – Activities – What’s my sale price? Y567

Calculating a percentage discount can be quite tricky. Your students need lots of opportunities to try different strategies, try to work things out mentally, perhaps use a calculator to check. What’s my sale price? is a partner activity for Grade 5/6/7 (Stage 3) students. Practise buying multiples of up to 6 objects and then calculating a given discount – 10%, 20%, 25%, 40%, 50% or even 75% off.

Complete with easy-to-read answer sheets so your students can work independently. There’s even blank proformas so your students can create similar activities themselves. Change the prices, change the discounts.

Great as part of a unit on discounts. Your students can collect plenty of shopping brochures and catalogues for more real-life examples.

## MEASUREMENT – VOLUME & CAPACITY – Photographs – Sydney Aquarium 8 million L

Sydney Aquarium at Darling Harbour opened in 1988 and is one of the world’s largest aquariums. Over 1 million people visit this attraction each year.  Most people spend about 2 hours there. It is open from 9:00 am to 4:00 pm each day. There are 4000 square metres of exhibition space, including 2 oceanariums.

Over 11000 creatures live there in about 8 million litres of water. How much water is this? How can we visualise it? For example, how many litres of water in a normal bath? How many bathtubs of water would it take to make 8 million L? How heavy will this water be?Is it sitting on the harbour floor or in a built environment?

What is the largest aquarium in the world? How does Sydney Aquarium compare in size? e.g. Georgia USA (24 million L), Dubai Mall (10 million L)?

Your students will find plenty more aquarium facts to explore and compare at http://en.wikipedia.org/wiki/List_of_aquaria

## GEOMETRY – 2D SHAPES – Photographs – 90 degree parking sign

Parking signs like this 90 degree angle parking sign can be found on many streets. A great way to discuss both 2D angles and Position/Location with your students. Why do we sometimes park side on to the curb, front on, rear end to the curb. What are the advantages and disadvantages of parking at a 90 degree angle to the curb? What other angles are possible? Which parks take up more room on a street? If you were a member of the local council, which parking sign would you like to see in your area? Look at the other parts of this sign. What does 4P mean? Why is there a time included? What does the green arrow facing to the left mean?  All of these questions are examples of the sort of discussion you can have as part of your daily mental warm-up. Or of course as part of a unit on 2D angles.

## NUMBER & ALGEBRA – PLACE VALUE – Photographs – Truck 808

Yet another photo to add to our vast place value collection. Numbers all around us. So what will your students do with this one? How does Truck Number 808 link to your maths session? For example, Place Value: How many other palindromic numbers ( the same number written forwards or backwards) are there between 800 and 900? What’s 100 more/less than this number? How many 10s altogether? (80.8) How many 100s? (8.08) 1000s? (0.808) Addition & Subtraction: if I just bought this one and I now own 808 trucks, how many more do I need to buy before I have 1000? Multiplication & Division: If I own 808 trucks, how many different ways can I put them into equal size groups? How many wheels in my fleet if there are 808 trucks and each truck has 12 wheels? If I need 2 drivers on a roster to drive each truck how many drivers do I need to employ?

## NUMBER – MULTIPLICATION & DIVISION – Grades 3/4 Counting Beetles Posters

Posters are an effective way to count daily with your Stage 2 (Years 3 & 4) students. Before students are ready to just say the multiples on their own, counting real-life objects, or pictures of real-life objects, can help your students develop more effective visual images of the multiplication process. Remember multiplication is just another form of addition, but we want our students to create neural pathways so that the numbers arrive automatically. Counting these posters daily is one way to make this happen. Count groups of 4 geckos from 4 to 40, groups of 6 leopards from 6 to 60, groups of 6 eggs, groups of 7 apples, groups of 8 beetles or groups of 9 hippos. Start at 90 and count back by 9s. Continue counting groups past the 10 x group as far as you can go. You can enlarge these six posters to A3 and laminate each one for better storage.

## NUMBER – MONEY ACTIVITIES – What’s my change from \$20, \$50, \$100 Grades 3/4/5/6

And there’s more! You can see I have been busy this week working on new money activities. And they now all link to the new ACARA Syllabus Content Codes. These What’s my change from \$20, What’s my change from \$50 and What’s my change from \$100, encourage your Stage 2 and 3 students to develop effective mental strategies for working with common shopping prices and then working out how much change is needed. They are suitable for pairs of students or small groups to use.