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NUMBER & ALGEBRA – Patterns & Algebra – Metal Fish Patterns (F/1/2)

Younger students need to experience patterning every week. They need to see the rhythm, the sequencing, the various possibilities. They need to be able to describe a pattern, predict what the next item may be, identify an item that doesn’t belong in a pattern. They can explore patterns in buildings looking at window repetitions, brickwork. They can explore patterns at a fruit shop where the fruit & vegetables are often laid out in regular, repeated patterns in shapes & colours & textures.

These metal fish are just one way to expose your students to looking for patterns in real-life. Which way do the fish face? Is there one of a kind or two or three? How do you know how many fish you need to put down before it is a recognisable and describable pattern? If one piece in your pattern is covered up, is it easy to see what this hidden part must be so that the pattern sequence is continued? There are no black and white answers to these questions but your students need to see this for themselves.

Metal Fish Patterns provides you with 36 small metal fish pieces and 6 sample pattern cards. All suitable for your 5-7 year olds.

NUMBER & ALGEBRA – MONEY ACTIVITIES – Stage 3 What’s Today’s Rate?

Investigating currency rates around the world is an effective way to practise multiplying and dividing decimal numbers by 10, 100 and 1000. Use this activity, What’s today’s rate? as a Mental Warm-up with your Stage 3 students at least once a week. Your students will become proficient at collecting online data and multiplying and dividing decimals in their head.

They challenge a partner to answer random questions related to the data they collect. They will see how each week our currency is worth more or less or may even stay at the same exchange rate. The decimal differences will make sense rather than just being a number on a screen or a page in a workbook.

GEOMETRY – 3D PHOTOGRAPHS – Edible Triangular Prism

How many 3D objects can your students name that are delicious to eat? Here is a slice of lemon tart from Tillerman’s Restaurant at Tea Gardens. Yum. It is definitely an edible 3D object. What is the mathematical name of this object? Can you describe at least 3 properties or facts about this object? e.g.The top and bottom (the bases) have the same shape, (a triangle), the sides are rectangular, two slices side by side still look like a triangular prism (just wider).

What shape are student sandwiches? What shape could these be? How can you describe fruit that your students bring to school? Students could also investigate the 3D Objects they discover for dinner tonight. You could then draw and graph the objects the next day to find out which object is the most common edible 3D dinner object.

GEOMETRY – POSITION PHOTOGRAPHS – Wooden Ball Triangular Pyramid

It’s quite difficult for us to imagine what something looks like from different viewpoints. Yet this is a wonderful skill we can try to develop in each of our students. A part of your daily mental Warm-ups, hold up a 3D object and ask your students to imagine what this looks like from on top or below of from the back. You might even ask them to sketch it on some scrap paper and then compare their sketches with a partner. Here is a triangular pyramid, for example, made from wooden balls.You can see it from 3 different angles.


Wooden ball triangular pyramid front view Bev Dunbar Maths Matters        Wooden Ball Tetrahedron Bev Dunbar Maths Matters copy

These balls demonstrate tetrahedral numbers too. The first 5 tetrahedral numbers are 1, 4, 10, 20 and  35. This one is made from 20 wooden balls stacked together. The base starts with 4 balls on each side.You need 35 wooden balls to make a triangular pyramid with sides 5 balls long. You need only 4 balls to make a triangular pyramid with sides 2 balls long at the base. One ball doesn’t really look like a triangular pyramid but the idea is there!!! By the way, in the Song “The 12 Days of Christmas my true love sent to me …” the total number of gifts is 364 – the twelfth tetrahedral number!


Measurement makes no sense when it is isolated from everyday events. When you study Volume and Capacity with your students always link your discussion to real life examples. Before investigating millilitres, for example, ask each student to bring in an empty plastic litre container, preferable a transparent one. Use your school’s marked litre and millilitre resources to measure and then mark out where multiples of 100 mL come to in each container. Ask your students to compare what these multiples look like in different-shaped containers. Can they then predict where it will come to in a new container?

Encourage them to visualise, to imagine where the finish line will be. Look at where 200 mL orange juice comes up to in this marked container, for example. You need your eye to be level with the line to get an exact measure.

Christmas Card

Duffy has created a very cute Christmas Card for you this year. We often visit Hawks Nest (a small sea-side town in NSW) which is famous for its small endangered koala population so Duff was inspired to have a koala as the central motif. Other Christmas characters can be found in Graphics – Special Occasion. You can also find links to useful Christmas Tree facts in the Maths Cafe.


Willow has only just turned 3 years old and she loves to read the Taronga Zoo Kids Map to discover her favourite animal spaces. She loves the giraffes in particular and carries her toy giraffe with her wherever she goes.

Map reading is an effective skill we use in our daily lives e.g. to read a transport map to figure out which station, stop or ferry wharf we need to get out at. You need to know which way is to the left and right on your map, even if you don’t have the words “left” and “right” fully understood. You need to understand that specific symbols refer to paths, areas and directions.

If Willow can maneuver herself and her Grandma around a zoo when she is three years old, imagine what she will be able to do when she is 5 and in Kindergarten. Current technology presents us with Google Maps, locations of holiday houses, shops and a friends house at the flick of an ipad or iphone.

What do we need to do in our schools to make map reading a relevant part of our maths sessions?


I have just been serenaded for 30 minutes by this magnificent butcher bird. He seems to show no fear of humans and let me take his photograph at close range.

Butcherbirds are Australasian songbirds with a complex range of beautiful songs. They get their name from hanging their prey by a twig hook or in a tree crevice. They often live in dense forests but can also be found in suburban backyards.  They are quite large with bodies between 30 – 40 cm long and they have a heavy hook-tipped beak. Females lay between 2 – 5 eggs in the nest in a fork of a tree about 10 m from the ground. They breed from August to December and live together in family groups of up to 10 birds. Young birds leave the nest at about 4 weeks old.

MATHS GRAPHICS – 3D OBJECTS – 6 new solids

Duffy has been hard at work creating lots of new graphics. These are his latest – six 3D Objects for your students to compare, discuss and describe.  They replace our earlier versions on the activity for Stage 1 students 3D Objects Mental Warmup Cards, where previously Bev had used just simple diagrams from Microsoft Word. Hmm … Duffy’s are heaps better! So professional.

GEOMETRY – 3D OBJECTS – What 3D Object am I?

We live in a beautiful 3D world and your students need to explore, talk about, describe and sort 3D objects – real life ones, whenever possible. But they also need to interact with photographs, pictures and diagrams of 3D objects too. These 3 new activities, What 3D Object am I ? and What 3D Object am I? PICTURE CARDS and Sorting 3D Objects for your Stage 1 students provide photocopiable resources using photographs and diagrams for pairs and small groups to use over and over again. They can close their eyes while a partner reads out some verbal clues. Can they visualise which object is being described? Or can they give their own verbal description based on just looking at a diagram of a 3D object. We’ve provided everything you need, even suggested ANSWERS and sample definitions. Plenty here to keep your 3D maths sessions full of discussion.

For example, Duffy is wearing a hat shaped like a cone. A cone has one curved surface that meets at a point. It also has one flat surface shaped like a circle. It has no straight edges. It has no corners.

Did you know that corners are formed only when 2 or more straight lines or faces meet. There are no straight edges or faces to form a corner in a cone. The point is created by a curved surface. This point is called an apex.

Fractions Decimals Percentages PHOTOGRAPHS – Discount Signs

Shopping is a fantastic way to talk about real-life mathematics. These 4 Shopping Discount signs can be used in a multitude of ways in your classroom. For example, use a real store catalogue with one of these signs. What is the current price? What will it be with another 40% off? What strategy will you use to work this out? Is there more than one way? Does one strategy work better than another for you?

Or use one of our 1000s of maths photographs and allocate a range of prices for these items. Next select one of the shopping discount photographs and discuss what this means. Will the prices be higher or lower with this discount? Is it more than half price of less than half price?

Or your students can draw their own shopping items and then allocate prices. Swap drawings with a partner, select a shopping discount and work out the sale prices for each item.

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?


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.


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.