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!

]]>Have you been to New York? I haven’t … but people in the know say that you should visit this award-winning small museum, the National Museum of Mathematics. It is interactive and a great place for your children to explore. Puzzles, computer graphics and books on origami. It even has a special tricycle with square wheels.

This museum is located at 11 East 26th Street in Manhattan and is open from 10:00 am to 5:00 pm, seven days a week, 364 days a year. It is only closed for Thanksgiving Day!

]]>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.

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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.

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- Why Solve Problems? Explains which personal skills help you solve problems and what a problem solving cycle looks like.
- Common Problem Solving Strategies The 8 suggested strategies are: Visualise it, Make a table or graph, Guess and check, Break it into smaller parts, Work backwards, Look for a pattern, Eliminate possibilities.
- Types of Problems More than 140 sample problems include 1-step, 2-step, more than 2-step, multiple choice and open-ended problems.

The book includes detailed, suggested strategies, as well as **TRY THIS** and **CHALLENGE** activities to test your understanding. **Answers** are at the back of the book. It is suitable for students, teachers and parents working with Stage 2 or 3 students. This Guide is packed full of easy-to-understand explanations, real-life photographs and graphics. The book includes curriculum correlation charts. The book also showcases 7 outstanding male and female problem-solvers from across the world.

Click here to buy a copy directly from the publisher or to view sample pages.

]]>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.

]]>- 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.

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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.

]]>While researching the history of division recently, I came across this old photograph of a Hospital School in Vienna, 1921. If you look carefully you see the students attempting to calculate 6975 ÷ 235.2. Obviously about 100 years ago we did not have calculators available to students to help them work out their division. Notice also that there is no real-life link, just the algorism waiting to be solved. The students have pen and paper ready and they also seem to be listening to the student at the front who may be trying to explain to the rest of the class how he will work it out.

My worry is that this sort of experience still happens today. We no longer need to calculate such an example using pen and paper as we have a calculator on our phone or computer that can do this for us. We also need a real-life context so that this calculation makes sense to our brain and is not just a meaningless number.You could ask your Stage 3 students to brainstorm for 1 minute with a partner as many different examples as they can. For example, there is a length of timber that is 6975 cm long and we need it cut into 235.2 cm lengths. How many lengths will you get? Or you have 6975 mL and you need to pack it into containers that each hold exactly 235.2 mL. How many containers will you need? But notice how this actual calculation is pretty obscure. It is not something you will come across every day.

And we still need to estimate our answer so that we can check we pressed the correct buttons. For example, 6975 is reasonably close to 7000. And 235.5 is closer to 250 than 200, if we round to the nearest 50. There are 4 groups of 250 in 1000 so there will be 7 x 4 = 28 groups of 250 in 7000. So I would expect to get an answer round about 28.

When I press 6975 ÷ 235.2 on my calculator it shows 29.6556122. I know this rounds up to 29.66 as a 2-place decimal or to 30 if I want no remainders. So my estimate was a useful check that my calculation was correct. Division estimates are a little tricky as you don’t need to round to the nearest 100, 1000 or 10 000 but to the nearest easy multiple. In this case 7000 was OK but if your calculation was 4530 ÷ 72 then an effective estimate would be 4200 ÷ 70 which you can then calculate mentally. 72 was rounded to the nearest 10, but then 4530 was rounded to an easy-to-think-about multiple of 7 and 42 is closer to 45 than 49 is to 45 so 4200 was a suitable number to round down to. I can then mentally calculate 4200 ÷ 70 to get 60. The calculator shows 62.9 so my estimate was in the right ball park.

So, what do we want our students to learn?

This is a difficult question to answer today as the world changes so rapidly. We are not sure what the world of our students will look like in 20 years time. But we are pretty sure that, in terms of number calculations, estimation is a vital skill and an understanding of what happens to numbers when you round up or down is a vital part of this skill. Once we go beyond our basic number facts and extended number facts, we no longer need to do the actual calculations ourselves. Those pages and pages of complex number calculations no longer have a central role in our primary classrooms.

We want students who are confident problem solvers, who can work co-operatively and explain processes. We want students who can tackle relevant, real-life problems, who can persist and not give up easily. Is this the focus in your maths sessions?

]]>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?

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