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Each year Bev Dunbar analyses the Year 3 and Year 5 NAPLAN Numeracy papers, looking for where students appear to have a major blockage to their understanding. For example  the results for Question 21 in the 2017 Year 3 paper  demonstrate that many Stage 2 students are insecure about how number sentences work.

This Stage 2 activity (Years 3/4), Match my Group (Division Number Sentences), helps these selected students realise that each part of a number sentence has meaning. If you rearrange the position of digits and symbols, then your number sentence may not make any sense. You can’t just put them wherever you like.

It also helps students realise that they need time to think about the actions in a number sentence. If they see the number 42 and the number 6, for example, do you add, subtract, multiply or divide them? You can’t just rush in with the first thing that comes into your head.

Each of the 4 stories in this activity is a single step story. Your students need to be able to manage linking their story and number sentence before tackling more complex events. You need to make time for your students to talk to each other, explain their thinking strategies, to work co-operatively on each activity. You can’t rush their understanding. You need that “aha” moment when they work out that actions matter, the placement of digits and symbols matter. Maths matters!

For the last 15 years Bev Dunbar has been analysing the NSW NAPLAN results, looking for the “big picture” information to help all teachers better understand student misconceptions and blockages to understanding. When you look at your NAPLAN results, you are looking at individual students in your class and whether your school achieved at, below or above State averages. This information helps you plan targeted strategies for student improvement.

However here at Maths Matters we look at the whole state results, in our case that’s NSW. Fortunately NSW results are almost identical to the Australian results so we are able to see how Australian students as a whole are tracking in their mathematical progess. But unfortunately … this is not a pretty picture. It appears that our students are not able to adequately demonstrate competency on key test questions. In other words, they are not able to demonstrate that they have achieved key content outcomes.

We can argue about the nature of the test and whether we agree or disagree about its continuation. That is another story. The fact is that our government collects yearly data and that yearly data tells us something.

We analyse every test question and categorise it by both Stage and also by Core or Advanced. We call a test item a Core Stage question if we think it is suitable for most students to answer. For example, in Year 3 a Core Question is one that covers Early Stage 1 or Stage 1 concepts that we expect most Year 3 students to answer. We have a cut off point of 80% for our definition of “most”. So one in five students might answer this Core Question incorrectly. These may be students who are anxious about the test, may be working at an even earlier Stage, may have language and reading difficulties and so on. But we believe the question is an effective one to ask this cohort. Other questions in the test paper may be at the same Stage but may have twists and turns or too many steps in their solution. We call these test items Advanced. We do not expect 80% or more students to answer these questions correctly. These questions help identify more advanced mathematical thinkers in your class, school, state or country.

The strange thing is though, the questions that make up a particular NAPLAN Numeracy test more often than not do NOT test Core Stage below content. Some even test our students on content that is two Stages above. We are not sure what this data is supposed to tell us. We are perplexed as to why these questions are included. If you study William Shakespeare’s plays at University, for example, you would not expect to be tested on the plays of Anton Chekhov, just to see if someone has that knowledge.

  • In the 2017 Year 3 NAPLAN Numeracy paper, only 44% of the questions were Early Stage 1 or Core Stage 1. That’s 16 out of 36 questions. And only 50% of these 16 questions were answered by 80% or more Year 3 students.


  • In the 2017 Year 5 NAPLAN Numeracy paper, 50% of the questions were Core Stage 1 or Core Stage 2. That’s 21 out of 42 questions. And only 43% of these 21 questions were answered by 80% or more Year 3 students.

If you would like to see our one page summary of this year’s Year 3 results, click here.

If you would like to see our one page summary of this year’s Year 5 results, click here.

The summary is compact, with test question numbers on the left and the NSW test results for each question in matching spaces on the right. We also include an analysis of key concerns, based on these results. These concerns highlight the “big picture” view. Your individual students may have been successful in answering a question, but the overall results might indicate misconceptions you need to be aware of. We then develop resources that help your students overcome these blockages to their understanding.


Our website is packed full of resources for you to use in your lesson planning. And even though we know you can manipulate our images yourself, we like to help make your life just that little bit easier by providing you with resources that are ready to use immediately. This new series of 1-10 blue sharks is such an example. We’ve repeated the shark image and saved it as 10 separate png images. You can now use these as part of your early addition and subtraction discussions. Here are 6 plus 8 sharks. That’s 14 sharks altogether.






We have also included the blue sharks on our MULTIPLICATION & DIVISION Photographs page as you could also reproduce each image to create as many multiples as you like. Here are 4 groups of 3 sharks, for example.


Learning to read and interpret road signs is an important part of helping your students to locate themselves in 3D space. Our resources include a wide range of road signs for class discussions with any age group. For example, here is an animal crossing sign. What does this sign mean? Why has it been put up on this road? What do you have to do? Will the animals come from the left, the right or straight ahead? Why do you think this? Where might you see a sign like this one? Do you only look out for cows and sheep? Why were these two animals selected for the sign?

If you know individual students are travelling along country roads, encourage them to take their own photographs of unusual road signs. Have they seen one about emus? Deer? Kangaroos? Koalas? Use these for related class discussions about the importance of road signs and the information they tell us.

The first of many NAPLAN 2017 follow-up activities to help your students remove blockages.  Only 48% of one large Year 3 cohort correctly matched a 2-digit addition and subtraction number story to the correct number sentence. The format of the question was slightly unusual and this seemed to have thrown the students off!!


Match my Story provides follow-up examples to discuss together with your Stage 1 students. It is also suitable for high and medium block Stage 2 students. Each set has more than one matching number sentence. It is vital to discuss both the ones that work and those that don’t. Help your students think more deeply about what they are learning.


This guide is a vital tool for all middle and upper primary students who want to be successful maths problem solvers. The book is divided into three sections.

  • 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.

Paper/rock/scissors is a game of chance between two people. On a signal you each make one of 3 shapes with your hand – rock (a closed fist), paper ( a flat hand) or scissors (a fist with two fingers making a V). The outcomes are that you make the same shape or a different shape. If the shapes are different then paper covers rock (paper wins), rock crushes scissors (rock wins) and scissors cut paper (scissors wins).

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.

Here is  an official website that demonstrates the rules of this game.

Duffy has just created a sweet set of children to help you talk about Chance with your students. What’s the chance of having a boy or a girl? Twins? Triplets? Quadruplets?

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.


Regular practice estimating volumes will help your students develop effective proportional reasoning. We use this skill when we think about multiplication and division. We also use this skill when we think about fractions. I am working on a whole set of these activities but this is the first in the STAGE 1 set. It will help your students think about fifths. It will help them understand how to mentally divide a length into 5 equal parts. Later sets will focus on dividing a given volume into halves, thirds, quarters and tenths.

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.