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Duffy has been busy creating more Australian animals for you. He has added a dingo, a goanna, an echidna, a hopping kangaroo and a wombat. Of course you can use these graphics in your literature or social sciences lessons too. But they are also a wonderful starting point for collecting many mathematical facts. How long do they live? How much do they eat? What is the average mass? Height? Length? Which parts of Australia do they live in? What might this look like as an area percentage? How many types of animals and birds like this are there? What is the estimated population size? What is the oldest one recorded? What is the largest one recorded?

 

For example, did you know that dingoes came from South East Asia? They are a subspecies of grey wolf and arrived in Australia about 5000 years ago, brought by Indonesian sea travellers. The average size is between 13 – 24 kg. And a dingo can turn its head almost 180 degrees, while we humans can only turn about 45 – 70 degrees. They live in packs of up to 12 dogs. They can live for up to 15 – 20 years in captivity but only about 5 – 10 years in the wild. In the 1940s a huge dingo fence was built to keep dingoes away from farmland. It was 8614 km long but has now been shortened to 5614 km. And it costs about $10 000 000 each year in upkeep.

Research shows that many primary students have difficulty working out time sequences when looking at and comparing two or more calendar dates. Your students need more experiences at thinking about the days, months and years and what each of these means in relation to a time sequence.

And it is no wonder students have difficulty with this concept. Our National Curriculum virtually ignores this skill and it is rarely mentioned in class programs.

How do you know which of two dates is more recent? What clues tell you which event happened further back in time?

Time is invisible. You can’t hold it in your hand, touch, smell or taste it. It is a human construct that gives meaning to our daily lives. Over 1000s of years humans in every culture have worked out different ways to mark time passing.

We watch the sun appear to rise and set and we call this a day. We watch the moon in its daily passage around the earth and notice it takes about 7 days to go from a new to a half moon, then another 7 days to go to a full moon. Another 7 days takes you back to a half moon then another 7 days takes you back to a new moon. We call these 7-day cycles weeks and the 28-day cycle we call a month. We work out that the earth rotates around the sun in about 12 months so we create a year. And because none of these observed events is as regular as we would like them to be, we have worked out a complex system to help us see patterns and make sense of these natural phenomena. We put all this knowledge together and call it a calendar.

The activity Who is older? has been designed to help your students think about comparing calendar dates with a partner. There are 7 pages, including 18 People Cards. Each person has a different birthday so there is plenty here to get your class started.

This is not a new resource but just a reminder that we have oodles of fantastic ideas to help you create effective maths lessons in your classroom. Calendars are hardly ever mentioned in the curriculum but knowing how to read them is an essential everyday skill. Every month, every class in your school can complete a blank calendar – one for themselves and one for class discussions. What month is it? What season is this? What day of the week does the month begin?

Just write the letters of the month in the balloons, then start writing in the numbers for the days of the week.

 

For more ideas like this see our Time activities, Time graphics or Time photographs.

A trip to the zoo is a fascinating way to explore the grandeur of life on our Earth. Here are 19 new zoo photographs   taken during a recent visit with our Canadian visitors. Each creature can be the centre of a whole week of mathematical investigations once you are back at school.

For example, leopards:

 

  • live in parts of Africa and Asia
  • are 1 of 5 species in the Panther family
  • can run at up to 58 km/h
  • can leap up to 6 m through the air
  • live for 12 – 17 years
  • males  have a mass of up to 31 kg
  • females have a mass up to 27 kg

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.