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.
]]>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.
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What if your students created their own book about geometry? What topics would they select? How would they illustrate it? Would they work on one book for the whole class or perhaps create a book in pairs? How many pages would it have?
Part of working mathematically is recording what you know and presenting it in a way that other people can read about your ideas.
Try to create at least one class book about mathematical concepts each term. You could lend your class book to other classes in the school and ask them for feedback too.
]]>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.
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Start with two identical size large equilateral triangles and place one upside down on top of the other. You might like to glue these together.You now have a 6 pointed star and the points are 6 smaller equilateral triangles.
Cut out 6 more triangles to fit these 6 smaller outer triangles and place them upside down on top of each one. Now you have created 18 tiny equilateral triangles.
Cut out 18 identical small triangles and place these upside down on each small triangle. Got the idea?
Stop whenever you feel the triangles are getting too fiddly to manage.
You have now created one of the most famous FRACTALS, the Von Koch Snowflake.
]]>Some interesting mathematical facts about dolphins:
– they are a type of “toothed whale”
– they grow up to 4 m in length
– they can swim for up to 100 km each day
– they get fresh water from their food (squid, fish)
– they can close down one half of their brain to “sleep” for 8 hours a day
– they can travel up to 35 km per hour and breathe through their blowhole
– this breath can help them dive for up to 4 minutes
– they can also hold their breath for up to 20 minutes
– they live for up to 40 years
Imagine all the wonderful classroom discussions with your students about these maths facts.What else can your students discover? Encourage your students to work in pairs to create a mathematical challenge based on these facts.
Remember it is vital to talk about what something ISN’T as much as about what it is. I just saw this ABC online video clip about Quarters. Everything there was fine. Cute female child’s voice over, clear graphics. All good. BUT … the biggest problem your students have in fractions is understanding far more than that, far more than just one explanation. What is NOT a quarter, what is NOT an equal part? What happens if there are only 3 equal parts? What happens if there are now five equal parts? Talking about “positive” things is only part of the solution. Talking about ‘negative’ things is also a vital component.
This video clip will be a fantastic starting point for a discussion with your class. Try to generate as many alternative questions that need answering. Get your students to explain to a partner what is and is not a quarter. Get them to draw pictures of what they think represents quarters and non-quarters. Try to spot misunderstandings that can then be shared with the whole class.
For more targeted fraction activities click here.
For more targeted fraction photographs click here.
For more targeted fraction graphics click here.
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For example, leopards:
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!
]]>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.
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.
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