Area is often a difficult substrand to photograph. Renovating a kitchen is a wonderful opportunity for Stage 3 students to see maths in real-life. And tiling the kitchen walls is a great way to think about many aspects of area.

How do you work out the area of each wall? What part of that area will need tiles (lots of Multiplication, Addition and Subtraction). Once you have your area worked out for one wall you then need to calculate the dimensions for any other wall too. What is the total area you want to tile? If you add an extra 10% for breakages and extra, how will you calculate your 10%?

And what about cost? What budget can you afford? If the tiles are $40 for one square metre, what is the total cost for your tiles? Do you need to round up or down to place your final order?

Often tile shops want you to buy by the box, not the square metre. If one box contains 1.5 square metres of tiles, how many boxes will you need?

And what about the cost of the tiler? If a tiler charges $75 to tile one square metre, how much money do you need to pay them for your job? Can you afford this?

Is it better to just paint the wall? Then you need to repeat all your calculations but using the cost of paint this time. If you need two coats and 1 litre does 15 square metres, how much paint will you need?

You can find more AREA Mental Maths Warm-ups here.

You can find suggested AREA Classroom Activities here.

Addition activities should be much more meaningful than just adding random numbers on a worksheet. Our mega June family birthday celebrations for 5 family members revealed our combined ages total 227. Imagine all the possible number combinations you can explore to create this total. Look at each person in the photograph. Estimate their ages and try to find a combination of 5 different numbers that add to 227. How many different combinations can you discover? The actual ages are Sofia = 1, Jess = 28, Patrick + 40, Bev = 68 and Eric = 90. Of course it is not important to discover this exact combination, as long as you find at least two that work.

Numbers are all around us. ThisNumber 75 is from a house in Bronte NSW. It is large, bold and beautiful. Imagine all the ways you can use this for a mental warm-up with Stage 2 or 3 students. You can count by 5s, 25s, 50s and 75s. You can discuss ways to add and subtract other 2-digit numbers to this mentally. You can list 75 things that start with “s” or “f”. You can put an alarm clock on for 75 seconds or 75 minutes and feel the time passing. You can look at a supermarket catalogue and find all the things you can buy for 75 cents (probably not so much these days!!!). You can estimate then measure things that are about 75 cm long. You can look at where 75 mL of water comes to in a variety of containers. You can ask 75 students at the end of recess to demonstrate different groups – e.g. on a signal they form into groups of 5 and count how many groups and how many leftovers to demonstrate 75 ÷ 5 = 17. Then try groups of 9? 75 ÷ 9 = 8 with 3 left. 12? 75 ÷ 12 = 6 with 3 remaining. 20? 75 ÷ 20 = 3 with 15 extras. What else might you try?

Place Value is one of the keys to success in mathematics. Studying this should be a regular part of your classroom activity. House numbers supply an endless variety of possibilities for Stage 1 students trying to understand how numbers to 1000 work. Ask each student to provide a photograph from their own home or apartment number, just like these two new ones I added today – 251 and 365.

What is the same about these two numbers?

They are both a 3-digit number, they are both more than 200 and less than 400, they both include odd and even digits, they both include the digit 5 but one is in the 10s place and one is in the 1s place, they are both odd numbers because the 1s digit is odd.

What else can your students discover? Where would you peg up these two number on a 1-1000 number line in your classroom? What do each of these numbers look like when modelled with Base 10 materials?

Use digit cards to model each number. What is the largest number you can make by rearranging these 3 digits? What is the smallest number you can make? How do you know this? Explain to a partner why you know your answer is the smallest (or the largest).

Every year at Maths Matters Resources we review and analyse the data for NSW Year 3 and Year 5 NAPLAN Numeracy. It is a unique service that provides you with a different way to think about your NAPLAN results. We believe it is most useful as it directs your attention to what really matters, not just whether your class or school is above or below a State average. And if you are from another state in Australia, the results can still be used effectively to compare with your own results.

We carefully look at the grade allocation for every question and then decide if it is correct (several questions have been incorrectly graded by the NAPLAN people …). If so, we then identify all the Stage below questions. For example, if your students are in Year 3, we look at any question graded as Stage 1 or Early Stage 1. For Year 5, we look at any question graded as Stage 1 or Stage 2.

We next consider if this question is one that we would expect 80% or more students to answer correctly. In other words, is this a basic or a core content question. These are the most important ones for your students to answer correctly. They indicate that your students have demonstrated an effective understanding of the stage below content. The 80% cut off mark still allows 1 in 5 students to answer incorrectly, for whatever reason. So what we expect is that 100% of these core/basic questions will be answered correctly by 80% or more students.

Unfortunately year after year we discover that too many students are not able to demonstrate this stage below understanding. And the 2018 results are no different.

Year 3:

42% were Core Stage 1 questions (15 out of 36 questions)

Only 73% of the Core Stage 1 questions scored ≤ 80% correct (11 out of 15 questions)

13% of these Core Stage 1 questions scored ≤ 50% correct (2 out of 15 questions)

Year 5:

48% were Core Stage 1 or 2 questions (20 out of 42 questions)

Only 70% of the Core Stage 1 or 2 questions scored ≤ 80% correct (14 out of 20 questions)

20% of the Core Stage 1 or 2 questions scored ≤ 50% correct (4 out of 20 questions)

We create follow-up NAPLAN activities to assist your students with any misunderstandings they may have. For example, you can find a targeted activity in Time Activities – Stage 1 ( F/1/2) that matches Question 31 : Year 3)

Our analysis helps you see exactly which aspects of Mathematics need more attention. These are the most urgent substrands that require your focus in Term 4 and beyond. For each Stage below question that did not get an 80% or more response, look at your school or class results to compare. These questions are marked in bold red and yellow background on the Year 3 and the Year 5 grid summary.

And please contact us if there is any way we can help you further with your own NAPLAN Numeracy analysis. We totally understand that NAPLAN is just one snapshot from all the work you do every year. But let’s look at the data and see what we can discover.

Here is a beautiful new set of Place Value discussion posters for Stage 1 students to help you think about groups of 10. Our focus was on Australian birds and animals. Counting by 10s to 100 is an important skill for Stage 1 or early Stage 1 students. Seeing what these multiples look like also helps build spatial thinking about numbers. Sometimes we have a group of 10 in a line, a huddle, even vertically. Touch each group of 10 as you count aloud, 10, 20, 30 , 40 …

Why not blow these up to A3 size as a classroom display. Or print them off for specific students to take home as practice items.

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.

A trip to the zoo is a fascinating way to explore the grandeur of life on our Earth. Here are 19 new zoo photographstaken 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.