# Maths Cafe

This is where you’ll find Bev’s latest thoughts, insights and relevant web links. As a Cafe, it’s a place for you to relax and browse. You’ll find interesting mathematics facts and snippets and helpful hints for making maths exciting and relevant. If you are a new subscriber it’s worth making a nice cup of coffee for yourself and checking out as many posts as you can – you never know what you’ll discover. Everyone can access this part of the website, even non-subscribers.

## The importance of estimating

Remember that it is often more important for your students to be able to estimate effectively than to calculate accurately. Encourage them to find strategies to help them estimate each day. For example, one strategy might be to visualise breaking up a large quantity into tenths. Roughly work out how many in that tenth and then multiply by 10 to get your estimate. How many bananas do you think are in this pile? How does your estimate compare with a friend’s estimate? Is it in the right ballpark? How do you know?

## Large Numbers Photographs

Keep on the look-out for fantastic photographs showing larger than normal occurrences of numbers in real-life. These will make your maths so much more meaningful … and memorable … for your students.

For example, I think this is definitely what you would call “an overcrowded train”. How many people do you think might be travelling on it? What strategy will you use to make your estimate?

## How many days old are you?

This activity is useful for almost any age group. Ask everyone to individually go to this website, put in their birth details on the left, press “Today” on the right and presto, you have it!

http://www.timeanddate.com/date/duration.html#

You can then ask everyone to sort the days into place value order. And what about sorting your weeks with your younger students or hours, minutes and seconds with your older students?

## London Numbers 1 to 365

At last, proof that I am not the only maths mad person around. Just discovered this lovely blog by photographer Roger Dean, who has photographed house and street numbers around London. His plan is to photograph each of the numbers to 365, one for every day of the year. Delightful.

http://london1to365.com

## Using the Money Photographs

Finding suitable money photos to help you and your students create your own real-life maths activities is easy. Out shopping, driving along in the country, in a supermarket., having breakfast in a cafe. And we are regularly adding more, like the 19 new photos from a recent visit to beautiful Morpeth, just outside of Maitland in the Hunter Region. Once you subscribe you can easily download the photos you need. Challenge your students to create their own activities, relevant to your focus for this week.

For example, these Lime Rock boiled lolly jars cost $5.50 each. The 40 lollies in each jar have a total mass of 110 g, so what’s the average mass? How much do you pay for just one lolly? How much will all 5 jars cost? If I want to put 5 pieces in a party bag for my birthday guests, how many jars do I need to buy if I am expecting 20 people?

What shape is each jar? Why would it be this shape? How much glass would be needed? Why select glass and not a cardboard box? If you design a box to hold 40 lolly pieces, what shape would you make it? Why? If these jars come in a large cardboard box that holds 60 jars, is it too heavy for you to carry safely?

What else can you invent with your students?

## Create your own activity using the Maths Graphics

Use each illustration in our Maths Graphics to create your own story problem, poster, worksheet or activity card. Make multiple clones for adding, subtracting, multiplying and dividing. The only limit is your imagination and the needs and interests of your students.

This is an example of a Counting Poster using a one of our People Maths Graphics.

Each day you can select a different number to count. For 5 year olds, tell the story of how much pocket money this girl gets each week. Count her money in multiples of $2 or $5 or $10.

For older students, today’s story may be about packing fruit into boxes. Every day she packs 25 boxes so count in multiples of 25.

Every day a different counting story. Every day a different counting multiple.

What story will you create today with your students?

## NSW Board of Studies K – 10 Mathematics Syllabus

You can access these documents directly by clicking here.

## ACARA National Mathematics F – Year 10 Curriculum

You can access these documents directly by clicking here.

## Exploring the days of the week in other cultures

**Where do the names come from? What is the origin of our days of the week?**

The moon travels around the earth in 7 day cycles as a new moon, half moon, three quarters moon and full moon. Most cultures in the world name a 7 day cycle.

Our Sunday of course is named after the **Sun**.

Then comes the **Moon** for Monday ( Moon Day).

Tuesday is derived from **Tyr’s Day**. Tyr was the god of single combat in old Norse mythology.

Wodin (or Odin) was the greatest Scandinavian God, the ruler of Asgard. **Wodin’s Day** became Wednesday in English.

Thursday gets its name from Thor, the ancient Scandinavian god of thunder. **Thor’s Day** became Thursday in English. Thor was the son of Wodin.You can see Thor, the god of thunder, with his hammer in this painting.

Friday gets its name from Wodin’s wife Frigg, so **Frigg’s Day** became our Friday.

And Saturday comes from **Saturn’s Day**, named by the Romans who believed the planet Saturn controlled the first hour of that day.

How do other cultures name their days? This will be a great Measurement activity for your students.

## Using the Place Value House Number Photographs

The **Place Value to 100 Photographs** and Place Value from 100 Photographs are great for your daily mental warm-ups, with any age group. For example this photograph shows Bev in Ubud, Bali, standing beside House Number 13. Show this on your smartboard and give your students 1 minute to face a partner and tell each other everything they know about this number. Your students’ responses will vary widely but here are some possibilities …

We live at house number 13 too. It is a 2-digit number, larger than 10, smaller than 20, in between 9 and 15. One is in the 10s place and 3 is in the 1s place. It’s an odd number because the last digit is odd. The last 2 digits of my phone number are 1 and 3. My brother is 1 year older than that. The two digits add to 4. If you add 10 it makes 23, if you remove 1 it is 12, if you add 1 it makes 14. Double it is 26. Take it away from 100 leaves 87. Multiply it by 10 makes 130, by 100 makes 1300, by 1000 makes 13000. I can buy a chicken salad lunch for $13. If I share it between 3 people each person gets $4.33. It’s a quarter of 52 so I would need 4 x $13 to buy my school uniform which costs $52. You’d need 3 cars to take 13 people to a party including the drivers. That’s the total number of sides on a hexagon and an octagon. It’s 13 kilometres to our nearest cinema. I can toss a beanbag 13 metres. There are 13 letters in my first and last name.

In other words, you want your students to creatively expand their thinking without the need for any restrictions. The sky is the limit. You could challenge your class by asking every student to say something different each time, all based on the starting point of 13. Encourage a mix of number facts as well as real-life links. We need them to see the relevance in as many places as possible.

Coincidentally there are 13 letters in the word “brainstorming”.

## Conservation of Number Checkup

What are you trying to do?

- Spot check your
*Low Block*Foundation/Year 1 (Early Stage 1 or Stage 1) students for their ability to conserve number, In readiness for a focus on simple adding and subtracting. These students should already be able to 1-1 match oral number words to objects accurately.

- To conserve number means that a young student understands a quantity does not change if it is rearranged, covered up or hidden behind a box. A student who can conserve number is ready for the concept of addition where you can count on to find the total of 2 groups. A student who can conserve number can also count back to find the difference between 2 quantities.

- A young student who cannot conserve number doesn’t understand that a quantity remains the same when it is rearranged. This student is able to 1-1 match number words to objects but continues to recount when objects are rearranged. These students solve addition problems by counting all objects one by one. This is a Count All strategy, which is NOT an addition strategy. You can’t expect these students to participate effectively in any addition or subtraction classroom experiences. You need to identify these students before you focus on any addition or subtraction experiences.

Suggested Checkup Process

You need:

- 12 colourful counters e.g. frogs, cars, fish …
- A few minutes for each student interview
- F/Year 1 (ES1/Stage 1) Conservation Checklist (available to subscribers in the Counting activity files)

What do you do?

- Ask the student to count out 8 objects for you and to place them on the table.
- Next tell the student that you are going to put these “frogs” together in pairs e.g. rearrange the 8 objects into 2 lines of 4.
- After the objects are rearranged, ask the student; “How many frogs are there now?” Notice the student’s response. Some students will automatically say “8” so you can confidently mark their name off as a conserver on your checklist.
- Some students will look at you as if to say “…but I already told you that…” but they will still recount. You need to rearrange the objects a third time, e.g. in a curve. Again ask: “How many objects are there now?” If they are a conserver they will definitely tell you “8”. You can then mark them off on your checklist.
- But if a student recounts all the objects this third time, it is a strong indication that they cannot conserve number. These students are not indicating their readiness to experience adding 2 sets together. They need to experience counting objects, covering them up and then saying how many there are altogether. They need to “trust” objects. It may take some time focusing on similar activities to this before they realize that the number of objects does not change if they are rearranged or hidden. These students are definitely not ready to investigate adding and subtracting objects from a given group.

## Blockages

When we talk about student ability levels, we often use terms such as low, medium and high ability. In itself a term like “low” conjures up images of students who do not have the capacity to learn as much as others. It implies that we as teachers have not much control over such a student’s learning, as if they are missing a “maths gene”. But what happens if a low ability student now understands that concept that was previously beyond their grasp. How do they go from being a low ability student in front of your very eyes to being a medium or high ability student, for that concept?

I find a more useful maths language term is “blockage”. Again we can categorise our students as low, medium or high block, but the terms “high” and “low” are now opposite in meaning to our previous focus on “ability”. A new image reveals itself. If a student has a high blockage, it implies far more action on our part as teachers. There are multiple things that can be blocking this student, including emotional and physical as well as conceptual issues. How can we unblock this student? What strategies have we tried already? What other strategies may be effective? What language structures have I used? What terms does this student misunderstand? And if they are able to tackle a misunderstanding effectively and now “get” what it is we are talking about, they are unblocked. Their ability hasn’t magically jumped from low to medium or even high. The emphasis becomes on what we can do and provide as teachers to remove each student’s blockage.

A medium block student has several misunderstandings and after some one-to-one questioning and discussion with you or fellow students they may discover their incorrect thinking. A low block student may have just one or two misunderstandings and can more quickly see how to change their thinking.

It’s a little bit crazy, but I think of blockages as transparent clingwrap. Imagine your students are sitting in front of you with different layers of clingwrap covering their eyes. They can all see something, but those with only one or two sheets of the clingwrap, your low block students, can see most clearly and can see perfectly once those few sheets are removed. Everyone has the possibility of understanding more. It does not mean that your high block students WILL understand, but the language of blockages gives us more confidence that they are capable of learning.

There is no maths gene that some students have and others don’t. What can we all do to help each student learn more effectively?

## SMART Tests Victoria

This is a new project developed by leading mathematics educators. You can access quick targeted maths assessments to reveal your students thinking at www.smartvic.com. The suggested age group is Years 7, 8 and 9 but you’ll find the test levels can also fit with the needs of some Year 5 and 6 students too. Read the accompanying article “Getting Smart about Assessment for Learning.” It is still a work in progress but it will keep you up to date with the latest thinking about assessment.

## Australian Primary Mathematics Classroom Journal

Does your school already subscribe to this fantastic journal from AAMT (Australian Association of Mathematics Teachers)? There are 4 issues each year of the Australian Primary Maths Classroom with plenty of practical articles to help you reflect on your primary classroom practice. It is only $60 per year. Or if you are already an AAMT member you get 50% off your yearly subscription. The editors are Linda Marshall and Paul Swan.

## Worldometer Statistics

If you haven’t discovered this website yet, the Worldometers are a fantastic resource for studying large numbers. They continuously update number facts related to populations, births and deaths, the number of cars and bicycles and even the number of mobile phones in the world.

You can investigate at the same time each day and ask students to create their own statistical facts, such as “Since yesterday, the world’s population has increased by …” or “There are almost 2 billion google searches made each day”.

www.worldometers.info

## Australian Maths Associations

Are you a member of your local Maths Association?

Australian Association of Mathematics Teachers (AAMT)

**Northern Territory** Mathematics Teachers Association of the Northern Territory (MTANT)

**NSW** Mathematical Association of NSW (MANSW)

**NSW** Primary Association of Mathematics (PAM)

**Queensland** Queensland Association of Mathematics Teachers (QAMT)

**SA** Mathematical Association of South Australia (MASA)

**Tasmania** Mathematical Association of Tasmania (MAT)

**Victoria** Mathematical Association of Victoria (MAV)

## Girl with macaws

Here’s another great photo to stimulate your students’ thinking about real-life maths. Enya has 2 macaws on her shoulders. Why is this part of our maths resources photographs? How can this be used to promote mathematical thinking? Most of our photographs at first glance don’t shout “Mathematics” to you. Try to leapfrog from the photo to a wide range of mathematical possibilities. This photo could be the start of a class brainstorm. How many macaw species are there in our world today? What is the heaviest macaw species? The lightest? Which macaw species has the longest wing span? In what countries can you find macaws in the wild? What percentage of the earth is this?

What is the heaviest macaw species? How far do they fly on average? What territory do they cover? What do they eat? How much do they eat in a week? How many macaws, on average, would you need to balance your own body mass? How many years do they live? What might a model macaw kite look like?

Each of these suggestions could be the basis of mathematical research in your classroom.

## Why did we include this graphic?

Although each graphic in itself may not appear too mathematical, let your imagination fly. Challenge your students to create a wide range of possible questions related to each one.

Look at this hen. How many different mathematical questions can you record in 1 minute?

How many hens can possibly fit in one square metre of a chook pen? Even so, what is the official number of hens allowed per square metre? How many eggs does a hen lay on average in one week. How many weeks would it take to lay 2 dozen eggs? How heavy is a hen? Is a rooster just as heavy or heavier? How long does a hen live? How many different breeds of hen are there in our world? What type of hen is the largest? The smallest?

How much food does a hen eat in one week? If a farmer has 100 hens, how much food is this in one month? If chook food costs $2.50 per kilo, how much does this cost this farmer for 1 month of chook food?

And I am sure there are plenty more questions you can think of!

## Why did we include this photograph?

When you look at each photograph it may not at first be obvious why it can be used for maths. We will leave it up to your imagination in most cases.

If you look at this sign, how many different mathematical possibilities do you see?

How many kilometres will you travel if you leave Orange and drive to Cowra? Is it further to drive from Bathurst to Orange or from Orange to Cowra? If you start at Bathurst in which direction is Orange? When was each of the 3 towns established? What is the current population of each town? If you keep driving past Cowra, what town will you pass through next? How far from Cowra is this town? Where does Highway 33 go to and from? What about Highway 31? About where would you be if you are 49 km from Bathurst?

What other challenges can you create using this photograph as the stimulus?

## Where to now with subtraction?

Bev wrote this article many years ago when she discovered so many students continued to find subtraction difficult to tackle even at the end of Year 6. It seems to boil down to 6 key issues that all schools need to consider.

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