Number Busting

Here is our first instalment of Numeracy News.

Each fortnight keep your eyes open for information on how we teach numeracy in the school and on ways you can support your child at home.   

This week our focus is ‘Number Busting’.  Number busting is a warm up strategy that each class in the school uses three times a week.  Students are given a starting number and are then to partition this number as many ways as they can in a given time.  Number busting is a fantastic way of revising and reinforcing different skills, techniques and concepts that are learnt in class.  

In blue are some cues you might like to use if you want to try some number busting at home.

Can you make your number with counters? (buttons, beads, peas etc)

How can you split your number into two groups, three groups, four groups etc.

Can you make a ____ pattern (+10, +20, takeaway, double and halve?)

Can you put your number on a number line?

Can you write a word problem for your number?

Three in a row bingo!

This week we are featuring a game which builds place value knowledge.  

The best thing is that it uses no special materials, just things you can find around the house.   W3 T2

Three in a Row Bingo

You will need a tape measure (over 100cm is best) some paper clips and a deck of cards.

* Shuffle your deck of cards.  

* The first player chooses two cards to make a two digit number.

* Player one may then use this number, or a number ten more or ten less than the number.

* Player 1 then finds the number on their tape measure and marks it with a paperclip.   

* Player two confirms that the clip is in the right place.  

Play alternates until one player places the third paperclip in a row (like connect four).  They are then the winner!

With your cards

Kings & Jacks =0

Queen = wild card (your choice)

Make the rules easier by throwing out the picture cards and drawing one at a time. Use 1 more one less rather than ten.

Make the game harder by making a custom tape measure (number line) and allowing negative numbers or decimals.

Love the game?  Made a modification of your own?  Share on the St Matthew’s Facebook page!

Where are the algorithms?

Primary maths - different to when you were at school?!   

Often students will be working on maths at home which may appear different to the way it was taught in the past. As research into mathematical learning grows, we aim to use the best strategies we can to build our students understanding.

So where are the algorithms? Isn’t that ‘real’ maths?

As outlined in the syllabus, first we focus on estimating strategies. If you are learning at home a great prompt is “what would you expect / estimate / think the answer could be?” “How could you prove that?” or “How could you work that out?”

Students may find writing out informal mental strategies to be more efficient than using formal written algorithms. For example, 8000 − 673 is easier to calculate mentally than by using a formal algorithm.  

So if your child is inventing strategies or using a more unconventional method encourage it!  We will teach the formal algorithm methods when the time is right, and the answer impossible to work out any other way!

Array Games

Warm Up Games - Times Tables  

Being able to quickly recall times tables is an essential skill for solving mental maths questions. However, the importance is not on being able to recall rote learnt facts but to understand what the fact means.  The following array activity can help children to remember and understand times table facts in  a visual way.

You will need

2 or more players, a selection of counters or small items (pasta is great) and a dice.

How to play

- Each player rolls a die and makes that many rows (e.g. 6)

- Roll the die again and place that many counters in each row (e.g. 5)

- How many counters all together?  Invite your partner to check.  (e.g. 30)

- Extension - write / say / chant the multiplication or division fact that matches the array.  (e.g. 6x5 = 30  5x6 = 30    30 ÷ 6 = 5    30 ÷ 5 = 6).

- The player with the most counters wins the round and the point.  The first to five points wins!

Make it a challenge by using a die with more than 6 sides.  There are lots of websites and apps that feature random dice spinners.  Try googling ‘virtual dice’ to get started.

Arrays in the Environment

An array of arrays!

In a previous post we focused on how to learn times tables using arrays.   

But St Matthew’s is looking for the most creative array!

We challenge you to look for arrays in the environment and take a photo.  Either upload to facebook or email them to stmatthews@parra.catholic.edu.au

Try adding a maths fact to match!

Happy Arraying!

More or less snap - A great at home game

This week our numeracy focus is on a game that you can play at home to develop mental computation skills.

More or less snap!

You will need a deck of cards and two players.

As usual in this game of snap you are looking to win the pile of cards on the table by snapping onto a 'match'.  However, in this game the rules have changed.  Try snapping if the card placed on top of the pile is one more or one less than the one underneath it.  

You could make this game harder by making the difference between the cards greater e.g. Three more or three less

Make the game easier by removing the picture cards.

This game helps with concepts of place value,  as well as addition and subtraction.

Happy Snapping!

What is an open ended task?

This week our numeracy focus is on a rich, open ended tasks.

What is an open ended task?

When teaching and learning in Mathematics at St Matthew's, throughout our diocese and the world the focus is on using questions that are open ended.

This means that there is either more than one way of working out the answer, more than one correct answer, or both!

In Infants an open question focusing on division may be something like:

A baker made 24 cookies.  How could he arrange them so that each baking tray he used had an equal amount of cookies on it?

In Primary a question focusing on multiplication could be:

I wrote a multiplication problem on the board but some of it was rubbed off.  I remember that I had a a seven in one of the numbers and that my answer had four digits. What could my equation have been?

This week students might like to share with you the questions they are working on in class!

Double, Half, Stay? Games for at home

Double? Halve? Stay?

At St Matthew’s we have been very lucky to have some amazing visiting teachers from different universities.  Here is a game Miss Van Der Berg has introduced to us which you might like to play at home.

You will need - Two dice (a spinner or dice app works just as well)

Two or more players

How to play  

Choose a starting number between 6 and 132

Player 1 rolls their dice to find out their number (e.g. One dice represents the tens digit and one the units digit.  e.g. 3 and 4 makes 34 or 43)

They can then choose to double it, halve it, or leave it as it is to get the closest to they can to the chosen number.

Each player has a turn.  

The person with the number closest to the starting number scores a point.

Everyone chooses a new starting number.

The player with the most points at the end of the game is the winner.  

Make it easier - Use only one die or a 10 sided die / spinner

Make it harder - Use three dice, one for a whole number and two for tenths and hundredths.

What a great game for a rainy day!

Mrs Usher

Estimating

Estimating

Estimating is an important strategy that we use more often in real life situations than precise calculations.

Over the next week and in the holidays look for opportunities to estimate quantities or totals. For our younger students they might estimate:

How many stairs in that staircase?

Total money in the coin section of a family members wallet.

How many books on a shelf?

How long until lunch?

Our older students might estimate:

The total of the grocery bill

The number of people living in their street

The sale price of a house

The duration of a trip or activity

Money in a full piggy bank

Build on the maths by asking students to prove or explain why their estimation is reasonable!

Happy Estimating!

Mrs Usher

Open Ended Fun

At St Matt’s we aim to make all of our maths activities ones which “enable students to develop a positive self-concept as learners of mathematics, obtain enjoyment from mathematics, and become self-motivated learners through inquiry and active participation in challenging and engaging experiences” (NSW Mathematics Syllabus 2014).

Below is a task that students and parents might like to try at home.  Like many great puzzles we hope it enables you to obtain enjoyment from mathematics! We are not sure of it's origin, but thanks to the Western Sydney University who used this with a cohort of teachers long ago!

The entrance to an ancient underground storehouse has been discovered.  Each room contains a different number of gemstones.

You may only visit 13 rooms before returning to the entrance otherwise you will be trapped forever.

There are no doors which go diagonally.

Which way will you go?

Battleships - Learning on a number line

Here is a  new game we have invented at St Matt’s. This game helps players to visualise numbers on a number line.  Remember to keep playing maths games often to keep your numeracy skills in top shape!

BATTLESHIPS!

Mark out your playing field - we used a strip along the tables 150cm long. Younger students could use a shorter length based on the numbers they are familiar with.

Sit alongside your partner so you are both visualising 0-150 in the same orientation.  Remove any tape measures from the field of play.

Player 1 gives three target numbers. Player 2 has to use a counter to 'bomb' those ships by placing them where they believe the number would be. When all three bombs are placed the tape measure is brought back in to check. A direct hit is 5 points and a hit within 5cm each side of the number gets 2 points. The player with the most points at the end of time wins.

Make the game more challenging by playing with tenths. Mark out 1-15 (making each multiple of 10 equal 1) and the number between become the tenths!

Enjoy!

Assessment and Tracking at St Matthew's

Maths Assessment Interview Success!

At the beginning of the school year all primary students in the Parramatta Diocese complete the Maths Assessment Interview. The Mathematics Assessment Interview consists of hands-on and mental computation assessment tasks where students can demonstrate mathematical understanding and preferred strategies for solving increasingly complex tasks.

The interview is allows us to:

• Collect detailed information on students’ understanding of Mathematics.
• Develop a detailed profile of student achievement.
• Inform focused teaching.
• Measure growth over time.

MAI interviews are completed at the same time each year so remember to keep an eye open in December for the interview booking information.

BIG numbers

BIG numbers!

Learning how to read large numbers is a big confidence booster for students and helps them to recognise the maths in real life.   

This week try looking for large numbers in your environment and 

reading them together.

Some places you can might find larger numbers are:

In the newspaper

On television

Real Estate windows / advertisements

3 digit numbers on car number plates

House numbers on long streets   

km on street signs 

Top scores on computer games

What others can you find?  Add your suggestions to the comment section!

Learning about time

What’s the TIME?

Telling time is one of those areas of Mathematics which has obvious links to everyday life.  However many students have difficulty in this area, particularly when reading analogue time.

What should they be able to do?  

The Mathematics Syllabus suggests that at least, students should be learning to read:

Kindy - o’clock time

Stage 1 - half and quarter hour time

Stage 2 - time at one minute intervals

Stage 3 - 24hr time

Some ideas for learning time at home include

• Have a range of clock types (including different number styles and those with a second hand) in use in your home.
• Give your student an analogue watch to wear each day.
• Have an analogue clock next to a digital one so every time it is used the correlation between the two is clear.
• When children ask for  the time or when giving time based instructions use a variety of language and descriptions of the time e.g. Your bed time is at 8:30pm, or half past eight.  You will need to brush your teeth 15min before at quarter past.
• Set your iphone / ipad / device clock to 24hr time

• Estimate, measure and talk about elapsed time, e.g. “I predict that it will take us 25min to get to school on this rainy day”  

When is the right time to learn about time? All the time!!

Friends of 10 apps

Friends of 10

‘Friends of Ten’ are whole number pairs that equal 10 (9+1  2+8  7=3  6+4  5+5)  These are an important set of number facts for students to understand and memorise. Here are some apps which can help practise ‘friends of ten’.

Rich, Open Ended Mathematics - Design a city

Rich, Open Ended Mathematics  

The latest research on learning in Mathematics supports an approach which encourages students to solve problems in a variety of different ways, using a variety of different strategies.

In Year Three students were asked to design a city using a combination of parallel and perpendicular lines, a variety of angles and a ruler.  Here are some of their solutions!  

Rich, Open Ended Mathematics - Cartesian Plane and Coding

Rich, Open Ended Mathematics  

The latest research on learning in Mathematics supports an approach which encourages students to solve problems in a variety of different ways, using a variety of different strategies. At St Matthew's we use this approach daily.

In Stage Three students have combined learning about the cartesian plane and computer coding to navigate with an Edison robot car.

Feedback in Mathematics

Feedback in Mathematics - More than ticks and crosses

Not all that long ago all students worked on the same problems, making marking a page of sums a reasonably simple exercise.  Now in classroom visits you will see something different!

Teachers now focus on feedback that is focused, timely and based on

strategies for improvement. This takes priority over rows of ticks and crosses or having every piece of working out corrected.

While much of the feedback we give is verbal, written feedback can be seen in books also.

For students privacy we won’t be publishing samples this week, but some examples include:

“Fred was able to skip count by 5s starting at 10. Your goal now is to try starting at 11”

“Wilma, you have used a graph well to record your results.  Don’t forget to label each axis”

“Betty, can you solve this problem another way?”

“Barney, you have made a great x10 pattern, what would happen if you multiplied by 11, or 20?”

Teachers may also annotate students work, particularly in the younger grades to show what they can do.

BamBam can count a collection up to 39

or

When solving subtraction questions Pebbles used a counting up strategy.

Have some questions?  Bring them to one of our numeracy workshops!

Mrs Usher

Apps for Arrays

There are a lot of great iPad Apps out there for Mathematics. Here are some we recommend for working with arrays.  

Times Tables with Arrays

In Term Three 2015 we had a fantastic parent workshop on arrays.  We plan to run one more workshop next term.  Email rusher3@parra.catholic.edu.au with your suggestions!

Making ‘Times Tables’ 

Times tables are one of those maths skills that not only help with mental computation, but help students feel confident when working mathematically. 

As well as memorising number facts, students must understand them.  

An array is a fabulous way of showing a ‘times table’ fact in a visual way. This can help students to see the multiplication. 

Here is a 5x10 array. It shows 5 equal rows and 10 equal columns. 

To support numeracy learning try making arrays at home 

Use items which are the same size, buttons, pasta shells, lego pieces. Different colours can be helpful for visualising but are not necessary.

Try using dice, number spinners etc to generate the number of rows and columns you are making.

Have paper ready so your child can record their array using numbers and symbols.

Try asking your child:

How can you count your array in a fast way?  (In this one I can count quickly by 5s, 10s or I can see five groups of ten).

Can you write a multiplication fact to match your array?

Is there a different fact that may be used but has the same answer?  (e.g. 5x10  10x5 )

If I made an array that showed 5X10, how can I quickly change it to show 9x5 or 5x11?

How many would you have if I added one more row?  One more column?  doubled my array?  

While covering part of the array ask “How many are there all together?” 

Try searching for arrays in the environment! There are more than you would expect!