What does a Mathematics Lesson at St Matt's look like?

What would I see if I joined in on a Mathematics lesson at St Matthew’s?

At St Matthew’s Mathematics is taught for at least one hour each day, every day in all classes.

All of our classes follow the same outline.

10-15min warm up - focused on whole number games and activities. These differentiated activities are open ended and encourage maximum participation from all students (e.g. no whole class turn taking games). This gets students focused, thinking hard and revises key number concepts.

30- 40min Rich Open Ended Task - With minimal discussion beforehand students are encouraged to do some ‘hard thinking’ about an open ended mathematics problem. Some confusion is important here as students look for solutions and pose questions about the mathematics. This enables teachers or peers to give a prompt or some feedback which can switch on a new way of thinking, leading to that ‘ah-ha! moment that is so rewarding.

10 - 15min Reflection - This is where the explicit teaching happens. Students are brought together to reflect on the maths with a focus on how and why solutions worked.  This leads specifically into more varied or challenging questions which build on the learning of the day. Students are then ready for more hard thinking the next day!

Don’t steal the learning, give students a chance to think hard about Mathematics.   

Students share their number busting solutions on a class white wall. Number busting is a high yield warm up activity completed 2-3 times a week. 

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?

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

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?

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!  

Open Ended Tasks

Open Ended Tasks

Tasks are open ended, and far more enjoyable, when there are many ways to

solve a problem, just like a puzzle or a brainteaser.

How would you solve this chance (and measurement) problem which was recently completed with great success in Stage Three? 

Spin that Wheel!

I designed a ‘spinner’ with the numbers 1-10

as the outcomes.

One outcome was more likely than all the others.

One outcome had a 25% chance of being chosen.

Three outcomes had an equal chance.

It was highly unlikely that I would spin the #4

What could my spinner have looked like?

Enjoy some hard thinking today!

Mrs Usher