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1. Maths processes and the strategies you might use
1. Maths processes and the strategies you might use
There are some maths understandings (content) below which need to be taught and practised by students, and some activities and strategies which support that content. Some activities and strategies are more engaging and therefore are remembered better by students. Teaching that is organised, consistent and involves repetition builds understanding and fluency as long as it is also engaging.
As you work through each consider:
what are the maths/numeracy processes being taught to the student?
what strategies might you use and why?
is this achieving the learning that is intended? If not, why not?
2. Recording our strategies and answers
2. Recording our strategies and answers
Young children's mathematical recording https://nrich.maths.org/6894
Primary Children's Mathematical Recording - https://nrich.maths.org/9871
Carruthers and Worthington suggest: ‘It is important that children are free to work out their own sense of calculations in ways they understand’ (2008).
Mathematical graphics support 'young children’s thinking when they are encouraged to use their own ways of representing their personal mathematical meanings’ (Worthington, 2007).
2a. Activity - Recording our working out and answers - what does the syllabus say?
2a. Activity - Recording our working out and answers - what does the syllabus say?
Check out the links below to find out when the syllabus wants students to move from informal written strategies/methods to formal written strategies/methods (algorithms) for:
1. addition and subtraction
2. multiplication and division
Number and Algebra
Check out what it says for each stage in relation to written methods and representing working and answers.
Look at the images below - which one would be done at which stage?
🔢 1. Addition and Subtraction
🔢 1. Addition and Subtraction
Stage 1 (Years 1–2)
Students develop and use a range of informal mental and written strategies to add and subtract.
They use objects, drawings, and number lines to model problems.
Stage 2 (Years 3–4)
Students use a range of efficient mental and informal written strategies.
Begin to use formal written methods (algorithms) for addition and subtraction, particularly with larger numbers.
Emphasis is placed on understanding place value and regrouping.
Transition point: Stage 2 – from informal strategies to formal algorithms begins.
✖️➗ 2. Multiplication and Division
✖️➗ 2. Multiplication and Division
Stage 1 (Years 1–2)
Students explore multiplication and division through repeated addition, equal groups, and arrays.
Focus is on informal strategies and understanding concepts.
Stage 2 (Years 3–4)
Continue with informal strategies (e.g., using arrays, doubling/halving).
Start using formal written methods for multiplication and division (e.g., vertical layout for multiplication, long division), especially for 2-digit numbers and beyond.
Transition point: Stage 2 – introduction to formal written methods starts, but conceptual understanding is still key.
Source:
Source:
NSW Mathematics K–10 Syllabus (2022)
Outcomes and Content Descriptions from Stage 1 & 2
3. Varying our strategies
3. Varying our strategies
The position of a digit in a number is important; it has a different value depending on where it is in the number. Numbers have names and we read them in particular ways.
Warm up game - 3 dice
Warm up game - 3 dice
Tell students that they will roll three dice. Each digit or number must be used to make a 3 digit number. We are making the biggest possible number with those three digits.
3 digit number
5 or 6 digit number
change the scoring system
make one number = 0
People numbers
People numbers
Give each student a card and ask them to write 1 digit/numeral on one side and one on the other. They must write two different digits/numerals.
They then choose which one they will use and hold the card with that digit/numeral facing out so others can read it.
Tell the students that they are going to use the four digits that they can see to make the biggest possible four digit number (they have to move around and make the number). Ask them now to move around and make the smallest possible four digit number. Ask them to move and make the largest even number. The smallest even number... etc
Questions and discussion points:
if we have a zero how can we use it?
if no-one is showing an even numeral (number) can we make a four digit even number?
how many even numerals (numbers) do we need to make an even number?
when a numeral moves to a different place in the number what happens to its value?
if no-one is showing an odd numeral (number) can we make a four digit odd number?
how many odd numerals (numbers) do we need to make an odd number?
What would the next number be?
What is the number before this number?
4. Practising adjustment or differentiation
4. Practising adjustment or differentiation
It is important that you know how to make a task more challenging or more easy, whilst retaining appropriate maths for the stage. What we mean by that is that if a student is finding a task easy, you might say "I will make it harder, I will get them to use multiplication instead of addition". However, depending on the stage they are in, they might not have been exposed to that maths before. The best way to differentiate or adjust an activity is to use the syllabus or the teacher as a guide.
For example, let's play the game Snake Eyes as described in the instructions, THEN, use the syllabus to adjust the game to another stage. Currently it is sitting at Stage 2.
change your target
use 3 dice and go to 4000
use one die
add (do your total) then allow check with calculator
2 x 6 you can double your score (66 becomes 132)
more than one venomous number,
throw a double you have to subtract the score.
start at target and go backwards
add the dice instead of using then as tens and ones.
Play different versions of Wishball - there are many different versions of the game designed for different stages.
Login to https://www.scootle.edu.au/ec/pin
using the PIN - EYCOLF
Play one and then work out what stage it would suit.
https://calculate.org.au/wp-content/uploads/sites/15/2020/03/yohaku-number-puzzles.pdf
5. Finding the right strategy for the child - which one suits you? Why is it important to approach all problems from different perspectives?
5. Finding the right strategy for the child - which one suits you? Why is it important to approach all problems from different perspectives?
Use the link below to work out which methods suits you best.
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