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# Teaching and Learning Sequence Adding and Subtracting (F - 6) Key Ideas

1.   Addition begins informally when students are working their way through the ‘making groups’ stage of learning.

• They learn to combine smaller groups to make larger groups and communicate their learning in words and using sentences.

• At this early stage of their learning, students do not use the operator symbols  and =.

• This is because students are still practicing and developing their number sense and these symbols add unnecessary cognitive load.

2.   When beginning addition with students, ask them to start with two groups [of counters], they don’t have to be equal,            and then combine the groups to make one whole group.

• Prompt students to organise their counters in a way that makes counting (or subitising) more efficient.

• As a scaffold, you may provide students with a tens frame and ask them to place their groups together on the one (or more) tens frame.

• To show the combined groups more explicitly, students could be prompted to collect separate-coloured counters for each group.

3.   When describing their additions, ask students to write down their processes using operator words such as, ‘and’,                  ‘more’, ‘altogether’, ‘makes’.

4.   Students are ready for the use of the operator symbols +, -, and = when they have shown proficiency in combining              groups and communicating the steps correctly both verbally and in writing.

Activity Videos Coming soon!

## Informal Subtraction

Key Ideas

1.   Subtraction using take-away

a.   Students are ready for subtraction by take-away when they are comfortable adding groups of different sizes without          group markers.

• When first introducing students to subtraction use the word take-away instead of subtraction.

• The term subtraction can be introduced when proficiency is shown in this area.

b.   When first learning subtraction as take-away, a degree of ‘number sense’ needs to be demonstrated by the                         students.

• Students need to make the connection that they must start with the larger group and then take away the smaller group.

• Allow them to explore this concept themselves using concrete materials instead of pointing it out for them. This will ensure a conceptual understanding of take-away with natural numbers.

• *Note: It is mathematically incorrect to suggest that they can’t take a larger number away from a smaller number (you can, it just makes a negative number).

c.     Once students have formed their larger group, they will physically take objects away to show their final amount.

d.     When describing their subtraction as take-away, ask students to write down their process initially using the word                take-away and then when more confident using different words like ‘less’.

2.   Subtraction using difference

a.   Students are ready for subtraction by difference when they are comfortable adding groups of different sizes without          group markers.

b.   Subtraction by difference is a comparison model.

c.   Students make groups and compare them to work out ‘how many more’ or ‘how many less’, one group is from                    another.

d.   This value will be the difference of the subtraction and can be worked out using the ‘adding on’ strategy, or by taking          away.

It will take time for students to develop the concept of adding and subtracting. Continuous exposure to problems, use of think boards to organise thinking and repeated use of concrete materials will help to support this development.

subtraction 1

Activity Videos Coming soon!

### Number Trails

• Number sequences

• Skip counting

• Odd and even numbers

Foundation

AC9MFN01

name, represent, and order numbers including zero to at least 20, using physical and virtual materials and numerals

Year 1*

AC9MFA01

recognise, copy and continue repeating patterns represented in different ways

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

*NOTE: This activity can be differentiated to include similar Number and Algebra content descriptors from

F - 6

### See and Say

• Ordinal numbers

• Sequences

Foundation

AC9MFN01

name, represent, and order numbers including zero to at least 20, using physical and virtual materials and numerals

Year 1*

AC9MFA01

recognise, copy and continue repeating patterns represented in different ways

AC9M1A02

recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

*NOTE: This activity can be differentiated to include similar Number and Algebra content descriptors from

F - 6.

### I'm Eight

• Part-part-whole

• Formal subtraction

Foundation

AC9MFN01

name, represent, and order numbers including zero to at least 20, using physical and virtual materials and numerals

partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts

Year 1

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

### ROWCO

• Recognising numbers

• Formal subtraction

Foundation

AC9MFN01

name, represent, and order numbers including zero to at least 20, using physical and virtual materials and numerals

Year 1

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

### Mancala

• Cardinality

• Trusting the count

• Informal subtraction

Foundation

AC9MFN01

name, represent, and order numbers including zero to at least 20, using physical and virtual materials and numerals

AC9MFN04

partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts

Year 1

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

### Strike-it-out

• Formal subtraction

• Number lines

Year 1*

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

*NOTE: This activity can be differentiated to include similar Number and Algebra: Addition and Subtraction content descriptors from F - 6

### What's the Difference

• Formal subtraction

• Number lines

Foundation

AC9MFN01

name, represent, and order numbers including zero to at least 20, using physical and virtual materials and numerals

partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts

Year 1

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

### Race To...

• Place Value

• Formal subtraction

Year 1

AC9M1N04

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10, and a variety of calculation strategies

Year 2

AC9M2N04

add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies

Year 3

AC9M3N03

add and subtract two- and three-digit numbers using place value to partition, rearrange, and regroup numbers to assist in calculations without a calculator

*NOTE: This activity can be differentiated to include similar Number and Algebra: Addition and Subtraction content descriptors from F - 6

References

Reys R., et.al, (2022) CHAPTER 8: Extending number sense: place value, Helping Children Learn Mathematics. John Wiley &amp; Sons Australia, Ltd.
Rogers, A., (2017), Teaching Place Value: A Framework, Prime Number: Volume 32, Number 1, pp 19-21. The Mathematical Association of Victoria.

Rogers, A. (2014). Investigating whole number place value assessment in Years 3-6: Creating an evidence-based Developmental Progression. [Unpublished PhD thesis]. RMIT University.

Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R. and Warren, E. (2011) Teaching mathematics: Foundations to middle years, Oxford University Press.

Van de Walle, J., Karp, K., M, B.-W. J. &amp; Brass, A., 2019. Primary and Middle Years Mathematics: Teaching Developmentally. Australia: Pearson

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