• ### Where are they now?

Addition: Uses make-to-ten strategy to mentally add single digit numbers and beyond ( e.g. 8 and 6, 18 and 6) Solves 2 digit addition problems with support , e.g. model 28 + 36 using MAB, 10 frames or Open Number Lines.

Subtraction: Uses make-back-to-ten, halving and/or place-value-based strategies to mentally subtract single digit numbers from 1 and 2-digit numbers. Solves 2 digit subtraction problems with support (eg, MAB and Open Number Lines)

• ### Where to next?

Addition: Uses number fact knowledge and renaming (grouping) to record solutions to problems involving 2 digit numbers. Uses number fact knowledge to solve single digit, multiple addend problems

Subtraction: Uses number fact knowledge and renaming (trading) to record solutions to subtraction problems involving 2 digit numbers. May use MAB initially

• ### Purpose

Addition and subtraction are an important part of the skill set of a numerate person and are foundational skills for the other operations (multiplication and division) as well as for the larger body of mathematics.

• ### Building Addition and Subtraction skills:

The skill of adding and subtracting draws on all of the skills studied in the whole number section, and a failure to progress will generally indicate that one or more of these skills needs to be revisited.

Understanding addition and subtraction begins with the realisation that the total of a collection changes when items are added or removed. The key skill at this stage is still counting, as students will initially use a ‘make all- count all’ strategy. That is, they will either add or remove a specified number of items from their collection, and then count the new collection starting at one to find the new total. Language is an important element at this level – linkng the idea of adding and removing items from a collection should be linked with words such as add, plus, take, minus and subtract and difference*.

Once students are familiar enough with counting to ‘trust the count’ they will be able to add and subtract by counting on or back from the total. This is a very inefficient way of adding and subtracting however and as soon as students ‘trust the count’, they should start to explore patterns. These will be visual initially, through subitising and investigating the ‘part-part-whole’ nature of number using counters.

Part-part-whole knowledge begins with exploring the structure of all the numbers to 10 – understanding that four is two and two or three and one for example. Part-part-whole knowledge can then be extended to larger numbers through an understanding of the base 10 and place value system ultimately leading to efficient mental methods of adding and subtracting.

*Difference is an important idea as it leads to the understanding that add and subtract are just two different ways of looking at the same thing. Addition and subtraction should be taught as part of a single concept where possible.

### Activities and Assessments (Designed to move students from step 7 to step 8)

Race past 90 and Back (supplemented)

Focus: Adding and subtracting two digit numbers to and from two-digit numbers with support (modified hundred chart) leading to written methods.

Race past 90 and Back game board

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Focus: Mentally keeping a progressive total of a series of single digit numbers.

How: See Card Flip Addition instructions

Numeral Cards 1-9

120 Straw subtract (supplemented)

Focus: Subtracting 2 digit numbers from 2 digit numbers with support (bundled straws) leading to written methods.

100 Straw Subtract score sheet

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Grab 100 (supplemented)

Focus: Subtracting 2 digit numbers from 2 digit numbers with support (bundled straws) leading to written methods.

How: See Grab 100 instructions

Grab 100 score sheet

Long Walk, Short Pier (supplemented)

Focus: Adding and subtracting 1 and 2 digit numbers to and from 2 digit numbers with support (number lines) leading to written methods .

Long Walk, Short Pier game board

Long Walk, Short Pier markers

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Draw Five – Difference Bingo

Focus: Subtracting 2 digit numbers from 2 digit numbers, practicing written and mental methods.

Draw Five – Difference Bingo score sheet