• ### Where are they now?

Addition: Uses doubles and near doubles strategy to mentally add selected 1 and 2-digit numbers ( eg, 8 and 9, 15 and 16). Use formal notation to record equations

Subtraction: Uses count on from (think of addition) strategy to solve difference problems involving numbers to 20 eg understand 13 – 11 is the same as saying 11 + = 13. Use formal notation to record equations

• ### Where to next?

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)

• ### 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 6 to step 7)

Ten Frames Addition Bingo (video example)

Focus: Building and consolidating a ‘make to 10’ stragegy to facilitate the rapid mental addition of two single digit numbers with carrying.

How: See Ten Frames Addition Bingo instruction sheet or view the video

Ten Frames Addition Bingo instruction sheet

Ten Frames Addition Bingo board

Ten Frames

Spinners

Race past 90 and Back

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

Race past 90 and Back game board

Spinner 0-9

Spinner 0-30

Focus: Finding the total of multiple single digit numbers by first identifying pairs to 10.

Seven Card Addition score

Numeral Cards 1-9

120 Straw subtract

Focus: Subtracting 2 digit numbers from 2 digit numbers with support (bundled straws).

100 Straw Subtract score sheet

Spinner 0-30

Spinner 0-9

Long Walk, Short Pier

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

Numeral Dot Addition game board

Long Walk, Short Pier markers

Spinner +/-

Spinner 0-20

Spinner 0-9

Salute

Focus: For the Players: Solving “difference” or “missing addend” problems for totals to 20 without the use of counters or visual cues; For the Dealer: Finding the total of two numerals (each in the range to 10) by using doubles, near doubles and part-part-whole knowledge.

How: See Salute instructions