• ### Where are they now?

Addition: Uses concrete materials where some items are concealed to solve addition problems to 20 using counting on strategies or part-part-whole knowledge. Poses and solves simple addition problems.

Subtraction: Uses concrete materials to solve simple subtraction problems (take 1, 2 or 3) or use materials to solve missing addend (5 and something makes 8) problems using ‘make-all/count-all’ strategy

• ### Where to next?

Addition: Uses count on from larger (add 1, 2 or 3) or part-part-whole knowledge to mentally add small collections to one and two digit numbers

Subtraction: Solves and poses ‘difference’ problems (1-10) using counting back (1, 2 or 3) from known or part-part-whole knowledge i.e. Solve missing addend problems (numbers to 10) mentally

• ### 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 4 to step 5)

Focus: Quickly finding the total of two numerals, where one is in the range to 3 – memorising addition facts.

Blank Beehives to 20 – Concealed Subtraction

Adapted from ‘Beehive’, Developing Efficient Numeracy Strategies Stage 1 page 34. NSW Department of Education and Training, Professional Support and Curriculum Directorate 2003

Focus: Subtracting a small number from a hidden collection. Learning to mentally subtract with less access to visual cues.

How: See Beehive Activity 4b

Beehives boards

Part-part whole board : Difference

Focus: Solving “difference” or “missing addend” problems for totals to 10 without the use of counters or visual cues.

Part part whole board

Spinner

Focus: Quickly determining the total of two small collections presented visually. Practicing and consolidating number facts and using these to develop efficient addition strategies.