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.
Where are they now?
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
Where to next?
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
Where are they now?
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?
Solves and poses ‘difference’ problems (1-10) using counting back (1, 2 or 3) from known or part-part-whole knowledge
ie. Solve missing addend problems (numbers to 10) mentallyPurpose
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:
Resources
Many of these activities are the same as those in the Part-Part-Whole section as the core concepts are identical. There is an added emphasis her on connecting these ideas to the language of addition and subtraction however.
Activities and Assessments
Addition Memory
Focus: Quickly finding the total of two numerals, where one is in the range to 3 – memorising addition facts.
How: See Addition Memory instruction sheet
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
Part-part whole board : Difference
Focus: Solving “difference” or “missing addend” problems for totals to 10 without the use of counters or visual cues.
Dot Addition Flash to 10
Focus: Quickly determining the total of two small collections presented visually. Practicing and consolidating number facts and using these to develop efficient addition strategies.
How: See Dot Addition Flash instructions
Add / Subtract 4
Activity based indicators that students have achieved the target understandings