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Make Sense of Number to Solve Problems
In order to meet the demands of being a worker, a learner and a family and community member, adults need to be able to solve operational problems with numbers.
Number strategies
Number strategies are the mental processes learners use to solve operational problems with numbers. They are strategies that make it easier to solve number problems without having to rely on poorly understood algorithms that may lead to confusion. Number strategies can be grouped into counting strategies and partitioning strategies.
Counting strategies
Counting strategies involve counting in 1s to solve problems, often with the support of objects (such as fingers).
| Counting all of the objects | This involves joining or separating sets to solve addition or subtraction problems. Learners count all the objects in both sets to find the answer. |
| Counting on | Learners count on or back to solve addition or subtraction problems. For example, instead of counting all objects to solve 8 + 5, the learner counts on from 8: 9, 10, 11, 12, 13. |
Partitioning strategies
Partitioning strategies are based on using knowledge of number properties to split numbers (partitioning) and combine them again in ways that make it easier to reach the solution. Partitioning strategies include the following strategies and can be applied to addition, subtraction, multiplication, division and proportional problems.
| Deriving from known facts | The learner derives unknown information from a known fact. A learner may solve 25 + 26 by using what they know (25 + 25 = 50), then adding 1 to reach 51. Similarly, if a learner knows 6 x 7 = 42, they can solve 6 x 70 = 420. |
| Place value partitioning | The learner breaks the numbers into 1s, 10s and 100s, adds numbers of the same place value together and then combines these numbers. For example:63 + 35 can be solved as (60 + 30) + (3 + 5) = 98.45 x 6 can be solved as (40 x 6) + (5 x 6) = 270. |
| Using tidy numbers with compensation | The learner rounds a number to the nearest 10 or 100, then compensates for what has been added or subtracted. For example, 73 – 29 can be solved as 73 – 30 + 1 = 44 and 64 + 28 can be solved as 64 + 30 – 2 = 92. Alternatively, the learner may make the compensatory adjustment at the start of the problem, for example, 73 – 29 can be solved as 74 – 30. |
| Using reversibility | The learner changes a subtraction problem into an addition problem in order to have an easier route to the solution. For example,66 – 48 becomes 48 + ? = 66; 48 + 2 + 16 = 66, so 66 – 48 = 18. |
| Halving and doubling (or dividing by 3 and trebling) | The learner uses knowledge of number doubling and trebling. For example,16 x 8 can be solved as 2 x (8 x 8) = 2 x 64 = 12816 x 4 can be solved as 8 x 8 = 643 x 27 can be solved as 9 x 9 = 81. |