The strategies presented are designed for use with early numeracy lessons, as such the focus is on basic strategies for addition. Subtraction strategies can be thought of as the opposite of addition strategies (Dole & McIntosh, 2004). Multiplication and division strategies are introduced in later years of schooling, once students have a firm grasp of addition and subtraction strategies (ACARA, 2014).
It is not intended as a list to be taught by rote, the strategies are included so that teachers can be aware of methods students are likely to develop and use if given the freedom to explore mental computation. "...there is a growing body of research that shows that children can develop their own efficient and skilled strategies spontaneously without instruction" (Carpenter, Franke, Jacobs, Fennema, & Empson, 1998; Heirdsfield, 2000; Kamii,
Lewis, & Jones, 1991; Kamii, Lewis, & Livingston, 1993, as cited in Varol and Farron, 2007). |
ALISTAIR MCINTOSH
"Good mental calculators use a range of mental strategies when performing calculations, drawing on conceptual understanding of numbers and operations and known relationships with the particular numbers and operations involved. Number sense and conceptual understanding are therefore essential pre-requisites for competency in mental computation." (McIntosh, 2004).
SHELLY DOLE
ALISTAIR MCINTOSH "Although there are 242 basic addition and subtraction facts to be mastered, the basic facts can be categorised by particular thinking strategies. Teaching thinking strategies for learning the basic facts of addition and subtraction reduces the number of facts to be learned, and the effort associated with memorising individual facts." (Dole & McIntosh, 2004).
|
STRATEGY
|
DESCRIPTION
|
EXAMPLE
|
COMMUTATIVITY
|
Understanding that a + b = c is the same as b + a = c
When students understand commutativity, the number of addition facts to be learned is halved |
7 + 14 = 14 + 7 = 21
|
SOURCE: DOLE & MCINTOSH, 2004
INVERSE
|
Understanding that two addition and two subtraction facts are generated through rearrangement.
When students understand inverse, learning subtraction facts can be relatively simple |
7 + 14 = 21
14 + 7 = 21 21 - 7 = 14 21 - 14 = 7 |
SOURCE: DOLE & MCINTOSH, 2004
COUNTING ALL
|
Counting all units from 1 to 14 and then counting on another 7 units
|
7 + 14 = 1, 2, 3, 4, 5, 6, 7 and then counting 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
|
SOURCE: CHESNEY, 2013
COUNTING ON
|
Choose the larger number and then count on from that number
|
7 + 14 = 14 + 7 = 14 and then counting 15, 16, 17, 18, 19, 20, 21
|
SOURCE: CHESNEY, 2013
SKIP COUNTING
|
Counting by multiples
|
7 + 14 = 7 + 7 + 7 = 21
|
SOURCE: CHESNEY, 2013
BRIDGING TEN
|
Use part of the second number to make the first number equal the next multiple of 10, then add the remainder of the second number
|
7 + 14 = (7 + 3) + 11 = 10 + 11 = 21
|
SOURCE: CHESNEY, 2013
SPLIT TENS
|
Using place value, the Tens and Units colums are added separately and then the totals combined
|
7 + 14 = (7 + 4) + 10 = 11 + 10 = 21
|
SOURCE: CHESNEY, 2013
COMPENSATION
|
A larger number than required is added on, and then to compensate for this, a value must be subtracted
|
7 + 14 = (7 + 20) - 6 = 27 - 6 = 21
|
SOURCE: CHESNEY, 2013
NEAR DOUBLES
|
Recognising that the numbers are almost the same, instantly calculating the double and adding the remainder
|
10 + 11 = (10 + 10) + 1 = 20 + 1 = 21
|
SOURCE: DOLE & MCINTOSH, 2004