Media > TDT > Mental computation

Mental computation

MC_A_AP_AP2_fig1

Sample of checklist showing four strategies (place value with tens first, place value with ones first, friendly numbers, inverse). Responses for four students with teacher notes and comments.

Mental strategy observation checklist.

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Problem of 28 + 36 shown as start at 0, jump 20 to 20, then jump 30 to 50, then jump 8 to 58 then jump 6 to 64.

Use of an empty number line.

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MC_B1_I1_E1_fig1

MC_BI_I1_E3_fig1

Hundred board starting at 26 and counting on to 32.

Hundred board showing counting on.

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MC_BI_I1_E3_fig12

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MC_BI_I1_E4_fig2

MC_BI_I1_E4_fig2

MC_BI_I2_E1_fig1

MC_BI_I2_E1_fig1

Array models illustrating commutative processes for multiplication.

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Problem is 28 plus 7, broken into 28 plus 2 plus 5 to equal 35.

Screen grab from L91 The part-adder: make your own easy sums.
Source: © Education Services Australia, 2011.

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The problem 24 minus 8 solved by subtracting 4 from 20 and then adding 4, with a diagrammatic representation.

Screen grab from L97 The takeaway bar: make your own easy subtractions.
Source: © Education Service Australia, 2011.

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Problem of 60 plus 40, broken into 60 plus four lots of 10, with a diagrammatic representation.

Screen grab from L92 The part-adder: make your own hard sums.
Source: © Education Services Australia, 2011.

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Problem of 90 minus 30, with a diagrammatic representation.

Screen grab from L98 The take-away bar: make your own hard subtractions.
Source: © Education Services Australia, 2011.

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Using a number line to add 43 and 50.

Screen grab 1 from Number line applet.
Material from NZ Maths website published by the New Zealand Ministry of Education. Reproduced with permission from the New Zealand Ministry of Education © Crown.

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Using a number line to subtract 50 from 137.

Screen grab 2 from Number line applet.
Material from NZ Maths website published by the New Zealand Ministry of Education. Reproduced with permission from the New Zealand Ministry of Education © Crown.

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Using a number line to subtract 63 from 127, first subtracting 60 and then subtracting 3.

Screen grab from Number line applet.
Material from NZ Maths website published by the New Zealand Ministry of Education. Reproduced with permission from the New Zealand Ministry of Education © Crown.

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A string of beads, alternating every ten beads from green to pink. The problem is to add 27 to 58. First peg is at 58 with a jump of 20 to reach 78, then a jump of 2 to reach 80 then a jump of 5 to reach the answer of 85.

Adding with a bead string (solution 1).

MC_GT_T1_E3_A4_fig2

A string of beads, alternating every ten beads from green to pink. The problem is to add 27 to 58. First peg is at 58 with a jump of 2 to reach 60, then a jump of 5 to reach 65 then a jump of 20 to reach the answer of 85.

Adding with a bead string (solution 2).

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Problem of 62 minus 28, with a diagrammatic representation of 28 added to 30 to give 58, leaving 4 to reach 62.

Screen grab from L112 The difference bar: generate hard differences.
Source: © Education Services Australia, 2011.

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Problem of 62 minus 28, with a diagrammatic representation of 2 added to 28 to give 30, leaving 32 plus the remaining 2 to reach 64.

Screen grab from L110 The difference bar: make your own hard subtractions.
Source: © Education Services Australia, 2011.

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A pair of counting strips marked from 1 to 15, the upper one showing the difference between 8 and 13 and the lower the difference between 10 and 15. Finding the difference between 8 and 13 is harder than finding the difference between 10 and 15.

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A pair of counting strips marked from 1 to 15, the upper one showing the difference between 8 and 13 and the lower the difference between 10 and 15. Each has a difference of 5.

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Sets the problem of working out the difference between 27 and 63 and suggests that the solution be in the form of 27 + ? = 63.

Screen grabs from L110 The difference bar: make your own hard subtractions.
Source: © Education Services Australia, 2011

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Beginning at 203 then subtracting 80 to reach 123, then 7 to reach the result of 116.

Number line for 'result unknown' problem.
Material from NZ Maths website published by the New Zealand Ministry of Education. Reproduced with permission from the New Zealand Ministry of Education © Crown.

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First number line showing jump from 74 to 135. Second number line showing jump from 218 to 153.

Number lines for 'change unknown' problems.
Material from NZ Maths website published by the New Zealand Ministry of Education. Reproduced with permission from the New Zealand Ministry of Education © Crown.

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Number line showing 56 subtracted from an unknown point to reach the result of 37.

Number line for a 'start unknown' problem.
Material from NZ Maths website published by the New Zealand Ministry of Education. Reproduced with permission from the New Zealand Ministry of Education © Crown.

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How many tiles do I need? A partial 6 by 5 array showing only the far left column and top row.

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Six eggs in a carton arranged in a 2 by 3 array.

An array of eggs.

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25 juice boxes arranged in a 5 by 5 array.

An array of juice boxes.

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16 chocolates arranged in a 4 by 4 array.

An array of chocolates.

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10 by 10 multiplication grid with product of 15 shown as 3 by 5 and 5 by 3, and product of 24 shown as 6 by 4 and 4 by 6.

Sample multiplication fact grid.

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10 by 10 multiplication grid with all products shown, and products of 28, 48 and 72 circled.

Completed multiplication fact grid.

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10 by 10 multiplication grid with different colours showing the zero products, the ones products, the double ones, the double twos, the double threes, the double fours, and the relating to tens.

Shaded multiplication fact grid.


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