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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.

MC_B1_I1_E1_fig1

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.

MC_B1_I1_E1_fig1

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.

MC_BI_I1_E3_fig12

MC_BI_I1_E3_fig12

MC_BI_I1_E4_fig1

MC_BI_I1_E4_fig1

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.

MC_BI_I2_E2_fig1

MC_BI_I2_E2_fig1

MC_GT_T1_E2_A1_fig1

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.

MC_GT_T1_E2_A2_fig1

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.

MC_GT_T1_E3_A1_fig1

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.

MC_GT_T1_E3_A1_fig2

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.

MC_GT_T1_E3_A2_fig1

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.

MC_GT_T1_E3_A2_fig2

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.

MC_GT_T1_E3_A3_fig2

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.

MC_GT_T1_E3_A4_fig1

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).

MC_GT_T1_E5_A1_fig1

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.

MC_GT_T1_E5_A1_fig2

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.

MC_GT_T1_E5_A2_fig1

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.

MC_GT_T1_E5_A2_fig2

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.

MC_GT_T1_E5_A2_fig34

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

MC_GT_T1_E6_fig1

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.

MC_GT_T1_E6_fig2

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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