**Learning and Teaching Resources for Mental Computation Strategies**

**Addition/Subtraction Clusters** (3 cards)

– Count on/back card for adding/subtracting 2

This card was created using 180gsm card and clip art images. The dimensions are 21cm X 30cm.

**PURPOSE:** Used for the addition strategy called ‘count on’, this card can also be used in subtraction as ‘count back’. It is used for adding or subtracting the numbers 0, 1, 2 and 3 to and from any number. It is not suitable for numbers larger than 3 as it takes too long and is inefficient. It is used to reinforce the counting on/back 2 from any number strategy. For example: ‘With the card closed, ask the children “how many sun’s can you see? How could we work it out?” 1, 2, 3, 4, 5, 6. There are 6 suns on the card. Open the card. How many more suns are there? 2. How many are there altogether? 8. There are eight altogether.’ This can be repeated in reverse for subtraction or counting back.

– Doubling/halving card for doubling/halving 6 or near 6

This card was created using 180gsm card and clip art images. The dimensions are approximately 21cm X 30cm.

**PURPOSE:** Used for the addition/subtraction strategy doubling and near doubling. The strategy can be used for any number but this particular card looks at the number 6. It is used to reinforce the strategy of doubling/halving or near doubling/halving. For example: ‘With the card closed ask the children “How many grasshoppers can you see? How can we work it out?” There are 6 grasshoppers. Open the card. “How many more grasshoppers can you see?” 6 grasshoppers. “How many are there altogether?” 12 grasshoppers. Double 6 is 12. Use this strategy in conjunction with a count on/back strategy for near doubling for example: 6 add 7 or 6 add 8.

– Use 10 card for adding/subtracting to 10

This card was created using 180gsm card and clip art images. The dimensions are approximately 21cm X 30cm.

**PURPOSE:** For use when adding/subtracting numbers to/from 8 and 9. It is used to reinforce the strategy that when adding to the numbers 8 and 9, it is easier to add to 10 first and then add the remaining amount to 10. For example: ‘Close the card and ask”How many snails can you see?” 9 snails. Open the right hand side and ask “how many more snails can you see?” 5. “How many snails are there altogether, how could we work it out?” Fold back the 1 on the right and fold down the 1 on the left (adding to the 9). There are now 10 and 4, which is easier to add than 9 and 5.’ Can also be used for subtraction by reversing ’14 subtract 4 is 10, subtract 1 is 9′.

**ACARA:** These strategies are developed in year 1 and 2 and cover the Australian Curriculum (2013) strands ‘Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012)’, ‘explore the connection between addition and subtraction (ACMNA029)’ and ‘solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)’.

**Multiplication/Division Clusters** (4 cards)

– Counting on card for use with groups of 10

This card was created using 180gsm card and clip art images. The dimensions are approximately 14cm X 30cm.

**PURPOSE:** This strategy is used to multiply by 10. The strategy is used to reinforce skip counting of lots of 10. This is a visual representation other than letting children use their hands to count their fingers (two hands is a lot of 10). For example: ‘If we have to count 2 X 10, we will count 10 two times, 10, 20.’

– Doubling/halving card for use with groups of 6

This card was created using 180gsm card and clip art images. The dimensions are approximately 21cm X 80cm.

**PURPOSE:** This card is used to reinforce the doubling strategy. It can be used to multiply any number by 2, 4 and 8. This particular card represents the number 6 X2, X4 and X8. For example: ‘With the card closed ask “How many caterpillars can you see?” 6. Open the first section and ask “how many more?”6. 12 altogether. Double 6 is 12. Open the next section of the card and ask “how many?” There are 6 lots of 4. If double 6 is 12, 4 lots of 6 is double 12. 24. Open the final section of the card. There are 8 lots of 6. If double 6 is 12, double 12 is 24, then double 24 is 48.’ This strategy can also be used in reverse as a halving strategy, starting at 48 and dividing by 6.

– Real world

These two card were created using 180gsm card and clip art images. The dimensions are approximately 10cm X 30cm each.

**PURPOSE:** Used to reinforce the number facts of 1 and 0 in a multiplication setting. It refers to real world because it is used to show that for example: ‘1 group of 6 is 6, and alternatively 0 groups of 6 is 0.’ The strategy would be used by physically showing a group of 6 and 0 groups of 6 with real world objects.

– Build up/down card for use with groups of 3

This card was created using 180gsm card and clip art images. The dimensions are approximately 21cm X 30cm.

**PURPOSE:** This card demonstrates the build up/down strategy for the number 3. It reinforces the strategy that each multiple of a number is just adding another group of that amount to the total. For example: ‘Close the card and ask “how many trees are there, how could we work it out?” Using a counting strategy, skip count in groups of 3 to 18 (3 X 6). Open the card and ask “how many more?” 3. Count an extra 3 and 7 groups of 3 is 21.’ I have chosen to use this particular card array design as it demonstrates one way in which 7 times tables can be introduced.

**ACARA: **These strategies are developed in year 2 and cover the Australian Curriculum (2013) strands ‘recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)’ and ‘recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)’.

**Reinforcing the inverse relationship between X and /**

I would introduce the process of ‘Partition’ (Jamieson-Proctor, 2014, page 3), as a type of division in that we have the total and number of groups but need to work out how many goes into each group. For example I am using the same Build Up/Down card where there are a total of 21 trees. Where in the multiplication strategy we counted 7 groups of 3 to get 21 trees, in this case we will divide the 21 trees among the 7 groups, but how many trees are in each group? The answer is 3. This demonstrates that there is an inverse relationship between multiplication and division by using the process of partition. A thorough look at how this would happen is as follows:

With the card open fully, the children revisit the multiplication strategy of building up in groups of 3 from 18 to 21. The teacher explains that although this is a form of multiplication it can also be used for division as well. The teacher explains that there are 21 trees and they need to be divided into 7 equal groups for replanting. We know the total and the number of groups but we have to find out how many in each group. As there are 21 trees on the card, in a lesson the teacher could provide a copy of the card to all students and on a separate piece of paper, get them to draw 7 large squares. Into each square they need to share out the trees, physically do it. Are there enough trees to be shared equally? Are there any left over? (Jamieson-Proctor, 2014, page 8) They should come up with 7 equal groups of 3. (Jamieson-Proctor, 2014, page 8). This is essentially a representation of a partition mat which shows the children this inverse relationship of multiplication and division.

**References**

ACACRA, (2013). The Australian Curriculum F-10: Mathematics. Retrieved 27th April 2014 from http://www.australiancurriculum.edu.au/mathematics/Curriculum/F-10

Jamieson-Proctor, R., (2014), EDX1280 Foundations of Numeracy Week 4 Lecture: Topic 4 Division. Retrieved 27th April 2014 from University of Southern Queensland, Faculty of Education, USQ Connect website:http://usqstudydesk.usq.edu.au/m2/pluginfile.php/276934/mod_folder/content/0/Division%20Lecture%20Notes.pdf?forcedownload=1