Adapted from Bern Long and Angela Rogers presentation, 2013 K. Chiodi

 Discuss with the person next to you what you think mental computation involves?  When should mental computation be taught?

 Mental computation is a calculation performed entirely in the head, with only the answer being written (Mcintosh, 2005)  Reading: Mental Computation and Estimation Read and then discuss at your table Victoria Department of Education and Early Childhood Development, 2009  Resource: Mental Computation: A Strategies Approach Alistair Mcintosh, 2004

 Mental computation is based on understanding.  Mental arithmetic is based on speed and accuracy related to memory. Research by Biggs (1967) revealed that: “Allocation of time to mental arithmetic bore no relation to attainment” “In other words, these daily speed and accuracy tests did not make the children noticeably more competent, but it did make them slightly more neurotic about numbers” (Mcintosh, 2004, 1)

 Warm Up activity using the Westwood Addition and Subtraction test.

 Introduce and make explicit the strategies we use to help us complete mental computations.  Memorisation of some basic facts required.  It is certainly desirable for children to know the addition facts to 20.  Mental computation strategies must be efficient and always allow us to arrive at the correct answer.  Strategies are necessary because they allow students not only to calculate simple 1-digit facts but also to calculate much bigger equations e.g ……

LevelMental Computation Link FSubitise small collections of objects (ACMNA003)(ACMNA003) 1Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015) 2Explore the connection between addition and subtraction (ACMNA029) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) 3Recognise and explain the connection between addition and subtraction (ACMNA054) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

LevelMental Computation Link 4Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) 5Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121) 6Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

The Addition and Subtraction strategies to be taught F – 6 Count on in ones Tens Facts Doubles (for addition) Doubles (for subtraction) Near Doubles (for addition) Near Doubles (for subtraction) Bridging to 10 Adding 10 Communitivity (counting on from the larger number) Count back Tens Facts (for subtraction) Subtract 10 Bridging 10 (for subtraction) Inverse – Think ‘+’

You can use your fingers to count on 0, 1, 2, 3  3+0=3  3+1=4  3+2=5  3+3=6 (also a double)

Start the biggest number and count on.  Eg: 2+7=9  We would start at 7 and count on

 Add 1,2,3 to a multi digit no. e.g. 3+35=  Add 10, 20, 30 to a multiple of 10 up to 90. e.g =  Add 10, 20, 30 to a multi digit number e.g =  Add 100, 200, 300 to a hundreds number  E.g =  Add 100, 200, 300 to a multi digit number e.g  Add 1000, 2000, 3000 to a single digit number  E.g =  Add 1000, 2000, 3000 to a multi digit number e.g =

 If you spin around addition equations you get the same answer.  This shows children the commutativity of addition equations = = 7

 Single digit with multii-digit  E.g. 4+64=64+4  Multi-digit with multi-digit  E.g =123+97

 Start with real world  We need to learn these doubles.  1+1=26+6=12  2+2=47+7=14  3+3=68+8=16  4+4=89+9=18  5+5= =20

 Double multiples of 10 up to 90 e.g Think… 5 tens+5 tens= 10 tens= 100  Double multiples of 100 up to 900 e.g = Think… 6 hundred+6 hundred= 12 hundred=  Double multiples of up to e.g Think… 6 thousand+6 thousand=12 thousand= 12 00

 Use doubles strategy with multi-digit and single digit numbers e.g  Use doubles strategy when adding multi-digit with multi-digit

 If we remember the doubles, we can work out these sums.  6+7=13  5+6=11  4+3=7  9+8=17

 Near doubles with multiples of 10 up to 90 e.g Think… 5 tens +5tens is tens and 1 more ten is 11 tens=110  Near doubles with multiples of 100 to 900 e.g  Near doubles with multiples of 1000 up to 9000 e.g  Use near doubles strategy with multi-digit and single digit numbers e.g  Use near doubles strategy when adding multi-digit with multi-digit

 These equations add to 10.  1+9=109+1=10  2+8=108+2=10  3+7=107+3=10  4+6=106+4=10  5+5=105+5=10

 Tens facts with single digits that add to 20 E.g  Tens facts with multiples of 10 that add to 100 E.g  Tens facts with multiples of 100 that add to 1000 E.g  Tens facts with multiples of 1000 that add to E.g  Tens facts with single digit that add with multi digit numbers E.g  Tens facts with multi digit with multi digit E.g 

 Seven, Eight, Nine are close to Ten.  9+2=118+6=147+6=13  9+3=128+7=157+5=12  9+4=138+8=167+4=11

 Bridging with multiples of 10 e.g think…4 tens +9 tens is 13 tens =  Bridging single digit numbers with multi digit numbers  E.g  Bridging multi digit numbers with multi-digit numbers e.g

 When we add ten, the ones number stays the same.  2+10=126+10=16  3+10=137+10=17  4+10=148+10=18  5+10=159+10=19

 Add 10 to multi-digit numbers e.g  Add 100 to single digit e.g  Add 100 to multi-digit e.g  Add 1000 to single digit e.g =  Add 1000 to multi-digit e.g

 To teach with understanding all strategies must be taught using visual aids and at any time when students are experiencing difficulties teachers must return to visual aids e.g. tens frames, bead strings, place value cards etc.

 2 dice are rolled  Write the number sentence on your playing board that corresponds with the strategy you used to work out the answer  The player to fill up their playing board first calls ‘Bingo’ and reads out their answers

 You can count back 0, 1, 2, 3 using your fingers or in your head  5-2=3  6-1=5

Count down to:  Beginning at the total, count down to the number being taken away. The answer is the number of steps this takes. For example, start at 18 and count down to 13, 17, 16, 15, 14, 13= 5 numbers counted back Count up from:  Beginning at the number being taken away, count up to the total. The answer is the number of steps this takes. For example, start at 17 and count up to , 19, 20, 21 = 4 numbers counted up

 Tens facts can help us work out the answer when we subtract from ten.  Eg. 10=5=5  10-6=4

 If you know 6+6=12, then you also know 12- 6=6  Eg: 4+4=8 so 8-4=4  10+10=20 so 20-10=10

 You can take away the ones number and it leaves you with just the tens.  Eg: 13-3=10  25-5=20

 Count back to the nearest tens number, then its easy to take away what is left.  Eg. 11-3=  First do 11-1=10  Then 10-2=8 (tens fact)

 If you know the doubles the near doubles can also help.  Eg. 12-7=  I know 12-6 (double)=6  Take one more = 5

ExplainHow did you figure it out? JustifyHow did you do it like that? CompareIs there another way? Which one do you like? I really like this strategy. What other problems will this strategy work for? Will it always work? Reasoning and reflecting Is your answer reasonable/ Could that be the answer? How do you know your right? ApplicationWhat would you use this for in the real world?