Year 5 and 6 maths

In year 5 children are expected to be at the Early Additive (stage 5) or Advanced Additive (stage 6).
In year 6 the children are expected to be at the Advanced Additive stage by the end of the year.

Early Additive (EA) is where they solve addition problems by splitting numbers.
E.g. Erin takes 37 minutes to run the cross country. Brian takes 9 minutes more than Erin. How long does Brian take?
Student: Thirty-seven plus three (breaking the 9 into 3 and 6) equals forty. Forty plus six equals forty-six.

Advanced Additive (AA) is where they can solve problems using a range of strategies.
E.g. There are 121 students at Sarah's school. Sixty-six of them are girls. How many are boys?
Student: One hundred and twenty-one minus sixty is sixty-one. Sixty-one minus six is fifty-five. (partitioning the number into tens and ones)

The key to moving from Early Additive to Advanced Additive is having a range of strategies the children can use quickly and easily, and also being able to select the right one for the problem.
Again knowing basic facts is vital in the children being able to quickly and easily use different mental strategies.

Because of the increased knowledge and number of strategies the children need to master at these higher stages it can take up to 18 months for a child to progress from one stage to another hence the expectation that the children move one stage within a two year period.

Basic Facts
As children move through the stages there are key groups of basic facts they need to master to enable them to quickly solve problems in their heads.  They need to have instant recall of these facts – not just be able to quickly work them out, but KNOW it.  Refer to the children’s “student profile” or “I can “ sheets in their portfolios.

By EA (stage 5) the children should have mastered the addition and subtraction facts to 5 then 10, doubles and halves to 20 and also groupings with 10 (e.g. 10+3=13).

During the EA stage children are expected to learn:
  All the facts from previous stages and:
  All addition facts to 20
  2x, 5x, 10x multiplication facts and matching division facts

During AA stage the children are expected to learn:
  All the facts from previous stages and:
  All subtraction facts to 20
  All basic multiplication facts to 10x10

Activities to do at home
Never say “I was no good at maths at school”.  This gives children the idea that maths is not fun or interesting and could affect their attitude.  Even if we as adults have negative memories of maths, we should try to be positive about it.  Remember, the way we were taught may have been quite different to the way maths is taught in schools today.  And you may be far better at maths than you realise!
Car journeys – we’ve travelled 25 km today.  If we travel that far tomorrow, how far will we have gone?  If we’d stopped 8 km back, what would the odometer reading be? (Children at this stage might mentally solve the problem by using 25 – 5 –3 = 17.  Taking away 5 first takes us to a ‘tidy’ number of 20, then their basic fact knowledge should help them know that 20 – 3 = 17.  Because they are part-whole thinkers they know that the 8 can be split into 5 and 3 to make working out the problem easier.)

Explain to your child the strategies you are using to work things out as they occur.  You may be surprised by the number of mental strategies you have.  See if your child can use your strategy and you use theirs.  See if they can think of other ways it could be worked out.  E.g. when shopping, you may have bought something for $12 and something for $9.  How would you work out the total in your head?  You may know that $12 and $8 is $20, then one more is $21. Or that $9 + $9 = $18, and $3 more is $21.

Children at this stage need to learn a lot about the Base Ten nature of our number system.   
Continue playing grouping to 10 games with iceblock sticks or haricot beans, etc. Try using 3 dice to make adding the totals a little more challenging.

Take opportunities to share your maths strategies with your child and encourage them to share their own.  Play board games and card games together– crib, 500, etc.

Making small flash cards of all the basic facts and then putting them into piles of those you know and those you don’t’ know.  Work on the pile you don’t know, gradually getting that pile less.

Continue reading large numbers up to trillions.  Use the odometer of the car and read these numbers.  What is one more?  One less?  Ten more?  Twenty more?  A hundred less?  A hundred more?

Gather some decimal numbers from magazines, newspapers, advertising flyers etc.  Place these in order.  Be careful to use more than just prices.  Do the same with fractional numbers.  

Use the car sales pages or house sale pages in a Saturday paper and get the children to say and then order some large numbers.  Which is the most expensive car?  The cheapest?