1. “How Does Your Child Learn Maths?” Dinah Harvey, Advisers Plus
“We want our children to understand
that learning is something they do,
it is not done to them”

2. How many cars will there be if the car park is full?
How do YOU solve this?
In the new car parking building there are 6 levels. On each level you can park 24 cars.
How many cars will there be if the car park is full?

3. A full maths programme Number Knowledge (includes basic facts)
Number strategies (+, -, X, ÷, fractions)
Geometry, Measurement, Algebra, Statistics
More than recall of facts and routine procedures – students can apply the learning they have in new situations
A “normal” child can be achieving at different levels or stages for different areas of maths

4. National Standards - making an OTJ
“In contexts that require them to solve problems or model situations….. independently and most of the time…..”
Based on a “Best fit” judgement
Numeracy strategy stage (verbal and written)
Application of Number skills – thinking with what they know – in context or in rich or open tasks. Achievement in the other strands – geometry, measurement, statistics and algebra
Externally referenced data e.g. PAT

5. National Standards - making an OTJ
Handwriting
Spelling / sight words
Punctuation / grammar
Writing a recount
Writing a story
Writing a poem
Writing what’s needed in the real world
Basic facts
Basic knowledge
Mental & written strategies to solve unknown problems(+, -, x, ÷, fractions)
Using strategies in other maths
Maths in the real world
Literacy
Numeracy

6. Stage 0 Cannot reliably count a group 1-1
(5 objects, wrong word order)
……..(doesn’t stop)
1-2/ (5 counts but only 4 objects)
Also learning to read the numerals & the words to 10

7. Stage 1 Can reliably 1-1 count to 10
Cannot join 2 separate sets( rename the second set)
How many have you got? 4 and 3, 43, ???

8. Stage 2 (after 1 year at school)
Reliably adds & subtracts to 10, then 20
Cannot count the objects if they are unseen can only be counted with objects (usually fingers or counters)
Cannot do “rabbits ears”
Learning to image patterns

9. Stage 3 (after 1 year at school)
Can count small unseen sets of objects using just the numbers
Always starts from 1 –often counts 3 times to count once
then then
Often “rocks”, stares, rolls eyes up or shuts eyes to concentrate on the count

10. Stage 4 (after 2 years at school)
Counts on or back from the biggest number
as 28 then 29, 30, 31, 32
Uses 1 as the count – often uses finger to “track” the count
Learns 10 as the unit to count with
as 33 then 43, 53, 63, 64, 65
Numbers to 100

11. Stage 5 (after 3 years at school & end of year 4)
Manipulates numbers to make the operation easier to work with
in many ways such as
8 + 8 – 1 (doubles minus…)
(doubles plus….)
(take 2 from the 7 to put with the 8)
– 2 ( round and adjust)
(2 + 3) (using 5’s)
Numbers to 1000

12. Stage 6 (end of year 5 & 6)
Addition and subtraction with any whole numbers to 1,000,000
Many strategies, including formal algorithm
62 – 39 as 62 – 40 +1
73 – 28 as
5006 – 1997 as
56–27 as = 54 then + 2 = 56 so its 29

13. Stage 7 (end of year 7 & 8)
Wide range of strategies for multiplication & division (includes formal equations)
9 x 24
189 ÷ 7
Addition and subtraction of decimals and fractions
7.3 – 2.96 mentally, with an effective strategy – no pencil and paper

14. Stage 8
Mental manipulations with fractions, decimals percentages and ratios
To make 8 t-shirts you need 6 metres of cloth. How many metres would you need to make 20 t-shirts?
Matiu started with a whole box and ate 5/9 of the chocolates. That left only 16 chocolates for Yves. How many chocolates were in the box at the start?

15. How do YOU solve these? 19 + 19 + 19 71 – 27 6 x 18 6.2 – 3.94
How do the people around you solve the following problems WITHOUT pencil and paper?
What strategies do they use?
Can you explain more than one efficient method?
What basic knowledge is needed first?
– 27
6 x – 3.94
5012 – ÷ 16
tenths?

16. “Thinking” Examples:
Design the seating arrangement in your new stadium. It seats 36 people around a hexagon shape

17. “Thinking” Examples:
From: What is the volume of the box with sides 2 x 2 x 9?
To: Working in pairs, create an open- topped box that will hold exactly 36 1cm cubes, using an A4 sheet of paper and sellotape.

18. “Thinking” Examples: From: 21÷3 =
To: At school we only have triangle shaped tables. One person sits at each side of the table. How many tables do we need for 20 children?

19. “Thinking” Examples From: 25÷ 4 = Four friends shared 25 balloons
To: Four friends want to “share 25” as equally as possible.
Four friends shared 25 balloons
Four friends shared $25
Four friends shared 25 biscuits

20. “Thinking” Examples:
Draw as many different digital clock times as you can which only use the digits 1, 4, 6, 8
You can use each digit more than once on your clock time.

21. “Thinking” Examples:
At the school gala, tickets for the ride are $2 for adults and $1 for kids.
If we make $14, who had a ride?
How many different ways can you do this? 

22. Learning Basic Facts
Essential at all stages but only part of the full maths programme
The goal is instant recall
More than just x tables(attached sheet)
Can be taught through games (dice, cards etc) as well as via on line activities OR rote
Teach the patterns and connections and understanding, don’t just test!
Make it a fun challenge

23. Want to know more? Go to www.nzmaths.co.nz and check out the links to:
Numeracy projects
Families
“Information” then “Links” for heaps of websites
“Google” Basic Facts games