“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”

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?

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

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

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

Stage 0 Cannot reliably count a group 1-1 1-2-4-3-5 (5 objects, wrong word order) 1-2-3-4-5-6-7-8-9……..(doesn’t stop) 1-2/3 -4-5 (5 counts but only 4 objects) Also learning to read the numerals & the words to 10

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

Stage 2 (after 1 year at school) Reliably adds & subtracts to 10, then 20 Cannot count the objects if they are unseen 4 + 5 can only be counted with objects (usually fingers or counters) Cannot do “rabbits ears” Learning to image patterns

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 1-2-3-4-5-6 then 1-2-3 then 1-2-3-4-5- 6-7-8-9 Often “rocks”, stares, rolls eyes up or shuts eyes to concentrate on the count

Stage 4 (after 2 years at school) Counts on or back from the biggest number 4 + 28 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 33 + 32 as 33 then 43, 53, 63, 64, 65 Numbers to 100

Stage 5 (after 3 years at school & end of year 4) Manipulates numbers to make the operation easier to work with 8 + 7 in many ways such as 8 + 8 – 1 (doubles minus…) 7 + 7 + 1 (doubles plus….) 10 + 5 (take 2 from the 7 to put with the 8) 10 + 7 – 2 ( round and adjust) 5 + 5 + (2 + 3) (using 5’s) Numbers to 1000

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 75 - 30 5006 – 1997 as 1997 + 3 +3006 56–27 as 27+27 = 54 then + 2 = 56 so its 29

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

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?

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? 19 + 19 + 19 71 – 27 6 x 18 6.2 – 3.94 5012 – 2997 368 ÷ 16 0.8 + 22 tenths?

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

“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.  

“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?

“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

“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.

“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? 

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

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