Transcript Warm up activity. When are they going to start learning proper maths? Using the first 3 problems as clues, what is the number represented as an “?” 1.

Warm up activity.
When are
they
going to
start
learning
proper
maths?
Using the first 3 problems as
clues, what is the number
represented as an “?”
1. 1/3 of 12 = 4
2. 9 + 7 =
16
3. 100 – 36 =
4. 56 + ? =
? = 200
64
256
1. 127 + 125 =
2. 378 – 153 =
3. 9 x 49 =
4. 20 x 342 =
5. 408 ÷ 12 =
6. 37.5% of $80 =
Do all the
odd
numbers!
No. However students shouldn't be exposed to
working form until they are “part wholing” (stage 6)
Premature exposure to this may restrict the
students ability and desire to use mental strategies.
Solve by
using
working
form
499
+
21
_______
Doesn’t it make
sense to change
it to 500+20
rather than
doing all the
renaming and
carrying stuff?
The Numeracy Development Project began with a pilot in
2000, since then its expanded to involve almost all of the
primary schools in New Zealand.
Its purpose is to promote quality teaching. It is designed
to provide different experiences in learning mathematics.
More emphasis is placed on the students making sense of
mathematical ideas and to develop abstract thnking.
Enjoy working with numbers
Make sense of numbers - how big they are, how they relate to other
numbers, and how they behave
Solve mathematical problems - whether real life or imaginary
Calculate in their heads whenever possible, rather than using a
calculator or pen and paper
Show that they understand maths, using equipment, diagrams and
pictures
Explain and record the methods they use to work out problems
Accept challenges and work at levels that stretch them
Work with others and by themselves
Discuss how they tackle mathematical problems - with other students,
their teacher and you!
Stage
Zero
One
Two
Three
Four
Five
Six
Seven
Eight
Overview
Emergent
One-to one counting
Counting on from materials
Counting on from One by imaging
Advance Counting
Early additive Part-Whole
Advance Additive Part-Whole
Advance Multiplicative Part-Whole
Advance Proportional Part-Whole
Students at this stage are unable to consistently count a
given number of objects.
1,2,3,5,9
Students can count a set of objects up to 10, but cant
join two sets together
6
Students can join two sets of objects, but rely on
counting physical materials (including their fingers)
5 and 3 more
is 8
Students can count all of the objects in addition and
subtraction problems in their mind
If I had 6 logs
and carried in
another 2,
how many
logs do I
have?
1,2,3,4,5,
6,7,8
Students here are able to count on or back from the
largest number rather than starting at zero
I counted 6
cars and 9
trucks. How
many
vehicles did I
count?
9,10,11,12
,13,14,15
Students are able to re-arrange numbers to make them
easier to solve using their doubles or teen numbers
There are 7 in
Team Red
and 8 in Team
White. How
many players
are there?
7+7=14,
so 7+8=15
Students can recombine numbers in a variety of ways to
answer problems. They can also solve fraction problems
by combining multiplication and addition facts
I had saved
$63, but
spent $29 on
my new
soccer boots.
How much do
I have left?
63-29=?
63-30+1=34
Students here have a vast range of strategies to call on
and will use the “smartest” one. Some equations may
require a combination of strategies in order to solve it
I divided an
orange and
ate 18
segments that
equalled 2/3.
How many
pieces were
there in total?
2/3 of __ = 18
½ of 18 = 9
3 x 9 = 27
2/3 of 27 = 18
Students are using estimations, fractions, proportions and
ratios.
Cayla’s
Clothing
Shop is
giving a
discount.
For a $75
pair of
jeans, you
pay only
$50. What
percentage
discount is
that?
$75 - $50 = $25
25 is 1/3 of 75
The percentage
discount is 33.3%
•Knowledge – Number identification,
number sequence and order, grouping and
place value, basic facts
•Strategy – Addition and subtraction,
Multiplication and Division, Fraction and
Proportions. These are known as
operations.
Strong knowledge is essential for students to broaden
their strategies. There are several key elements to each
stage that children must master to fully grasp the
strategy.
The Strategies build onto one and each other. These are
used to solve problems throughout the stages
Creates new knowledge through use
Strategy
Knowledge
Provides the foundation for strategies
This is a great game you can play at home with children who are
Stages 3-4, however it can be a challenge to anyone at any stage.
I’m going to revel ‘x’ amount of counters for a short time. There
wont be enough time to mental count them all so you’ll need to use
another strategy.
Are you ready??????
There are slight variations of these in later stages!
Doubles + - 1
8+9=
8 + 8 = 16
16 + 1 = 17
Compensation
Skip Counting
39 + 26 =
4x6=
40 + 25 = 65
6,12,18,24
Partitioning
Back through ten
43 + 25 =
84 – 8
40 + 20 = 60
84 – 4 = 80
3+5=8
80 – 4 = 76
60 + 8 = 68
Compensation
Equal Addition
324 – 86 =
89 – 54 =
324 – 100 = 224
90 – 55 = 35
Round &
Compensate
9x6=
10 x 6 = 60
224 + 14 = 238
60 – 6 = 54
Reversibility
Doubling and Halving
63 – 29 =
8 x 25
29 + 30 = 59
4 x 50 = 200
59 + 4 – 63
30 + 4 = 34
Your child will:
Enjoy working with numbers
Make sense of numbers
Solve mathematical problems
Calculate in their head rather than using a calculator or
pen & paper
Explain and record the methods they used to work out
problems
Accept challenges and work at levels that stretch them
Work with others and by themselves
Discuss how they tackle mathematical problems
There are 9 lollies in the jar, Mum gives me 8 more
to put in the jar. How many are in the jar now?
Solution: 9 + 8 =
•How did you work it out?
•What happened in your head
Share your thinking with the people
around you
Can you think of any other ways to solve the
problem?
“I count on from the
biggest number. I put
9 in my head and
counted on.
10,11,12,13,14,15,16,17
“I use my doubles 1.” I know 9+9=18
so…
18-1=17
9+8=
“I use my doubles +1.”
I know 8+8=16 so…
16+1=17
“I can make a 10 by
taking 1 from the 8 to
make the 9 a 10… s0
10+7=17
There are 53 people on the bus. 29 people get off.
How many people are now on the bus?
Solution: 53 – 29 =
•How did you work it out?
•What happened in your head
Share your thinking with the people
around you
Can you think of any other ways to solve the
problem?
I use place value.
53-20=33. Minus another
9.
I split 9 into 3 and 6.
So… 33-3=30
30-6=24
I use a number line
and reversibility
29 30
50
53
So… +1, +20, +3 = 24
I use tidy numbers:
53-30=23
23+1=24
53 – 29 =
I use equal addition
I change 53-29 to…
54-30=24
There are 4 packets of biscuits with 24 cookies in
each pack. How many cookies are there
altogether?
Solution: 4 x 24 =
•How did you work it out?
•What happened in your head
Share your thinking with the people
around you
Can you think of any other ways to solve the
problem?
I use tidy numbers: I
know 4 x 25 = 100 so…
100-(1x4)=96
I used place value.
4 x 20 = 80, and 4
x 4 = 16.
So… 80+16=96
4 x 24 =
I used doubling and halving.
Double 4 = 8, half 14 = 12.
8X12=96
I know
24 + 24 = 48.
So…
48 + 48 = 96
How important is equipment?
When children meet new mathematical ideas for the first
time, it is essential they explore those ideas using
equipment. Once they understand an idea they should try
to use it without the support of the equipment
What about times tables?
Children should be able to make sense of addition and
multiplication before they try to memorise their tables.
But when they do understand, it is important that they
learn these basic facts and can recall them instantly
What about calculators?
Children should do most calculations in their heads. They
should only use calculators when the numbers are hard.
What about bookwork?
Most children will have untidy sections in their maths
books or maths scrapbooks, especially where they have
been thinking about problems. They should also have tidy
sections, where they have written out important ideas or
results
Knowledge Building:
Counting: cars, shells on the beach, how many
times you can run around the house, counting
backwards etc
Numbers before and after: Letter boxes,
number cards, keyboard numbers, dice etc
Identifying numbers: Letter boxes, number
plates, speed signs, how many Km to go etc
Ordering numbers: Write some down on paper
and order
Knowing groups to ten: using the tens
frames, using fingers, cards, dice
Basic addition facts to ten
Recalling doubles
To become a Part-Whole thinker (Stage
5+) children need automatic recall of…
Facts to ten
Doubles facts
Ten and … (10+6=16)
To become a Multiplicative Thinker
(Stage 7+), children need to be able to
recall there times tables
Now try and crack these questions using some of the
strategies mentioned
127 + 125 =
378 – 153 =
9 x 49 =
408 ÷ 12 =
20 x 342 =
37.5% 0f $80 =
Here are some possible solutions. Can you name the
strategies used?
127 + 125 =
378 – 153 =
9 x 49 =
1. 125 x 2 + 2 = 252
1. 380-155=225
1. 9x40+(9x9)=441
2. 200+40+12=252
2. 153+225=378
2. 10x49-49=441
3. 130+125-3-252
3. 300-153+78=225
3. 9x50-9=441
20 x 342
1. 2 x 342=684 so 20 x 342=6840
2. 10x684=6840
408 ÷ 12 =
1. 408 ÷12 as 204 ÷6 as 102 ÷ 3 = 34
2. 12 x 30 = 360, 4 x 12 = 48 so 30 + 4 = 34
3. 12 ÷ 400 = 30r4, 12 ÷ 48 = 4. 30+4=34
37.5% of $80
10% of 80 = 8, so 30% = 24
5% of 80 is half of 10% so it must be 4
Half of 5 is 2.5 which is what we have left, so 2.5% of 80 must be 2
So… 24+4+2 = $30
Thank you for turning out to this evening, we hope you will
go away with a bit more knowledge on what your child is
learning.
Please stay and have a look around the class displays. We
have set up typical tasks children at various stages do and
maths games that help reinforce learning.