How we teach Maths in Grade 3/4

1. ADDITION & SUBTRACTION
in GRADE 3/4

2. Stepping Stones/Hurdles at this level:
• These are stages that children move through – some more quickly
than others.
Just like taking that first step, some children do it much earlier,
some children may take a little longer to let go of your hand or that
table edge they are clinging to. We see a lot of this with the use of
strategies , for example, with addition, where children use their
fingers instead of taking risks and trying new ways.
• However, some stones may become hurdles and children may stay at
that stage for a length of time. Teachers and parents will have to be
patient and show children different ways to manage these
difficulties. When we move children on before they are ready, we can
create problems for later.
• Students are monitored and assessed regularly – and it’s not just the
NAPLAN! Data from these assessments are used to determine at
what stage a particular student is at and the program is
differentiated to meet his/her needs.

3. Stepping Stone 1:
MOVING FROM CONCRETE TO ABSTRACT
UNDERSTANDING
• Place Value – where the place of a digit indicates its value
and understanding the significance of a “zero”, and the
use of a Base 10 system
• How do you visualise 19, 057? Large numbers are
difficult too visualise
• What does 50 metres look like? What is your reference
point? For example: think of the length of a swimming
pool
• What do you mean by 2/3? 6/10? What does 5/7 + 3/8
mean?

4. PLACE VALUE ACTIVITIES –
I had a group of students who were stuck at a particular point and
I knew I couldn’t go forward without re-establishing what they
had already learnt about counting by 10s, using materials to
represent the different elements of the place value system and that
you could rename a number in many ways e.g. 11 is 1 ten and 1
one as well as 11 ones, 345 is 3 hundreds, 4 tens and 5 ones as well
as 34 tens and 5 ones, etc. This is important groundwork which
would help students understand how to use conventional
algorithms appropriately. (I’ll talk about algorithms later.)

5. STEPPING STONE 2:
WIDER RANGE OF STRATEGIES TO LEARN TO
WORK WITH:
• Assessment conducted at beginning of the year – to establish what
strategies students were using and grouping students for explicit
teaching, then reassessing them to determine if they have moved
on. Students could be in different groupings based on what they
need to learn or work on.
• Range of strategies for addition – building on from what students
have learnt in the Early Years: counting all, counting on , counting
in groups, doubles, making to 10, making to 100, etc and then
generalising from known strategies e.g. I know that 2 x 4 is 8
therefore 2 x 400 must be 800, even though I didn’t learn the 2
times table to 400 but because I understand how the place value
system works.
• Subtraction is the inverse operation to addition – if you “master”
addition, the theory is that you also “master” subtraction. But
students seem to find subtraction quite difficult to visualise.
• Fact families – number facts to 20. (This helps with recognising
when a calculation may be inaccurate.) Knowing these also help
with faster calculations without reaching for the calculator!

6. STEPPING STONE 3:
REASONING AND LOGIC
Because you cannot see something, you need other ways to be sure that your
calculations are logical and reasonable
e.g:
• knowing that when you add 2 numbers together, the total has to be larger
than either of the original numbers (5 + 3 = 8) but this does not always hold
true for subtraction e.g. 11 – 3 = 8.
• knowing that when you add or subtract a “0”, you get the original number.
• when you add 2 odd numbers, you will always get an even number, etc.
• Estimating skills are very important – they help to check if your answer is
accurate. e.g. 456 x 3 would be round about but less than 1500 because 456 is
less than 500 and if I wrote that 25.2 x 1.3 = 327.6 , I should question that
because 25 x 2 would only give me 50. Estimating is especially important
when children are using calculators because it is very easy to punch in the
wrong digits or put in too many 0s, etc and children tend to think the
calculator is always right!

7. STEPPING STONE 4:
PROBLEM SOLVING
Now that students have mastered each particular process, do
they necessarily know when to use each one?
Sample problems:
• I went to the market and bought 5 apples and 6 bananas. How
many things did I buy? Pretty straight forward : 5 + 6 = 11
• Kate and Jane participated in a marathon. Jane ran ½ as fast as
Kate. If Kate ran at 7 km/h, what was Jane’s speed? What does half
as fast mean? Was Kate faster or Jane faster? What does km/h
mean? What process do I need to use to find the answer? Can you
imagine a student who comes from a non-English speaking
background or is a little weak or slow in reading having to deal
with this? He/she may be a Maths wiz but might find it difficult to
work this out.

8. Then you get something like this:
• During the 100 meter dash in the 1988 Olympic Games in Seoul,
Florence Griffith-Joyner was timed at 0.91 seconds for 10 meters.
At that speed, could she pass a car traveling 35 km per hour in
a school zone? First response will probably be “Huh???”
SEVERAL STEPS FOR PROBLEM SOLVING:
• Interpreting the problem – what information is essential? What
do I need to find out?
• Strategies for solution – what processes can I use? Which is the
most efficient way of doing this?
• Estimating the answer – is my answer logical?

9. STEPPING STONE 5:
ALGORITHMS –
• These are merely conventional ways of setting out our calculations so
that everyone can understand them. In Maths, symbols are part of a
universal language and we have to learn to follow the conventions.
• Students often have a very strong understanding of how to add 2-digit
numbers in their heads or even horizontally –
e.g. 27 + 45, I know that 2 and 4 make 6, and the 7 and 5 make 12 so it
must be 72 but we then impose a structure upon their reasoning and
throw them off track with the “ do the left column first and then you
carry that number over there and then you add those numbers
together”.
• If students how a strong understanding of how the place value system
works, then using the algorithm makes sense to them and they are not
then merely a series of steps.

10. With subtraction, it gets even more complicated. You borrow but
you never return anything! Or you “decompose” or whatever
method your own teacher taught you……remember the frustration
when you didn’t get the “right answer”? How come when you
borrow a number from the left hand column and put it in the right,
it’s not 1 + 5 but it becomes 15?
1
6 5
- 3 7
____
We introduce the algorithms only after we have done the
groundwork with understanding place value and developing strong
estimating skills.

11. Last Stepping Stone:
THE MATHS CURRICULUM & THE REST OF THE
CURRICULUM!
There is a set quantity of material in the curriculum to be “covered”
at any grade level . As I mentioned at the beginning of the evening,
there is the continuum of logical progression for developing
understanding of concepts but we know that in life, nothing ever
develops in the way it should – some students fly through the
stages, some stumble and others can get quite stuck at a particular
point!
While we try to teach students at their pace, at the back of our
minds is the pressure of teaching them to meet the requisite
standards because they are in Grade 3 or 4 or 5 or whatever and we
don’t want to put a “D” on the reports. And it is understandable
when parents and we teachers get frustrated when a child doesn’t
move forward at the pace we expect.