This document contains a math problem solving journal from students in class 1/2A and 1/2B. It includes summaries and diagrams from 10 different math problems the students worked on, including problems about tripods, hanging washing, arranging milk bottles, making bear coats, and more. For each problem, 1-3 students explained their thinking and approaches to solving the problem, often using drawings, diagrams, or written explanations.

1. Our Maths Problem
Solving Reflective
Journal
By 1/2A and 1/2B
1

2. Good mathematicians:
2

3. We discovered that when we draw a diagram it
is different to a picture:
3

4. Contents Page:
Problem: Page:
Tripods 5
Mrs Parore’s Washing 9
Strawberry and Chocolate Milk 12
Buttons and Bears 16
Fair Exchange 20
Three Cold Kittens 23
Pizza and Things 27
Pizza and Things Extension 30
More Lollies 35
More Lollies Extension 39
4

5. Tripods
Our Problem
5

6. Li Ya used the counting frame to make groups
of 3 legs to pretend to be the tripod.
Aby did 18 dots to pretend to be the legs and
then circled them in groups of 3.
6

7. Alisha and Ada discovered that they
could use the same strategy to help
them solve the second part of the
problem.
Naomi and Ada labelled their tripods
to show how they counted by 3s to
solve the problem.
7

8. Naomi was trying to work out
how many legs are needed to
make 12 quadpods. She decided
a quadpod has 4 legs (used
Italian - quattro - to work it
out). She was counting in 4s to
make the models. In total she
would need 48 legs.
8

9. Mrs Parore’s Washing
The start of our problem. Dailoli knew the answer straight away
because all he needed to do was count by 2s. 9

10. The second part of our problem
asked how many pegs would be
needed to hang 4 towels if she
used 3 pegs per 2 towels. A few
people were confused at first and
drew 4 towels; 3 pegs on 2 of the
towels and 2 pegs on the other 2
towels.
Imogen, Thomas and LiYa were thinking and trialling different diagrams until
they found one that they thought could make sense. LiYa had felt frustrated and
went to join their group to see if they could work together on solving it. 10

11. We discovered that 6 pegs
were needed to hang 4
towels if you put the peg on
the corner between two
towels BUT...
…By joining ALL the towels together,
Rebecca was able to use 5 pegs,
which meant she saved 3 pegs. This
meant that she found a better peg-
saving method of hanging out the
washing!
11

12. 12
Mary the milk lady has a square milk crate
that would hold four bottles. In how many
ways can she fill it with strawberry and
chocolate milk bottles?
•
Strawberry and Chocolate Milk

13. 13
Some people chose to use the letters "S" for
"strawberry" and "C" for "chocolate" to show
where the bottles were in the crate.

14. 14
Other people chose to use colours to
represent the strawberry and chocolate milk.

15. 15
Some children managed to solve the problem and work out that there
were 16 possible solutions! Tom did his very systematically - this means
he didn't change the number of bottles until he was sure he'd found all
the different solutions.
Mohamed discovered that a 3 by 3 crate will go 3 squares across and 3
squares down. This means there will be 9 squares in the crate!

16. 16
Buttons and Bears
Mother Bear is making her 5 bear
cubs new coats. The coats have 3
buttons each. How many buttons
does Mother Bear need?

17. 17
Ada, Naomi, Tom and
Imogen modelled putting
the buttons into groups
so that they could be
counted by 3s. The total
number of buttons
needed was 15.

18. 18
Imogen, Ada
and Mohamed
were able to
produce a
drawing to
explain their
thinking and
how they
counted by 3s.

19. 19
Dailoli knew the answer straight away by
adding 3, so used an addition number
sentence to show his thinking.
Tom knew the answer straight away
after counting in his head by 3s. He
wrote down the counting sequence
that he said in his head.

20. 20
Fair Exchange
Mary wants to swap money with her brother.
Exchange 5 coins for a $5 note so that both
children get the same amount.
EXTENSION: I went shopping at the
supermarket and bought items that gave me
the smallest amount of change possible from
$20. What might I have bought?

21. 21
Tyler explained that five $1 coins is
the same as $5, and $2 + $2 + $1 +
50c + 50c will make $6, so the
bottom one is too much.
The correct answer should be $1 +
$1 + 50c + 50c + $2.
Lelah was trying to write 50 cents,
but had written $50. She learnt
we can write 50 cents like this: 50c
or $0.50.

22. 22
Leila was trying to make the closest
amount to $20 possible so that she still
received some change. Leila made a
total of $19.99 and was really excited
until she worked out 1c pieces aren't
around anymore, so her answer didn't
work. Next time she is going to try and
buy items that add to $19.95.
Annie, Alisha and Eva discovered
when there is a total like 19.8 on
their calculator, in money this
means we pretend there is a zero
on the end to make $19.80.

23. 23
Three Cold Kittens
Winter has set in. The three little kittens are very cold and
they need mittens. Mother Cat decided to make mittens.
It takes two balls of wool to make mittens for one kitten.
How many balls of wool will Mother Cat need to make
mittens for three little kittens?
Mother Cat went shopping to buy balls of wool. One ball
of wool costs $1. How much money will mother cat have
to spend to buy all the wool she needs?

24. 24
Tom discovered that you need to read
the question carefully and look for key
details. Tom had accidentally mis-read
how many balls were needed to make
one pair of mittens. Once he read this, it
was easy to solve and fix!
Imogen drew a diagram to show the kittens,
two balls of wool and the counting pattern
(by 2s). Rebecca solved it the same way.

25. 25
Ada chose to draw a diagram.
Her thinking was: two balls of
wool makes one pair of
mittens, so that is 6 altogether.
Naomi chose to show her thinking in
words and numbers rather than a
diagram.

26. 26
Dailoli chose to use
multiplication (3 kittens times 2
balls of wool each is 6
altogether). Three "groups of" 2
is the same as 2+2+2.
Leila and Kira chose to use concrete materials
to show their thinking. They thought it was
easier to show their thinking this way. They
chose to use blue bears to be the kittens, and
a yellow bear for the mum. They chose to
show different coloured balls of wool so you
could easily see what balls of wool were for
which kittens.

27. 27
Pizza and Things
Our local Pizza Place has only two tables but they
are quite big. If each table holds 7 people, how
many people can be seated altogether?
The Chicken N Chips next door to the Pizza Place
also has two identical tables. The Chicken N Chips
can seat 16 people. How many people can sit at
each table?

28. 28
Annie drew 7 seats around each table and
knew that 7+7=14.
Harry decided to use two colours to show the
difference between the tables. He then
realised he needed a second table because it
said the Pizza Shop had two tables.
Imogen and Li Ya decided to draw a table and
then use counters to be the 7 seats around
each table. Then could then easily see
"double 7" is 14.

29. 29
Noah realised that 7+7=14, but also knew that was
the same as 2x7. The 2 is the 2 tables, the 7 is the
number of seats at each table.
Eva and Annie solved the first part of the problem
easily. Eva realised that the Chicken restaurant
could only have 16 people. They then used counters
to try and make two identical tables that equalled
16 people altogether. They found they could sit 8
people at each table.
Noah had made an error reading the question and
had done 2 tables of 16 people (which makes 32),
but now realises he could solve it as 2x8=16.
Tom H chose to solve the problem in quite a
different way. He used tally marks to draw 16
people and then shared them equally between the
two tables. He still got the same answer.

30. 30
One night, 57 people wanted to be seated at the
local pizza shop for dinner. How many tables will
the owners of the pizza shop need?
If the chicken and chip shop had 7 tables full of
people, which shop had the most people?

31. 31
Eva and Annie used counters to make 7 chairs
around each table, leaving a gap between
them. They were then starting to draw their
tables in their books.
Aby, Lelah, Li Ya and Rebecca got 57
unifix in towers of ten and then
sorted them in 7s. They discovered
they could make 9 tables.

32. 32
Imogen looked like she was doing
fractions, but she was actually
counting by 5s. She knows 5 is 2 less
than 7 so she found counting by 5s
and then adding 2 on to each made
the counting easier for her. This wasn’t
helping her to solve the problem so…
Imogen then decided to sort the
counters so that there were 7 on
each. She has made an array.

33. 33
Noah and Tom's early work. They
first thought there were 8 tables
but noticed they had made a
mistake counting. Kristin
challenged them to prove that they
had 57 people altogether without
counting one-by-one and this led
to...
Tom getting the idea of labelling
each table in the counting by 7s
pattern: 7, 14, 21, 28, 35, 42, 49,
56...57. This helped them to realise
their mistake.

34. 34
Alisha, Naomi and Ada all used a similar
strategy to work out that the pizza shop
needed 9 tables, but the 8 tables of the
chicken shop only held 56 people. So, the
pizza shop had more!

35. 35
• On Monday, their Mum gave Sam and Sylvia 7 lollies. Sam got 2 lollies. How many lollies did Sylvia get?
On Monday their mum gave Sam and Sylvia 7
lollies. Sam got two lollies, how many lollies did
Sylvia get?
Their Mum gave Sam the same number of lollies
each day up to (and including) Friday. How many
lollies did Sylvia get that week?
More Lollies

36. 36
Tom thought it would be good
to use a number sentence to
show his thinking because he
knew there was a total of 7
lollies, and a number fact he
already knew was 5+2 so he
knew how many Sylvia would
be getting.
Li Ya did a similar thing to
Tom but counted on her
fingers from 2 to see how
many lollies Sylvia would be
getting.

37. 37
Aby decided to do a table to organise her thinking. She wrote down the numbers
1-7 for the number of days in the week, and then counted by 5s to show how
many lollies Sylvia was getting. Aby realised a problem – she was only meant to
count the lollies from Monday to Friday, and she had accidentally included the
weekend as well. Aby knew she didn’t need to do the whole problem again, she
just crossed off 2 days.

38. 38
Imogen had started to create a grid or table to show the days of the week and
how many lollies Sylvia and Sam would get each day. She found out that when
she counted by 5s (for the lollies that Sylvia was getting) from Monday to
Friday, she got 25 (5, 10, 15, 20, 25).

39. 39
If Sam collected 56 lollies over two weeks, how many
lollies would he get each day?
If Sylvia received 63 lollies over two weeks, how many
more lollies did Sylvia get than Sam?
More Lollies Extension

40. 40
Naomi worked out that 2 weeks was 14 days so she started off trying to put 8 lollies
in each group. That was only enough for 7 days (I week). She then knew to halve the
amount in each of the groups, which meant Sam was getting 4 lollies each day for 2
weeks.