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Our Maths Problem Solving Reflective

Journal

By 1/2A and 1/2B

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Good mathematicians:

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

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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

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Tripods

Our Problem

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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.

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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.

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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.

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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.

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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.

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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!

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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

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

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

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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!

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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?

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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.

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

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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.

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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?

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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.

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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.

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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?

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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.

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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.

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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.

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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?

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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.

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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.

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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?

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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.

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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.

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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.

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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!

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• 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

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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.

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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.

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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).

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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

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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.