# Problem Solving

This Professional Learning Community (PLC) has been created to provide a forum for discussing problem solving activities. Each month we will post two new problems, a level 1 problem, a level 2 problem and a level 3 problem. Please use the threads to tell us how your students solved the problems. We will include some of the solutions at the bottom of each problem on the site. Don’t forget to include your students name, (age if you wish) and the school that you are in when you post their strategies on how they solved the problem.

There is also a thread where you can share good problems that you have used, and a thread for general discussion about problem solving.

The posts in this PLC can be viewed by anyone, but if you wish to post a comment yourself you will need to sign in to the nzmaths website. If you do not have an account you can create one for free. Please feel free to comment on any of the links provided.

If you join this PLC, you will receive email notifications whenever a new page is listed here, or whenever a user comments on the pages already listed.

For information on using PLCs please visit:

http://nzmaths.co.nz/using-professional-learning-communities

Happy problem solving! We look forward to seeing the range of methods and approaches students use to solve these problems.

## Level 3 problem February 2015

*Level 3 String Problem*

*Level 3 String Problem*

### Pale has a piece of string 24 centimetres long. He ties the ends together and then lays it out so that it makes a rectangle. He notices that the length of the long sides is twice the length of the short sides.

### How long are the sides of the rectangle?

## Level 2 problem February 2015

__Level 2 String Problem__

__Level 2 String Problem__

### Chris has a 20cm long piece of string. He wants to cut it into two pieces that are different lengths.

### If each piece needs to be an exact number of centimetres in legth, how many different ways can he cut the string?

## Level 1 problem February 2015

*Level 1 String Problem*

*Level 1 String Problem*

### A 30cm long piece of string is cut into two pieces. One piece is twice as long as the other.

### How long is the longer piece?

## Level 3 problem December 2014

*The 500 Problem*

*The 500 Problem*

### Here’s a subtraction problem.

### In the two subtraction sums below, a and b each stand for digits.

### If the two subtraction sums give the same answer, what digits do a and b stand for?

## 500 | ## 5ab |

## Level 2 problem December 2014

__Little Magic Squares__

__Little Magic Squares__

### Tui has just discovered magic squares. Magic squares are grids of numbers where the numbers in each row, column and diagonal all add to give the same sum.

She decided to make all of the 3x3 magic squares that she could just using the numbers 1, 2 and 3.

How many could she make?

## Level 1 problem December 2014

*Well, Well!*

*Well, Well!*

### Freddo has had a nice swim in the bottom of the well and decides that now is the time to get out.

Freddo climbs 3m up the wall of the well and then rests.

But the wall is slippery and he then slips down 1m. He is so tired he goes to sleep for the rest of the day.

The next day he does the same thing - climbs up 3m, slips back 1m, and goes to sleep.

## Level 3 problem November 2014

__My Dogs__

__My Dogs__

### I have three dogs. If I add their ages together I get 15.

If I multiply their ages together I get 45.

How old are my dogs?

## Level 2 problem November 2014

__A Fishy Problem__

__A Fishy Problem__

### Millie has just got a new pet fish.

The pet shop owner told her that she needs to put the fish into exactly one litre of water.

The problem is she can only find two containers.

One holds seven litres and the other holds four litres.

Can you use these two containers to put exactly one litre of water into the fish tank?

## Level 1 problem November 2014

__Gremlins__

__Gremlins__

### Oh no, gremlins have been in and covered up some numbers on the chart. Can you put the equations back together?

## Level 3 problem September 2014

__Lollies, Lollies, Lollies__

__Lollies, Lollies, Lollies__

### On Monday, Sam, Sunny and Sylvia shared some lollies that their mother had given them.

Sunny got twice as many lollies as Sam.

Sylvia got three times as many lollies as Sam.

## Level 2 problem September 2014

__Grandpa's Chocolates__

__Grandpa's Chocolates__

### Grandpa has five pockets in his jacket.

In one pocket he has one chocolate. In another pocket he has two chocolates.

In another he has double that many chocolates.

In yet another he has double that many and in the fifth pocket he has double that many again.

How many chocolates does Grandpa have in his jacket?

## Level 1 problem September 2014

__Strawberry and Chocolate Milk __

__Strawberry and Chocolate Milk__

### Mary the milk lady had a square milk crate that would hold four bottles.

### In how many ways can she fill it with strawberry and chocolate milk bottles?

## General discussion

Please use this thread for any general discussion about problem solving.

## Problem sharing thread

Please use this thread to share and discuss any good problem solving activities that you have found.