## Final Maths Challenge

This is the final maths blog of the academic year. So to mark this special occasion I have asked Mrs Hannah Hukins to be a guest blogger. For those who do not know her, she is both a a parent and teaching assistant. In addition, she has a maths degree and simply LOVES maths!

### Mrs Hukins: This week’s challenge involves colour!

This puzzle is all about colouring in using the fewest colours possible without any sections next to each other being the same colour. Take a look at this pattern.

We could colour it in like this using 4 colours

But could we use fewer than 4 colours and still not have any sections touching with the same colour? How about this?

I don’t think we can use less than 2 colours can we?

Now have a go with the following patterns – do as many or as few as you like. But remember, no sections next to each other can be the same colour, but you’re trying to use as few colours as possible.

Maybe you could try drawing your own patterns and colouring them in.

This bit of maths is useful for people who make maps – take a look at this map of the world, how many different colours have been used?

It’s not many is it, given that there are nearly 200 countries in the world!

## I look forward to seeing your lovely colouring in!

Mrs Hukins

#### NEXT ONE – KS2 Come along…..

Quirkville is a town which lies on the river Grimble, it has 2 islands, connected by 5 bridges as shown below.

The people of Quirkville like walking but they are wondering is it possible to walk along ALL the paths and bridges and get back to their starting point without walking along the same path or bridge twice? We could draw a simple diagram to represent the islands, paths and bridges as shown here

To answer the people of Quirkville’s question, we could see whether we can draw the shape that diagram makes without taking our pencil off the paper…. have a go and see whether you can? Try starting at different points? Can you do it if you start at point A? What about point F?

Mrs Gilhouley and Mrs Mackelworth both live in Quirkville, on the river banks; they decide to build bridges from their houses to their favourite island…

Now can the people of Quirkville walk along every path and bridge without walking the same path or bridge twice? Again we can draw a simple diagram and see if we can draw the shape it makes without taking our pencil off the paper, is it possible?

Did you manage it?

Without the extra bridges it IS possible if you start at point F or C

This is one way of doing it

But with the extra bridges added it is NOT possible…. Why is that? Let’s look at some other shapes and see if you can draw them without taking your pen off the paper, how about this one – it is possible, challenge your friends to see whether they can do it!

Can you do it? Hint – try starting at point D or E

To work out why it works with some shapes and not others, we need to look at the points where the lines (or paths and bridges) meet – the mathematical word for the points is the vertices (the singular of vertices is vertex) – and we need to see how many lines come out of each vertex. If we look back to our first diagram there are 6 vertices (A – F); 4 vertices have 2 lines coming out of them (A, B, E and D) and 2 vertices have 3 lines coming out of them (F and C). If you remember, we had to start drawing from F or C, why is that?

Look at these shapes and then fill in the table below.

 Shape number How many vertices? How many vertices with an odd number of lines? How many vertices with an even number of lines? Can you draw it without taking your pencil off the paper? 1 2 3 4 5 6 7 8

The big question is, can you work out how you can tell whether you will be able to draw the shape without taking your pencil off the paper or not? Try drawing some more complex shapes that will work. Send your answers to [email protected] you can also email me if you have any questions or want a hint.

I hope you enjoy this puzzle – this is part of an area of maths called graph theory which I actually studied at university.

Mrs Hukins

## Solutions to Maths Challenges Week 7

Thank you to the children who entered this week’s maths challenges. It looked quite straightforward on first appearance but it was actually quite tricky indeed to solve.

Harrison in Year 1 found a way to start with the blue triangle and by changing one property only end with the red circle. Well done Harrison.

Rory found two possible solutions.

Well done Rory, what tenacity.

Primrose found three solutions to the puzzle for challenge one! And with the help of her family was able to solve Challenge 2.

Congratulations to everyone who took part this week.

## Week 7 – Maths Challenges

```Remember to send solutions to [email protected] by 3pm next Wednesday.
Simply write the type of maths challenge e.g. First Maths challenge, Junior Maths Challenge or Senior Maths challenge
in the subject bar. Tell me your class and if you are happy for your work to be published on the blog.
I look forward to seeing your ideas and solutions. If you can attach your work, that would really help!```

Hello! I hope you had a lovely half term break and have settled back into learning smoothly once more. Did you try any of the puzzles I blogged over half term?

Did you like my jokes? If you have a maths related joke, please send it to me – I would love to hear it.

### First Challenge

This week it’s a tricky one! It is called Chain of Changes. There’s a help sheet in case you would like to cut out the shapes.

### Senior Challenge

What time is it? It’s hard to know the day let alone the time these days! This is a particularly tricky problem for Sam. Good luck!

## May Half Term

### Hello Math-e-magicians!

#### It’s half term next week, but that’s no reason to abandon maths and puzzling, if, like me, that’s your thing. But first a couple of jokes!

Here are links to activities that you may wish to try…

General maths puzzles:

https://www.mathinenglish.com/PagePL3P21to25.php

Love emoji maths? Try this: https://www.solvemoji.com/

Rainy day? Online games: https://www.transum.org/Software/Puzzles/

#### Something of a challenge to think about….

You have a bucket, a container which holds 5 litres of water and container which holds 3 litres of water. You have nothing else.

How can you make the bucket contain EXACTLY 7 litres of water?

#### Number Sticks

Collect lots of sticks or twigs. Can you make the numbers 1-9 using the sticks? BUT the rule is, you need to make the number 1 with one stick, the number 2 with two sticks and so on. Is it possible? If it helps, you can use sticks of any size.

#### Finally…

Here’s an interesting idea – can you find other ways to write numbers? This is written in Korean and shows us not only how to say the number but how it is written. I wonder what you will discover…

Have a lovely break,

Mrs G

Maths is beautiful and I love books too!

## Solutions to Week 6 – Counters

Hello everyone,

Thank you to everyone who had a go at last week’s maths challenges.

Here are some of the solutions:

#### First Challenge

This involved biscuits and decorations. Rory, in Year 1, used wooden blocks and Lego to solve this.

And here is another classmate using paper, sparkly pipe cleaners and REAL chocolate buttons to give us her solution. Yum Yum!

Arlo, Year 2, found the solution too. He knew there was only one biscuit with all three decorations on it.

But my question is WHY does biscuit 12 have all three decorations of icing, a cherry and a chocolate button?

Well it’s all to do with factors! Thank you Rory – you picked this up too.

There is one biscuit with all three decorations and that is because 12 is in the 2, 3 and 4 times table. Take a look:

#### Junior Challenge

Click on the link below for a solution from a keen Year 4.

Week 6 Junior

Have a look at this!

#### Senior Challenge

Jamie has used 15 moves but he knows that it can be done in 14 moves. Jamie’s family have set themselves a half term challenge of cracking this – Good Luck – Buena Suerte!

#### Bonus Challenge

I love these sorts of challenge and so does Eloise in Year 6! Here is what she discovered:

## Week 6 – Counters

### Hello Everyone!

```Remember to send solutions to [email protected] by 3pm next Wednesday.
Simply write the type of maths challenge e.g. First Maths challenge, Junior Maths Challenge or Senior Maths challenge
in the subject bar. Tell me your class and if you are happy for your work to be published on the blog.
I look forward to seeing your ideas and solutions. If you can attach your work, that would really help!```

Thank you for the feedback on codes week. What a lot of keen code breakers we have.

This week I have decided to go with the theme of counters. All the challenges use counters or can be solved using counters. What could you use if you don’t have counters? Why not try, bits of paper, coins, stones or pebbles, I wonder what creative ways you will find to solve these puzzles.

## Week 5 – Code Crackers – Solutions

Thank you for your replies to last week’s challenges. We have a lot of keen code crackers at St. John’s.

## First Challenge

We had picture algebra here – this just goes to show how early we introduce children to algebra. It is not something for older children, we actually start this in reception class.

Aalim in Class 1 tried this and did very well. The ‘monster’ pictures were particularly hard to work out. Have a look and you will see why.

Aalim then went on to try the first two Junior challenges. What tenacity! (see below)

Max S tried these too. What careful calculating.

He then went on to do some more and even set some questions of his own for his family! Well done Max S – good job.

Rory in Class 1 also tried this. What careful, neat work. He tells me it was a little bit like the Morse code he did with his granny last week on Facetime. Yes, it is! It’s a good idea to work out the answers before you put them onto the sheet too.

Zach in Class 1 tried this. Miss Giles will be pleased to see your partitioning of 22 – well done!

## Junior Challenge

Aalim solved the first two – here are his workings.

Rory went on to this challenge too. I think everyone has really enjoyed the codes this week.

With the help of a clue, Rory was then able to work out the tricky challenge at the bottom!

Eloise in Class 6 tried also this. The first two puzzles are warm ups for the older children. The final one provides the challenge! Well done, Eloise.

Teddy in Class 2 also had a go – well done, Teddy.

Jamie in Class 4 was the only person to do the Junior Challenge Plus. Well done Jamie – I thought this was rather tricky!

## Senior Challenge

This relied on noticing two of the mathematical patterns. Once you work out that the square has to have the value 2, this helps you with square x orange triangle. That is how I started, did you?

Eloise tried the Senior Challenge.

So did Alex from Class 5

And Mikalya from Class 6,

Jamie from Class 4 tried this out too!

## Week 5 – Secret Mission: Crack the Code!

Hello Everyone!

```Remember to send solutions to [email protected] by 3pm next Wednesday.
Simply write the type of maths challenge e.g. First Maths challenge, Junior Maths Challenge or Senior Maths challenge
in the subject bar. Tell me your class and if you are happy for your work to be published on the blog.
I look forward to seeing your ideas and solutions. If you can attach your work, that would really help!```

Thank you to all my regular contributors and welcome all newcomers!

This week, in honour of the 75th anniversary of VE day and thinking about ways that maths helped to bring an end to the Second World War, we will be acting as mathematical code breakers!

In addition, I would like to celebrate the phenomenal achievements of Alan Turing and The Bletchley Park group. You might like to find out more about this by visiting: https://bletchleypark.org.uk/our-story to see where it all began. Or try some of the code breaking resources on the website at https://bletchleypark.org.uk/learn/resources/ve-day-learning-resources an example of which is at the end of the blog.

## First Challenge

Enjoyed that? Want a bit more of a challenge?

## Junior Challenge

Come on you can do it!

Want to stretch your code breaking abilities?

## Senior Challenge

Step up the next Alan Turing! Good luck – this will take real perseverance and tenacity.   Why not try this with family, grandparents, friends and relatives. OPEN TO ALL.

### Message from me  –. — — -.. .-.. ..- -.-. -.-

One of the puzzles on the Bletchley Park Website:

## First Challenge

Max S in Year 1, solved this puzzle.  He used flash cards with the numbers on to add with, along with a little help from the numicon. He then went onto find 3 other totals using the cards. Well done Max!

I was delighted to see that Aalim in Year 1, used the coloured blocks – this is EXCELLENT. Often something amazing happens when we solve problems in this way – the brain sees maths in a special way and our brain grows.

Rory, in Year 1, also solved the puzzle. He decided to use dominoes. He tried out the different combinations of numbers adding these up to see which totals he could find. He found that over time the more sums he did, the easier the sums became and the more quickly he could find the answers he wanted. Well done, Rory! Great puzzling!

Zach in Year 1 also solved this. If you look carefully you can see how he started with the number 8 and generated many of the answers using this as a starting base. Great thinking!

## Junior Challenge

Aalim also enjoyed cracking the codes. I know this is very popular with many people – especially me! Starting with the four circles is key to this puzzle. From there it is possible to reason the remaining answers.

Teddy, in Year 2, took this on and solved it correctly. If you lok carefully you can see the TOP TIP! Thank you Teddy.

Jamie, in year 4 also enjoyed this and

## Senior Challenge

Mikayla was quick off the mark this week with her solution. She quickly realised that no house number could be higher than 8 as it would take the total of all the eight house greater than 36. She also worked out which combinations could NOT go together. She used my suggestion of cutting up the paper squares and reasoning her way to the final solution. Thank you for sharing your approach – this really helps others to consider ways to solve problem like this. Congratulations.

Eloise in Year 6 solved this too. Well done!

Alex, Year 5, also attempted this. It is a tricky problem, so very well done, Alex. As you can see, this arrangement of houses is different from Mikayla’s and Eloise’s but still solves the problem correctly. As in life, there are often many ways to solve the same problem.

Very excited about tomorrow’s challenges. I am releasing them early as we have VE day on Friday! Might there be a link? Who can guess what it will be?

## Maths Challenges – Week 4

### Welcome to this week’s maths challenges. They have come out a little earlier than usual as next week is a 4 day week –  so feel free to get started!

```Remember to send solutions to [email protected] by 3pm next Wednesday.
Simply write the type of maths challenge e.g. First Maths challenge, Junior Maths Challenge or Senior Maths challenge in the subject bar.
Tell me your class and if you are happy for your work to be published on the blog.
I look forward to seeing your ideas and solutions.
If you can attach your work, that would really help!```

## First Challenge

Tricky one this week, my keen mathematicians. Try your best – stick at it.