Category Archives: Problem Solving

More Maths in Art

Good afternoon everyone!  Another maths in art post from me today!  I was inspired by Mrs Piper’s Scribbly Bugs and the work of artist Alex Kohnahin to make these symmetrical insects.

 

Something is symmetrical if one side is a mirror image of the other side.  Lots of shapes can be symmetrical, and you can make symmetrical patterns.  You also find symmetry in nature.  A good example of this is the butterfly – its wings are mirror images of each other.  However, other insects are often symmetrical too.  Can you think of or find other examples?

The artist Alex Kohnahin created beautiful, extraordinarily detailed drawings of insects, and they are all symmetrical.

I thought it might be fun to create our own pictures inspired by him.  I’ve included step by step instructions below.  If you make them why not display them with your Scribbly Bugs?

 

First take a piece of plain white paper and fold it in half.

Starting at the fold/closed edge, draw half of your insect.  You can use curly lines and patterns like Alex Kohnahin does, but you will have to re-draw anything you do here, so it might be a good idea to keep it simple!

Then turn the paper over so your drawing is face down.

You will see the outline of your drawing on the other side. Trace over your drawing.  To make this easier you could put your piece of paper in a window – the light shining through will make it easier to see your lines.  I made a light box using a clear plastic container and the torch on my phone!

Once you’ve traced over your lines, open up the paper and you should have created a symmetrical drawing!

Now, you can add colour!

I’d love to see any creatures you create so remember to comment here, send me an email, post on Twitter or on Teams.

Have a lovely afternoon!

Miss Mitchell

Art in Maths!

Good morning everyone!  Another lovely sunny day!  I hope everyone enjoyed Sports Day yesterday.  Something different from me today – using two of my favourite things – art and maths! Can you draw a curve using only straight lines?  Sounds impossible doesn’t it!?  However, it can be done!  The basic technique is called curve stitching and once you have learned it, you can use it to create all sorts of different patterns.  My instructions are quite long and have lots of photos, so I’ve uploaded a word document with the instructions.

I’ve also linked to two videos – the first shows the basic technique and the second shows how to use it to make a pattern.

How to Draw a Curve Using Straight Lines.

Video One – https://youtu.be/xY2U28etO0A

Video Two – https://youtu.be/4rDDa3AbRvI

If you decide to have a go, I’d love to see your pictures so remember to email them, post them in Teams, on the blog or on Twitter (remembering not to add names to photos please)

Have a great day!

Some Puzzles to Solve!

Good morning!  I hope you are all well this week and had a lovely long weekend 🙂

Some puzzles for you to have a go at today!  These are all about guessing a number and I think the most effective strategy to solve them is going to be trial and error.  Remember this is where you make a guess and see if you are close to the right answer.  If your answer is too big, try a smaller guess, if your answer is too small try a bigger guess!  This is a good strategy to try if you really don’t know where to start with a problem.  Remember as well, that it’s good to always read the question properly before you start and then again once you’ve had your first guess!

There are different levels of problems to try, read through and see which you want to have a go at J

 

Problem One

Q.1      I am even.

I am less than 20.

I have 2 digits.

One digit is twice as big as the other.

What number am I?

 

  1. 2 Reece and Luke are given £13 pocket money between them each week.

Reece gets £5 more than Luke.

How much pocket money does each get?

 

Q.3      Can you come up with your own guess the number problem for us to solve?  Post them in Teams, on the Blog or email them too me so that people can have a go at solving your problem!

 

Problem Two

Q.1      I am thinking of a number.  It is between 25 and 32.

Its tens digit is smaller than its ones digit.

If I halve my number, I get an even number.

Guess my number!

 

Q.2.     I am thinking of a number.  It is greater than 50 and less than 100.

You can divide it by five.

Its digits add up to 8.

Guess my number!

 

Q.3      I think of 10.  I halve it.

I add 10.

I subtract 7.

What is left?

 

Q.4.     Can you come up with your own guess the number problem for us to solve?  Post them in Teams, on the Blog or email them too me so that people can have a go at solving your problem!

 

Problem Three

These are somewhat trickier.  First choose a number to start with and work out the sums.  For example you might try 8 for the first question. First you look at “twice my number minus 7”. This would give you 8×2=16, 16-7=9.  To check if this is right, you need to see if the number you started with (8) add 5 is the same as the answer you got for the first part of the question.  8+5=13 however the answer we got the first time was 9 so the starting number cannot be 8.  You could now try starting with another number – do you think the number would be higher or lower than 8?

For each clue guess the number I am thinking of.

Q.1      Twice my number minus seven is equal to my number plus five.

Q.2      Three times my number minus eight is equal to my number plus 6.

Q.3      My number multiplied by 5, plus five, is 20 less than eight more than my number

multiplied by six.

Q.4      Can you come up with your own guess the number problem for us to solve?  Post them in Teams, on the Blog or email them too me so that people can have a go at solving your problem!

 

If you are replying in Teams please try and tag me so that I don’t miss your reply!

 

Happy puzzling!

Miss Mitchell

 

 

Something different…

Something different from me today – not a puzzle to solve!

As it is VE Day I thought I’d share a song which was very popular during World War 2 and which I really enjoy. The singer, Dame Vera Lynn, is 103 and will be leading a singalong from her house this evening as part of the VE Day celebrations! The lyrics, although obviously written about the war are also I think still very relevant today.  I hope you enjoy it!
Hope everyone is well and has a lovely weekend!
Miss Mitchell

Problem Solving

Good morning all!  I hope you have all had a lovely few days enjoying the sunshine and are rested and ready to learn!

Today I have a problem that can be solved by using strategies we have covered before in class.  You could draw a diagram, make an organised list, work systematically or use trial and error.  Whichever method or methods you choose please try to write down and show how you worked out your answer.  As I’ve said in class, I am interested in the strategies we use in problem solving – and we often use smaller numbers in order to help us focus on that.

There are three problems to try.  The second has many possible solutions – how many can you find?  You can try any or all of the problems and I look forward to seeing your solutions!

Problem One – Heads and Feet

On a farm there were some hens and sheep.

Altogether there were 8 heads and 22 feet.

How many hens were there?  How many sheep?

 

Problem Two – Noah’s Ark

Noah saw 12 legs walk by into the ark.

How many creatures could he have seen?

How many different answers can you find?

Can you explain how you found out these answers?

What if Noah saw 18 legs?

 

Problem Three – More Heads and Feet!

On a farm there are chickens and sheep.

I count 48 heads and 134 legs.

How many chickens and how many sheep are there?

 

Good luck and remember you can email me, contact me on Teams or leave a comment here on the blog!

Miss Mitchell

Something different!

Good morning everyone, hope everyone is well.  Something different today! Inspired by some of the learning I’ve seen on Teams this week I thought I’d share my favourite website for learning how to do origami!

https://www.origami-fun.com/origami-for-kids.html

This link will take you straight to the page for origami for children, but if you explore the site there are lots of other models to choose from – including some trickier folds.

I love origami – I find it fascinating that it is possible to turn one piece of paper into so many different models.  Not only is it fun, but it lets you develop lots of really useful skills too – it is great for concentration, patience and reasoning amongst other things.  All in all a good brain workout! I know that lots of you enjoy origami too so hopefully you enjoy this link!

Yesterday I made a crane which is a very traditional Japanese origami model.  Japanese tradition says that if you fold 1000 cranes you will be granted a wish, but I think that might take me some time! They are often seen at Japanese weddings, because they are good luck. They are hung on strings, 40 cranes to a string.  A little maths puzzle – how many strings would you need to have 1000?  Send me your answers on the blog, by email or on Teams!

If you have a go at some Origami I’d love to see – please post or send pictures!

Happy folding!

Solutions!

Good morning everyone!  Thank you for sending me your answers.  The solutions to Friday’s post are as follows!

Puzzle 1 – The answer is 13 triangles – a lot of people got this one!

Puzzle 2 – The answer is 40 – some people got very close to this one!  I have attached a picture which shows the solution – which ones did you miss?

Puzzle 3 – The answer is 204.  This was very hard and required a lot of patient counting!

For all of these puzzles I think the best strategy is to make an organised list and to work systematically (strategies we’ve used in class!)

For example with the chessboard – you could count the number of 8×8 squares (there is 1), then the number of 7×7 squares (there are 4) , then the number of 6×6 squares (there are 9) and so on , until you get to the number of 1×1 squares (there are 64).  Finally, add the totals for the different sizes of squares together to get the answer. The picture showing the answer for puzzle 2 shows this strategy pretty clearly.

The brainteaser was a trick question I’m afraid!  The answer is 1. This is because once you’ve taken 5 from 25 you have 20 – so you can’t take any more 5s from 25!

I’ll be posting some more puzzles and problems for you soon, so keep your eyes peeled!  Either email me your answers (look for the owl icon!) send them in Teams, or comment on the blog 🙂

 

A Little Challenge!

Good morning all!  I hope you are all having a lovely Friday.

Just for a little fun I thought I would set you all a little challenge this morning!  These are classic puzzles which at first glance appear easy but are trickier than you think.  They get trickier as they go on, but the same method will solve them all. See how you get on!  I’ve rounded off with a little brainteaser.  Good luck, and as always please share your solutions and methods with me!

Puzzle 1

Count how many triangles you see in the picture above.

Puzzle 2

Count the squares in the picture above!

Puzzle 3

Getting much trickier now…! How many squares can you count on a chessboard? Clue…there are a lot!

And finally…just for fun!

What is the maximum possible number of times you can subtract number 5 from number 25?

Have a great weekend everyone!

Problem Solving!

Good afternoon everyone!  Hope everyone is having a good day!

Another little problem solving challenge for you!  This one is a fab way to practice your number bonds.

Calculation Families

A calculation family or fact family is made up of four number sentences that all use the same numbers.  Two number sentences use addition and two use subtraction. For example:

3 + 7 = 10

7 + 3 = 10

10 – 3 = 7

10 – 7 = 3

Can you make the fact families for these number sentences?

  1. 8 + 2 = 10
  2. 7 – 3 = 4
  3. 12 + 8 = 20
  4. 20 – 5 = 15
  5. 12 + 5 + 3 = 20

Can you come up with your own?

Things to Think About!

How will you know what you have found all the solutions?

Can you start with one operation?  Focus first on addition then subtraction maybe?

Will you start with any particular number?

How many number sentences will you have for question 5?

 

If you want to practice your fact families some more, Topmarks has a great game here:

https://www.topmarks.co.uk/number-facts/number-fact-families

You can choose which numbers to focus on.

Good luck and I’d love to see your solutions!

Miss Mitchell

Problem Solving

Good afternoon everyone!  Hope you are all well and having a good week so far.  I have attached some number puzzles for you.  If you fancy a challenge have a go!  These puzzles can be solved using strategies we have done in class – either by working in an organised way or by using trial and error. If you need any help just let me know. I’d love to see your solutions so please send them to me or comment below.  Good luck!

Highest Total

Working from left to right, calculate the numbers in the order shown.

Replace each question mark with a mathematical sign (+, -, x, ÷)

Plus, minus, multiply and divide can each be used once only.

What is the highest number you can possibly score?

7  ?   6   ?   3   ?   1   ?   5 =

 Magic Squares

In a Magic Square, every row, column and diagonal all add up to make the same total.

In a traditional 3 by 3 magic square, the digits 1 to 9 are used to make totals of 15, like the one below.  Each digit can only be used once.

However, other totals can be used and larger grids – for example 4 by 4 or 5 by 5.

 I have attached some different magic squares.  Have a go at completing them.

Can you come up with your own magic squares for us to solve?

Magic Squares