# Maths Investigations

This week, I'd like you to have a go at some investigations, using and applying some of the Maths you have learnt over the year.  You will need to think about working systematically (eg. starting with the smallest number and working upwards or grouping similar things together) and using your reasoning and problem solving skills.  There are four investigations and you can choose which you do on each day.

Dominoes!

If you have a set of dominoes at home, great, you may find them helpful and you could start with playing a game of dominoes!  If you would like a printable set of dominoes so you can play at home, I have attached one on a pdf below.

If you don’t have a set of dominoes, here is an interactive version to help you with the investigations below:

https://nrich.maths.org/6361

There are three parts to the investigation.  You can do some or all of them, it's up to you and according to how much time you have!

https://nrich.maths.org/9965

Part 2: Next, try to complete the Double 3 down problem on this link.  Record your arrangement of dominoes by drawing them or taking a photo.

https://nrich.maths.org/146

Part 3: If you want a more challenging problem, have a go at solving this problem called Amy’s dominoes.  It uses a 0-6 set of dominoes and you have to think about the different values that each domino has (eg. 2 + 5 = 7, 2 + 6 = 8)

https://nrich.maths.org/1044

Garam Puzzles!

Garam puzzles are named after the person who invented them.  They involve using your basic number facts to solve a puzzle by filling in the gaps.

The Garam puzzles have blanks which have to be filled in using the digits 0-9 to make all the number sentences correct.  The website talks you through how to complete them.  Then there are interactive ones to complete on the website or I have attached some printable ones for you.

This involves lots of reasoning skills, thinking to yourself “Well, this must be this because it’s the only number to make the number sentence true.  So that means the missing number in the next statement will be…..”.  We usually start in the top left hand corner but definitely wherever they have provided you with a completed number sentence or one that is just missing the answer.

Can you make up your own Garam puzzle for us to have a go at?

Money, Money, Money!

I’d like you to use your money knowledge to complete one or some of the investigations on the pdf below.

For the tea shop investigation, there are 3 different levels, you would only need to do one of them (*** is easier than *).

For the “I need 10p investigation”, think about which money amounts would be made using a 10p, for example 90p would be made using a 50p and two 20ps as this uses a smaller number of coins than replacing a 20p with two 10ps. However, 80p would have to use a 50p, 20p, 10p to use the smallest number of coins.

For the presents investigation, you will need to use some addition and also a bit of trial and error to find the amounts!

Mobile Maths!

For this investigation, you are going to use your subtraction knowledge and the number arrangement on a mobile phone.

Have a look at the activity (page 2 of the pdf is the children’s instructions for the investigation).  Try some different combinations of numbers and see if you notice any patterns.  These could be patterns or links between the chosen number and the answer or a pattern or link between the answers and other answer.

Don’t forget to use column subtraction, exchanging when the digit on top is smaller than the digit below.  If you need a recap of column subtraction, please watch the video below.