X marks the spot.
Symbols can be a nightmare for children struggling with maths. That's because its a new language - a maths language. And, as with learning any new language it takes time. For some children it is more difficult than for others and they will need to find ways to help them remember.
With Tiny, it was X marks the spot to tie in with his love of pirates. The division symbol is a little harder at the moment for him to remember. When we start to look at fractions again, it might become clearer.
Last weeks review.
Multiplication and Division
It was a lovely easy start to the week which meant that Tiny gained more and more confidence. This was a good thing after finding the money week very difficult.
The problems I drew in his book he found very funny and decided that he would like to do some himself.
This was a great way of reinforcing that each group had to have an equal amount.
Playing about with the Numicon always goes well.
He enjoyed this, but did become very tired of the writing in his book so I wrote some of the calculations for him.
5+5+5+5+5+5+5= 7 X 5
Use these symbols to make these statements correct.
More symbols, but these ones he knows and understands. < > =
3 X 5 ____ 5 + 5 + 5 + 5
2 X 2 ____ 2 + 2
Using arrays allows children to explore the commutative relationship between multiplication facts - i.e. 5 X 2 = 2 X 5
We used arrays a lot toward the end of the week. By grouping the cubes together and then making sure they made a rectangle, Tiny was able to work out his multiplications.
I gave him ten cubes and asked how many arrays could he make?
After a few tries he worked out that he could get 2 X 5 and that was the same as 5 X 2. What did surprise him was making an array in one long column - 1 X 10.
Often the one times table is not explained well enough.
The same as the 0 X 10 = 0. A lot of children get questions like this wrong in test.
We didn't get onto our array town this week. We can always come back to that for a quiet activity another time.
(Draw an image and write a calculation to represent the problem)
1. With ten cubes how many arrays can you make? We also tried it with 12 cubes.
I introduced the word FACTOR at this time, but only briefly.
Example: All the factors of 12
2 × 6 = 12,but also 3 × 4 = 12,and of course 1 × 12 = 12.
So 1, 2, 3, 4, 6 and 12 are factors of 12.
2. There are 3 dolls in each basket. There are four baskets.
How many dolls are there all together?
3. There are 5 children sitting down for tea. They all have 3 sandwiches each. How many cakes did they eat altogether?
For both these problems we used Numicon and could do them easily.
He was doing so well I decided to find out if he would cope with work from a textbook. He has a fear of working from textbooks, as he says they are boring. This is a page from a year 3 textbook. He only managed the first half of the page before losing concentration, but it was such an achievement for him to even attempt it.
Sharing (Division) we did not manage to get onto last week because we spent a lot of time reinforcing multiplication. So we will start with that this week.
So Now Onto This Week
Division and Multiplication
It is important the division is related to multiplication, and wherever possible I will be re-capping on some of the work we did last week.
We're going to start off with this problem that we didn't manage to get done last week.
Ask questions like 'How many petals altogether?'
'If there were 30 petals, how many flowers would there be?
There are 35 fingers. How many hands?
Write and draw the calculations.
Sharing is Caring
Tiny needs to be able to make equal groups using one to one correspondence. First in practical contexts and then pictorially.
Now is the time to introduce the division symbol.
This is the kinds of things we will be talking about: How many do you have to start? How many equal groups are you sharing between? How many are in each group? etc.
I write up pages of work in his exercise book at the start of each week. That makes it easier for me on a day to day basis. If he is finding the work on one page to difficult, then we will try to find another way to solve the problem - or we will skip that page and come back to it later.
These are some of the things he has in his book for this week to do.
Can You share 12 cubes into 3 groups?
How many do you have in each group?
Draw what you have just done.
Continue with sharing problems and discuss them being related to multiplying.
Have fun with numbers, counters, objects, cakes and chocolate this week.
Whatever you can share (divide) is good. Even dividing up the dinner into equal portions is great for the concept of sharing.
Can you use a bar model again to help you work these problems out?
Janet has 15 sweets and shares them between 3 friends. How many sweets do the each get?
(demonstrate how to write it out as a division sentence)
Mark has 20 toy cars and shares them between 10 friends. How many cars do they get each?
Now instead of using the bar model all of the time - now use Numicon or cubes.
What is 40 divided by 2? (explain what you did)
Can you work out this problem in the same way?
60 divided by 3
I use lot's of images in his book and encourage him to draw images of his own.
For this problem we are going to be making equal groups again. But this also reinforces problem solving.
I will first ask him to identify the numbers in the word problem and highlight them.
Don't forget to ask these questions all the time.
The top problem says -
Pencils come in packs of 20. We need to put 5 in each pot.
How many pots will we need?
This page is going to be about trying different ways to work out equal sharing.
Using a number line can be quite effective as they get more familiar with them.
They can always draw their own number line to help them solve problems with bigger numbers.
This problem says -
You can use a number line to work out equal groups.
For the first one I will show how to jump along the number line in jumps of 2.
Then we will count the number of jumps to give us the answer.
Reasoning and Problem Solving
(I have written these problems into his exercise book)
1, Is this true of false? - Every number in the 5 times table is odd.
2, Tubes of bubbles come in packs of 2 and 5.
You have 22 tubes of bubbles.
How many of each pack could you have?
3.Every number in the 2 times table is even. Is this true or false?
4. The ride on the Ghost Train cost 90p.
Derek finds a 20p coin.
He puts this coin with his three other 20p coins.
Does he have enough to ride on the Ghost Train?
All of these will need support and the use of equipment to be able to answer them. It is good for Tiny to face what he will think are impossible problems.
As we work on them together he will see that you can find an answer if you work through problems step by step.
Finally back to sharing and grouping.
I have written these problems in his book for us to work through together.
1. Share 15 counters into 3 piles. (now I will ask him if he knows how to write that down as a maths sentence. i.e. 15 / 3 = ( I have used the regular division sign in his book, not the computer division sign)
2. Can you use a bar model to divide 20 between 4?
What other number sentences can you make using this bar model?
(20 / 4 = 5 20 / 5 = 4 5 X 4 = 20 4 X 5 = 20)
3. Can you use a bar model to work this out?
Janet had 15 sweets and shares them between 3 friends. 15 / 3 =
4. Mark has 20 sweets and shares them between 10 friends. Show this on a bar model.
20 / 10 =
5. Use Numicon to work out the answer to this problem.
40 / 2 =
Explain what you did.
6. Can you work out this problem in the same way?
60 / 3 =
7. Jelly beans come in packs of 20.
We need to put 5 jelly beans into each party bag.
How many party bags will we need?
(20 / 5 = )
I know there seems to be a lot of repetition this week, but for Tiny there needs to be. A lot of children need to tackle the same problem in different ways. Tiny has a LOT of problems with maths, and the biggest problem he has is fear of not be able to do it and getting in wrong.
By working together and talking a lot about what we are doing as we are doing it, it is helping him grow those new connections in his brain. Every time he tackles a problem, it is helping him for the next time he see a similar problem.
Eventually he will find a way of solving the problems that is quicker and easier for him.
He is making so much progress. In less than a year he has come from not even being able to add the simplest of numbers to now doing multiplication and division.