You need a full understanding of number to be able to enjoy maths. Yes, I did say enjoy maths. A full understanding involves knowing what numbers and symbols mean. That might sound obvious, but its the hardest thing to learn. Once we have a true understanding of number we begin to see patterns - and when we see patterns we can start manipulating those numbers and having fun with them.
This is a few of the things it would be great to have in your arsenal to start this understanding.
A set of Numicon, Blank number lines, Arrow cards, Blocks, Lego or Duplo bricks, A collection of small objects (could be animals, buttons, straws etc), Rulers, Playing cards, Dice, Dominoes, Counters, Blank cards and Post-it notes.
If you have some, or all of them, then we are ready to go.
I am going to be working at Year 2 level with Tiny and the first week of the new year we are going to be doing a recap of place value.
Starting at Year 2 level when he should be in year 4 seems to be putting the expectations down very low.
Its not
Because he missed the general understanding of number early on he needs to revisit it and become more confident with number.
We are going to spend this week playing with number, and reinforcing what we were looking at towards the end of 2018.
I hop you use some of the ideas here - but the most important part about the whole week is the discussion that goes with the work. I will be listening for Tiny's explanation of what he is doing and encouraging him to explain his thinking.
Day One to Day Five: When he has had enough for the session - I will stop. If he want's to carry on then we will.
We are going to be partitioning numbers into 10's and ones. And we are going to do it using objects.
First of all we need a part whole model.
Do this by using 3 sheets of coloured paper and set them out on the table so they form a triangle.
Like this:
Using the part/whole model we are going to be adding counting blocks. Or see link below to cut out some paper versions of counting blocks.
Talk about the rods representing 10 and the small cubes representing ones.
Ask if they can put the rods into the first box and the small cubes into the second box.
Talk about how you can write four different math sentences for this part/whole model
40 + 7 = 47
7 + 40 = 47
47 - 7 = 40
47 - 40 = 7
Do this a few more times making it into a game.
Here are some ideas for the numbers you might use.
20 + 4 = 70 + 3 = 50 + 8 = 61 = 60 + __ 83 = ___ + 3
At the moment keep the partitioning simple just in tens and ones. Build up some confidence.
This game is how were going to start our session.
Next we are going to use symbols to
represent tens and ones - something like this.
This is the first time in this session that I am going to ask Tiny to do any written work in his book.
I have drawn some fruit at the top of the page with amounts underneath.
After doing the first example for him, he will now complete the rest himself using any symbols he wants to represent tens and ones.
Next we will talk about everything being 10p cheaper.
I want him to explain to me how he is going to work it out. (I'm looking for the fact that just the tens will change and the ones will stay the same)
Now for some problem solving.
I want Tiny to use the fruit examples to make up some sums.
He still has his blocks to help him, but I want him to use numbers to write out the maths sentence.
Ex: 15 + 15 + 35 =
Using the blocks gives him the chance to group 10 small blocks into a ten rod to be able to group his tens and ones.
By adding the 3 lots of 5 we will talk about the ones changing into 1 ten and 5 ones. Once that is done - then we can see how many tens we have and how many ones and write down the total. 6 tens and 5 ones (65)
He can make up some of his own combinations before moving onto the next problem.
The next problem on the page involves understanding that the tens are getting smaller, but the ones stay the same.
Back to whole/part models. For this we will still be using our 3 pieces of paper and our tens and one blocks to help us (more for the confidence).
Now we are partitioning numbers in a variety of ways, not just as tens and ones.
For example 74 is made up of 7 tens and 4 ones or 6 tens and 14 ones or 4 tens and 34 ones etc.
Once you have used the whole part models that you have drawn - then have a game with making different combinations of numbers to get the same answer and then write them down as number sentences.
Ex: 20 + 17 = 37
17 + 20 = 37
37 - 20 = 17
37 - 17 = 20 I know its a lot of repetition - but make it into a game.
I will be asking Tiny to give me a target number and I will see what combinations I can make to form a number sentence etc. And then it will by my turn.
Next we will start on our column addition and subtraction.
Again, we start by using symbols. This builds on all the previous skills and I will be encouraging him to start to formally present his work in the correct place value columns.
Talk about how many tens there are and how many ones. write the number after the equals sign next to the grid. I.e. 48 for the first example.
Next go onto doing an adding grid and demonstrate how to write it out in numbers.
For the last example I want him to notice that the operation has changed. This will lead onto recognising that different symbols create different results.
I have a large piece of card with the columns drawn in so that Tiny can still use his apparatus to help him work out the next problems.
I have deliberately mixed the operations so that he has to check the symbols.
I've kept it simple at this stage because I want to make sure that he has a full understanding of the calculation.
Hopefully he will want to make up some of his own, but if he doesn't we will leave it at that for now.
Now we can use our hundred square. He loves to use the one online as it is so interactive. Here is the link.
This is a fantastic hundred square that is interactive. Well worth downloading and adding to favourites
https://www.primarygames.co.uk/pg2/splat/splatsq100.html
Ask questions like:
What is ten more than 27?
What is 30 more than 34?
What is ten less than 86?
etc.
A great game to play with a hundred square that he loves goes like this.
Roll two dice and add up the numbers.
Starting from one - move that total.
The next person rolls 2 dice and adds up the numbers and moves the total.
The first person to reach 100 is the winner.
You can play this game on the Splat 100 square because it is so interactive.
The last problem involves using the 100 square to fill out the grid.
Add what numbers you want to the grid and have a race to see how quickly it can be filled.
There are some good games to play on the NRICH website. Here Is one I found for this week.
This is taken from the NRICH website https://nrich.maths.org/
What's the Difference? (7-8 years) 2-4 players
Materials: A pack of 20 to 30 dot cards (1 to 10 dots in dice and regular patterns), counters.
Rules: Spread out 10 cards face down and place the rest of the cards in a pile face down. The first player turns over the top pile card and places beside the pile. He/she then turns over one of the spread cards. The player works out the difference between the number of dots on each card, and takes that number of counters. (E.g. If one card showed 3 dots and the other 8, the player would take 5 counters.) The spread card is turned face down again in its place and the next player turns the top pile card and so on. Play continues until all the pile cards have been used. The winner is the player with the most counters; therefore the strategy is to remember the value of the spread cards so the one that gives the maximum difference can be chosen.
Variations/Extensions
Try to turn the spread cards that give the minimum difference, so the winner is the player with the fewest counters.Roll a die instead of using pile cards. Start with a set number of counters (say 20), so that when all the counters have been claimed the game ends.Use dot cards with random arrangements of dots.