Counting on & Square numbers

Z has known how to count up to 100 for a while... I'm not sure where she learnt it - from her sisters probably! And has recently randomly started doing addition on her fingers, e.g. she'll come to me while I'm cooking and say "4 plus 3 is 7!" while holding up her fingers to show me... So I thought I should probably put some effort in too and help her addition skills improve. 😅

Firstly, she hadn't got the hang of counting on when doing addition - i.e. she would count the fingers on one hand from 1 before counting on the fingers from the other hand, rather than just start at 4 and count on from there. So I asked her "What's 7 plus 7?" Of course, she couldn't do it on her fingers because she didn't have 7 fingers on each hand!

So we took out the multilink cubes and she chose two colours - red and black - to represent each number in my questions. She counted out 7 red cubes and 7 black cubes, then (starting from 1 again!) counted them all to 14. I covered the red pile with my hand and told her we know this pile is 7, so we don't need to count it again! And modelled counting on with the black blocks to get to 14.

We did another couple of questions like this with the blocks (e.g. 8 + 4, 6 + 9, so answers between 11-20) and I would cover the larger number with my hand after she'd counted out the blocks so she could count on with the smaller number. Then I would uncover the pile and she could count them all to check her answer was correct.

Then I asked her if she needed to count out the blocks for the bigger number at all, because I was covering the pile anyway! And she said no, but where should she put the number then? I lightly squeezed the top of her head with my hand and said to put the number in there (I found when teaching the twins when they were younger that this physical action helped them!).

I asked her what 8 + 5 was. Which was the bigger number? 8. So where does it go? In your head (*squeeze for emphasis)... Without prompting she then counted out 5 blocks. I touched her head to remind her 8 was in there then she used the blocks to help count on to 13. 😄

Final stage: I asked her if she could do bigger numbers like 15 + 4 then? And could she use her fingers to help in case she didn't have any blocks? She touched her own head (15 in here...) and counted on to 19 using 4 fingers. Last question, 22 + 8? Same method, she worked out it was 30! MashaAllah. 💪 When Papa came home later she was happy to show him she could now do maths with bigger numbers! And I was happy to see she'd retained what I'd taught her earlier. 😂💕

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While I had the blocks out, I decided to use them afterwards for the twins as an introduction to square numbers.

They have a multiplication grid poster in their bedroom and F had asked that morning why the numbers in a diagonal line were coloured differently to the rest. M straightaway answered because they were in a pattern of 1 x 1, 2 x 2, 3 x 3... So we went downstairs and I wrote these out to 5 x 5 on the whiteboard, with the answers, and an array of dots for each one to explain why they were called square numbers.

Fast forward to these blocks again - so several hours later - I asked the twins to use them to make as many square numbers as they could while I put A down for her nap.

MashaAllah they made these (and were also able to tell me they had used 91 blocks because there were 9 left over!) so I thought I'd quickly recap area while here...

E.g. how many cubes are in the square for 6 x 6? 36. So if I had a field and one side of the field was 6m, what would the area of the field be? They quickly answered 36 (and I filled in the m² units for them - I'm not interested in units at the moment so didn't want to dwell on them at this point). I asked similar questions for other square numbers in the context of word problems such as areas of walls, books, rooms, boxes, etc. Then to be sneaky I threw in a question on perimeter. They both fell for it. 😂 But when I repeated the question emphasising the word perimeter they laughed at themselves and were able to give the correct answer. MashaAllah. 😁😁

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While we're on the subject of maths, I'm going to put this here as a nice reminder of how the twins have different personalities and ways of thinking... Some of their answers to a worksheet they did the next day...

F, trying her hardest, but sometimes not seeing the wood for the trees:

M, being calm, laid-back and not making life difficult for herself:

😂👍

Maths Update: Times Tables (2x, 5x, 10x)

We've been focusing on multiplication and the times tables facts for the past couple of weeks. The NC for Year 1 introduces the 10x, 5x and 2x tables, which the girls are familiar with now, and the NC for Year 2 mentions them again - so I wanted to concentrate on quicker recall to help with their mental maths.

We began by recapping multiplication theory i.e. What does 2 x 5 mean? It means counting the number 2 five times. This is the same as 5 x 2, counting the number 5 two times - all demonstrated physically with cubes first then as dots on the whiteboard.

Over the week they then did a mixture of worksheets, oral questions, online games (we've signed up to education.com as someone organised a cheap HE lifetime deal!) and simply chanting both as facts (2 x 1 is 2, 2 x 2 is 4, etc) and as sequences (2, 4, 6, 8, etc) forwards and backwards as and when fit with our schedule - to give them plenty of practise and repetition in a variety of ways.

These were mainly to do with the 2x and 5x tables since, after a quick verbal quiz, they showed they understood the pattern for multiplying by 10, i.e. the number becomes 1 place value bigger - an easy trick being to put a 0 at the end (language is important here! I made sure not to say "add a zero", since mathematically adding 0 to a number means it stays the same! And I emphasised it's the place value which changes, which is an important building block for when they move onto decimal numbers in the future inshaAllah). They're able to recall/work out the 10x table up to 10 x 12, as well as calculate random whole numbers x 10, e.g. 24 x 10 = 240, 523 x 10 = 5230, etc. at a good speed, mashaAllah.

I printed out a multiplication square each for them each, up to 12 x 12, which I'm planning for them to keep until they memorise all their times tables... So a few years inshaAllah! I glued the square into a piece of coloured card, to help it last longer, and so there's also space to keep a log of which times tables are tested when. When they're able to quickly recall a multiplication fact, they can colour the corresponding square in - so the goal is to have the whole sheet coloured in. By quickly, the aim is for them to have memorised the fact rather than count it out each time, so I guess under 3 seconds? Instantly, ideally! But they're still young so inshaAllah with more repetition over the years, the speed of recall will only increase. (The girls asked me if I knew my times tables to which I said yes... When did I start learning them? Probably at around their age and I remember having a sheet like them at school to colour in too! So how long did it take for me to finish colouring them all in? I suppose around Year 3 or 4? So around 7 or 8? To which they both laughed because why did it take me 3 years just to learn this tiny square of numbers? F then said she'd definitely finish it all before she was 7. Lol. 😂)

You can download the multiplication square we used here, though a quick Google search will probably turn up many others!

As a craft activity to visually represent the multiplication families, we used pony beads to make "bracelets" for the 2x, 3x, 4x and 5x tables. So for the 2x table, they needed to use 2 beads of the same colour together, then 2 beads of a different colour, then 2 beads of a different colour, etc. etc. until they had a chain of 12 sets of 2 beads together. Then I helped them tie the elastic off into a bracelet. For the 3x table they used 3 beads of the same colour together, for the 4x table 4 beads and for the 5x table 5. So they could see visually the difference in size between 12 x 2, 3, 4 and 5 and I showed them how they could use the relevant beads as a kind of number line to help them count the answer to e.g. 3 x 6 or 7 x 5 etc. The activity itself was good fine motor practise as well as a lesson in concentration! M made the 2x, 3x and 4x bracelets in the same amount of time as F took to do the 5x as she kept getting distracted. 😅

We also played some card games to help practise faster recall, similar to the card games we made up for learning the number bonds to 10: Snap, where instead of saying "Snap!" for a matching suit they needed to say the answer to the multiplication fact for the card on top (e.g. if we were practicing the 2x table and the 10 of clubs was played followed by the 4 of clubs, the first person to shout the answer to 2 x 4 and touch the cards would win them), and also just a speed competition whereby I would shuffle the cards then hold up the one on top - the first person to say the answer (for whichever times table we were practising, e.g. if we were doing the 5x table and I held up the 6 of diamonds, the first one to shout "30!") would win the card, the winner being the person with the most cards at the end.

I made a quick worksheet of word problems, based on the 2x, 5x and 10x tables, set in Chuggington - as this is the current favourite TV show for the girls! Using their interests is an easy way to get them excited and keep their focus for a task. 😂

You can download the worksheet here.

Finally, I linked it all to division as the inverse of multiplication, ie 2 x 3 = 6 so 6 ÷2 = 3... demonstrated with physical objects first before using drawings and lastly just number sentences. With this knowledge they were then able to quickly answer missing number problems for multiplication (eg 5 x ? = 35) as well as division problems (18 ÷ 2 = ? 60 ÷ ? = 6) while practising their 2x, 5x and 10x tables at the same time.