Adding two 2-digit numbers

The prerequisites for this activity were to be able to add together multiples of 10 in their head and know how to count on using a 100 square.

I decided to focus on mental methods for adding 2-digit numbers as I feel it's important they understand the basics before moving on to the quicker (and arguably easier) standard written methods.

The method I taught them to use is pictured above, which I went through on the whiteboard using coloured pens for simplicity. First, I wrote out an example question with the Tens in red, the Units in purple and the equation signs (and subsequent answer) in blue: 14 + 48 =

I told them the first step was to look at the Tens. What are the Tens? 10 and 40. So what is 10 + 40? 50. I wrote this sum underneath in red, to keep the colour co-ordination.

Next, look at the Units. What are they? 4 and 8. Which Unit is bigger? The 8.

So keep the Tens total (50) and add on the bigger Unit (8) to get 58. I wrote this underneath, colour co-ordinated.

How many Units are left to add on? 4. So I wrote 58 + 4 =

They could then use their 100 squares to find 58 and count up 4 more squares to calculate the total. 62. So I wrote 62 as the answer to both 58 + 4 and the overall question of 14 + 48.

Reading through, this looks like it took a long time to explain! But it really didn't, and with a few more examples and me reminding them of the steps the girls soon got the hang of this method. This is my personal method of choice for mental addition, which is the reason I taught it to them. As they get older and their mathematical understanding strengthens, insha'Allah, then I'll introduce the alternative methods for them to choose from. 😊

After two examples using numbers of my choice (one where the Units total to within 10, another where they didn't), I asked the twins to choose numbers at random for me to use in the questions - otherwise I wouldn't have used 49 + 94 as an example since it goes into the Hundreds! But Alhamdulillah, this was the last example we did together and they understood it fine. 👍

The next day - while leaving the examples on the whiteboard for reference - I gave them the pictured double-sided worksheet to do (taken from Schofield&Sims - KS1 Problem Solving 2). We did the first side (5 questions) together, with me scaffolding their thinking by reminding them of the steps to the method, and I helped with the first couple on the next page too. Then I let them try the last few by themselves and they were both able to do the final two questions completely independently, MashaAllah. 💕

Greater than & Less than (> & <)

I began by leaving the above picture and sentence on the whiteboard for the first half of the day... The girls were intrigued: Why did I write it? What's it for? Why does the crocodile always want more?? I just told them it always did... SNAP! 🐊

When we were ready for our "lesson" later in the day, I asked them how many monkeys were on the left? 3, so I wrote it underneath. How many monkeys were on the right? 1, so I wrote that underneath too. Which side did the crocodile want to eat? The one with more, so 3 - and I drew the > symbol in between in the same colour as the crocodile. Then I read the number sentence out loud to them: 3 is greater than 1. This > symbol means greater than. So what if there was 1 monkey on the left and 3 monkeys on the right? I wrote the numbers underneath with a blank space in between. Which side will the crocodile face now? MashaAllah the girls understood and told me he would face the other way, so I filled in the blank and read this number sentence out too: 1 is less than 3. The < symbol means less than.

The crocodile always wants more! His open mouth will always go towards the bigger number. SNAP! 🐊

Leaving that on the board, we then got the toy animals out and I gave the girls a < card each (they could flip it over to make it >!). I laid out two groups of animals and the girls needed to decide which card to put in the middle. After each question, we "read the sentence" out loud, i.e. "5 is greater than 2". After a few of these, with the toy crocodile then without, I repeated the activity using the number pieces from their Melissa & Doug jigsaw (only because I didn't feel like writing out numbers if we already had some!).

I took the opportunity to practise their mental maths too by getting them to compare the total on each side rather than just a number. 👌

Finally, they were able to complete the top half of the worksheet they did the other day on adding/subtracting 1s and 10s to 2 digit numbers (Collins Easy Learning - Mental Maths (Ages 5-7)).

More work with 10s

Just another self-reference post to show progress...

We did some more work on 2-digit numbers and adding/subtracting 10s. One of the girls found this a little more difficult than the other (the other was fine with an explanation then onto the worksheet) - I needed to model it for her a little more both with the multilink cubes, the abacus and writing colour coded examples on the whiteboard - so she could see visually that when adding/subtracting by 10 only the Tens are affected and the Units don't change at all. (Letts Make It Easy... Maths & English (Age 5-6) & Collins Easy Learning - Mental Maths (Ages 5-7))

We also did some work on the 10x table, by which I gave them the worksheets (Schofield&Sims - KS1 Problem Solving 2 & Letts Make It Easy... Maths & English (Age 5-6)) and the multilink cubes sorted into sticks of 10, read through the first question together as an example then left them to it... MashaAllah they were finished both sides within 10 minutes and without using the cubes at all! One of them laughed at me that I thought it would take them longer and they both laughed at me for taking the cubes out. 🙈 I tested them orally to check understanding and yes, they had either memorised or could quickly calculate their 10x table up to 10 x 10. 👌 Out of curiosity, I asked them what was 11 x 10? They weren't sure until I wrote it down for them to see, at which one of them got it straightaway. So I continued, then what was 20 x 10? That same twin understood it was 200 and 30 x 10 was 300 and so on; the other didn't get it - but that was just extra for my own curiosity. Not really something expected of them at this age! MashaAllah, I'm still super proud of them both. 💕

Number Bonds to 20

Building upon our work on learning the number bonds to 10 (posted about here and here) and their understanding of partitioning, we then expanded this knowledge to calculate and so memorise the number bonds to 20 - with the overall aim of improving their mental maths skills.

I began by giving them a quick oral quiz on which numbers "matched" with each other to give a total of 10, i.e. "What do you add to 2 to make 10?" We then revised what they knew about partitioning numbers into tens and units by going through a couple of examples together on the whiteboard - stopping on the number 20.

I then explained to them how they could use the number bonds to 10 to calculate what number they needed to make a total of 20, because 20 is simply 10 more than 10! I gave them a couple of examples on the whiteboard (e.g. see picture above) then quizzed them to check their understanding.

Finally, I gave them some pages photocopied from Letts Make It Easy... Maths & English (Age 5-6) and Letts Monster Maths - Maths (Age 5-6) to recap and reinforce.

The bottom of the first page (left) was a good opportunity to teach them the importance of showing their working out, in terms of keeping track of what they're doing and working things out step by step, in order to pick up on where they might have made a mistake.

Place Value and Partitioning

We recently bought this wooden abacus as both a learning tool for the twins and a toy for the 2 year old. Since the older two can count confidently back and forth to 100, I thought now was a good time to introduce larger numbers and place value to them.

I explained to them how to use an abacus to represent larger numbers, writing a colour-coded list on the whiteboard to clarify and make clear the pattern:

1s = units
10s = tens
100s = hundreds
1,000s = thousands
10,000s = ten thousands
100,000s = hundred thousands
1,000,000s = millions
10,000,000s = ten millions
100,000,000s = hundred millions
1,000,000,000s = billions

 I stopped there since our abacus has 10 rows, but I was pleased when they asked if ten billions came next, then hundred billions and what was after that? MashaAllah they're both very logical in their thinking (to make up for their lack of artistic flair lol).

Over the next few days we played with the abacus, taking turns to make numbers for each other to read - first only using the top 2 rows, then the first 3 and finally the first 4) - or saying a number and getting the other to make it on the abacus.

Once they were confident with this, I modelled on the whiteboard how to partition two digit numbers into tens and units, i.e.

          Tens       Units
12  =    10     +     2
          (1 ten  + 2 units)
58 =     50     +     8
          (5 tens + 8 units)
93 =     90     +     3
          (9 tens + 3 units)

etc. then carried on the list, leaving the Tens and Units columns blank for the girls to try and fill in together. I made sure to get them to further split the Tens into e.g. 5 tens = 50 which helped practise their 10x table too.

We repeated this over a couple of days, with different numbers on the whiteboard each morning for them to fill in independently, going up to 3 digit numbers on the last day for an extra challenge. 💪

To summarise and check their understanding, I then photocopied the relevant pages from Letts Monster Maths - Maths (Age 5-6), Collins Easy Learning - Mental Maths (Ages 5-7) and CGP Key Stage One Maths - The Question Book onto a double-sided page, for them to work through together and then file away in their folders - pictured at the start of this entry.

Since then, they've continued to play with the abacus both alone and with each other, repeating our games from earlier. 😁😁