Mastery in Subtraction

After a week of looking at formal written methods of subtraction I wanted to see how deep their understanding really was. So using some of the questions from the Maths Hub I posted a few questions onto Seesaw and asked them to record their answers and explanations.


Here is an example from Andrey which shows his understanding of solving addition and subtraction two step problems in contexts, deciding which operations and methods to use and why.  



Baimonn explains how to work out the missing numbers in a subtraction sum. This shows a deep understanding of using the inverse relationship between addition and subtraction, and also the column method. 




CC explains how to work out a 2 step problem that involves adding and subtracting.




What was great about this activity was it also showed me which children still needed some work on their understanding of a subtraction written method.

Kamilla was so close here. You can hear her brain ticking as she thinks about the first units column, showing her understanding of using inverse and the concept of borrowing. 


Using a formal method in her book was not a problem, but being presented with the problem in a different context proved that we need to take another look at applying skills and understanding. 



Some confusion between the operations. This also shows me that there is not the depth of number sense that I thought there originally way. Taking another look at place value and using the manipulatives is a must when we review this.

Diving deeper into understanding of multiplication.

Thursday 6th October

Diving deeper into understanding of multiplication.

This has been a tricky week. Started off with looking at table facts, where the children were with them and which ones they still had to learn. Need to communicate this further with parents so they are aware of which tables their child need to learn. Will send home a booklet and some games.

I wanted to know what the children thought multiplication was. So I asked them to draw 5 x 2. The answers were interesting. This was the answer from most of them. I think only one child drew an array, and another 5 groups of 2.

So this gave me some idea of what we needed to do. Arrays were revisited - although when I said that word most of them looked at me blankly! I wanted them to first see an array as a multiplication sum and then to use that to understand the commutative property of multiplication. However, I think I moved too quickly and did not make sure of their complete understanding as the following day I went into associative property and ended up with 15 confused children and a frustrated teacher!

Time to rethink my planning...

Split into 2 groups, no whole class teaching this time around.
Commutative property with Ms Nocha - 2 dice, write the sum, draw the array. Change the order of the dice, write the sum, draw the array = what do you notice. They gave verbal feedback, noticing that it made no difference what order you put the numbers in, the product was the same.

















Associative Property with me - 3 dice, write the sum, group them (using brackets), draw the array, work out the answer. Group them in a different way, or change the order, write the sum, draw the array, work it out - what do you notice. They wrote a sentence to explain.
 = success.

Went back to asking them what they would draw for 5 x 2 = an array or 5 groups of 2 were the answers! Hurrah! What properties do you notice about multiplication - again the answers I was looking for.

The best bit was on the way to lunch we looked for arrays around the school. Hayley then made my day...

Using games to help with reasoning

Monday 26th September

Using games to help with reasoning

Great to see lots of reasoning today whilst children were 'playing' games that involved using mental subtraction strategies that had been explicitly taught last week.

For 'Strike It Out' it was interesting to see Kamilla using the strategy of thinking about the outcome of the difference between her two numbers before committing to her answer. 

Nour, who had been trying to use a written formal method for 'mental' subtraction last week could now see that counting up as an effective method last week, was able to use this when she was finding the greatest difference between 2 out of 3 of her playing cards. 

After about 5 minutes of staring at a number fact family, Kimberly was able to see that by changing numbers around you can create 4 different number statements using 3 numbers (add/subtract only). 

Playing games with maths has become a regular Monday morning session and the discussion of maths and the language that was being used - 'I have the biggest difference', 'oh, I can change the numbers around and make...' is proving to be a great insight into their understanding of numbers.