How to explain that 'equals' means 'the same on both sides' to 7yo DD?

[Satina]

Y2 DD is reasonably good at maths, but for a long time got the same style of question wrong:

Unknown + number = another number.

She could easily solve it with simple numbers that she knows so, when presented with

12 + ? = 26, she automatically knew the answer was 14, but couldn't explain why.

With bigger numbers such as 58 + ? = 117, she would just get confused.

She's now discovered with such questions she should just take the smaller number from the bigger number and then gets the answer correct, but again can't explain 'why'.

I've tried telling her that an equals sign means 'the same on both sides'. I've drawn scales with 3 apples, plus an unknown weight on one side and then 30 apples on the other side of the scale and asked how she'd find how many 'apples' the unknown weight equates to. She easily new to take three apples off each side. She can't however apply this to sums.

Any tips? YouTube videos? Ways of explaining 'You take the same number off both sides of the equation to keep the equation balanced' then you get the answer.

I'm keen for her to actually understand what she's doing, rather than just remembering tricks.

Thanks.

Stop using the word equals for a while.
So three 'is the same' or whatever she understands as 3
3=3
3+1 is the same as 4
Try using counters and an old fashioned scale with an = stuck in the middle.
Be practical and use maths language then colour in, then use numbers

Build with Lego bricks? Money with notes and coins to show equivalence (e.g. £10 note = 10 £1 coins, could then place another = and build it in 50p pieces)? I always built numbers with my class when they struggled with a concept. To make it quicker you could always cut up paper and build with that or (if child is ready) use different colours for different values (e.g. red could be units, white could be tens). Egg boxes could also work (e.g. 2 half dozen boxes = 1 dozen box).

Sounds to me like she's nearly there if she understands she needs to take the number on one side away from the number on the other side to get the answer.

In the example you've given, can you explain to her that what she's doing is calculating 58 less on both sides. So without the 58 on the left, you'd also need to take 58 from the other side?

Or explain it as "sign swapping", so if it's +58 on one side of the equal sign, it becomes -58 if you want to take it to the other side. Appreciate that might be more what you refer to as a trick rather than proper understanding.

swap equals for "Is the same as" or "is"

3+2 is the same as 5, etc.

"Equals is just another word for "is" - get her using "is" until she's confident, then reintroduce "equals".

My kids' school has got ride of the word "units" - they now talk about 100s, 10s and 1s instead of H,T,U. It's much easier to explain new ideas using words they already know.

If she understands numberlines, you could do 3 + 2 is 5. Then hide the 3 on the same numberline and figure it out x+2=5 by counting backwards by 2 from 5. And you can extend that approach by "a few" each time (5+4, 7+6, 13+5, 19+12, etc), until she understands what she is drawing.

Anything where she can see and do it herself will probably work better than explaining. In an average class of 30, I think only about 2/3 get 'explaining' - the rest need training (understanding it at each stage - so in my example you definitely would show the subtracting 2 and point out it;s subtracting) and then they fill in the abstract rule for themselves with time. And you have to give them the right examples to allow them to fill it in.

We are at a slightly lower level but we use "add" and "take away" instead of saying "plus" and "minus" because DS gets those terms but not the other ones.

He actually understands the word "equal" in other contexts (e.g. these two shapes look the same so they are equal).

I am a ta and have worked in year 2. Number bonds to 10 are good for demonstrating this. I use Lego bricks in different colours or if you can get multi link cubes from school in different colours use those.

So say 6+4=10 build a tower with 6 red bricks and another with 4 green ones. Start by showing that if you combine the towers they make 10 altogether. You can turn them the other way so 4+6 also = 10. Then ask what happens if you start with 10 and take 4 green ones away you are left with 6 red and if you take 6 red ones away you are left with 4 green. You can do this with all the numbers that make 10 to show it works for them all. You will be teaching your DD that addition can be done in any order and that subtraction or taking away is the inverse or opposite of addition. I always told children that the numbers stick together like glue. Once she understands the relationship between the numbers you can show her that it works for other calculations as well. So do addition and subtractions within 20. Build it up slowly and she will get there. You can then move onto bigger numbers.