Balancing equations

This was a mental starter recommended by our previous maths consultant. Begin with a simple equation such as 5 =5 and ask for their initial thoughts. Is it wrong or just unusual?

The children were initially puzzled but then decided that it was not wrong, just different to what they expected. I then asked them to change one side so that the sentence stayed correct. They suggested 4 +1 so I changed the right hand side which surprised them as they had expected me to change the left to make a normal calculation.

                                                 5 = 4 +1

I then asked for suggestions for the left hand side. Initially they suggested other single numbers so the equation could not be correct. Then one child asked if it had to be a single number. Once they realised that they could substitute another calculation they began to see what I was after.

I asked what the = symbol stands for and received the quick reply that it tells you where the answer is. Anothe child then pointed out that it really stands for ‘the same as’. There were several intakes of breath and whispers of ‘I get it now’.

We quickly moved through a range of calculations to make 5, changing one side at a time. They moved into decimals as they ran out of simple addition sums they could make. I asked if they thought there would be more possible addition calculations or subtractions. They worked out that there were only a few whole number addition calculations possible but an infinite number of subtraction ones. There were so few addition sums because 5 was such a low number.

Then a child asked if they  could use negative numbers and the ball started rolling again as they found a variety of calculations that would satisfy the statement.

In 10 minutes we had done mathematical reasoning, decimals and negative numbers. I felt it was a really successful mental and oral starter. We could have extended it further by moving into algebra eg 5 = (n + 5) – n.

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2 thoughts on “Balancing equations

  1. I really like this. It is an activity that promotes thinking rather than regurgitating, and as you pointed out, it can go anywhere you take it.

    Also very interesting to read that your class (like millions of others) think that “=” means “write the answer here”.
    I enjoyed this – thanks!
    AJ x

    1. Thanks for comment AJ. It is nice to know that I’m not just talking to myself. Although it would probably still be a useful exercise in clarifying my ideas.

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