Simultaneous Equations Questions

[stroudydad]

The KS2 algebra content is as follows:

Year 6
Pupils should be taught to:
● use simple formulae
● generate and describe linear number sequences
● express missing number problems algebraically
● find pairs of numbers that satisfy an equation with two unknowns
● enumerate possibilities of combinations of two variables.

There is no ‘formal’ solution of equations - the non-statutory guidance says:
● Pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:
● missing numbers, lengths, coordinates and angles
● formulae in mathematics and science
● equivalent expressions (for example, a + b = b + a)
● generalisations of number patterns
● number puzzles (for example, what two numbers can add up to).

So that would be 'equivalent expressions' which is fine.

Or is it??!!

[Guest55]

It's really pre-algebra in my opinion. Certainly no setting up and solving equations which is what was suggested for this question.

When the 11+ is set only Year 5 content should be tested ie no algebra at all.

[stroudydad]

It's really pre-algebra in my opinion. Certainly no setting up and solving equations which is what was suggested for this question.

When the 11+ is set only Year 5 content should be tested ie no algebra at all.

So does no algebra mean no pre-algebra too??

[stroudydad]

So,
A rectangular garden has width Xm. It's length is 5m more than its width and area is 126m2.

Which eaquation is correct.
x(x+5)=126
x+x+5=126
2(2x+5)=126
(x-5)x=126
x+5=126

Is that not algebra?

[Bluearrow]

It's really pre-algebra in my opinion. Certainly no setting up and solving equations which is what was suggested for this question.

When the 11+ is set only Year 5 content should be tested ie no algebra at all.

So does no algebra mean no pre-algebra too??

I think the school teaches the concept of algebra, but very little on using algebral method to solve word problems. As for 11+ test, some questions will be easier to solve using algebral method, even though you can still solve the problem without using it.

The good thing about algebra is it simplifies a complicated word problem into an equation, which can be routinely solved with standard operations.

I do teach my DD algebra as I think she understands the concept. Therefore she will have more choices when solving word problems.

[loobylou]

When dd was doing the 11+ about 5 years ago, she asked for my help on a maths question. I started getting bogged down with algebra and trying to show her how to do it. It wasn't working (my teaching or her learning!) so I gave up and asked the tutor the following week - she told me that algebra was never required and showed us the trial and improvement method. It was a complete revelation - it had never occurred to me to do it that way. Dd did it that way from then on and did fine.
I am certain she never had a question quite like the one above with the garden area.

[Bluearrow]

I agree with you. When I helped my DS with his 11+, I did not teach him algebra because I knew it would confuse him. I tried to explain the question using the "normal" method, sometimes drawing graphs to help. He only started to learn algebra in Y7. It really depends on the child.

[stroudydad]

So,
A rectangular garden has width Xm. It's length is 5m more than its width and area is 126m2.

Which eaquation is correct.
x(x+5)=126
x+x+5=126
2(2x+5)=126
(x-5)x=126
x+5=126

Is that not algebra?

This question is taken from a cgp CEM practice book:-)

[RedDevil66]

Delighted to see that it has generated some debate.
Just to clarify I asked for materials for practice of this type of question. While I did use an algebraic method, I'm aware that not all children will be able to solve it using this method. I was looking for a quick and efficient way of tackling these type of questions.

Bar modelling also will achieve the same result as will other reasoning methods. However it may only be one question among 50 and as with all maths questions, working quickly and not deliberating too long on one question is key.

I appreciate all the responses. It has been fun looking at them

[Guest55]

CGP has obviously made an error stroudydad - that question is not appropriate.

The Primary NC changed about four years ago so some material published earlier than that may have errors. Remember question books may not be written by people who actually know much about Primary maths ...

Algebra can confuse a problem and is not easy to teach properly. Throwing 'x' at a problem usually does not help - many children end up afraid of algebra.