Material developed by Paul Dickinson, Steve Gough & Sue Hough at MMU Easy To See Material developed by Paul Dickinson, Steve Gough & Sue Hough at MMU

Thank you Sue, Steve and Paul would like to thank all the teachers and students who have been involved in the trials of these materials Some of the materials are closely linked to the ‘Making Sense of Maths’ series of books and are reproduced by the kind permission of Hodder Education

Note to teacher This section is designed to encourage students to notice that some equations are easy to solve and do not require any complex manipulation to reach a solution. If students can read and make sense of an equation they may have a chance of seeing the solution immediately. A common teacher strategy is to cover up the unknown part of the equation and ask what number must be underneath.

Easy to see Sometimes, when you look at an equation carefully you can see the solution straight away. For example, if x + 5 = 19, then it must mean that x is equal to 14 (because 14 + 5 = 19). When we can see the solution quickly like this we say the solution is EASY TO SEE. This section reminds students that some equations are very easy to solve if they are able to read the equation with a little understanding. Students are encouraged to consider first whether a solution is “easy to see”. In the first example, cover up with your hand/finger the x in the x+5=15 and ask “what must be under my hand to make this maths statement true?”. The problem becomes, “what added to 4 makes 15?”. The second problem becomes, “what do we take 7 from to leave 9?”. For many students this is a lot simpler than adding 7 onto each side because there is -7 to get rid of etc., and they are also a lot less likely to make an error. If x+4=15, what is x? If x-7=9, what is x?

Easy to see The solutions to the equations on the left are all easy to see. For each question, write down the value of x. These questions can be completed very quickly, perhaps using mini whiteboards. Question 5 may require some discussion due to the conceptual difficulties in understanding around subtracting but making larger. (Answers: Q1. x=20, Q2. x=9, Q3. x=7, Q4. x=3, Q5. x=-2, Q6. x=6, Q7. x=-1, Q8. x=-7)

Easy to see When you start to use this method, more equations become easy to see. For example, if 18-2x=4, 2x=14 so x=…. Explain the example above These more complicated equations can still be easy to see. In the example, if you put your hand/finger over 2x and ask “what must be under my hand to make this maths statement true?”. The problem becomes, “what must be subtracted from 18 to get 4?”. When students answer 14, you take your hand away to reveal 2x therefore 2x=14, x=7. It is particularly useful for fractions. For example, in question 7 you put your hand over x/2 and recognise that the value under you hand is 9. the problem then becomes, “what number divided by 2 leaves us with 9?” (Answers: Q1. x=9, Q2. x=7, Q3. x=4, Q4. x=5, Q5. x=35, Q6. x=-2, Q7. x=18, Q8. x=15) Use the easy to see method to solve the equations on the right

Easy to see These equations are slightly more difficult. However, they are still quite simple if you use easy to see Again, fraction equations like question 1 often prove challenging to middle ability students. However, if they cover up x and ask “what number do I divide 8 by to leave 2?”, it becomes a much easier question. Question 4 would start with the student seeing that the contents of the bracket must be 10, so x squared would be 9 etc. (Answers: Q1. x=4, Q2. x=3, Q3. x=2, Q4. x=3, Q5. x=3, Q6. x=2)

Easy to see (Summary) When you look closely, some equations are simple to solve…the solution is “easy to see”. Putting your finger over the x can often help you find the answer 12-x=7. In this case, covering up x, the equation is 12 take away something equals 7 32/x = 8. This reads: 32 divided by what number gives 8?