1. Functional Skills Maths Using reverse calculations and rearranging formulae
September Kindly contributed by Mrs Rajal Naik, the Manchester College.
Search for Rajal on
Please refer to the download page for this resource on skillsworkshop.org for detailed curriculum links and related resources. The formula cards mentioned in this PPT are available separately.
Functional Maths - Coverage & range statements
L1 Use simple formulae expressed in words for one- or two-step operations
L2 Understand and use simple formulae and equations involving one- or two-step operations
Functional Maths - Process skills
L1[2] Use appropriate checking procedures [and evaluate their effectiveness ]at each stage
Adult Numeracy
N1/L2.4 Evaluate expressions and make substitutions in given formulae in words and symbols to produce results
N1/L2.2 Carry out calculations with numbers of any size using efficient written and mental methods (c) Know and use strategies to check answers
References: Excellence Gateway (2009), Skills for Life, Core Curriculum
Ofqual (2009), Functional Skills criteria for English, Mathematics and ICT
Sep Kindly contributed to by Mrs Rajal Naik, The Manchester College

2. Rearranging Formulas and the use of Reverse Calculations
by Mrs Rajal Naik

3. Introduction In functional skills exams you may be asked to
check your own answers using reverse calculations
make any part of the formula the subject
The following presentation will demonstrate both of these topics.
At level 1 and level 2 it is essential that students understand the term reverse calculation and the use of it in finding out if they have calculated their sum correctly, without asking their teachers to check it for them. At the end of the year when they are asked to check their answers, students will be expected to use this method at level 1 and level 2. So this presentation will give them a quick introduction to it.

4. Terminology What is the subject of the formula?
This is the main term you are trying to find the value for. E.g. in area = length x width, area is the subject.
The subject is the last and final part of the formula left on one side of the equal side, with all other terms on the other side.

5. Finding a Part of the Formula
When we want to find a part of the formula e.g. in A=L x W, we need to rearrange it, to find the length i.e. make the length the subject of the formula , we do this in the following way.
AREA =
LENGTH
WIDTH X
You want the length to be the only term on the other side of the equal sign, and the area and the width on the same. Since the width is multiplying, it changes to division when it goes over to the other side.
Now use the cards to work out the Area or perimeter of the rectangles or squares.

6. What is reverse calculation
Reverse calculations are used to check your own answer, by reversing each step in the calculation.
When you move a positive value to the other side of the equals sign, the value becomes negative and vice versa.
When you move a multiplication to the other side of it, the value becomes a division and vice versa.
Explain the use of reverse calculations as a self check tool. Explain the importance of conserving the values on either side of the calculations, and that positive is opposite of negative and negative is opposite of positive.
Multiplication is opposite of division and vice versa.

7. Rules when rearranging the formula ( reverse calculation - easy method)
The following examples demonstrate this. Remember both side of the equation must balance at the end, If your answer is correct. 48 6 × = 8
Remind them that, 6 x 8 =48 and that 48/8 =6 and 48/6 =8. Explain of the steps equate, so the sum is correctly worked out. 26 35 - 9 = = +

8. Rules related to rearranging the formula (the harder but correct method)
When we rearrange a formula, we can work out what the reversed value of each bit of the sum will be, by either adding, taking away, dividing or multiplying both sides of the formula to preserve the equation. The following formula for circumference demonstrates this, when making the d, the diameter the subject. C = π d
Since we need to get rid of pi, and it moves to become a divisional value, on being reversed. This determines what we do with the rest of the sum, which is divide each side by pi, thus cancelling it out on one side only to leave the diameter as the subject of the formula.
÷ both sides by π C ÷ π π C = d
Cancel each other out So π

9. Use the cards to help you rearrange the formula.
Now try these
Reverse the following equations to make 5 the subject in both of the following equations.
1) a) 7 x 5 = 35, so 5 =?
b) 30 ÷ 5 = 6, so 5=?
2) Area = length x width. If area to be plastered is 38m2 and length of plasterboard is 9.5 m what is the width of the plasterboard? Rearrange the formula to find the width.
Use the cards to help you rearrange the formula.
Get them to work out the values in pairs using the formula cards, to firstly rearrange the calculation correctly and then to find the value by inserting in the correct numeric values in each place.