Percentage change and best buys
This lesson took place on Wednesday 23rd March 2022 at Grantham College.
I observed three girls, G1, G2 and G3.
9:04
The lesson starts.
G1 has not yet arrived. She has let the teacher know that she will be late.
The teacher asks the students to write down what they know about percentages.
This is what G2 has written.
9:08
The teacher introduces Explore 1, asking the students to use any method they like to work out the length of the brown tape.
9:10
G3 uses a calculator to find 50/100.
9:12
G2 has found half of 120 and added it to 120.
9:14:28
G3 appears confused.
She seems to know her approach is incorrect and asks G2 for help.
G2 explains what she did and G3 writes this down.
9:17:23
The TA has visited G2 and said she could also have multiplied by 1.5 because ‘it is one and a half’.
She does this.
He then suggests she could try dividing 120 by 100, asking her what percentage that gives. She appears not to understand but eventually says ‘one’.
He asks her to multiply this by 150 because she is looking for 150%.
G1 arrives.
9:22:43
The teacher puts up the slide showing the three approaches on the handout.
9:25:55
G2 explains to G1 what they have been doing.
G1 also halves 120 and then adds.
G2 has matched the diagrams to the approaches.
9:27:04 – 9:32:39
The teacher has put up the slide with Nel’s approach.
He asks the students to consider what Nel has done, and circulates and discusses with the small groups.
He holds a class discussion.
G2 writes 15 x 10 = 150.
9:32:39 – 9:39:20
The teacher has put up the slide with Reuben’s approach.
He asks the students to consider what Reuben has done, and circulates as they do so, asking questions and checking understanding.
He holds a class discussion.
G2 writes 120 by 1.5 which gives you 180.
9:39:20 – 9:42:33
The teacher has put up the slide with Saskia’s approach.
He holds a class discussion.
He asks what Saskia would have been looking for if she divided by 4, emphasising that the students need to understand why Saskia divided by 2.
9:42:33 – 9:44:36
The teacher holds a class discussion about the diagrams and the meaning of a 50% increase, saying that they have already covered most of this in their discussions.
9:44:36
The teacher asks the students to work in pairs to work out which is the better offer: Offer 1 and Offer 2.
He asks them to use diagrams.
9:46:45
G1 appears to know that 20% of 180 is 36 and uses a calculator to add 36 to 180.
The teacher arrives and she explains to him what she has done.
He asks her to explain to G2 and to ‘try to represent it as a picture’.
9:48:18
The TA has arrived.
G2 has written down the question but she has not started an answer.
9:51:46
The TA asks how G2 would find 20%.
She suggests halving it, and he says that she needs to find 20%.
She suggests: ‘do 10% and do 10%’
He encourages her to write this down.
9:51:58
G3 has written 180 = 20 x 9 and 180 ÷ 9 = 20.
9:52:52
G1 has worked out both offers.
(Offer 3 is the same as Offer 1).
9:54 – 9:56
G3 has drawn a diagram.
The teacher has arrived and explains Reuben’s approach, suggesting that G3 could also use a multiplier.
9:54 – 9:56
He talks her through finding 20% as a decimal and then adding it to 1, to get 1.2.
He shows her how Reuben multiplied the original by 1.5 and asks her what she thinks she should do now.
She asks if she should multiply 180 by 1.2
9:57 – 10:01
The teacher has asked the students to draw a diagram.
The TA helps G1 with a diagram.
He points out that there are five lots of 20% in 100%, so the number line should have five divisions and one more for the extra 20%.
10:02 – 10:05
G2 has drawn the same diagram for Offer 1 as G1.
She has also drawn an incorrect diagram for Offer 2.
10:03
G3 has worked out Offer 2 by finding 1% and multiplying to find 20% and then subtracting.
10:08 – 10:11
The teacher holds a class discussion, going over the 20% offers.
10:11:13
The teacher asks the students to work out the price per metre.
10:12:48
G1 and G2 appear to be stuck.
The teacher visits.
10:14:02
G3 has written 10% =
10:16:33
G2 has used a calculator to divide 120 by 100.
10:16:53 – 10:19:26
The teacher has drawn a diagram.
He asks the students ‘what sum can you do with 240 and 120’.
He talks the class though how to find the price per metre, pointing out how the units indicate what the divisor should be.
10:22
The teacher has handed out the sheet with Nel’s and Reuben’s suggestions, and some A3 paper.
G1 tears the sheet.
10:23:34
G2 appears to be stuck.
She looks at the approaches sheet.
10:25:54
The teacher arrives and asks the students which one they are working on.
They tell him Offer C.
He asks which approach they will use and they point to Reuben’s approach (using a multiplier).
He asks what the multiplier will be, and they say they don’t know.
He asks what the multiplier was when the increase was 50%, and they say 1.5.
He asks again what the multiplier will be if the increase is 60% and they say 1.6.
He asks what the original amount is, and what they need to multiply it by, and as they respond and write it down he finishes by saying ‘and that gives you the answer’.
10:31:36
G1 has worked out that a 60% increase in length gives 192 (metres).
10:32:41
G2 asks G3 if you need to divide to find the price per metre.
G3 tells her to divide 240 by 120 (the divisor should be 192).
G2 writes this down and uses a calculator to do the division (even though the teacher’s division is still on the board.)
10:33:50
G3 has worked out both of Reuben’s suggestions (Offer C and Offer D).
For Offer C, she has used a multiplier. She has also found the price per metre using the original length of 120m.
For Offer D she has found 1%, and then 35% and subtracted. She has not found the price per metre.
10:34:01 – 10:35:07
G1 has asked the teacher for help to find the price per metre.
The teacher says they should use the same approach as on the board.
He suggests that they convert the £2.40 into pence and types 240 in the calculator. He asks them what the new length is and they say 192. He says that gives 1.25p. He says ‘that is 1.25 pence per metre’.
10:38:36
G1 has packed up.
She has not written anything on the sheet.
10:40:52 – 10:45:27
The teacher holds a class discussion.
He goes through the answers for Offers A, B, C and D.
10:45:29
The teacher hands out the sheet with the exam questions.
He asks them to work individually.
10:51
G1 writes Jan’s store.
The teacher asks her to show her working.
G1 and G2 discuss what to do (in whispers).
They write the same answers. They appear to be confused between pounds and pence.
10:51
G3 has worked out the new price correctly.
10:55
G2 has written some correct calculations for Jan’s store.
She has not found the unit costs, but the answer Jan’s store is correct.
10:56 – 11:00
The teacher discusses the answers.
G1 and G2 make no changes to their answers.
The teacher finishes the lesson by reviewing the objectives and asking the students how they feel about percentages.