Category Archives: Algebra

63. How to make GCSE past papers fun

Well folks, the end is in sight! Soon Y11 will be on study leave. Sure, there will be those conscientious few who come in for help or revision sessions, but the majority of pupils need the next month to considate their learning and be ready for their exams.

Are these teenagers buzzing with energy and keen to work? No.

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They are tired of being told about exam technique and interpreting questions. They are fed up with assessments and coursework. They are irritable with every non-teenager who mentions exams and ‘this is your future’. And most of all they are just tired because they are working late on deadlines that are suddenly tomorrow, rather than 6 months away.

How can you make yet another GCSE paper interesting?

It’s time to cut up the exam paper (see Foundation GCSE analysis for first scissor session).

Now this task will need some prep work. It is an adaptation of a Maths Relay.

Equipment
*Enough copies of a GCSE paper for 1 between 2 or 3.
(Variation: A set of themed questions, for example 15 questions on Algebra of graduated difficulty)
*Roughly three copies of the mark scheme.
*Your best 3 or 4 students to help manage the task. Alternatively,  mathematically minded sixth former or spare teacher would do. You could even put two classes together.

Optional: A spreadsheet with the pairs of students in the first column

Prep Work
You need to slice the papers into individual questions. Lay out the piles in number order across a desk.
The desks in the room need to be arranged to allow pair/group work and also movement around the room.
Your helpers need to be briefed about the activity.

Activity
Each pair is given the first question face down. When you say ‘Start’, they may write down their names on the question and answer the question.
When they have an answer, they must bring it to be checked.

Correct: it is ticked and they are issued with the next question.
Wrong: it is crossed and they try again.
Wrong twice: they are issued with the next question.

By using your most able student as checkers, you are enabling them to practise effectively checking work quickly and give hints. If they can check their own work in exams quickly, then they will have more time to answer harder questions. By giving hints they are consolidating their learning. Of course, the rest of the class can’t complain that the brightest will win as they are not taking part.

Differentiation
If you have a mixed tier/ability class you can colour code two exam papers: yellow for foundation, pink for higher. They can still race each other but at a more appropriate level.

About that optional spreadsheet
Set up a spreadsheet with the first column for names, the next 15 columns labelled 1-15 and the last column for the total.
Once a question is finished with you record correct/wrong with a 1/0 . You can then keep track of who is on which question with what success rate.

The more ICT-friendly teacher could use conditional formatting to highlight the cells and which team is winning.

Management
I have found it easiest to use helpers for checking and leave the spreadsheet recording to the class teacher. This allows the teacher to oversee and troubleshoot as required.

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Review
I’ve done this with low-ability Y11 last lesson on a Friday and was stunned at the engagement. Although that might have had something to do with the prize of first choice from a box of fondant fancies …

61. St George’s Day Investigation

Here is a quick St George’s day area investigation for the 23rd April.

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What size cross must be drawn for the areas of red and white to be equal?

Assume the flag is a rectangle and the strips of the cross are the same width.

KS2/3: investigate by counting squares or working out areas.

KS3/4: extend to an algebraic solution if appropriate

If you like this post why not follow Maths Sandpit on twitter: @Ms_KMP

47. Light bulb moment

Here is a ridiculously simple classroom tip that was thought up by one of my pupils today.

 

Situation

The class were using past GCSE questions, compiled in a Word document, photocopied back to back and stapled.

 

Problem

After completing a table of values, the question said ‘Use the graph paper below…’, except the graph paper had ended up three sides of A4 away due to a crazy quirk of Testbase (GCSE exam question software) and Word. Cue much mumbling and enough paper shuffling to make me think a hamster was rearranging his bedding!

 

Solution

One pupil simply asked if she could take a picture of the table of values, so she wouldn’t have to keep flipping pages.

 

So simple … pure genius!

 

Within 5 minutes, the class were quietly doing very accurate cumulative frequency diagrams, without silly mistakes and rustling.

16. Library Fines (Sequences)

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County Library
The first day a book is overdue, you are charged 4p. Each day incurs another 4p.
What are the charges for the first week?
(4, 8, 12, 16, 20, 24, 28)
What is the Nth term?
(4N)
How much would you be charged for being 25 days late?
(100p)

Village library
The village library charges 10p for the first day and 3p for every subsequent day.
What are the charges for the first week?
(10, 13, 16, 19, 22, 25, 28)
What is the Nth term?
(3N+7)
What is the charge for 30 days?
(97p)
How many days late is one book if the fine is more than £2?
(Solve 3N+7>200)

Look back at both libraries. Under what conditions do the libraries have the cheapest fines?
(1-6 days: County Library
7 days: same
8+: Village library)

Extension
Why do the libraries have the same charge on the 7th day?
Prove it algebraically.
(Solve 3N+7=4N)

You can also extend this investigation to looking at calendar dates, with one library open 5 days a week and the other being open 6 days with fines only applying when libraries are open. How would this affect the ‘cheapness’ of fines when days are included?

Adaptations
This method can be used for car hire, mobile phone comparisons, energy bills because sequences link so well with graphs of real life problems.

15. Algebra bingo

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When you are teaching simplifying, most published worksheets and textbooks contain pages of themed or mixed questions. It’s not exactly thrilling stuff.

How about a bit of friendly competition?

Equipment
You just need a set of simplifying questions with answers. Any textbook with the answers in the back would do or project the answers on the board.

Set Up
Ask each student to pick eight answers from a specified set.

Play
The teacher reads out a question. The students simplify it and circle if they have it. First player to get all eight wins.

You could repeat this, increasing the difficulty or change to a different theme eg substitution.

The nice thing about this activity is you are in control of the level of difficulty and you can adapt it as you go on. The game element is engaging and the sneaky thing is that everyone has to do every question to have a chance to win.