This post isn’t a resource, more of a source of ideas. We tell students that maths is about problem solving, but how many problems are fictitious?
Here is a problem, taken directly from ‘real life’ when a friend was making custard on sunday evening.
Do you think the instructions are wrong?
Does 2.75 litres of water seem right? Use the whole packet? How much is in the packet?
The custard powder had been bought from the wholesalers. It was such good value because it was a catering pack.
- If the pack weighs 605g, how much would you need for one portion?
- How much water would you need?
- How could you decide if 55ml was a decent size portion?
- How many pint jugs would the fifty-five 55ml portions fill?
If you have access to a wholesaler or talk nicely to the canteen, you will be surprised how much proportion work you can find in catering size value packs
By the way, my friend did a couple of calculations and a bit of estimating resulting in a large, but tasty, bowl of custard.
In an ideal world you would issue a homework sheet with a deadline and then dutiful students would hand in beautiful pieces of work on the specified date.
- the work is handed in
- the work is handed in late
- the work isn’t handed in because they’ve lost it
- the work isn’t handed in because they’ve left it at home
- what homework, I’ve got nothing in my planner?
I have a standard practice of printing 10% (or more) extra worksheets than I need given the track record of some of my students. Let’s just say lunch detentions happen so regularly for certain bods that they are referred to as ‘lunch dates’, much to the amusement of their friends! The annoying bit is finding/handing out the spare sheets and chasing deadlines. There is also the classic response of ‘I couldn’t get a new sheet because I couldn’t find you, Miss’.
I found this genius gadget in my local Asda (Walmart), but you could recreate it with laminated card and a pin-board.
- In each day section I record the homework set on that day – addresses the issue of not knowing there was homework.
- Each week I transfer last week’s deadlines across – no excuse for not knowing when work is due in.
- Underneath each day I pin a plastic wallet with the spare copies (but not the master copy) of the worksheet set – students can access spare sheets whenever they need to and I can find them quickly too (no more rummaging in folders/drawers)
- The board is stuck on the wall, near the main board so it is in the eyeline of the students – a constant reminder.
I’ve been using it for a month now and students are already helping themselves when they lose sheets. It’s also a much quicker reminder for me too.
The last word of this post has to go to my Year 11 frequent homework dodger:
‘We’ve got no excuse for not doing our homework now, have we Miss?’
Here’s a problem on averages that has been used by many teachers over the years. I like the additional ‘sting in the tail’ as it really makes pupils think about real life and it is an instant use of calculating the mean from an ungrouped frequency table.
Image Credit: www.vivcorecruitment.co.uk
A job advert says that the average worker at OfficesRUs earns over £30 thousand pounds.
- Director £100,000
- Manager £50,000
- Sales Person £35,000
- Clerical Assistant £22,000
- Trainees £15,000
Is the advert true?
If pupils calculate the mean they will find it is £44,400 – this makes the advert true
But why would a company have the same number of employees at each pay grade?
OfficesRUs is a clerical agency, offering temporary clerical staff for other businesses. Their staff numbers are:
- 1 Director £100,000
- 4 Managers £50,000
- 8 Sales People £35,000
- 200 Clerical Assistants £22,000
- 4 Trainees £15,000
Is the advert still true?
My class worked out how much each pay grade would get and added them to find the total salary cost. Some pupils then divided by 5, but discovered that the mean would be far greater than the Director’s salary. They then realised they had to total up the employees too. The mean turned out to be less than £30,000. This then leads to a discussion of which measure of average is best in this situation.
This is the working out from my board. The original problem is in black, with the sting and working in red. We linked the individual pay grade calculations to the work we had done on means from ungrouped frequency tables. The layout of the calculations is very similar to our tables.
This was a really good investigative starter to bridge between a theory and problem solving lesson. You could get pupils to see if they can find any examples of job adverts with average salaries in and make up their own problems.
I take no responsibility for this blog post. It is all down to the amazing teachers I work with. We have recently had our Year 6 open day and one of the activities was this amazing tessellation:
As you can see each rhombus has a pattern or picture which links to the next rhombus. You can stand in front of the full wall display and spend ages tracing the different routes across the wall. The clever use of colour means that from a distance the wall pops out as 3D cubes. Older students at school have commented that the display is ‘Awesome!’ and ‘Amazing!.
It was inspired by Vi Hart’s videos on snakes and doodling: YouTube
It’s been a while since I’ve done a step by step instruction post, so I thought I would share this lesson on questions and surveys.
- To understand bias in questions
- To consider how to structure answer options.
- Exercise books or paper
- Ruler/straight edge
Write out your usual headings: title, date, objective etc. Cut across the page to the spine. Stick the title page to the lower page.
Fold the lower half of the page in half and cut down the fold.
Fold the loose piece of paper into four equal pieces. Mark the fold positions in the book.
Draw horizontal lines across both the upper and lower pages. Cut the upper page to the spine along those lines to make four flaps.
Continue the horizontal lines on the lower page under the flaps
Label the flaps as shown
Give examples of bad questions, good questions, bad response boxes and good response boxes
Under each flap justify why each question or response is good or bad.
My class really enjoyed this activity – one of them even wrote it in their feedback. The following are examples from my class. You might even spot some RAG123 on their pages. Follow @ListerKev or search #rag123 on Twitter to find out more.