A quick idea for you today:
What is the cheapest each item could have been?
Which of these is the odd one out?
Why is it the odd one out? What discount does it represent? What is this as a decimal or percentage?
Keep your tags the next time you go to the sales – you never know what questions you’ll find.
I found this really useful book set on a second-hand market stall in the summer. I felt it was worth a look for £3.
It is Aba-Conundrums by Evelyn B. Christensen, published by Fat Brain Toy Co. The set includes a soroban, 120 number puzzles (& solutions) on spiral-bound dry-wipe card and dry-wipe pen.
The problem solving elements of the tasks are really good for improving basic number skills.
After boring four generations of my family with it, I did a bit of web-searching and came across the Soroban Cymru website – don’t worry if you don’t ‘siarad Cymraeg’, it’s in English.
I think proper use of sorobans could be a really useful tool for developing the understanding of number in low ability Year 6/7. I know they are used by all abilities in Asia, but pupils here don’t generally know how to use a soroban correctly and it could be a way to make numbers more interesting for those who disconnected from maths at a young age. I’m certainly going to try it out this term.
You can get basic sorobans on Amazon from about £2.50.
I’ve become increasingly interested in an inquiry based approach to learning maths after completing the ‘How to Learn Maths’ course.
Today I tried out a more problem-based approach with a Year 9 class. Last lesson we had recapped prior learning of equivalent fractions, simplifying and multiplying fractions. We had looked at using reciprocals in division. The starter today could easily have been 5 minutes with mini-whiteboards, but instead I gave them to following problem:
There is no ‘one correct answer’. The only limit was their mathematical imagination. After about twenty minutes we discussed each other’s answers on the board. If an answer was wrong, it was considered and corrected – rather than being dismissed or ignored. Walking around the room I was amazed – the level of engagement had increased and pupils were explaining their ideas. I could get a feel for who understood and who just followed procedures (and came unstuck when asked to do something different).
Of course, some pupils said ‘I can’t do it!’. They were met with the sympathetic response of ‘Can’t do it, doesn’t work anymore. Challenge is good for you’. Surprisingly, they either got on with it, started working with a friend or asked for pointers on how to start the problem.
I was really impressed with the students’ reaction to the task and by what I learnt about their understanding. Why not try it yourself on your next topic?
If you remember ‘The Wonder Years’ you are probably old enough to remember grunge the first time around and television programmes that didn’t involve so called ‘Reality TV’.
So what happens to female child stars?
Some have a rocky youth, work really hard and become hugely successful (Drew Barrymore). Some have a rocky youth and become hugely notorious (Lindsay Lohan). Some work really hard, do research, writing and acting, have a theorem named after them and become advocates for women and maths education!
Step forward Danica McKellar!
Apart from playing ‘Winnie Cooper’ in ‘The Wonder Years’, Danica is also a successful mathematician. She has written four books aimed at promoting maths to high school students, in particular girls. I strongly suggest you have a look at them or get your school library to purchase them as they are full of inspirational ideas and new ways to think about ‘dusty’ topics.
Her books to date are:
Girls Get Curves: Geometry Takes Shape (2013)
Hot X: Algebra Exposed! (2011)
Maths Doesn’t Suck: How to survive year 6 through year 9 maths without losing your mind or breaking a nail (2010)
Kiss my Math: Showing Pre-Algebra who’s boss (2009)
We’ve all seen the question about using a worded problem to work out the cooking time of a chicken. So dull and in many respects irrelevent – cook books & websites don’t write a big description. This is more like real-life:
Extract from the ‘Reader’s Digest Cookery Year’
Butcher’s label – no cooking instructions
Equipment
Pictures of labels from fresh meat* (actual labels are a hygiene hazard) – you might want multiple copies
Some cookbooks or tables of temperatures for cooking
Cards saying ‘Delicious’ or ‘Food poisoning!’
Calculators
*Be aware of pupils’ beliefs regarding meat – you don’t want to cause offence
Activity
1. Give out the cooking instructions & labels from the meat, ensuring the actual type of meat is on them.
2. Get pupils to decide how they want to cook their meat. You may also want to specify the cooking method to ensure variety in the,solutions.
3. Pupils calculate the appropriate times.
4. Each person (or group) presents their answer to a group (or the class). The other pupils hold up ‘Delicious’ if they agree or ‘Food poisoning!’ if they disagree. This can lead to a discussion as to why.
5. This can then be extended to look at writing formulae for cooking times.
Vegetarian Option
This task is easily adapted for any vegetarian recipe where weight is important eg Roast squash.
Don’t forget all the work on time and unit conversion that can be included!
This week I gave a talk to a group of PGCE/Schools Direct associates about innovation and ‘keeping it fresh’. One of my points was you should ‘Keep the good ideas and bin the rubbish/pointless ones’. This is one of my ideas I kept – first used in the late 1990s!
Background
Wassily Kandinsky was an artist, born in Russia in 1866. He died in France in 1944. He is credited with being the first artist to explore purely abstract work. Researching him is a nice homework task which can add to the final work.
Farbstudie quadrate mit konzentrischen ringen
This work has been reproduced thousands of times -you can see it everywhere from student bedrooms to upmarket coffee shops. The original was completed in 1913. It roughly translates as colour study squares with concentric circles.
Investigation
You will need:
Squared paper (or plain)
Coloured pencils or pens
1. Show the class the painting and discuss how the colours are arranged.
2. How many ways can you colour in one square with one colour? 1
3. How many ways can you colour in two concentric squares with two colours? 2
4. Repeat for three colours and ask for predictions. The usual prediction is 3, the answer is 6.
5. Repeat the process and ask them if they can see a pattern forming. Encourage them to be methodical.
The colour patterns form a set of factorial numbers. Finding out about factorials could be a good extension task.
After the work is completed you’ve potentially got a great wall display, a cross-curricular link to art and an understanding of combinations/factorials.
Variation
This also looks rather cool done with concentric equilateral triangles or hexagons on isometric paper.
Here’s a simple starter/revision activity. All you need is Post-it notes.
Hand out Post-its as the class arrive.
Once they have got their things out they each write four questions on a topic of your choice. Encourage them to make the questions challenging. Once that’s done tell them they need to write the answer lightly in pencil on the back.
Stick all the Post-its on a table or wall.
Everyone then collects a Post-it (or Qwiz-it) to answer (not their own).
Once they’ve answered, they can check their answer. If the answers don’t match, who is correct? Why?
This can lead to discussions about question-style, methods, misconceptions and understanding.