Suggestions for lesson starters:
The following lesson starters were offered by delegates attending a recent mathematics course of mine. Any errors or omissions are entirely my responsibility (sorry) and if you have any further ideas or you want to comment on how well (or badly) these were received then please get in touch.
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TO BE UNDERTAKEN INDIVIDUALLY
Bottles of beer
A bottle of beer costs £3 and the beer costs £2 more than the bottle. How much does the bottle cost?
nb The answer is not £1
Code Breakers
Given that A=26 and Z=1, can you write your name in digits?
Crossing the river
Two adults and two children have to cross a river. They have a boat which will carry one adult or two children. How do they cross the river?
Dates
In 1999, Christmas day fell on a Saturday....In which year did it last fall on a Saturday? In which year will it next fall on a Saturday?
Days
How many days in a year?
How many days in a leap year?
How many days since last Christmas?
How many days until next Christmas?
Decimal practice
Write down two numbers on the board and ask pupils to write down a number between them. Repeat the process.
Dogs and fleas
Two dogs are 100m apart and start to run towards each other at a speed of 10m/s. A flea flies at 20m/s from dog to dog. How far does the flea fly before the dogs meet?
Eggs
You need to boil an egg for 11 minutes (are you sure?) but you only have a 3 minute egg timer and a 7 minute egg timer. What do you do (use a watch)?
Four 2's
Use four 2's to make as many numbers as you can betweeen 1 and 10, 1 and 100, etc.
Four fours?
Four pupils each give random digit. Pupils use these four digits with any operations to make as many numbers as they can (in a fixed time or for the next lesson or …).
Handshakes
A room contains 5 people. Everybody shakes hands with everybody else. How many handshakes?
Holes
How much earth in a hole measuring 1m by 2m by 3m?
How many squares
How many squares can you see in this diagram?
What about a 4x4, 5x5, ….?
What about a chessboard?
You could also try this with triangles.....
Largest (or smallest)
What is the largest or smallest number you can get using all of the digits 1, 3, 5 and 7 (or any other combination of digits)?
nb This activity might be time constrained at the beginning of the lesson – remember powers for largest numbers!!!
Last lesson
Start the lesson by asking them to write down five things they remember from the last lesson.
Make numbers
Using the numbers 1, 3, 9 and 27 (or any other set of numbers), how quickly can you make the numbers from 1 to 20?
Missing signs
The following is written on the board
1 2 3 4 5 = 1and pupils have to fill in the missing signs…..how many different solutions can you find?
Quick add
How quickly can you add
1 + 2 + 3 + …….. + 8 + 9 + 10
1 + 2 + 3 + …….. + 48 + 49 + 50
1 + 2 + 3 + …….. + 98 + 99 + 100
Quick multiply
How quickly can you multiply
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 x 0
Sequences
A sequence of numbers is written on the board and pupils have to fill in the missing gaps
Snails pace
A snail climbs 2m each day but slips back 1m each night. How lomg will it take the snail to climb a wall 10m high?
String
A piece of string is placed around the equator (imagine the world to be a perfect sphere) and then an extra 6 inches is added to its length. The string is now placed so it is the same height off the ground around the equator. How high off the ground is the string?
nb I was given the answer (thank you) but I encourage you to find the answer out for yourself…remember what I said about ‘awe and wonder’!!!!
This year, next year, last year
The year 1998 has a sum of 27 when the digits are added together
When will the next time be when the digit total is 27?
When was the last time?
The year 1999 has a product of 729 when the digits are multiplied together
When will the next time be when the digit product is 729?
When was the last time?
Today’s date
Use the digits of today’s date as a starter for various number puzzles…
eg How many numbers can you make from 1 to 20
or How many numbers can you make using all of the digits
TO BE UNDERTAKEN AS A CLASS
Add ons and take aways and …..
The teacher gives a starting number (or a pupil can choose the starting number for added involvement!) and pupils have to add on 7 (or 8 or 9 or….)
The teacher gives a starting number and pupils have to take away 7 (or 8 or 9 or….)
The teacher gives a starting number and a rule such as ‘multiply by 2 and add 3’ ….
nb These activities can be undertaken by moving from pupil to pupil (in order or randomly) or else by getting all pupils to say the numbers …a bit noisy bur remember that noise does not necessarily equate to indiscipline!!!
Countdown
Pupils choose five numbers (these might have conditions on them such a one number bigger than 50 or one number less than 10 ….) and a target number is chosen. Pupils can use any combination of operation to reach the target number. The winner is the closest to the target number (or the first to finish …).
Five in a line
Pupils each have a five by five card (with numbers on it) and play the game in pairs using three dice. The dice are thrown and the pupil uses the numbers on the dice with any operations to make a number on the card. Counters are used to cover the number and the winner is the first person to get five in a line.
Four in a line (a bit like five in a line)
Pupils play the game in pairs using three dice and a five by five card (or six by six or …..as above). The dice are thrown and the pupil uses the numbers on the dice with any operations to make a number on the card. Different coloured counters (one for each pupil) are used to cover the number and the winner is the first person to get four (five…) counters in a line.
Hangman (or Hangperson)
The teacher thinks of a shape (or a solid) and pupils ask questions to which the answer is ‘yes’ or ‘no’ such as:
Does the shape have straight sides?
Has the shape got equal sides?
Has the shape got parallel sides?
Has the shape got reflection symmetry?
Has the shape got rotation symmetry?
nb Pupils might also try out this activity in groups – ask them to consider what questions are efficient in getting to the answer quickly
SOME OTHER SUGGESTIONS
Challenge the Champion
A knock out tournament where pupils compete in pairs answering mental arithmetic questions (best of three). Subsequently, in each lesson, the first five people who ask can ‘challenge the champion’
nb I am told that this challenge is particularly popular in years 7 and 8
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