1. Expressions
[ A1.2 Core Plenary]
The algebraic “sentences” 4x + 3 and 4x + 3 = 19 can be written in words as:
‘The sum of four times a number and three’ and
‘Four times a number added to three gives nineteen’
1) Write these in words – there are several different ways. Find as many as you can. (a) x + (x + 1) + (x + 2) (b) (x + 2)(x + 1) (c) x(x + 1) = 20 (d) 9(2x + 1) (e) x + y = xy (f) (x + 1)2 = 10
2) Write these as algebraic sentences. (a) The sum of two numbers is ten. (b) A number squared is two less than six. (c) Ten times a number is equal to the square of one more than the number. (d) Subtract six times a number from twice the square of the number. (e) Multiplying the square of a number by three and then adding two to the product gives twenty.
3) Make up some similar problems to those in 2) for yourself.
Preamble
Some problems involving children looking closer at algebraic and numerical statements. Preparatory work for setting up equations. Suitable for individuals or pairs.
Possible content
Writing algebraic expressions in words and vice versa, using brackets, expanding brackets.
Resources
None
Solution/Notes
Children’s own responses, for example: (a) the sum of three consecutive numbers (b) the product of two added to a number and one added to the same number (c) a number added to one, then multiplied by its original value gives twenty (d) nine times the sum of twice a number and one (e) the sum of two numbers is equal to their product (f) a number added to one and the result all squared is equal to 10.
Children may well use different variables than x etc. (a) x + y = 10 (b) (c) (d) (e)
3) Children's own work
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010