Year 7 Algebraic Expressions Dr J Frost Last modified: 4 th May 2016 Objectives: Appreciate the purpose of algebraic variables and simplify algebraic expressions. Substitute into algebraic expressions. Form algebraic expressions from worded information.

INTRO :: What is algebra? Source: Google Algebra concerns representing missing information. Put simply, we use letters, known as variables, to (usually) represent numbers. Usually the value of variables are not initially known, but we hope to combine available information to find their value. Examples:

INTRO :: Examples of algebraic expressions Your age in 4 years time. Twice your age. A third of your age. ? ? ?

INTRO :: Two stages of algebraic problems [JMC 2008 Q18] Granny swears that she is getting younger. She has calculated that she is four times as old as I am now, but remember that 5 years ago she was five times as old as I was at that time. What is the sum of our ages now? Worded problem Stage 1: Represent problem algebraically Stage 2: ‘Solve’ equation(s) to find value of variables. These next few lessons we’ll be looking at Stage 1. Stage 2, ‘solving’, we’ll do later this year. Being able to do these two stages for difficult problems is a vital skill for Maths Challenges/Olympiads. We won’t solve this now, but how would we approach such a problem?

Algebraic Simplification – Adding/Subtracting ? How does this ‘simplify’? Why conceptually does it work? ? More Examples: ?

x2x2 x2x2 2x 2 -3x 2 3x 3 -x 3 y2y2 y2y2 5xy 2 4x 2 y 2x 2 y +4 x x 9x 5xy ACTIVITY :: Collecting Like Terms Instructions: In pairs, discuss which terms you think might be ‘like’ terms, i.e. they could be combined together into one when adding/subtracting. Therefore, terms are ‘like terms’ if: The involve the same variables and powers. ?

Quickfire Examples ? ? ? ? ?

A common Schoolboy Error TM ?

ACTIVITY :: Addition Pyramids You should have printed the following pyramids. Each block is the sum of the two below it, e.g. as per on the right. Can you fill in the missing blocks? ? ? ? ??? ? ?? ?? ? ?? ?? ? ?

Multiplying ? ? ? ? ? ? ? ? ?

Test Your Understanding (so far) ? ? ? ? ? a b c d e Simplify the following.

Division ? Fractions are ultimately just divisions. How did we simplify this fraction? Can we apply the same principle to algebraic division? ? ? ? ? ? ?

Test Your Understanding ? ? ? ?

Exercise 1 1 Simplify the following, or write ‘already simplified’. a b c d e f g h i j 2 a c e g i j k l b d f h 3 a c e g i j b d f h k 4 a c b d ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Substitution 12?36?

Substitution Bro Tips: Start by working out each of the terms first (mentally if you can) leaving the +/- symbols between as they are. Don’t try to do all at once. ? Terms ? ?

Another Example ? ? ? ? ? ?

Test Your Understanding ? ? ? ? ?

Formulae ? ? ?

Exercise 2 1 a b c d 2 a b c d e 3 4 a b c d e 5 6 a b c d e ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Forming Expressions [JMC 2008 Q18] Granny swears that she is getting younger. She has calculated that she is four times as old as I am now, but remember that 5 years ago she was five times as old as I was at that time. What is the sum of our ages now? Worded problem Stage 1: Represent problem algebraically Stage 2: ‘Solve’ equation(s) to find value of variables. Remember this problem? We’ll be looking how we can turn worded information into algebraic expressions.

Forming Expressions ? ? ? ? ? ? Later this year you’ll properly learn how to ‘expand brackets’. ?

A Harder One “The sum of 5 consecutive whole numbers is 285. What is the smallest of these numbers?” Option 1 Option 2 ? ? ?? ? ? Why might Option 2 might make the later ‘solving’ stage easier?

Check Your Understanding A B C D ? ? ? ? ? ? ? ? ?

Exercise ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Questions on provided sheet.

Exercise ? ? ? ? ? ? ?

Exercise ? ?