Mathematics • Year 7 • Unit 2 • Lesson 1
What is Algebra?
Build the basics: name the parts of an algebraic expression (variable, constant, coefficient, term), tell expressions apart from equations, and turn short English phrases into algebra.
1. I do, fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. For the expression 5a − 3b + 7, (a) how many terms are there, (b) what is the coefficient of a, (c) what is the constant term, and (d) what is the variable in the second term?
Step 1, Split the expression into terms.
5a | −3b | +7 → 3 terms
Reason: terms are separated by + and − signs. The sign belongs to the term that follows it, so the second term is −3b, not just 3b.
Step 2, Coefficient of a.
In 5a, the number multiplying a is 5 → coefficient = 5
Reason: the coefficient is the number that sits in front of a variable. 5a means 5 × a.
Step 3, Constant term.
+7 has no variable → constant term = 7
Reason: a constant term is a term that is just a number, no x, a or b attached.
Step 4, Variable in the second term.
Second term is −3b → variable is b
Reason: pick out the letter inside the term. The minus sign and the 3 belong to the term, but the variable itself is just b.
Answer: (a) 3 terms (b) coefficient of a = 5 (c) constant term = 7 (d) variable = b.
2. We do, fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. For 4x + 6y − 9, find: (a) the number of terms, (b) the coefficient of x, (c) the constant term, (d) the coefficient of y.
Step 1, Split into terms:
_______ | _______ | _______ → ____ terms
Step 2, Coefficient of x:
In ______, the number in front of x is ______, so coefficient of x = ______
Step 3, Constant term:
The term with no variable is ______, so the constant term is ______
Step 4, Coefficient of y:
In ______, the number in front of y is ______, so coefficient of y = ______
3. You do, independent practice
Show your working under each question. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation, single step
3.1 Is each of these an expression or an equation? (a) 3x + 4 (b) 3x + 4 = 19 (c) 5n − 1 1 mark
3.2 In the term 7m, what is the coefficient and what is the variable? 1 mark
3.3 Rewrite using algebra shorthand (no times sign): 6 × y. 1 mark
3.4 What is the hidden coefficient of x in the term x? What about −x? 1 mark
Standard, combine two ideas
3.5 For the expression 8a − b + 12, list (a) the number of terms, (b) the coefficient of a, (c) the coefficient of b, (d) the constant term. 2 marks
3.6 Translate each phrase into algebra. Use n for "a number". (a) "a number plus 9" (b) "double a number" (c) "7 less than a number". 2 marks
Extension, push your thinking
3.7 Look at the expression 2x + 3y − x + 5. (a) How many terms are there? (b) What is the coefficient of y? (c) Which two terms have x as the variable? (d) What is the hidden coefficient of the term −x? 3 marks
3.8 A friend writes "x4 + 2 = 14" on the board. Two things are unusual about how they have written it. Find both, fix them, and rewrite the equation correctly. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do (4x + 6y − 9)
Step 1: 4x | +6y | −9 → 3 terms.
Step 2: In 4x, the number in front of x is 4, so coefficient of x = 4.
Step 3: The term with no variable is −9, so the constant term is −9.
Step 4: In 6y, the number in front of y is 6, so coefficient of y = 6.
3.1, Expression or equation?
(a) 3x + 4 → expression (no equals sign). (b) 3x + 4 = 19 → equation (has equals sign). (c) 5n − 1 → expression.
3.2, Parts of 7m
Coefficient = 7. Variable = m. (7m is shorthand for 7 × m.)
3.3, Algebra shorthand for 6 × y
6y. In algebra we drop the × sign and put the number in front of the letter.
3.4, Hidden coefficients
The coefficient of x in the term x is 1 (because x means 1x).
The coefficient of x in the term −x is −1 (because −x means −1x).
3.5, Parts of 8a − b + 12
(a) 3 terms: 8a, −b, +12.
(b) Coefficient of a = 8.
(c) Coefficient of b = −1 (the term is −b, which means −1b).
(d) Constant term = 12.
3.6, Translating phrases
(a) "a number plus 9" → n + 9.
(b) "double a number" → 2n (double = multiply by 2).
(c) "7 less than a number" → n − 7 (less than reverses the order, start with n, then take 7 away).
3.7, Parts of 2x + 3y − x + 5
(a) 4 terms: 2x, +3y, −x, +5.
(b) Coefficient of y = 3.
(c) The two x-terms are 2x and −x.
(d) The hidden coefficient of −x is −1.
3.8, Two unusual things about "x4 + 2 = 14"
(1) The coefficient should be written before the variable, not after. "x4" should be "4x".
(2) Writing a variable next to a digit (like x4) can look like the number "x4" or like x×4, it's ambiguous. The convention is always coefficient-then-variable to avoid confusion.
Corrected: 4x + 2 = 14.