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.