S1 Maths — Algebraic Expressions: Lesson Prep Guide for Tutors (like terms, minus before a bracket, negative substitution)

2026-11-14

Tutor lesson-prep guides · Secondary Maths

Asked for the value of 3x squared minus 2x plus 1 when x is minus 2, students answer 15, two marks short, because they square the 2 and keep the minus. This lesson separates three skills, collecting like terms, the minus in front of a bracket, and substituting a negative, and leaves one sentence for each.

Objectives — By the end students can: (1) simplify 3a + 5b – 2a + 4b to a + 9b and state that only the same letter may be collected; (2) expand 4(2x – 3) – 3(x – 5) to 8x – 12 – 3x + 15 and then to 5x + 3, stating that the minus changes every sign inside; (3) evaluate 3x squared – 2x + 1 at x = -2 as 17, stating square first, then multiply, and a negative times a negative is positive.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Like terms	Can 3x and 3y be added together?	No, the letters differ
Multiplying negatives	What is -2 times -2?	+4, two negatives give a positive
Distributing	Expand 3(x + 2)	3x + 6, the 3 multiplies both terms

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Guess first	Write 3a + 5b – 2a + 4b and ask whether it can be made shorter	Name the two pairs that can be collected
5-14 min	Collecting like terms	Use three colours for a terms, b terms and numbers, model 3a – 2a = a and 5b + 4b = 9b	Write a + 9b themselves
14-24 min	The minus before a bracket	Model 4(2x – 3) – 3(x – 5): multiply in first, then hand the minus to both terms	Write 8x – 12 – 3x + 15
24-33 min	Substituting a negative	Write x as (-2), then substitute term by term: 3 x 4, -2 x (-2), +1	Get 17 and show one middle line
33-41 min	Three questions alone	Hand out one simplify, one expand, one substitute, and check for missing brackets	Bracket before calculating
41-45 min	Exit check	Three oral questions: can they be collected, does the minus reach both terms, what is (-2) squared	Answer aloud with a reason

03 Teaching script (read it out)

Scene 1: Act 1: only the same letter may be collected

“There is exactly one move in simplifying: collect like terms. 3a and 5b cannot be added, because one is a and the other is b. But 3a and -2a give a, and 5b and 4b give 9b. So the whole expression is a + 9b. Circle the a terms in one colour and the b terms in another, and never let two colours touch.”

Students repeat: only the same letter may be collected

Scene 2: Act 2: a minus in front of a bracket changes every sign

“Take 4(2x – 3) – 3(x – 5). The 4 multiplies in to give 8x – 12, that part is safe. The minus in front is not just minus 3, it is minus the whole bracket, so the 3 multiplies in and every sign flips: -3x + 15. Together that is 8x – 12 – 3x + 15, which collects to 5x + 3. The usual mistake is flipping only the first term and writing -15, which subtracts twice.”

Students repeat: minus before a bracket flips every sign

Scene 3: Act 3: bracket the negative before you substitute

“At x = -2 we want 3x squared – 2x + 1. Step one is to write the number as (-2), brackets and all, before any arithmetic. So 3 x (-2) squared is 3 x 4 = 12, then -2 x (-2) is +4, then add 1, giving 17. If you type 3 x -2 squared into a calculator it squares first and gives -12, and the answer falls apart. Rule: substitute a negative, bracket it, then square.”

Students repeat: bracket the negative, then square

04 Question types and worked steps

Type	Example	Steps	Answer
Collect like terms	Simplify 3a + 5b – 2a + 4b	(1) Circle terms with the same letter (2) add or subtract the coefficients (3) keep the letter (4) write in alphabetical order	a + 9b
Expand and simplify	Simplify 5(3x – 2) + 4(1 – 2x)	(1) Multiply each term in (2) keep the signs visible (3) collect (4) count the terms	15x – 10 + 4 – 8x = 7x – 6
Minus before a bracket	Simplify 2(3y + 4) – (y – 6)	(1) Read the minus as -1 times (2) flip both signs (3) collect (4) test with y = 1	6y + 8 – y + 6 = 5y + 14
Substitute a value	Find 3x squared – 2x + 1 when x = -2	(1) Write (-2) in brackets (2) square first (3) multiply by the coefficient (4) add and subtract last	3 x 4 + 4 + 1 = 17

Sanity check (teach this): Reasonableness checks: after simplifying, each letter should appear once, and a + 9b has two terms, so a leftover 3a means collecting is unfinished; coefficients come from adding and subtracting, 3 – 2 = 1, so 5a means the wrong direction; an expansion keeps the right number of terms, and 4(2x – 3) must give two; substituting x = 1 gives 5(1) + 4(-1) = 1 on the left and 7 – 6 = 1 on the right, so the simplification is sound; a square is never negative, so 17 above 1 is plausible.

05 Independent practice (3 questions)

Question	Answer	What to watch
Simplify 2(3y + 4) – (y – 6)	6y + 8 – y + 6 = 5y + 14	An answer of 5y + 2 means only the first term in the second bracket was flipped
Find the perimeter of a rectangle with length x + 5 and width 2x – 1 when x = 4	Perimeter = 2((x + 5) + (2x – 1)) = 6x + 8, which is 32 at x = 4	The simplified expression must be written before the substitution
Find (a + b) divided by (a – b) when a = 5 and b = 3	(5 + 3) divided by (5 – 3) = 8 divided by 2 = 4	Without brackets this becomes 5 + 3/5 – 3 = 2.6

06 Common mistakes and what to say

Mistake	Student writes	Say this
Collecting different letters	“3a + 5b – 2a + 4b is 10ab.”	“a and b are different things and never merge into ab. Split into two groups: one a and nine b, so a + 9b.”
Flipping only the first term	“4(2x – 3) – 3(x – 5) is 8x – 12 – 3x – 15.”	“The minus goes into the whole bracket, and -3 times -5 is +15. Writing -15 subtracts twice and loses 30.”
No bracket on a negative	“At x = -2, 3x squared is 3 x -2 squared = -12.”	“Write (-2) first, then square: (-2) squared is 4, times 3 is 12. You kept the minus until the end, which is the wrong order.”
Multiplying coefficients instead of adding	“3a – 2a is 6a.”	“Collecting means adding and subtracting coefficients, never multiplying. 3 minus 2 is 1, so the answer is a.”

07 Homework (paper, section and question numbers)

Redo Act 1: circle the like terms in 3a + 5b – 2a + 4b in two colours and write the simplified result — Chapter practice, question 1
Do three expansions with a minus before a bracket and test each one with y = 1 — Chapter practice, question 2
Preview: substitute x = -3 into 2x squared + 3x – 1 and show one middle line — Chapter practice, question 3

08 Exit check (last 5 minutes)

Question	Answer	Decision
Can 3a and 5b be collected, and why?	No, the letters differ, and only like terms collect	Answering yes means Act 1 again
Simplify 4(2x – 3) – 3(x – 5)	5x + 3, both signs in the second bracket flip	An answer of 5x – 27 means Act 2 again
What is 3x squared – 2x + 1 when x = -2?	17, after bracketing the negative and squaring first	An answer of 15 means Act 3 again

09 Tutor FAQ

Why not teach moving terms across the equals sign now?

Moving terms belongs to solving equations, and mixing the two in one lesson makes students treat the equals sign as an instruction. It comes in the next chapter.

My student types -2 squared and gets -4. What do I do?

Use it: show the calculator reads it as minus (2 squared), which is why the bracket comes first. One demonstration and every later substitution is safe.

Must the simplified answer be in alphabetical order?

Not strictly, but keep one order across the chapter so marking and self-checking stay quick.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.