What you'll learn
A number sentence is a mathematical statement written with numbers and symbols, such as 7 + 8 = 15 or 4 × □ = 20, and algebraic thinking means working out the value hiding in the empty box or letter. The key to the whole topic is that the equals sign means "the same as", not "here comes the answer" — both sides of a number sentence must balance. So in 7 + □ = 15, the box must hold 8, because 7 + 8 is the same as 15. This guide covers reading and writing number sentences, using inverse operations to find a missing number, working with a letter instead of a box, substituting a value into an expression, following the correct order of operations, using function machines, and turning a word problem into a number sentence you can solve. Number is 19 of the 40 items on the SEA Mathematics paper, and this topic is also the first real step towards secondary-school algebra.
Key terms and definitions
Number sentence — a complete mathematical statement, such as 12 − 5 = 7 or 3 × n = 18.
Equals sign (=) — means the two sides have the same value. It does not mean "write the answer here".
Unknown — the value you are looking for, shown by a box, a shape or a letter.
Expression — a piece of mathematics with no equals sign, such as 3n + 2.
Equation — an expression set equal to something, such as 3n + 2 = 17.
Inverse operation — the operation that undoes another. Subtraction undoes addition; division undoes multiplication.
Substitute — to put a given number in place of a letter. If n = 5, then 3n means 3 × 5 = 15.
Function machine — a diagram in words that takes an input, applies one or more operations, and gives an output.
Inequality — a sentence using < (less than) or > (greater than) instead of =, such as □ < 10.
Core concepts
The equals sign means balance
Think of a pair of scales. Whatever sits on the left pan must weigh the same as whatever sits on the right pan, or the scales tip.
This matters because of a very common question type:
8 + 4 = □ + 5
Many children write 12, because they read the equals sign as "the answer goes here". But the left side is worth 12, so the right side must also be worth 12, and 12 − 5 = 7.
Saying the sentence aloud as "eight add four is the same as something add five" fixes this almost immediately. The words "is the same as" are the repair for the most persistent misunderstanding in primary mathematics.
Using inverse operations to find the unknown
Every missing-number sentence is solved by undoing what was done.
| Sentence | Undo with | Answer |
|---|---|---|
| 7 + □ = 15 | 15 − 7 | □ = 8 |
| □ − 6 = 21 | 21 + 6 | □ = 27 |
| 4 × □ = 32 | 32 ÷ 4 | □ = 8 |
| □ ÷ 5 = 9 | 9 × 5 | □ = 45 |
Always check by putting your answer back into the original sentence. For □ ÷ 5 = 9, test 45 ÷ 5 = 9. ✔ This check costs five seconds and catches every error.
Two-step sentences
When two things have been done to the unknown, undo them in reverse order — last thing first.
For 3 × □ + 4 = 22:
- The last thing done was "add 4", so undo it: 22 − 4 = 18. Now 3 × □ = 18.
- The remaining thing is "multiply by 3", so undo it: 18 ÷ 3 = 6.
So □ = 6. Check: 3 × 6 + 4 = 18 + 4 = 22. ✔
Think of it as taking off shoes and socks. Socks went on first, so shoes come off first.
Letters instead of boxes
A letter does exactly the same job as an empty box. In n + 9 = 20, the letter n stands for one particular unknown number, and n = 11.
Two writing conventions are worth learning now:
- 3n means 3 × n. The multiplication sign is left out.
- n² means n × n.
So if n = 4, then 3n = 12 and n² = 16.
Substituting a value
Substitution means replacing the letter with the number you have been given, then working the sum out.
If a = 6, then:
- a + 7 = 13
- 5a = 5 × 6 = 30
- 2a − 3 = 12 − 3 = 9
- a² = 36
Write the multiplication sign back in as soon as you substitute. Turning 5a into 5 × 6 rather than "56" removes the commonest slip.
Order of operations
When a sentence has more than one operation, they are not done left to right. The order is:
- Brackets first.
- Then multiply and divide, working left to right.
- Then add and subtract, working left to right.
| Calculation | Correct answer | Common wrong answer |
|---|---|---|
| 5 + 3 × 2 | 5 + 6 = 11 | 8 × 2 = 16 |
| 12 − 2 × 4 | 12 − 8 = 4 | 10 × 4 = 40 |
| (12 − 2) × 4 | 10 × 4 = 40 | — |
| 20 ÷ 4 + 6 | 5 + 6 = 11 | 20 ÷ 10 = 2 |
Function machines
A function machine takes a number in, does something to it, and passes the result out.
Input → × 3 → + 2 → Output
Put 5 in: 5 × 3 = 15, then 15 + 2 = 17. The output is 17.
To go the other way, reverse the machine and reverse each operation. If the output is 26: 26 − 2 = 24, then 24 ÷ 3 = 8. The input was 8.
Check forwards: 8 × 3 = 24, and 24 + 2 = 26. ✔ Working a function machine backwards is the same skill as solving a two-step equation, just drawn differently.
Inequalities
Some sentences use < or > instead of =. The wide end of the symbol always faces the bigger number: 9 > 4 and 4 < 9.
A sentence like □ + 3 < 10 does not have a single answer. Any number under 7 works, so the largest whole number that fits is 6.
Writing a word problem as a number sentence
This is where most of the marks are, and it is a translation exercise.
- "how many altogether", "total", "in all" → add
- "how many left", "how many more than", "difference" → subtract
- "each", "groups of", "per" → multiply
- "shared equally", "split between", "how many each" → divide
Riya had some money. She spent $35 and has $18 left. The sentence is m − 35 = 18, so m = 53.
Write the sentence down before solving it.
Worked examples
Example 1: A two-step missing number
Find the value of the box: 4 × □ + 3 = 27.
Undo the last operation first. Three was added at the end, so take it away from both sides: 27 − 3 = 24. The sentence is now 4 × □ = 24.
Now undo the multiplication: 24 ÷ 4 = 6.
So □ = 6.
Check by substituting back into the original: 4 × 6 + 3 = 24 + 3 = 27. ✔
Example 2: Turning a word problem into a number sentence
Shanice picked some mangoes. She gave 7 to her neighbour and had 18 left. Write a number sentence for this and find how many mangoes she picked.
Let m stand for the mangoes she picked. She gave some away, so the operation is subtraction:
m − 7 = 18
Undo the subtraction by adding: 18 + 7 = 25.
Shanice picked 25 mangoes.
Check the story, not just the sum: 25 mangoes take away 7 leaves 18. ✔ Reading the answer back into the original sentence is what proves it.
Example 3: A two-step money problem
Devon buys 3 exercise books that all cost the same, and a pen costing $8. He spends $50 altogether. How much does one exercise book cost?
Let b stand for the cost of one book in dollars. Three books cost 3b, and the pen costs 8, so:
3b + 8 = 50
Undo the addition first: 50 − 8 = 42. So 3b = 42.
Undo the multiplication: 42 ÷ 3 = 14.
One exercise book costs $14.
Check: 3 × $14 = $42, and $42 + $8 = $50. ✔
Common mistakes and how to avoid them
Reading the equals sign as "write the answer". Putting 12 in 8 + 4 = □ + 5. Fix: read the sentence aloud with "is the same as" where the equals sign is.
Using the same operation instead of the inverse. Solving 4 × □ = 32 by multiplying. Fix: ask "what was done to the box?" then do the opposite.
Undoing the steps in the wrong order. In 3 × □ + 4 = 22, dividing by 3 first. Fix: undo the last operation first, like taking shoes off before socks.
Working left to right when there is a multiplication. Answering 16 for 5 + 3 × 2. Fix: scan the line for × and ÷ before starting, and do those first.
Reading 3n as a two-digit number. Fix: put the × back in as soon as you substitute — 3n with n = 5 is 3 × 5.
Not checking the answer back in the sentence. Fix: substitute your answer into the original and confirm both sides match. This is the fastest reliable check in the whole paper.
Guessing at word problems instead of writing the sentence. Fix: write the sentence with a letter first, even if the answer feels obvious.
How parents can help at home
You do not need to remember algebra to help with this. What your child needs is practice in one particular habit: writing the sentence down.
Play "guess my number". "I'm thinking of a number. I add 6 and get 19. What is it?" Then make it two steps: "I double it and add 3 and get 17." (The answer is 7.) This is exactly what the exam asks, in a friendlier voice.
Use the scales idea. If you have kitchen scales, put something on one side and ask what would balance it. The picture of two sides being equal is what makes the equals sign make sense.
Ask them to say the sentence aloud with "is the same as". Every time your child reads 9 + 5 = □ + 4 as "nine add five is the same as something add four", the misunderstanding weakens.
When they are stuck, ask "what was done to the number, and what undoes it?" Those two questions solve nearly every item in this topic, and you do not need to know the answer to ask them.
Shopping is full of these. "Three of these cost $36 — what is one?" "You spent $22 and have $8 left, so how much did you start with?" Real money in TT dollars makes the letters feel like something rather than nothing.
Exam technique for number sentences and algebraic thinking
The SEA Mathematics paper is weighted 100 marks, against 60 for ELA and 40 for ELA Writing. It has 40 items worth 75 marks, with 19 of those items in Number, so sentences of this kind appear every year.
Write the number sentence on the paper before solving it, even for a multiple-choice item. The working space is there, and an unwritten sentence is where the mistakes live.
Substitute your answer back into the original sentence every time. If both sides do not match, you have found your own error before the marker did.
Scan for × and ÷ before you calculate anything in a mixed line, and look for brackets first of all.
In multiple-choice items the wrong options are built from the standard errors — the left-to-right answer, the same-operation-instead-of-inverse answer, the answer to the first step only. Matching an option is not proof that you are right.
If a question gives a letter and a value, write the substitution out in full with the multiplication signs restored. It takes a few extra seconds and it prevents the 3n-becomes-thirty-something slip.
Quick revision summary
- The equals sign means "is the same as"; both sides must balance.
- Find an unknown by using the inverse operation: + undoes −, × undoes ÷.
- In a two-step sentence, undo the last operation first.
- A letter does the same job as an empty box; 3n means 3 × n and n² means n × n.
- Substitute by replacing the letter with the number and restoring the × sign.
- Order of operations: brackets, then × and ÷, then + and −.
- 5 + 3 × 2 = 11, not 16.
- A function machine run backwards uses reversed operations in reverse order.
- In < and >, the wide end faces the larger number.
- Translate word problems: total means add, left means subtract, each means multiply, shared means divide.
- Always substitute the answer back into the original sentence to check.