Ratio, proportion & algebra
Introduction to Algebra: Missing Numbers, Sequences and Simple Rules
Year 3 · Year 4 · Year 5 · Year 6
- ✓By the end of this lesson students will be able to understand that a letter or symbol can represent an unknown number.
- ✓By the end of this lesson students will be able to solve missing number problems using inverse operations.
- ✓By the end of this lesson students will be able to identify the rule in a linear number sequence and find missing terms.
- ✓By the end of this lesson students will be able to use simple formulae to calculate values when given the value of a variable.
Key concepts
A variable is a letter or symbol (like x, y, a, or even a question mark or an empty box) that stands for a number we don't know yet. It's a placeholder for an unknown value.
A missing number problem is an equation where one of the numbers is unknown, and you need to find its value. For example, 5 + ? = 12.
Inverse operations are pairs of operations that 'undo' each other. Addition is the inverse of subtraction, and multiplication is the inverse of division. We use them to solve missing number problems.
A linear number sequence is a list of numbers that follows a pattern where the same amount is added or subtracted each time to get from one term to the next. This 'same amount' is called the term-to-term rule.
A simple formula is a rule written using letters and symbols that shows how different quantities are related. For example, if you buy 'n' apples at 50p each, the total cost (C) could be written as C = 50 × n.
Key facts to remember
- 1A letter or symbol in maths can represent an unknown number.
- 2To solve for a missing number, use the inverse operation (e.g., if it's 'add', use 'subtract').
- 3An equation means that what is on one side of the '=' sign is equal to what is on the other side.
- 4A linear number sequence increases or decreases by the same amount each time.
- 5A formula is a rule that uses letters to show how different quantities are connected.
- 6Always check your answer by substituting it back into the original problem.
Worked examples
Example 1
Solve the missing number problem: 17 + ? = 25
Answer
? = 8
Always check your answer: 17 + 8 = 25. This is correct.
Example 2
Find the missing numbers in the linear sequence: 5, 10, __, 20, __, 30
Answer
The missing numbers are 15 and 25. The complete sequence is 5, 10, 15, 20, 25, 30.
Make sure the rule works for all numbers in the sequence.
Example 3
If 'c' stands for the cost of one comic book, and each comic book costs £3. What is the total cost (T) if you buy 4 comic books? Use the formula T = c × number of comic books.
Answer
The total cost (T) is £12.
In algebra, 'c × 4' can also be written as '4c'.
Common mistakes
- ✗Thinking that a letter always stands for the same number in every problem.
- ✗Not using the correct inverse operation when solving missing number problems.
- ✗Guessing the rule for a sequence instead of carefully checking the difference between terms.
- ✗Confusing addition with multiplication when a letter is next to a number (e.g., thinking '3a' means '3 + a' instead of '3 × a').
- ✗Not performing calculations in the correct order (e.g., for 5 + 2 × 3, doing 5 + 2 first).
Exam tips
- ★Read the question carefully to understand what each letter or symbol represents.
- ★Show all your working steps clearly, as this can earn you marks even if your final answer is incorrect.
- ★Always check your answer by putting it back into the original problem or sequence to see if it makes sense.
- ★Look for patterns and rules in number sequences before trying to fill in missing terms.
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