Introduction to Algebra
Introduction to Algebra covers the Year 6 skills of using a letter to stand for an unknown number, forming a simple equation from a word problem or a number machine, and solving it using inverse operations.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the problem and decide what the unknown value is, then give it a letter, such as n.
- Translate the words into a number sentence (an equation) using that letter, in the same order the words describe.
- Solve the equation using inverse operations: undo addition with subtraction, undo multiplication with division, and undo the steps in the reverse order to how they were applied.
- Work through a two-step equation one operation at a time, simplifying the equation after each step.
- For a sequence, find the term-to-term rule first (what is added or subtracted each time) before trying to find a specific term.
- Check your answer by substituting the value back into the original equation or sequence rule to see if it works.
Worked example
A number machine multiplies a number by 4 and then adds 7. The output is 39. Work out the input number, n.
- Write the machine as an equation: 4n + 7 = 39.
- Undo the last step first: subtract 7 from both sides, 4n = 32.
- Undo the multiplication: divide both sides by 4, n = 8.
- Check by substituting back in: 4 x 8 + 7 = 32 + 7 = 39, which matches the given output.
Practice questions
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Q1If p + 9 = 17, what is the value of p?Show answer
Answer: 8
Q2If 5t = 45, what is the value of t?Show answer
Answer: 9
Q3Write an expression for 'a number, n, doubled and then add 3'.Show answer
Answer: 2n + 3
Q4The perimeter of a square is given by P = 4s, where s is the side length. Find P when s = 7cm.Show answer
Answer: 28cm
Q5Continue this sequence: 3, 7, 11, 15, ___Show answer
Answer: 19 (the rule is add 4 each time)
Q6Solve 2x - 5 = 11.Show answer
Answer: x = 8
Q7If y - 6 = 14, what is the value of y?Show answer
Answer: y = 20
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A number machine takes a number, multiplies it by 3 and then subtracts 4. The output is 23. What was the input number? Show your method.
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The rule for a sequence is 'start at 5 and add 6 each time.' a) Write the first four terms of the sequence. b) A pupil says the 10th term will be 60. Explain whether the pupil is correct, showing your working.
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Free printable worksheet
Want more practice on paper? Download the introduction to algebra worksheet pack - 10 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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