Pre-Algebra and Sequences
Pre-Algebra and Sequences builds on introductory algebra with harder Year 6 objectives: finding pairs of whole numbers that satisfy an equation with two unknowns, systematically listing all the possibilities for a given condition, and describing and extending more complex linear sequences.
Method
- Identify what is unknown in the problem and how many separate unknowns there are.
- For an equation with two unknowns, list possible whole-number pairs systematically, starting from the smallest sensible value and increasing in order so no pair is missed or repeated.
- Check each pair actually satisfies every condition given in the question, not just the first one.
- For a sequence, find the term-to-term rule (what is added or subtracted each time) by comparing consecutive terms.
- Describe the rule in words, stating both the starting value and what changes each step.
- To find a specific term without listing every term, work out how many steps from the start it is, multiply that by the step size, then adjust for the starting value.
Worked example
Find all pairs of whole numbers a and b, both greater than 0, that satisfy a + b = 9, where a must be a multiple of 3.
- List the multiples of 3 that are less than 9: these are 3 and 6.
- If a = 3, then b = 9 - 3 = 6.
- If a = 6, then b = 9 - 6 = 3.
- Check both pairs: 3 + 6 = 9 and 6 + 3 = 9, so both satisfy the equation.
- So the pairs are a = 3, b = 6 and a = 6, b = 3.
Practice questions
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Q1Find one pair of whole numbers x and y (both greater than 0) that satisfy x + y = 12.Show answer
Answer: Any valid pair, e.g. x = 5 and y = 7.
Q2A pattern of triangles is made from matchsticks: 1 triangle uses 3 matchsticks, and each extra triangle added in a row uses 2 more matchsticks. How many matchsticks make 5 triangles?Show answer
Answer: 11 (3 + 2 x 4)
Q3The rule for a sequence is 'start at 4 and add 5 each time.' Find the 6th term.Show answer
Answer: 29 (4 + 5 x 5)
Q4If 2a + b = 16 and a = 3, find the value of b.Show answer
Answer: b = 10
Q5Find two whole numbers that multiply to give 24 and add to give 11.Show answer
Answer: 3 and 8
Q6Continue the sequence 2, 6, 10, 14, ___ and state the rule.Show answer
Answer: 18; the rule is add 4 each time.
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
a and b are whole numbers greater than 0. a + b = 15 and a is double b. Find the values of a and b. Show your method.
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A sequence of dot patterns has: pattern 1 with 5 dots, pattern 2 with 9 dots, pattern 3 with 13 dots. a) State the rule for going from one pattern to the next. b) How many dots are in pattern 8? Show your working.
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Free printable worksheet
Want more practice on paper? Download the pre-algebra and sequences worksheet pack - 8 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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