The first algebra: letters for numbers
Class 6 Maths · Algebra · 36 questions with answers
A letter in algebra is a number we have not been told yet - not a label for an object. Getting that framing right in Class 6 is what makes Class 8 equations feel like reasoning instead of like following steps.
- Writes an expression from a sentence
- Substitutes a value into an expression correctly
- Reads an equation as a statement of balance rather than an instruction
Exercise 1 of 3 · 12 questions
Write an expression for each. Use n for the unknown number.
Write the answer · Warm-up
Here’s one done for you
Five more than a number → n + 5. Careful with 'three less than a number': it is n - 3, not 3 - n. English puts the 3 first and the maths puts it second, and that reversal catches almost every child at least once.
- 1)Five more than a number
- 2)Twice a number
- 3)Three less than a number
- 4)A number divided by four
- 5)Two more than three times a number
- 6)Seven less than half a number
- 7)Ten more than a number
- 8)Five times a number
- 9)A number decreased by nine
- 10)One third of a number
- 11)Four more than twice a number
- 12)Six less than five times a number
Answers
- 1) n + 5
- 2) 2n
- 3) n - 3
- 4) n ÷ 4 or n/4
- 5) 3n + 2
- 6) n/2 - 7
- 7) n + 10
- 8) 5n
- 9) n - 9
- 10) n/3
- 11) 2n + 4
- 12) 5n - 6
Exercise 2 of 3 · 12 questions
Find the value when n = 6.
Write the answer · Guided
Here’s one done for you
4n when n = 6 → 4 × 6 = 24. The letter simply stands in for 6, so replace it and calculate. Note that n - 11 gives -5, which is a perfectly good answer - children often assume they have made a mistake when the result is negative, and that is where the integers work above pays off.
- 1)n + 9
- 2)4n
- 3)n - 11
- 4)2n + 3
- 5)3n - 8
- 6)n/2 + 5
- 7)5n - 6
- 8)n × n
- 9)(n + 4)/2
- 10)10 - n
- 11)2(n + 1)
- 12)n/3 + 7
Answers
- 1) 15
- 2) 24
- 3) -5
- 4) 15
- 5) 10
- 6) 8
- 7) 24
- 8) 36
- 9) 5
- 10) 4
- 11) 14
- 12) 9
Exercise 3 of 3 · 12 questions
Find the value of the letter that makes each statement true.
Write the answer · Practice
Here’s one done for you
x + 7 = 15 → the equals sign means both sides are worth the same. Something plus 7 is 15, so x is 8. Do not teach 'move it across and change the sign' yet - at Class 6 the useful question is 'what would make this true?', and that keeps the balance idea intact for Class 8.
- 1)x + 7 = 15
- 2)5y = 40
- 3)a - 9 = 4
- 4)3m + 2 = 17
- 5)p/4 = 6
- 6)x + 13 = 20
- 7)7y = 63
- 8)b - 14 = 6
- 9)4m - 5 = 23
- 10)q/6 = 5
- 11)2k + 9 = 25
- 12)c + 2.5 = 8
Answers
- 1) x = 8
- 2) y = 8
- 3) a = 13
- 4) m = 5
- 5) p = 24
- 6) x = 7
- 7) y = 9
- 8) b = 20
- 9) m = 7
- 10) q = 30
- 11) k = 8
- 12) c = 5.5
While your child works
- Never explain 3a + 2a as three apples plus two apples. It works for a term and then makes a × a = a² impossible to understand.
- 'Three less than a number' is n - 3, not 3 - n. English and maths put the numbers in opposite orders and this reversal catches nearly everyone.
- Read the equals sign aloud as 'is the same as'. It stops a child treating an equation as an instruction to compute.