Subtraction within 20
Subtraction within 20 is taking one number away from another where the starting number is no more than 20, and covers two meanings children often experience as separate skills: 'take away', removing objects from a group, and 'find the difference', comparing two amounts.
Before you start
Make sure you're comfortable with these topics first:
Method
- Start concrete with take-away: count out the starting number of objects, physically remove the amount being subtracted, and count what is left - this models the take-away meaning directly and is where every child should begin.
- Introduce find-the-difference with a separate, side-by-side concrete model: line up two rows of objects (e.g. two towers of cubes of different heights) and count the gap between them, so the child sees this gives the same kind of answer as take-away even though nothing was removed.
- Use a number line for both meanings at the pictorial stage, but draw the jumps differently: for take-away, jump backwards from the starting number; for find-the-difference, mark both numbers on the line and count the space between them forwards. Seeing both on the same tool helps the child connect the two ideas.
- Teach bridging through 10 for subtraction the same way as for addition, but working backwards: for 14 - 6, first subtract enough to reach the nearest ten below (14 - 4 = 10), then subtract what is left of the 6 (4 has been used, 2 remains, so 10 - 2 = 8).
- Keep bonds-to-10 recall central to this: a child who is not instant with bonds to 10 will not be able to bridge-subtract quickly, since every bridging step relies on knowing how far a number is from the nearest ten.
- Move to the abstract stage - a bare number sentence (16 - 9 = ?) or a missing number in another position (? - 5 = 8, meaning 'what did I start with') - once both meanings and the bridging strategy are secure without the number line.
- Watch for the common error of subtracting the smaller digit from the larger digit regardless of position once children start seeing numbers written in columns (e.g. treating 14 - 8 as 'take the 4 from the 8' and getting 4 instead of 6): at this stage, keep working with the whole numbers on a number line rather than introducing column subtraction, which comes later.
Worked example
Work out 15 - 7 by bridging through 10.
- Start at 15.
- Work out how far 15 is from the nearest ten below: 15 - 5 = 10, so 5 is the first part to take away.
- Subtract that first part: 15 - 5 = 10.
- Work out what is left of the 7 to subtract: 5 has been used, so 2 remains.
- Subtract what is left: 10 - 2 = 8.
- So 15 - 7 = 8.
Practice questions
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Q1Work out 18 - 5.Show answer
Answer: 13
Q2Work out 14 - 6 by bridging through 10.Show answer
Answer: 8 (14 - 4 = 10, then 10 - 2 = 8)
Q3Fill in the missing number: 16 - ? = 9.Show answer
Answer: 7
Q4Freya has 17 party bags and gives 8 away. How many party bags does she have left?Show answer
Answer: 9 party bags (17 - 8 = 9)
Q5One tower is 12 cubes tall. Another tower is 5 cubes tall. What is the difference in height between the two towers?Show answer
Answer: 7 cubes (12 - 5 = 7)
Q6Work out 20 - 6.Show answer
Answer: 14
Q7Hamza has read 9 pages of his book. The book has 20 pages. How many more pages does he have left to read?Show answer
Answer: 11 pages (20 - 9 = 11)
Q8Fill in the missing number: ? - 4 = 12.Show answer
Answer: 16
Exam-style questions
Written in the style of a KS1 Maths exam paper, with a full mark scheme.
Work out 15 - 8 by bridging through 10. Show each step.
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Niamh has 19 conkers. She gives some to her brother and has 11 left. How many conkers did she give her brother? Show your working.
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One shelf has 16 books on it. Another shelf has 9 books on it. How many more books does the first shelf have than the second shelf? Explain whether this is a take away or a find the difference question.
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Free printable worksheet
Want more practice on paper? Download the subtraction within 20 worksheet pack - 7 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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