Idea Transcript
Subtraction Year 1 Key Vocabulary
Key skills for subtraction at Y1: Given a number, say one more or one less. Count to and over 100, forward and back, from any number. Represent and use subtraction facts to 20 and within 20. Subtract with one-digit and two-digit numbers to 20, including zero. Solve one-step problems that involve addition and subtraction, using concrete objects (ie bead string, objects, cubes) and pictures, and missing number problems. Read and write numbers from 0 to 20 in numerals and words.
Understanding the operation Understand subtraction as: Taking away Comparison (finding the difference)
Begin to relate subtraction to ‘taking away’ using objects to count ‘how many are left’ after some have been taken away.
6–2=4 This will be introduced practically with the language ‘find the difference between’ and ‘how many more?’ in a range of familiar contexts. “Seven is three more than four” “I am three years older than my sister. How old am I?” “Four is three less/fewer than 7.”
Read, write and interpret mathematical statements involving subtraction (-) and equals (=) signs. 14-3=11 9=16-7 Examples 3 less than 4 is 11. 14 take away 3 is/equals/is the same as 11. If I subtract 3 from 14 it equals 11. 14 minus 3 leaves us with 11. The difference between 14 and 3 is 11.
Number facts
Represent and use number bonds and related subtractions facts to 10 and 20.
Mental Strategies
Subtract one digit and two digit numbers to 20 including 0.
Solve one step problems that involve subtraction using concrete objects in pictorial representations and missing number problems such as 7= 9 -
Represent and use number bonds within 20 Partition a given number of objects (up to 20) into 2 groups e.g. Partition 15 into 7 and 8, 9 and 6 …. COUNTING BACK (SEQUENCING): 15-3 (by counting back 3 in ones; 14, 13, 12)
WITH JOTTINGS: 15 – 6 (by counting back in ones or partitioning 6 to bridge the tens boundary; -5, -1) Progress to crossing the tens boundary COUNTING UP 9 – 6 (by counting up from 6 to 9 in ones; 7, 8, 9) WITH JOTTINGS: 19 – 14 (by counting up from 14 to 19 in ones; 15, 16, 17, 18, 19) USING KNOWN FACTS AND PLACE VALUE: 16 – 4 6 – 4 = 2 so 16-4 = 12
Subtraction Year 2 Key Vocabulary
Key skills for subtraction at Y2:
Recognise the place value of each digit in a two-digit number. Recall and use subtraction facts to 20 fluently, and derive and use related facts up to 100. Subtract using concrete objects, pictorial representations, 100 squares and mentally, including: a twodigit number and ones, a two-digit number and tens, and two two-digit numbers. Show that subtraction of one number from another cannot be done in any order. Recognise and use inverse relationship between addition and subtraction, using this to check calculations and missing number problems. Solve simple addition and subtraction problems including measures, using concrete objects, pictorial representation, and also applying their increasing knowledge of mental and written methods. Read and write numbers to at least 100 in numerals and in words.
Understanding the operation
Show that subtraction of one number from another cannot be done in any order recognise that 5-3 is different from 3-5
Recognise the inverse relationship between addition and subtraction write the related number sentences 5+2=7 2+5=7 7=5+2 7=2+5 7-2=5 7-5=2 2=7-5 5=7-2
Shake tray
Number facts Recall and use subtraction facts to 20 fluently, and derive and use related facts up to 100 e.g. 15 subtract 8
4 less than 12
80 minus 30
90 take 50
Using diennes, money and year 1 images. ‘Ten times bigger/smaller.’ What patterns can you see? Know complements to the next multiple of 10 e.g. 52+☐ = 60
52+☐ = 80
Know pairs of multiples of 10 with a total of 100 and derive related subtraction facts e.g. 100-10, 100-20, 100-30 … Mental Strategies
Subtract using concrete objects, pictorial representation and mentally including 2 digit and ones. 17 – 7
17 – 9
58 -7 Encourage counting back mentally.
Multiples of ten and ten.
30-10 =
2 digit and tens. 38 – 20 = 56 – 30 =
2 digit and 2 digit. 47 – 23 =
Use of Diennes and Numicon but not bead strings 0-100 complete number lines/tracks.
COUNTING BACK (SEQUENCING): 57 – 20 (by counting back in tens; 47, 37)
WITH JOTTINGS: 57 – 23 (by partitioning the second number and counting back; -20, -3) Begin by not crossing the tens boundary 42 – 17 (by partitioning the second number and counting back; -10, -2, -5) Progress to crossing the tens boundary COUNTING UP: 31 - 28 (by counting up from 28 by bridging the tens boundary; +2, +1)
WITH JOTTINGS: 65 – 47 (by counting up from 47 by bridging the tens boundary; +3, +10, +5) ADJUSTING: 16 – 9 (by subtracting 10 and adding 1)
WITH JOTTINGS: 45 – 19 (by subtracting 20 and adding 1)
USING KNOWN FACTS AND PLACE VALUE: 57 – 4 7 – 4 = 3 so 57 – 4 = 53
Jottings
Continue to use visual images below, even with larger numbers
Subtraction Year 3 Key Vocabulary
Key skills for subtraction at Y3: Subtract mentally a: 3-digit number and ones, 3-digit number and tens, 3-digit number and hundreds . Solve problems, including missing number problems. Find 10 or 100 more or less than a given number. Recognise the place value of each digit in a 3-digit number . Counting up differences as a mental strategy when numbers are close together or near multiples of 10 (see examples above) Read and write numbers up to 1000 in numerals and words. Practise mental subtraction strategies, such as subtracting near multiples of 10 and adjusting (e.g. subtracting 19 or 21), and select most appropriate methods to subtract, explaining why. Understanding the operation
Estimate answers and use inverse operations to check.
Understand that the principles of the commutative and associative laws do not apply to subtraction recognise that 41-35 is different from 35-41 recognise that if calculating 19-6-3 the order matters (we cannot calculate 6-3 first) Number facts (as year 2 images and visuals) Continue to recall and use subtraction facts to 20 fluently, and derive and use related facts beyond 100 e.g. 16 subtract 9, 150 minus 70, the difference between 80 and 170, 30 fewer than 110 Know pairs of two-digit numbers with a total of 100 and derive related subtraction facts e.g. 100-79, 100-43, 100-12 …. 100 – 63 = 100 – 37 =
Mental Strategies Subtract numbers mentally, including: * a three-digit number and ones * a three-digit number and tens * a three-digit number and hundreds
COUNTING BACK (SEQUENCING): 164 – 40 (by counting back in tens; 154, 144, 134, 124) WITH JOTTINGS: 375 – 47 (by partitioning the second number and counting back; -40, -5, -2)
COUNTING UP: 102 – 97 (by counting up from 97, bridging the hundreds boundary; +3, +2) WITH JOTTINGS: 343 – 170 (by counting up from 170, bridging the hundreds boundary; +30, +100, +43)
ADJUSTING: 234 – 99 (by subtracting 100 and adding 1)
WITH JOTTINGS: 387 – 59 (by subtracting 60 and adding 1)
USING KNOWN FACTS AND PLACE VALUE: 268 – 5 8-5=3 so 268-5=263
Written methods
59 – 35 = 24
50 + 9 - 30 + 5 20 + 4
Introduce this method with examples where no exchanging is involved. When learning to exchange, explore partitioning in different ways so that pupils understand that when you exchange, the value is the same i.e. 72 = 70 +2 = 60 + 12 = 50 + 22 etc. Emphasise the value hasn’t changed, we have just partitioned it in a different way.
Introduce exchanging through practical subtraction. Make the larger number with Diennes, then subtract 47 from it.
Once pupils are secure with understanding the exchanging, they can use the partitioned column method to subtract any 2 and 3 digit numbers.
Subtraction Year 4 Key Vocabulary
Key skills for subtraction at Y4: Subtract by counting on where numbers are close together or they are near to multiples of 10, 100 etc. Children select the most appropriate and efficient methods for given subtraction calculations. Solve addition and subtraction 2-step problems, choosing which operations and methods to use and why. Solve simple measure and money problems involving fractions and decimals to two decimal places. Find 1000 more or less than a given number. Count backwards through zero, including negative numbers. Recognise place value of each digit in a 4-digit number Round any number to the nearest 10, 100 or 1000 Solve number and practical problems that involve the above, with increasingly large positive numbers.
Understanding the operation Estimate and use inverse operations to check answers. Continue to understand that the principles of the commutative and associative laws do not apply to subtraction recognise that 92-56 is different from 56-92 recognise that if calculating 73-27-8 the order matters (we cannot calculate 27-8 first) Number facts
Continue to use knowledge of subtraction facts and place value to derive related facts e.g. 8000 subtract 3000, 1700 minus 800, the difference between 700 and 1400, 300 fewer than 1200 Know complements to the next multiple of 100 e.g. 367 + ☐ = 400
Mental Strategies
739 + ☐ = 800
Continue to practise mental methods of subtraction with increasingly large numbers
COUNTING BACK (SEQUENCING): 564 – 150 (by partitioning the second number and counting back; -100, -50)
WITH JOTTINGS: 732 – 137 (by partitioning the second number and counting back; -100, -32, -5)
COUNTING UP: 607 – 288 (by counting up from 288, bridging the hundreds boundary; +12, +7)
WITH JOTTINGS: 6070 – 4987 (by counting up from 4987, bridging the thousands boundary; +13, +1070)
ADJUSTING: 1487 – 199 (by subtracting 200 and adding 1)
WITH JOTTINGS: 442 – 79 (by subtracting 80 (-40, -40) and adding 1)
USING KNOWN FACTS AND PLACE VALUE: 7000-600 1000-600=400 so 7000-600=6400
Written methods
Partitioned column subtraction with exchanging (decomposition). As introduced in Year 3 but moving towards more complex numbers and values. Use place value counters or Diennes.
Partitioned column method, with up to 1 d.p.
78.4 – 26.7 = 51.7 70 + 78 + 10.4 - 20 + 6 + 0.7 50 + 1 + 0.7
Beginning to introduce compact method, alongside the partitioned column method.
Subtraction Year 5 Key vocabulary
Key skills for subtraction at Y5:
Subtract numbers mentally with increasingly large numbers. Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use and why. Read, write, order and compare numbers to at least 1 million and determine the value of each digit. Count forwards or backwards in steps of powers of 10 for any given number up to 1 million. Interpret negative numbers in context, counting forwards and backwards with positive and negative integers through 0. Round any number up to 1 million to the nearest 10, 100, 1000, 10 000 and 100 000.
Understanding the operation Use rounding and estimation to check answers to calculations and determine, in a range of contexts, levels of accuracy . Number facts Continue to use knowledge of subtraction facts and place value to derive related facts with numbers to one decimal place 1.2 subtract 0.7, 1.8 minus 0.9, the difference between 2 and 1.3, 0.3 fewer than 1.7 Know complements to 1 0.78 + ☐ = 1
0.52 + ☐ = 1
Recall pairs of three-digit numbers with a total of 1000 and derive related subtraction facts 1000-453, 1000-239, 1000-712 …
Mental Strategies Subtract numbers mentally with increasingly large numbers Subtract tenths, and one-digit whole numbers and tenths
COUNTING BACK (SEQUENCING): 4.7 – 1.5 (by partitioning the second number and counting back; -1, -0.5) WITH JOTTINGS: 19.2 – 2.7 (by partitioning the second number and counting back; -2, -0.2, -0.5) COUNTING UP: 7.2 – 6.8 (by counting up from 6.8 by bridging the units boundary; +0.2, +0.2) WITH JOTTINGS: 8.3 – 4.8 (by counting up from 4.8 by bridging the units boundary; +0.2, +3.3) ADJUSTING: 8.3 – 1.9 (by subtracting 2 and adding 0.1)
WITH JOTTINGS: 12.6 – 3.9 (by subtracting 4 and adding 0.1) USING KNOWN FACTS AND PLACE VALUE: 15 – 0.3 1-0.3=0.7 so 15-0.3=14.7
Written methods
Subtract with up to 4 digit numbers and decimals up to 2 d.p. Children who are still not secure with number facts and place value will need to remain on the partitioned column method until ready for the compact method. Remind children at 5 digit to use a comma to separate the thousands.
336.54 – 122.61 = 214.2 300 + 30 + 56 + - 100 + 20 + 2 + 200 + 10 + 3 + = 213 + = 214.2
1
0.5 + 0.04 0.6 + 0.01 0.9 + 0.03 1.2 (mental calculation across units boundary)
Subtraction Year 6 Key Vocabulary
Key skills for subtraction at Y6:
Solve addition and subtraction multi-step problems in context, deciding which operations and methods to use and why. Read, write, order and compare numbers up to 10 million and determine the value of each digit Round any whole number to a required degree of accuracy Use negative numbers in context, and calculate intervals across zero. Children need to utilise and consider a range of mental subtraction strategies, jottings and written methods before choosing how to calculate.
Understanding operation Use their knowledge of the order of operations Understand that when there are no brackets in an expression, do multiplication or division before addition or subtraction Understand that if the operations are at the same level of priority, work out the example from left to right Number facts Continue to use knowledge of subtraction facts and place value to derive related facts with numbers to two decimal places 3.09 subtract 0.04, 0.16 minus 0.08, the difference between 0.2 and 0.12, 0.06 fewer than 0-19 Know complements to the next whole number 4.83 + ☐ = 5
7.125 + ☐ = 8
Mental Strategies Perform mental calculations, including with mixed operations, large numbers and decimals Calculate intervals across zero e.g. The drop in temperature from +5 to -3 (use negative number line to show visually)
COUNTING BACK (SEQUENCING): 7.87 – 2.03 (by partitioning the second number and counting back; -2, -0.03) WITH JOTTINGS: 16.3 – 3.55 (by partitioning the second number and counting back; -3, -0.3, 0.25)
COUNTING UP: 6.14 – 5.76 (by counting up from 5.76 by bridging the units boundary; +0.24, +0.14) WITH JOTTINGS: 8.3 – 4.54 (by counting up from 4.54 by bridging the units boundary; +0.46, +3.3) ADJUSTING: 7.65 – 0.99 (by subtracting 1 and adding 0.01) WITH JOTTINGS: 15.4 – 3.09 (by subtracting 3.1 and adding 0.01)
USING KNOWN FACTS AND PLACE VALUE: 1.63 – 0.8 16-8=8 so 1.63-0.8=0.83
Written methods With increasingly large and complex numbers and decimal values. Pupils should be able to apply their knowledge of a range of mental strategies, mental recall strategies and informal and formal written methods when selecting the most appropriate method to work out subtraction problems.