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1 Addition Vocabulary NB:H=hundreds/T=Tens/O=ones number bonds, number line, add, more, plus, make, sum, total, altogether, double, how many more?, column addition, partition, counting on, efficient method, order of operations, increase Objective and Strategies Concrete Pictorial Abstract Introduction of the = sign/develop understanding of equals. Introduce the = sign and start with examples like 5 = 5 using different objects. Use a balance to illustrate. Use the = sign in different places in pictorial problems sometimes have the total box at the beginning. For example, draw how many more you need to make the sets equal. = Use the = sign in different places For example 3 = = 3 throughout EY-KS1 and KS2. - missing number problems are introduced in Year 1. For example, 3 +? = 5 Combining two or more parts to make a whole. Horizontal recording of an addition calculation. Use different objects toys/cubes/stones/shells etc. to combine two or more groups and develop the language of addition e.g. how many more? / How many altogether? / What is my total? Place the = sign in different places. Word problems e.g. You have five apples and I have three apples. How many apples altogether? Word problems e.g. You have five apples and I have three apples. How many apples altogether? Introduce the symbols = start to relate to the calculation Initially, record how many in each set, then complete the calculation. Children/adult draw the apples. Note: children can still draw their own pictures if needed or use fingers but will count all objects. 3+2= Matching games / loop games = 6 and how many 10=5+5 more make 10? Missing number problems 6 + = 10 Children count out 6 cubes how many more do I need to have 10 in total? Draw 6 circles how many more do I need to make 10? Missing number problems solved using fingers. 1

2 Partitioning a whole into 2 parts/ number bonds. Looking at patterns, for example, using Multilink /Numicon Looking at patterns colouring combinations Mental recall of number bonds. Manipulating number bonds e.g. if I know = 7, I must know that = 7, Also 7-4 = 3 and 7 3 = 4 Fact families. 8 1 Writing all the number bonds systematically. Interactive games. Counting on from the bigger number in ones. Horizontal recording of an addition calculation To bridge from counting on, use concrete objects on a number line. Alternatively, use a bead string. Missing number problems Rapid mental recall of one more than. Mentally counting on to find the total = 9 in head count on as child holds up finger -10, 11, 12, 13, 14, 15 Using mental skills to aid solving horizontal addition calculations. For example: Use concrete objects to find the total of three single digit numbers. Use knowledge of number bonds to find patterns. For example: Add together three groups of objects. Draw a picture to recombine the groups to make 10. Adding 3 single digit numbers by looking for = 17 Put 4 and 6 Add together three numbers, using knowledge of number

3 number bonds. Regrouping. together to make 10. Add on = Start with the bigger number and use the smaller number to make 10. In Year 2 introduce missing numbers. For example: = 100, 7 + 4= 11 If I am at seven, how many more do I need to make 10? How many more do I add on now? Adjusting Use multilink/bundles of straws/base 10 that breaks up to add a near multiple of ten. Physically adjust by adding or subtracting one. Add 9 or 11 by adding 10 and adjusting by 1. Using a number line or 100 square. Solve mentally. Add a 2 or 3 digit number using a number line and partitioning. Horizontal recording of an addition calculation. Use bead strings to show the groups of ten and ones = = = 57 Initially use a numbered number line to add on in steps of tens and ones, or hundreds, tens and ones. Then progress to using blank number lines. Jumping on in steps mentally = Well I know 34 plus 3 is 37 and 37 plus 20 is 57. This can also be used for money and time. Introduce the column method by partitioning into tens and ones and recombine = Moving to: Draw base 10 / place value coins For example: Progress to the written method. For example, = 89 Add together the ones first, and then add the tens. Use bundles of objects

4 e.g. straws, then progress to Base 10 blocks before moving onto place value counters = TO + O = TO + TO = HTO + HTO = Column method with regrouping. Physically make both numbers on a place value grid using objects. Children can draw a pictoral representation of the columns and place value counters to further support their learning and understanding. Start by partitioning the numbers before moving on to clearly show the exchange below the addition. Add up the ones and exchange 10 ones for one 10. 2,634 +4,517 Add up the rest of the columns, exchanging the 10 counters from one column for the next place value column until every column has been added. This can also be done with Base 10 to help children clearly see that 10 ones equal 1 ten and 10 tens equal 100. As children move on to decimals, money and decimal place value As the children move on, introduce decimals with the same and different number of decimal places. Money can be used here Note: In written column addition, leave a space for carrying numbers to the next column. Numbers are carried above and crossed out when added. 4

5 Subtraction Vocabulary NB:H=hundreds/T=Tens/O=ones Subtract, subtraction, take-away, less than, less, minus, how many fewer? Count back, Half, find the difference, column method, efficient method, order of operations. Objective and Strategies Concrete Pictorial Abstract Introduction of the = sign Introduce the = sign and start with Use the = sign in different places in pictorial Use the = sign in different places /develop understanding of equals. examples like 5 = 5 using different objects. problems sometimes have the total box at the beginning. 3 2 = 1 1 = 3-2 Draw how many more you need to make the sets Include missing number questions. equal Taking away ones. - Horizontal recording of a subtraction calculation. Use a balance to illustrate. Use physical objects, counters, cubes etc. to show how objects can be taken away. Cross out drawn objects to show what has been taken away. Write a number sentence to record the calculation = = = 2 Songs using concrete objects/children Counting back from a given number in ones. - Horizontal recording of a subtraction calculation. Start with 1 less. Use a number line to match the objects to the numbers. 5 3 = Lay out 5 cubes on a number line and take away 2. Use bead strings / multilink to physically move back. Use a number line to count back in ones. Not bridging 10 then bridging = 9 Mentally count back in ones from a given number. 8 3 = 8, 7, 6, (use fingers to illustrate the 3) I am left with 5 5

6 Use number bonds (also known as fact families) to develop children s understanding of the relationship between addition and subtraction. other part? Use multilink to explore number bonds. If 10 is the whole, and 6 is one of the parts. What is the Use pictorial representation to show the relationship between number bonds. Write down fact families using 3 numbers If I know 9 2 = 7 Then 9 7 = = = = Use picture cards to help create the fact families. Find the difference. Horizontal recording of a subtraction calculation. Compare amounts and objects to find the difference. Count on to find the difference. For example, find the difference between 11 and 5 using a number line. Solve word problems involving finding the difference. For example: Hannah has 23 sandwiches, Helen has 19 sandwiches. Find the difference between the number of sandwiches. Use cubes to build towers or make bars to find the difference. Use basic bar models with objects to find the difference. Draw bars to find the difference between 2 numbers. 19 in head count up to 23 (may use fingers to help find the difference.) 20,21,22,23 The difference is 4. If I spend 13p and give the shop keeper 20p, how much change will I have? 6

7 Counting back in steps of ones and tens. - Horizontal recording of a subtraction calculation. Use multilink, Base 10, bundles of objects, etc. to subtract a two digit number from another number. Subtract on a number line by counting back in ones and tens. For example, = 34 Mentally count back in ones and multiples of tens to subtract a two digit number. Could use a 100 square for Support = I know 57-3= =34 Take the ones away first then the tens. Use partitioning to subtract two or three digit numbers. This will move onto column subtraction method without exchanging. Column method. Use concrete objects as bundles to subtract groups of hundreds / tens / ones. Drawing base 10/place value coins to help them move from the concrete to the abstract. Write number sentences to show the partitioning of numbers. For example: TO - O TO - TO HTO - TO HTO HTO ETC = 23 Mentally use the following method, which subtracts the ones then the tens children physically take away the ones then the tens

8 Column subtraction method with exchanging. Use of counters may still be used with a place value chart. Always start by subtracting the ones. Draw a place value chart and draw representations of counters. Always start by subtracting the ones. Extend larger numbers and decimals = 1552 Extend larger numbers and decimals. 8

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