Start with the bigger number and use the smaller number to make 10. Adding three single digits 4 + 7 + 6= 17 Put 4 and 6 together to make 10. Add on 7. Following on from making 10, make 10 with 2 of the digits (if possible) then add on the third digit. Combine the two numbers that make 10 and then add on the remainder. Column method- no regrouping 24 + 15= Add together the ones first then add the tens. Use the Base 10 blocks first before moving onto place value counters. After practically using the base 10 blocks and place value counters, children can draw the counters to help them to solve additions. T O Column method- regrouping Make both numbers on a place value grid. Add up the units and exchange 10 ones for one 10. 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. 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. As the children move on, introduce decimals with the same number of decimal places and different. Money can be used here.
As children move on to decimals, money and decimal place value counters can be used to support learning. Subtraction Objective and Strategies Concrete Pictorial Abstract Taking away ones Use physical objects, counters, cubes etc to show how objects can be taken away. 6 – 2 = 4 Cross out drawn objects to show what has been taken away. 18 -3= 15 8 – 2 = 6 Counting back Make the larger number in your subtraction. Move the beads along your bead string as you count backwards in ones. 13 – 4 Use counters and move them away from the group as you take them away counting backwards as you go. Count back on a number line or number track Start at the bigger number and count back the smaller number showing the jumps on the number line. This can progress all the way to counting back using two 2 digit numbers. Put 13 in your head, count back 4. What number are you at? Use your fingers to help.
Column method without regrouping Use Base 10 to make the bigger number then take the smaller number away. Show how you partition numbers to subtract. Again make the larger number first. Draw the Base 10 or place value counters alongside the written calculation to help to show working. This will lead to a clear written column subtraction. Column method with regrouping Use Base 10 to start with before moving on to place value counters. Start with one exchange before moving onto subtractions with 2 exchanges. Make the larger number with the place value counters Start with the ones, can I take away 8 from 4 easily? I need to exchange one of my tens for ten ones. Now I can subtract my ones. Now look at the tens, can I take away 8 tens easily? I need to exchange one hundred for ten tens. Now I can take away eight tens and complete my subtraction Show children how the concrete method links to the written method alongside your working. Cross out the numbers when exchanging and show where we write our new amount. Draw the counters onto a place value grid and show what you have taken away by crossing the counters out as well as clearly showing the exchanges you make. When confident, children can find their own way to record the exchange/regrouping. Just writing the numbers as shown here shows that the child understands the method and knows when to exchange/regroup. Children can start their formal written method by partitioning the number into clear place value columns. Moving forward the children use a more compact method. This will lead to an understanding of subtracting any number including decimals.
Multiplication Objective and Strategies Concrete Pictorial Abstract Doubling Use practical activities to show how to double a number. Draw pictures to show how to double a number. Partition a number and then double each part before recombining it back together. Counting in multiples Count in multiples supported by concrete objects in equal groups. Use a number line or pictures to continue support in counting in multiples. Count in multiples of a number aloud. Write sequences with multiples of numbers. 2, 4, 6, 8, 10 5, 10, 15, 20, 25 , 30
Division as grouping Divide quantities into equal groups. Use cubes, counters, objects or place value counters to aid understanding. Use a number line to show jumps in groups. The number of jumps equals the number of groups. Think of the bar as a whole. Split it into the number of groups you are dividing by and work out how many would be within each group. 28 ÷ 7 = 4 Divide 28 into 7 groups. How many are in each group? Division within arrays Link division to multiplication by creating an array and thinking about the number sentences that can be created. Eg 15 ÷ 3 = 5 5 x 3 = 15 15 ÷ 5 = 3 3 x 5 = 15 Draw an array and use lines to split the array into groups to make multiplication and division sentences. Find the inverse of multiplication and division sentences by creating four linking number sentences. 7 x 4 = 28 4 x 7 = 28 28 ÷ 7 = 4 28 ÷ 4 = 7 Division with a remainder 14 ÷ 3 = Divide objects between groups and see how much is left over Jump forward in equal jumps on a number line then see how many more you need to jump to find a remainder. Draw dots and group them to divide an amount and clearly show a remainder. Complete written divisions and show the remainder using r.