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**Spaldwick Number strategies**

+ - x ÷ = Spaldwick Number strategies A step by step guide to helping your child with their maths at home by using the same methods taught to them at school.

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**+ + + + + + + Total ADDITION Add Make The sum of… How much more is…?**

How many more make…? Make + +

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**Step 1: Learn numbers up to 10 and 20.**

11 12 1 2 3 4 13 14 5 6 7 8 15 16 17 9 10 18 19 20

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Step 2: Adding up to 20 eg Put the biggest number in your head (7), add on (4) using unifix cubes, your fingers, pictures or any other apparatus.

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**Step 3: Know your number bonds to 10 and 20.**

= 20 = 20 = 20 = 20 = 20 = 20 = 20 = 20 = 20 For example: 1 + 9 = 10 2 + 8 = 10 3 + 7 = 10 4 + 6 = 10 5 + 5 = 10

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**Step 4: Using a number line**

Step 4: Using a number line. From the biggest number ‘add on’ the smallest number in unit steps. Eg = 13 +1 +1 +1 +1 +1 +1 5 7 10 13 15 20

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**Step 5: Number line addition by adding on tens and units.**

Starting with the biggest number in the sum, add on in ‘chunks’ of tens and units. Eg = 55 +10 +10 +1 34 44 54 55

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**Step 6: Partitioning. Split the numbers up into tens (T) and units (U)**

Step 6: Partitioning. Split the numbers up into tens (T) and units (U). This is the first step to using column addition. For example: = = 70 = 11 = 81 81

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Step 7: Column Addition For example: = 62 T U 3 5 2 7 6 2 1 This method then expands to more complex sums such as those involving hundreds (H) and thousands (TH) or decimals in tenths (t) and hundredths (h). The ‘1’ in 12 has a value of ten so is carried over to the tens column to be added at the end.

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**- - - - - - - leave SUBTRACTION minus Take away How much fewer?**

How many less is… than…? How many are left over? - Find the difference between… How much fewer? - -

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**Step 1: Learn numbers up to 10 and 20.**

11 12 1 2 3 4 13 14 5 6 7 8 15 16 17 9 10 18 19 20

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**Step 2: Subtraction by drawing pictures, using apparatus or using fingers.**

Eg – 5 = 3

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**Step 3: Subtraction using a number line.**

Put the biggest number on the right and subtract in single unit steps. If understand number bonds, jump to the nearest ten. Eg. 14 – 8 = 6 -1 -1 -1 -1 -1 -1 -1 -1 6 14

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**Step 4: Subtracting TU and TU on a number line.**

Using a number line put large number on the right then partition second number and jump back that number of steps, starting with tens then the units. *Children need experience of oral counting and 100 square knowledge of counting back in tens eg. 91, 81, 71, 61 etc* Eg. 55 – 12 = 43 -10 -1 -1 43 44 45 55

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**Step 5: Finding the difference between two numbers**

Eg

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**Step 6: ‘Finding the difference’ between two numbers on a number line.**

Biggest number on the right, smallest number on the left. Count on from the smallest number to the nearest ten, then add on in tens, then add on the rest of the units. Then count up the ‘jumps’. Eg. 48 – 23 = 25 = 25 + 10 + 8 + 7 23 48

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**Step 6: Column subtraction**

Eg. 47 – 29 = 18 T U 4 7 2 9 1 8 3 1 Sum is ‘exchanged’ so that 47 is turned into because 7 – 9 is not possible.

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**x x x x x x x Groups of MULTIPLICATION times arrays Lots of**

Repeated addition x Multiply by x x Multiple of

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**Step 1: Using apparatus, pictures and toys to put into groups of a number.**

Eg. Sort these people into groups of 3. How many groups are there? How many people are there altogether? 5 groups 15 people altogether

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**Step 2: Repeated addition on a number line.**

Eg. 5 x 3 = 15. Starting from zero, add on 5 lots of 3. + 3 + 3 + 3 + 3 + 3 3 6 9 12 15

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Step 3: As arrays 3 x 5 = 15 5 x 3 = 15

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**Step 4: Learn your times tables up to 10**

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Step 5: Learn that when you x 10, you make all the digits once to the left and have a zero at a ‘place holder’ if needed. You do not just add a zero because once you start multiplying decimals by 10, adding a zero would not make the number ten times bigger. Eg. 32 x 10 = 320 H T U 3 2 H T U . t 3 2 (x 10) (x 10)

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**Step 6: TU x U Grid Multiplication**

Partition (or split up) the two digit number to make the sum more manageable and x by the smallest number. Eg. 45 x 3= 225 x 5 40 200 25 5 If your child knows that 4 x 5 = 20 then they just need to x the answer by 10 to get 40 x 5. 225

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**Step 7: Standard Short Method**

Eg. 32 x 23 STEP 1: 3 2 x 2 3 Multiply 32 by 3, starting with the units column. 3 x 2 = 6 3 x 30 = 90 9 6

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**Step 7: Standard Short Method continued…**

3 2 x 9 6 Now multiply 20 by 32 20 x 2 = 40 20 x 30 = 600 = 640 STEP 3: 3 2 x 9 6 Finish the sum off by adding the totals together using column addition.

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**x x x x x x x divide DIVISION share Divided by Divided into**

Share equally divide x DIVISION Divided into Equal groups of x x x Divided by

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**Step 1: Sharing out toys, cubes and any other apparatus.**

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**Step 2: Repeated subtraction on a number line.**

15 ÷ 3 = 5 - 3 - 3 - 3 - 3 - 3 3 6 9 12 15

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Step 3: A grouping/sets 15 ÷ 3 = 5

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**Step 4: Recognising division facts as the inverse of multiplication facts (times tables)**

4 x 5 = 20 so ÷ 5 = 4 6 x 7 = 42 so ÷ 7 = 6 8 x 9 = 72 so ÷ 9 = 8

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**Step 5: Extended number line division.**

Eg. 42 ÷ 3 = 14 3 x table facts 1 x 3 = 3 2 x 3 = 6 4 x 3 = 12 10 x 3 = 30 - 30 - 12 10 lots 4 lots 12 42 Count up the ‘lots’ of 3 you have taken away.

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**Step 6: Column Division Eg. 42 ÷ 3 = 14 42 - 30 (10 lots) 12**

3 x table facts 1 x 3 = 3 2 x 3 = 6 4 x 3 = 12 10 x 3 = 30 42 - 30 (10 lots) 12 12 (4 lots)

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**Step 7: Long Division Eg. 345 ÷ 25 STEP 1: 1 5 3 4 5 STEP 2: 2**

15 won’t divide into 3, so look at the next digit and divide 34 by 15. STEP 2: 2 2 x 15 = 30 Write the 2 above the 4. Then take 30 away from 34 to find the remainder.

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**Step 7: Long Division Continued**

2 3 0 4 5 “Bring down” the 5 next to the 4, ready to divide 15 into 45. 3 x 15 = 45 Write the 3 above the 5. There are no more numbers to bring down, so the final answer is 23 STEP 4: 2 3 3 0 4 5

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