Welcome to our Maths Workshop

To encourage and support our children to reach their full potential. To follow current National Curriculum objectives. To provide opportunities to challenge all our children. To provide reasoning & problem solving opportunities. Regular times table practice. Aims

What do we want our children to learn by the end of primary school?

Why are some of our children stuck? Poor understanding of place value Reliance on naïve counting strategies (fingers & noses) Limited understanding of structures and relationships between numbers Limited mathematical vocabulary and use of mathematical language Not seeing themselves as mathematicians

Mental Maths An expectation now that all children now times tables up to 12x 12 by the end of year 4. Regular practice of times tables & associated division facts, outside the maths lesson. Times table rock stars Regular opportunities to count.

How do we teach Maths at Gledhow Primary School?

Early Bird Maths in Years 1 -6 To ensure fluency 20 minutes every morning. 100 minutes extra a week. An extra 65 hours of Maths a year.

Concrete The use of real objects for mathematical representation.

Pictorial (Iconic) The use of pictures or equipment to represent real objects.

Abstract Mathematical concepts represented in an abstract way without the use of equipment

What does = mean?

Where do you see your word in everyday life? Mathematical symbol Describe what your word means. Other (mathematical) words related to your word Use your word in a statement Picture or diagram

“If in doubt use a number line!” All 4 operations can be carried out on a number line

Addition Using a number line In jumps of 1, put the biggest number first then count on. 7+4 =

Refine to partitioning the second number only. Add the ‘ones’ first then the ‘tens’ Moving on to an open number line. Add the ‘ones’ first then the ‘tens’:

Subtraction Finding the difference – ‘counting on’ children should be encouraged to add on when the 2 numbers are close together eg. 396 – 387= Number line underneath for subtraction 11 – 7=

Subtracting two numbers with a larger difference. Subtract using a number line, drawing the lines underneath. Subtract the ‘ones’ first.

Moving onto using an open number line:

Multiplication Arrays and repeated addition     4 x 2 or 4 + 4     2 x 4 or repeated addition 2 + 2 + 2 + 2

6 x 3= 16 x 3= 10 x 3 6 x 3 30 48

Division Grouping – There are 6 sweets. How many people can have 2 each? (How many 2’s make 6? Count in 2s)

Understand division as sharing and grouping 18 ÷ 3 can be modelled as: Sharing – 18 shared between 3 Grouping - How many 3’s make 18?

Sharing - 16 shared between 3, how many left over? Remainders 16 ÷ 3 = Sharing - 16 shared between 3, how many left over? Grouping – How many 3’s make 16, how many left over? e.g. 16 ÷ 3 = 5 r1

Sharing and grouping 30 ÷ 6 can be modelled as: grouping – counting in multiples of 6:

41÷ 4 = 10 r1 10 x 4 r 1 40

Time problems 13 c Number lines are excellent for time problems Eg. The bus leaves at 8:48 am and arrives at 1:12pm. How long is the journey? Negative number problems Eg. What is the difference in temperature between -6 c and 13 c? - 6 c 0 c 13 c

Moving on from the number line Expanded Method 358 + 73 = 431 “358 + 73 is approximately 350 +70 = 420” Partition the numbers to add: 300 + 50 + 8 + 70 + 3 300 +120 +11 = 431

Moving towards:   324 + 65 = 324 + 65 9 80 300 389

Formal written Method Estimate and check 2789 + 1642 4431 1 1 1 The children are to check their answer using the inverse operation.

Extend to numbers with any number of digits and decimals with 1 and 2 decimal places. 124.9 + 117.25 = 242.15 124.90 add in a zero to keep the place value + 117.25 242.15 11

Expanded Method for subtraction Not bridging 10 198 - 124 = 100 + 90 + 8 100 + 20 + 4 70 + 4 = 74  

Bridging 10 191 – 136 = 80 100 + 90+ 11 100 + 30 + 6 50 + 5

Formal written method for subtraction 8 1

Estimate and check Children are taught to estimate their answer first: 3352 – 2178 = “3352 – 2178 is approximately 3300 - 2000 = 1300”iis 3352 – 2178 is approximately 3300 – 2200 = 1100 Use decomposition 2 14 1 3 3 5 2 2 1 7 8 1 1 7 4

34590 – 1247.5 = - 3 4 5 9. 0 1 2 4 7. 5 2 2 1 1. 5 add in a zero to keep the place value

Grid Method **Remember to add the numbers inside 35 x 2 = 70 Partition **Remember to add the numbers inside the grid ie: 60 + 10 = 70

Add the numbers inside the grid 500 150 + 20 670

2660 then add the two numbers + 76 together to find 2736 answer. 1 2660 76 2660 then add the two numbers + 76 together to find 2736 answer. 1

Formal Method (short multiplication) 125 X 7 1 3 875

Formal Method (long multiplication) 1 2 5 X 1 7 1 3 8 7 5 12 5 0 1 21 2 5

Multiplication with decimals When multiplying a decimal the children should first multiply the decimal number by 10, 100 or 1000 to make it a whole number

eg Because the decimal number was multiplied by 10, the final answer should be divided by 10.

2 3 7 - 1 8 0 ( 20 x 9) 57 - 54 ( 6 x 9) 3 Answer: 26 r 3 Chunking 237 -:- 9= 1 1 2 3 7 - 1 8 0 ( 20 x 9) 57 - 54 ( 6 x 9) 3 Answer: 26 r 3

Bus stop / Formal Method using place value counters

Formal method (bus stop) Short division 3 2 8 3 4 5

Formal method (bus stop) long division 36 72 97 257 108 - 72 - 252 144 25 5 180 216 252   jottings can be written to the side/underneath Quotients expressed as fractions or decimal fractions 977 ÷ 36 = 27 5/36 or 27.14

31 159 62 - 155 jottings 93 4 124 155

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