Supporting Your Child at
KS3
Maths
Arithmetic – Addition
Skill Mental Addition
Method Calculation Strategy 14 + 6 Counting On… 14,15,16,17,18,19,20
Informal Method
24 + 32
Formal Method
46 + 58
Partition Method… 20 + 30 = 50 4+2=6 50 + 6 +
46 28 74 1
16 + 23
47 + 29
Practice and Fluency 26 + 52
Stretch and Challenge Fill in the missing digits to make the addition correct
6 4 + 2 6 7 5
Hint Use fingers to count forward, or count on six in your head Partition calculations: adding ten together, then units. Start at the right most column, adding units together. Don’t forget to carry when the total for a column is bigger than 9
183 + 57
Arithmetic – Subtraction
Skill Mental Subtraction Informal Method
Method Calculation Strategy 22 - 5 Counting back… 22, 21, 20, 19, 18, 17 55 - 24 54
= 31
24
Formal Method
245 - 127
3 1
-
15 - 9
55
245 127 118
Practice and Fluency 73 - 49 153 - 86
Hint Use fingers to count backwards, or count back five numbers in your head If you find subtraction difficult, just turn it into an addition. Just ask yourself how much you must add to the second number to reach the first. Start at the right most column, subtracting units. Don’t forget to borrow from the next column when the digit underneath is bigger than the digit above it.
253 - 159
Stretch and Challenge Susan wins £5000. She gives £1754 to her brother. £1245 to her sister. She then splits the rest between her two children equally. How much do each of the children get?
Arithmetic – Multiplication
Skill Mental Multiplication Informal Method
Formal Method
Method Calculation Strategy 8x6 Completing the 8 or 6 times table 8, 16, 24, 32, 40, 48, 7x9 Use 10 times or 5 times and work backwards or forwards from there: 7 x 10 = 70, 7 x 9 = 63 5 x 9 = 45, 6 x 9 = 54, 7 x 9 = 63 42 x 68 42 x 68 336 2520 2856 2 8 16
40 x 8 320
2 x 60 120
40 x 60 2400
x
8x6
12 x 15
Hint Learning your times tables will help with these calculations Always remember that a number multiplied by 10 has a 0 at the end. 5 times a number is half of 10 times the number This method is called column multiplication. The calculation is split up into more manageable pieces. Here 8 is multiplied by 16 2 and then 40. Then + 320 60 is multiplied by 2 336 and 40. The results of these 120 are then added + 2400 together to get the 2520 final answer.
Practice and Fluency 22 x 37
Stretch and Challenge
102 x 413
Alice is organising a concert. In the concert hall there are 32 rows of seats. Each row has 89 seats. All of the seats are taken. She sells the tickets for ÂŁ21. How much money does she make?
Arithmetic – Division
Skill Mental Division
Calculation 72 ÷ 8
Formal Method
2115 ÷ 9
Formal Method
142 ÷ 4
72 ÷ 6
120 ÷ 15
5
What is as a decimal? 8
Method Strategy Hint Reverse the calculation Learning your times 8 x ? = 72 8 x 9 = 72 tables will help with these calculations 9 goes into 2 zero times 9 2115 and leaves a remainder of 2. Write 0 on top of your 0235 bus stop and carry the 2 3 4 9 2115 remainder over. Now divide 21 by 9. Continue this until your division is complete. Remember to carry over the remainders. 0 3 5remainder2 When we complete a 1 2 4 1 4 2 bus stop division that has a remainder we need to work out the 0 3 5.5 actual answer. 1 2 2 4 1 4 2.0 Add a decimal place and 0’s to your original number until you have a whole number Practice and Fluency 2936 ÷ 8
Stretch and Challenge
1957 ÷ 5
Fractions
Skill Fractions of amounts
Simplifying fractions
Calculation 5 Find of 24 6
Simplify
12 36
Method Strategy
A division followed by a multiplication
If you have to draw the situation that’s fine.
Firstly, divide 24 into 6 parts. To fine one sixth. (24 ÷ 6 = 4) The question has for 5 sixths. So we multiply 1 sixth (4) by 5. (4 x 5 = 20)
Draw a bar that weighs 24kg. Chop it into 6 bars, each weighing 4kg. Choose 5 of the parts, totalling 20kg.
Find a common factor of 12 and 36 and divide the bottom and top by it.
The quickest way to fully simplify a fraction is to divide the numerator and denominator by the highest common factor (the highest number that foes into both numbers)
Keep going until there are no more common factors. ÷2 = ÷6 =
2
Find of 18 3
Hint
6
18 1 3
Practice and Fluency 3 8 Find of 54 Simplify 9
24
Simplify
Stretch and Challenge 3 Alex has £48. He gives Beth of his money. 8
How much money does Alex give Beth? What is Beth’s amount of money as a fraction in its simplest form?
15 36
Decimals
Skill Ordering Decimals
Method Strategy
Calculation
Order the Make the number of following from decimals places equal and smallest to biggest place vertically. 0.3, 0.23. 0.38, 0.300 0.48, 0.122 0.230 0.480 0.122 Then compare to put in order of size:
Add/Subtract 23.56 + 3.8 Decimals
0.122, 0.23, 0.3, 0.38. 0.48
23.56 + 3.80 27.36
14.98 - 3.12 11.86
Practice and Fluency
Order the following Order the following from small to big from small to big 0.4, 0.7, 0.2, 0.41
0.4, 0.7, 0.2, 0.41
Hint
Look for the number with the most decimal places. Here it is 0.122 with 3 decimal places. Make all the decimals have this amount of places. Finally, just treat the places after the decimal point as ‘normal’ numbers. e.g. 122, 230, 300, 380, 480 Make all the numbers have the same amount of decimals places by adding zeros. Then use the formal column method. Remember to line up the decimal points
Add the following;
Subtract the following;
23.7 + 45.9
29.4 – 15.9
Stretch and Challenge
Chloe has a ribbon 8 metres long. She cuts two pieces from the ribbon. The first piece was 1.28 metres long. The second piece was 0.65 metres long. How much ribbon is left?
2 STAR PROBLEM
1 STAR PROBLEM
Are you up for the challenge?
4 STAR PROBLEM
3 STAR PROBLEM
Support Materials In addition to the help and support found in this booklet, a range of online education platforms are used within the SDCC Mathematics department to support with your child’s learning. Many of these are interactive and students’ results are recorded directly after the completion of assignments or revision. The primary one used for intervention support, independent practise and homework is:
Hegarty - www.hegartymaths.com
Unique ID’s will be set-up in September
The following websites are recommended for the quality of their explanations, resources and accessibility. These websites can be accessed from today and may help over the summer. BBC Bitesize - www.bbc.co.uk/education Corbett Maths - www.corbettmaths.com
Any questions or concerns, feel free to contact; mhussey@sdcc.net - Mr M Hussey, Curriculum Manager Mathematics ddyer@sdcc.net - Mrs Dyer, MAT transition leader for Mathematics