1. Skills we will review
Each session will be part taught / part worksheet/past paper
Name of place value Positive/ negative numbers Multiples of 10 calculations = most of them Roman numerals Divisibility rules Factors / Primes Time (24hour, analogue etc) Angle facts Geometry Word problems comparing 2 or more values Calculate one value from others word problems Sequences / Linear sequences / Word problems Explain Fractions Compare Fraction/Decimal/Percent Imperial/Metric

2. Place Value. Important. You know this
Each step left is 10x bigger Right align numbers (they push into the decimal) Comma after every 3 digits from right of decimal 23,000,000 'Fill out' a number with trailing zeros to make easier to compare (then pretend the decimal isn’t there) 0.500, 0.250, (1/2, 1/4, 1/8) Place value headings:
10,000
1,000
100 10
1/10
1/100
1/1000
1/10,000

3. Positive /Negative numbers
Add/Subtract
Start at first number. Move with the next. Signs always belong to the number to the right    -4-5 = (-4) (-5) = -9     (start at –4, take 5 (5 steps left)
Signs don't always predict if answer positive or negative
See Snape powerpoint on school website for reminder
Multiply / divide
Look at sign of both numbers to decide sign of answer:   
+ and +   = +  , - and - = +    same sign = positive answer
+ and - = -  ,    - and + = -     different sign = negative answer

4. Multiples of 10
Many, MANY, calculations are simply times tables with an extra zero £4.80 ÷ 4 (based on 48 ÷ 4) £360 ÷ 12 (based on 36 ÷ 12) Also 14 x 4 …. 7 x 8 18 x 3 …. 9 x 6

5. Roman numerals. Use language you know
I 1 V 5 X 10 L 50 (how will you remember this 50 lovely lollies?) C 100 (centigrade, centurion, century, centimetre) D 500 (shape works for 5, how remember 500) M 1000 (millimetre, millennium)
Numerals are always 1’s, 10’s etc or 5’s Digits should get smaller from left to right MCCXII Up to 3 of one type of digit Eg I, II, III Any smaller put with the number to the right. M C XC IV You can only minus 1 of a type of digit IV

6. Divisibility rules
2 – number is even 4 – number is even after it’s been halved 5- ends in 5, ends in 0
3 – digits add to 3 (or in no in 3 x table) = 15 = 3 6 – 3x divisibility rule and even – digits add to no in 9 times table – digit in middle is sum of digits outside 352 , 264

7. Factors / Primes
Factors The small it that goes into other number Factor bug
Prime numbers Factor of 1 and itself ONLY Not 1 (only 1 factor) 2 (only even factor)
Prime Factors 12 12 1 12 6 2 2 6 3 4 2 3
Work logically so you don’t miss any
So prime factors for 12 are 2 x 2 x 3

8. Time
Analogue PAST all way up to half past then TO Quarter, half, number of minutes Digital Hour:minutes Always from the last hour Always am/pm if not 24 hour
24 hour No two times can be the same Always 2 digits for hours am/pm Midnight is 00:00 1 minute past 00:01 Lunch 12:00 4 o’clock tea 16:00

9. Angle facts
Sum of Internal Triangle 180o Any quadrilateral 360o Straight line 180o External Continue straight line from angle External +internal = 180o Sum of external always 360o
Angles around a point (360o) Angles where 2 lines meet Angles on parallel lines Angles in shapes
Exterior
Interior

10. Geometry Circle parts Area of triangle
Area of parallelogram (base x HEIGHT)
Area vs perimeter

11. Word Problems part 1
Picture the problem – what’s logical (dad weighs more) Draw bars to represent value compared to each other Keep picturing Check plausibility or backstep answer (Math-aids worksheet)
1. Carmen weighs 53kg. Her sister weighs 18kg less.
She said: ‘Together, we weigh 23kg less than our Dad!’
How much does their Dad weigh?
2. Katie picked 632 strawberries. She ate half of them on Monday and half of what was left on Tuesday. How many were left on Wednesday?

12. Word Problems part 2 compare one object to another known
You are given 2 number facts. One is for many of 1 object, one is for (some of) that object and another Work out value of single type of object, put into sum of mixed price. = £4.80 = £2.40
1. Carmen weighs 53kg. Her sister weighs 18kg less.
She said: ‘Together, we weigh 23kg less than our Dad!’
How much does their Dad weigh?
2. Katie picked 632 strawberries. She ate half of them on Monday and half of what was left on Tuesday. How many were left on Wednesday?
Find one of
Take that from this total

13. The nth position is (3x the position) +1
Sequences
Linear
4, 7, 10, 13
Look for the difference (3)
Look how it’s shifted from 1x the difference: 1 x 3 = 3, so we had to add 1 extra
So for this sequence:
Tn = 3n + 1
The nth position is (3x the position) +1
The 100th number
T100 = (3 x 100) + 1
T100=301
Not always linear
Look for the pattern
Square numbers (1,4,9,16)
Triangle numbers (1,3,6,10)

14. Explain
When you are asked to explain give number examples of why something must / must not be true.
Easier if proving false – show one example where it breaks the rule.

15. Sequence /Linear equation Word Problems
Always does something many times then adds/subtracts amount
Often buying tickets/work paid for/ products made
Tickets for boat trip
Window cleaning
Cakes made
Look for discounts or something you need to buy one of (a box, insurance etc)

16. Fractions (picture it!)
Make whole number into fraction . Put it over 1
26 =
Equivalent – cut up slices = more small slices
3 4 = 6 8
Improper/Top Heavy – cut whole’s into pieces, add to the pieces you already have
= = 10 3
Add
in English this ‘and’ that
Make slices same size (same denominator) add how many parts you have
𝟐 5 + 𝟐 5 = 𝟒 5
= 𝟖 12 + 𝟗 12 = 𝟏𝟕 12 =1 5 12
Subtract (you may need to turn whole numbers into fractions)
Multiply
Multiply fractions smaller than 1 = make smaller (a small part of a small thing)
in English ‘lots of’ or ‘of’ x is half of 4 5 (picture it)
Multiply numerator, multiply denominator
1 2 x = 1∗4 2∗5 = 4 10
Divide
Dividing fraction smaller than 1 = make bigger)
3 4 ÷ … How many 1/8’s in ¾
Turn over 2nd fraction and multiply
3 4 ÷ = x = = 6

17. Compare fraction/decimal/percent
1 10 = = 1 5 =0.2 Convert fraction to over 10 (tenths), 100 (100ths etc) = = 𝑡ℎ𝑠 Work out % = work out tool kit of: 10%, 5%, 1% build up using these parts 37% of % = 48 5% = 24 1%=4.8 Total =
Know common fractions as decimals
½ = (0.500)
¼ = (0.250)
1/8 = (0.125)
¾ = (0.750)
1/3 = 0.333
2/3 = 0.666
% = multiply decimal by 100 (move decimal 2 places)

18. Convert. Picture the amounts
Convert. Picture the amounts. Metric = measurements with 100, 1000s (kilo, centi, litre) Imperial = measurements with really odd amounts (5280 feet in a mile!)
Metric to imperial Learn these. (It’s the most boring bit, but you need them) Lengths Inch ≈ 2.5 cm Foot = 12 inches Yard = 3 feet Mile ≈ 1.6 km Weight Pound (lb) ≈ 0.45 kg Pound (lb) = 16 ounces (oz) Stone = 14 pounds (lb) Liquid /Volume Pint ≈ 0.56 litres
Metric
Tell yourself
Will there be more or few when I’ve converted
(2.35km to meters) = more
2. What multiple? There are 1000 meters in a km
3. Write number with extra zeros…’bounce’ right number of places
3 jumps for 3 0’s in 1000