Download Skills we will review - Hambridge Primary School

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
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, 0.125 (1/2, 1/4, 1/8)
Place value headings:
10,000
1,000
100
10
1
.
1/10
1/100
1/1000
1/10,000
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
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
Roman numerals. Use language you know
I
V
X
L
C
D
M
1
5
10
50
100
500
1000
(how will you remember this 50 lovely lollies?)
(centigrade, centurion, century, centimetre)
(shape works for 5, how remember 500)
(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
Divisibility rules
2 – number is even
4 – number is even after it’s been
halved
5- ends in 5, 0
10 - ends in 0
3 – digits add to 3 (or in no in 3 x
table) 54231 = 15 = 3
6 – 3x divisibility rule and even
3426
9 – digits add to no in 9 times
table 2727
11 – digit in middle is sum of digits
outside 352 , 264
Factors / Primes
Factors The small it that goes into other
number
Prime Factors
Factor bug
12
1
2
12
6
12
6
2
3
4
Work logically so
you don’t miss any
2
3
So prime factors for 12
are 2 x 2 x 3
Prime numbers
Factor of 1 and itself
ONLY
Not 1 (only 1 factor)
2 (only even factor)
3
5
7
11
13
17
19
23
29
31
37
31
47
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
Angle facts
Sum of Internal
Triangle 180o
Any quadrilateral 360o
Straight line 180o
Angles around a point (360o)
Angles where 2 lines meet
Angles on parallel lines
Angles in shapes
Exterior
External
Continue straight line from angle
External +internal = 180o
Sum of external always 360o
Interior
Geometry
• Circle parts
• Area of triangle
• Area of parallelogram (base x
HEIGHT)
• Area vs perimeter
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?
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
Find
one
of
Take that
from this
total
= £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?
Sequences
Not always linear
• Look for the pattern
• Square numbers (1,4,9,16)
• Triangle numbers (1,3,6,10)
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
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.
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)
Fractions (picture it!)
Make whole number into fraction . Put it over 1
26
1
26 =
Add
• in English this ‘and’ that
• Make slices same size (same denominator) add how many parts you have
𝟐
𝟐
+5
5
𝟒
=5
Equivalent – cut up slices = more small slices
2 3
𝟖
𝟗
𝟏𝟕
5
+ =
+
=
=1
3 4 12 12 12
12
3
4
= 68
Improper/Top Heavy – cut whole’s into pieces, add to the pieces you already have
1
33
9
1
=3+3 =
10
3
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)
1
2
4
5
4
•
in English ‘lots of’ or ‘of’
•
Multiply numerator, multiply denominator
1
2
x
4
5
1∗4
x
is half of 5 (picture it)
4
= 2∗5 =10
Divide
Dividing fraction smaller than 1 = make bigger)
3 1
÷
4 8
… How many 1/8’s in ¾
Turn over 2nd fraction and multiply
3 1
÷
4 8
=
3 8
x
4 1
=
24
4
=6
Compare fraction/decimal/percent
1
= 0.1
10
2
1
= = 0.2
10 5
Know common fractions as decimals
• ½ = 0.5
(0.500)
• ¼ = 0.25
(0.250)
•
1/8
= 0.125
• ¾ = 0.75
•
1/3
= 0.333
•
2/3
= 0.666
(0.125)
(0.750)
Convert fraction to over 10 (tenths), 100 (100ths etc)
17
68
=
= 0.68 68 100𝑡ℎ𝑠
25 100
Work out % = work out tool kit of:
10%, 5%, 1% build up using these parts
% = multiply decimal by 100 (move decimal 2 places)
37% of 480
10% = 48
5% = 24
1%=4.8
Total = 48 + 48 + 48 + 24 + 4.8 + 4.8
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
1. 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
0002.350.00
3 jumps for 3 0’s in 1000