Download Numeracy Booklet[1]

[1]
Estimation & Measurement
MNU112M, MNU113M, MNU217M, MNU218M, MNU219M, MNU315M
[2]
Rounding
MNU301A
[3]
Addition, Subtraction, Multiplication & Division
MNU103C, MNU203C, MNU303C, MTH403C, MTH205C
[4]
Scientific Notation / Standard Form
MTH405G
[5]
Fractions
MNU105H, MNU208H, MNU308H, MTH309H, MTH310H, MTH407H
[6]
Percentages
MNU208H, MNU308H, MNU406H, MNU209H
[7]
Proportion
MNU311J, MNU408J
[8]
Time
MNU214L, MNU216L, MNU314L, MNU413L
[9]
Algebraic Expressions, Equations & Formulae
MTH222R, MTH320R, MTH321R
[10] Co-ordinates
MNU206D, MTH230U, MTH429U, MTH430U
[11] Data & Analysis
MNU124W, MNU232W, MNU233W, MNU325W, MNU432W
[1] Estimation and Measurement

Estimate / measure height and length in mm, cm, m
and angle sizes in degrees
eg

Estimate / measure weight in g and kg, area in cm2, m2 and hectares
and volume / capacity in cm3, m3, ml and l
eg

length of pencil ≈ 10cm
width of desk ≈ 0.5m
diameter of 1p coin ≈ 15mm
bag of sugar ≈ 1kg
area of window ≈ 4m2
volume of drinks can ≈ 300ml
Learn equivalences
10mm
1000mm
1cm3
1000cm3
10000m2
=
=
=
=
=
1cm
100cm
1ml
1000ml
1 hectare
=
1m
=
1l
MNU112M, MNU113M, MNU217M, MNU218M, MNU219M, MNU315M
[2] Rounding

Round to the nearest whole number, 10 or 100
eg

Round to any number of decimal places or significant figures
eg




74 to the nearest 10 ≈ 70
347.5 to the nearest whole number ≈ 348
7.51
≈ 7.5 (1dp)
3.14159 ≈ 3.142 (3dp)
≈ 3.14 (3sp)
0.00231 ≈ 0.002 (1sf)
When the next number is a 5 always round up
Always round your final answer to the same level of accuracy as your starting values
Never round as you go along – just at the end
Watch out for necessary rounding
eg. If 90 children and 4 teachers go on a trip, how many 40-seater coaches would be needed?
94  40 = 2.35 coaches
which has to be rounded up or some people will be left behind !
MNU301A
[3] Addition, Subtraction, Multiplication & Division

Subtract using decomposition (as a written method)
eg
271
- 38
2 33

Do not borrow and pay back

Calculate using alternative mental methods when appropriate
eg
478 – 99
= 379 by subtracting 100 then adding 1
eg
1+2+3+ ………+8+9+10
= 11 x 5
= 55

Use correct order of operations

Remember BODMAS (or BOMDAS)
Brackets
Order
Divide
Multiply
Add
Subtract
eg
18 – 7 x 2
= 18 – 14
=4
eg
(14 + 12)  (6 – 4)
= 26  2
= 13
MNU103C, MNU203C, MNU303C, MTH403C, MTH205C
[4] Scientific Notation or Standard Form

Write large or small numbers in standard form and vice versa
eg
24500000 = 2.45 x 107
0.000988 = 9.88 x 10-4

Write as a x 10n where a is between 1 and 10

Use a calculator to carry out calculations involving standard form
eg
(3.2 x 106) x (1.7 x 10-2)
= 3.2 E 6 x 1.7 E (-) 2
= 54400
= 5.44 x 104

To avoid confusion do not use 10x on calculator

Different calculators have different displays - learn how yours works
MTH405G
[5] Fractions

Find simple fractions of a quantity
eg
1
of 70
5
2
of 120
3
= 70  5
= 120  3 x 2
= 14
= 80

Divide by the denominator, multiply by the numerator

Use equivalence of widely used fractions and decimals
x5
eg
3
= 0.3
10
3
15
=
= 0.15
20 100
x5

Add and subtract fractions
eg
3
1
4
+1
2
5
eg
2 1
3 4
=3
5
8
+1
10
10
=
8
3
12 12
=4
13
10
=
5
12
=5
3
10

Common denominator for adding and subtracting

Never use decimals in a fraction question
MNU105H, MNU208H, MNU308H, MTH309H, MTH310H, MTH407H

Multiply fractions
eg
1
1
5
x
4 7
2
1
7
x4
3
8
=
5
5
x
4 7
=
7 39
x
3
8
=
25
28
=
91
8
= 11






3
8
Cancel numerators and denominators first if possible to simplify figures
Always write final answer as a mixed number
Always give your answer in its simplest form
Never cancel two numbers on the top / or bottom
Never use a common denominator when multiplying
Divide fractions
eg
2
3
5

4
6
=
11
63
x
42
5
=
33
10
=3
3
10

To divide, invert second fraction and multiply

Don’t use a calculator for calculations involving fractions
[6] Percentages

Find 50%, 33⅓%, 10% and 1% without a calculator and use addition to find other amounts
eg

2
40
=
= 40%
5 100
23% of £300
= 0.23 x £300
= £69
Express fractions as percentages using a calculator
eg
A caravan was bought for £3000 and sold for £3250.
What was the profit as a percentage of the cost price ?
Profit = £3250 - £3000 = £250
Profit % =

250
= 0.0835 = 8.3%
3000
Carry out calculations involving percentage increase and decrease
eg


15% of £360
= 10% of £360 + 5% of £360
= £36 + £18
= £54
Find percentages with a calculator
eg

eg
Express some fractions as a percentage without a calculator
eg

50% of £240
= ½ of £240
= £120
Increase £350 by 15%
1.15 x £350
= £402.50
Always change percentages to decimals when using a calculator
Never use the percentage button on your calculator
MNU208H, MNU308H, MNU406H, MNU209H
[7] Proportion

Use the unitary method (ie. find the value of one first, then multiply by the required value)
eg
Direct
If 5 bananas cost 80p, what do 8 bananas cost ?
Bananas
5
1
3
Cost
80p
80  5 = 16p
16p x 3 = 48p
 3 bananas cost 48p
eg
Inverse
The journey time at 60km/h is 30 minutes, so what is the journey time at
50km/h ?
Speed
60
1
50
Time
30 mins
30 x 60 = 1800 mins
1800  50 = 36 mins
 The journey time at 50km/h is 36 minutes

Always communicate answer

Don’t round until the last stage
MNU311J, MNU408J
[8] Time

Convert between 12 and 24 hour clock
eg
2327 = 11.27pm

Do not write 2327pm

Calculate duration in hours and minutes by counting up to the next hour then on to the
required time, including pm → am times
eg
20mins
10.40pm
15mins
11.00pm
4.00am
5hrs

= 5hrs 35mins
Remember the cross-eyed frog !

Never use subtraction to find time intervals

Change minutes to hours and hours to minutes

4.15am
eg
27 mins = 27  60hrs
= 0.45hrs
eg
0.2hrs
= 0.2 x 60mins
= 12mins
Use the link between time, speed and distance to carry out related calculations
Speed = 42 km/h
T
Distance = 800km
D
S
800
=
42
=
0.0476 x 60 = 3mins
= 19.0476….hrs
= 19hrs 3mins
MNU214L, MNU216L, MNU314L, MNU413L
[9] Algebraic Expressions, Equations and Formulae
Solving Equations

By balancing / using the flag method

Performing the same operation to each side of the equation

Doing ‘undo’ operations eg undo ‘+’ with ‘-‘

Using statements like “multiply both sides by …”
eg
2x + 3 = 9
-3
-3
2x
= 6
2
2
x
= 3

One equal sign per line, written underneath each other

Work down the page

Write the letter ‘x’ differently from a multiplication sign

Never change side, change sign

Do not write ‘nonsense’ statements, such as 2x = 6 = 3
Formulae




Write down the formula first
Substitute clearly
Simplify the expression
Communicate answer fully
eg
The length of a string smm for the weight wg is given by the formula
s = 16 + 3w
Find (i) s when w = 3g
(ii) w when s = 20.5mm
(i)
s = 16 + 3w
= 16 + 3 x 3
= 16 + 9
= 25
 length of string is 25mm
(ii)
s = 16 + 3w
20.5 = 16 + 3w
-16
-16
4.5 = 3w
3w = 4.5
3
3
w = 1.5
 weight of string is 1.5g


Always show all steps in working
Always substitute first, then re-arrange as necessary to solve the equation
MTH222R, MTH320R, MTH321R
[10] Co-ordinates

Cartesian Co-ordinates are pairs of numbers separated by a comma and enclosed in
brackets. Each pair of numbers gives the position of a point relative to an origin O,
eg. (3, 4) is 3 units to right along the x-axis and 4 units in the positive y-direction and
(-3, -2) is 3 to the left and 3 down.

The points are marked where the lines cross, and not in the spaces.

The order matters in that (3, 4) is not in the same place as (4, 3).
(Remember : along the corridor then up (or down) the stairs !)
MNU206D, MTH230U, MTH429U, MTH430U
[11] Data and Analysis





Use a pencil and ruler
Give the graph a title
Label lines
Label the frequency up the side
Label on lines, not on spaces
Bar Graph

Construct and interpret bar graphs
Quantities of Litter
eg


Make sure each bar has equal width
Label each bar in its centre
Line Graphs

Construct and interpret line graphs
The distance a gas travels over time has been recorded in the table below
Time (s)
Distance (cm)
0
0
5
15
10
30
15
45
20
60
25
75
30
90
Distance travelled by a gas over time


Plot points neatly using a cross or dot
If the lower point of a graph has been
missed out, use a jagged line to show
this
eg
Scatter Graph

Construct and interpret scatter graphs

Draw a line of best fit when there is a correlation
Pie Charts

Construct pie charts involving simple fractions, decimals or percentages
eg
30% of pupils travel to school by bus
10% by car, 55% walk and 5% cycle
Bus
Car
Walk
Cycle

30% of 360 = 108
10% of 360 = 36
55% of 360 = 198
5% of 360 = 18
360
 Check
Construct pie charts of raw data
eg
20 pupils were asked “what is your favourite subject ?”
Replies were Maths 5, English 6, Science 7, Art 2
Maths
English
Science
Art
5  20 x 360 = 90
6  20 x 360 = 108
7  20 x 360 = 126
2  20 x 360 = 36
360
 Check
MNU124W, MNU232W, MNU233W, MNU325W, MNU432W
Elements Informing the Numeracy Framework for Action
Numeracy across
the curriculum
Teacher
knowledge of
mathematics
learning and
inclusive teaching
Improved
student
outcomes in
mathematics
and numeracy
capabilities
Understanding
numeracy
Numeracy
leadership
© ‘Framework for Action 2007-2010’ Queensland Government