Bridge of Weir Primary School Gryffe High School Houston Primary School Cross Curricular Methodology Maths and Numeracy Contents Place Value Addition Subtraction Multiplication Division Time Scientific Notation Ratio Percentages Equations and Formulae Statistical Graphs S1 and S2 Maths Course Summary
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Cross Curricular Methodology Maths and Numeracy...Place Value Multiplying by multiples of 10, 100 and 1000 The decimal point is fixed. The decimal point doesn’t move. Only the digits
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Bridge of Weir Primary School
Gryffe High School
Houston Primary School
Cross Curricular
Methodology
Maths and Numeracy
Contents
Place Value
Addition
Subtraction
Multiplication
Division
Time
Scientific Notation
Ratio
Percentages
Equations and Formulae
Statistical Graphs
S1 and S2 Maths Course Summary
Introduction This is the 2nd Edition of the Numeracy and Maths methodology document. The aim of this document is to promote the use of common methodologies in numeracy and mathematics across the school in order to improve the educational experience of pupils. Bridge of Weir and Houston Primaries have also been aware of the Maths Department’s methodologies in certain topics for a number of years and have been involved in ongoing discussions and development so that this document reflects joint Primary and High school approaches and methodologies. It is hoped that this awareness raising will result in all teachers adopting the same approaches thus improving consistency of teaching across the curriculum. The document also attempts to raise awareness as to when certain topics are covered by the Maths department, as it may well be the case that it is not the Maths department that introduces a particular topic for the first time in High School. Hopefully this document will help you, or at least encourage you to consult with the Maths Department. The process is intended to be a collegiate one and your comments, contributions and questions are always welcome.
Place Value
Multiplying by multiples of 10, 100 and 1000
The decimal point is fixed. The decimal point doesn’t move. Only the digits move.
To multiply by 10 every digit is moved one place to the left.
To multiply by 100 every digit is moved two places to the left.
To multiply by 1000 every digit is moved three places to the left.
Example 1 (a) 351 × 10 (b) 34∙67 × 100
Th H T U ∙ 1
10
1
100
1
100
3 4 6 7 ∙
Th H T U
3 5 1 0 Move one place to the left Move two places to the left
3 4 ∙ 6 7
7
3 5 1
(c) 45 × 50
Most pupils when
multiplying by 50
will multiply by 5,
then by 10.
(d) 2∙3 × 400
Most pupils when
multiplying by 400
will multiply by 4,
then by 100.
45 × 5 = 225
225 × 10 = 2250
2∙3 × 4 = 9∙2
9∙2 × 100 = 920
But don’t discourage this
45 ×50
2250
Multiply by 10, then by 5
Or vice versa. Or vice versa.
Dividing by multiples of 10, 100 and 1000
To divide by 10 every digit is moved one place to the right.
To divide by 100 every digit is moved two places to the right.
To divide by 1000 every digit is moved three places to the right
Example 1 (a) 351 ÷ 10 (b) 34∙67 ÷ 100
Some pupils have great difficulty grasping the process of moving digits and find it
easier to “move the decimal point”.
It was agreed (Primary and High school) that teachers should use their professional
judgement as to when the “moving point” should be resorted to.
Th H T U ∙ 1
10
1
100
Th H T U ∙ 1
10
1
100
1
1000
1
10000
3 5 1
3 4 ∙ 6 7
7 0 ∙ 3 4 6 7 3 5 ∙ 1
Move one place to the right Move two places to the right
(c) 45 ÷ 50
Most pupils when
dividing by 50 will
divide by 5, and
then by 10.
45 ÷ 5 = 9
9 ÷ 10 = 0∙9
Or vice versa.
Addition
Carrying tens, hundreds etc. will be done on top of the sum line.
Subtraction
All pupils will subtract by the method of decomposition.
Multiplication
Carrying tens, hundreds etc. will be done on top of the sum line.
Example: 342 × 9
3 4 2 3 4 2 3 4 2
+ 81 9 + 1 81 9 + 1 81 9
1 4 3 1 4 3 1
3 4 2 3 4 2 3 4 2
× 1 9 × 3 1 9 × 3 1 9
8 7 1 3 0 7 8
3 34 12 3 34 12 23134 12 23134 12
1 8 9 - 1 8 9 - 1 8 9 - 1 8 9
3 5 3 1 5 3
Division
Example: 342 ÷ 4
Time
12 hour clock times should be written with am/pm and dot between hours and
minutes e.g.
3.12am 10.15am 7.35pm
24 hour clock times should be written with four numbers with space between hours
and minutes e.g.
03 12 10 15 19 35
Calculation of time duration
Use horizontal line broken into stages of time. Stages are broken into minutes
and/or hours depending on duration.
In Gryffe we encourage to go to the next hour, then hours, then remaining minutes:
Using the balancing approach to change the subject of a formula
(e.g. to x).
𝑝 = 𝑎𝑥 + 𝑏 𝑃 = 𝑥
𝑅
−𝑏 − 𝑏 𝑅 × 𝑃 = 𝑥
𝑅 × 𝑅
𝑝 − 𝑏 = 𝑎𝑥 𝑃𝑅 = 𝑥
𝑝
𝑎 −
𝑏
𝑎=
𝑎𝑥
𝑎
𝑝 − 𝑏
𝑎 = 𝑥
This is also an
example of the
minimum amount of
working specified by
the SQA
Maths does not teach cross-multiplication
- Except when using the Sine Rule (November S4)
To deal with a problem such as:
or
Note on calculator use:
Calculators are only used in maths when it is appropriate.
Much of the work done in Maths does not require calculator use
and the use of calculators is not encouraged when their use is
not necessary.
Maths Timeline: Simple Formulae – From August S1: collect terms,
evaluate expressions, evaluate formulae. Change of subject S4.
𝑅
120 =
55
175
120
1×
𝑅
120 =
55
175×
120
1
120𝑅
120 =
6600
175
𝑅 = 264
7
𝑅 = 37 ∙ 7
Statistical Graphs
Most work done by pupils in S1 and S2 involves interpreting graphs not drawing them – with the exception of some time spent on Pie Charts and Scatter Diagrams. Bar Graph/Chart A bar chart is a way of displaying discrete or non-numerical data. That is data which is in separate categories. For example: Type of housing - flat Food content - protein
An equal space should be between each bar and each bar should be of an
equal width. Leave a space between the y-axis and the first bar.
Housing: Area A Number
Equal Width
Equal Spacing
Title
Label Axes
Histogram
A Histogram is often confused with a bar chart. More appropriately used
when data is continuous.
Continuous data are data that have no precise fixed value and are
usually measured to within a range. Such data includes height
(measurable to the nearest unit, a millimetre for example).
Data displayed in a histogram can be grouped.
As with a bar chart a histogram should have a title and appropriate x and
y-axis labels.
There should be no space between each bar. Each bar should be of an
equal width.
Maths Timeline
Bar Graphs – Information Handling – February S1 and December S2
Pupil Absence
Pupil Height
8
8
Number of
Pupils
7
Number of
Pupils
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
0-4 5-9 10-14 15-19 20-24
0-4 5-9 10-14 15-19 20-24
Number of days absent
Height (CM)
Line graphs compare two quantities (or variables). Each variable is plotted along an
axis.
A line graph should have a title and appropriate x and y-axis labels.
Pie Charts
A pie chart is a way of displaying discrete or non-numerical data.
A pie chart uses fractions or percentages to compare data.
In the construction of pie charts the maths department uses protractors and fractions
of 360°. A whole circle is then split into sectors representing those fractions.
A pie chart needs a title and a key.
T emp e r a t u r e C°
Time
37.50%
12.50%
21.90%
28.10%Banana
Orange
Apple
Pear
Favourite Fruit
Scatter Diagrams
A scattergraph allows you to compare two quantities (or variables). Each variable is
plotted along an axis. A scattergraph should have a title and appropriate x and y -
axis labels. For each pair of data items a point is plotted e.g. (maths score, physics
score). The points are not joined up.
A scattergraph allows you to see if there is a connection (correlation) between the
two quantities. If a correlation exists a line of best fit can be drawn on the diagram.
A line of best fit can be drawn using an “average point”: (mean x, mean y). However,
a line of best fit is only ever required to be drawn in maths at General level and at
Intermediate 2 where a “reasonable line” is acceptable.
Only pupils at Credit/Int 2 level are expected to find the equation of the line.
Maths Timeline
Line Graphs - February S1
Pie Charts - February S1
Scatter Diagrams (incl. line of best fit) - December S2
Gradient and Equations of Lines - End of S3/Beginning of S4
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120
Physics and Maths test scores
P h y s i c s
Maths
Line of best fit.
S1 Course Summary Level 3 Book R1
Unit 1 Algebra 1 mth3-14a/mnu3-03b Dewey Filing System mnu2-02a.3-03b Symmetry mth2-19a.3-19a.4-19a Whole numbers and decimals mth4-19a/mnu3-01a.3-03a.3-03b Health and Well Being 1 hwb2-36a.3-34a.4-34a/mnu3-20a Sequences, multiples and factors mth3-05a.3-05b.3-06a/mnu3-03a.3-03b.3-04a Egyptian Mathematics mth1-12a
Unit 1 Test before October Mid Term
Unit 2 Fractions mth3-07b.3-07c.4-07b/mnu3-07a Negative Numbers mnu2-04a.3-04a Long Multiplication mnu3-03b Algebra 2 mth3-15a.4-15a Angles mth3-17a Babylonian Mathematics mth1-12a
Unit 2 Test – Mid December
Unit 3 Coordinates mth2-18a.3-18a.4-18a.4-18b Measurement mnu2-11b Division and Long Division mnu3-03b Percentages mnu2-07b.3-07a Information Handling mth3-20a.3.20b.2-2a.3-21a/mnu4-20a.4-20b Greek Mathematics mth1-12a
Unit 3 Test – Early March Unit 4 2D shape mth2-16a.3-17a/mnu3-11a Time, distance and speed mnu3-10a Ratio mnu3-08a 3D shape mth2-16a.3-11b/mnu3-11a Formulae mth3-13a.3-15b Scale Drawing mth3-16a.3-17b.3-17c Unit 4 Test – End May
Unit1 Algebra 1 mth3-14a Sets of numbers mnu2-04a.3-04a/mth3-05b.4-06a.4-06b Area mnu3-11a/mth2-16a.3-11a.3-17a. Health and Well Being 2 hwb Decimals and significant figures mnu3-01a.3-03a/mth3-03b.4-03b. Formulae and sequences mnu3-03a.3-03b/mth3-06a.3-14a. Chinese Mathematics Unit 1 test middle/end of September
Unit 2 Fractions and Percentages mnu2-07b.3-07a Algebra 2 mth3-15a.4-15a Enlarging and Reducing mth3-17c.4-17c Proportion mnu3-08a.4-08a Unit 2 test middle of November Unit 3 Information Handling mnu3-20a.4-20a/mth3-20b.4-20b Algebra 3 mth3-15a.4-14a.4-14b.4-15a Circle mth4-16b Probability mnu3-22a.4-22a Unit 3 test end of January Unit 4 Time, Distance and Speed mnu3-10a.4-10b Pythagoras’ Theorem mth3-15a.4-16a Straight Line Graphs mth4-13b.4-13d Angles and Scale Drawing mth3-16a.3-17b.3-17c Unit 4 test end of March Literacy Outcomes permeating the course: lit3-04a.3-05a.3-09a.3-21a.3-24a