Scheme of Work - Year 9

Scheme of work for text Active Maths 3

Chapter

Title

Content

National

curriculum level

Number of weeks

Additional resources in folder

Comments

IT Opportunities

1. Arithmetic1

· Basic principles

· More calculator buttons

· % profit and loss

· Problem solving

· Revision exercises

2 weeks

See Hard Drive Word

· Test Chapter 1

Single lesson

2.Graphs

· Basic principles

· Graph relationships

· Understanding graphs

· Investigating graphs

· Travel graphs

· Revision exercises

2 weeks

· Bottles ws

· Use a spread sheet to investigate graphs initially

· Basic algebra test 1

Single lesson

3. Algebra

· Basic principles

· Brackets

· Symbolic expression

· Problem solving

· Simplifying algebraic fractions

· Solving algebraic fractions

· Simultaneous equations

· Inequalities

· Revision exercises

3 weeks

· Inequalities ws

Hard Drive: Publisher

Finding nth term of sequence

Investigation: Number Walls allows extension in algebra

· Text uses substitution, worth looking at but teach elimination

Use AM 4 Ex 33-35

Omnigraph: Solution of simultaneous equtions graphically

· Test Chapter 1 to 3

Double lesson

Test Chapters 1 to 3 Approximately October half term

Investigation (see above)

Basic test 2

Single lesson

4. Geometry 1

· Basic principles

· Angles of a circle

· Similar triangles

· Gradients

· Revision exercises

2 weeks

SSM16,SMM17

SSM18

5. Trigonometry

· Basic principles

· Tangent and ratio

· Sine and cosine ratio

· Miscellaneous problems

· Revision exercises

3 weeks

· Students may not have met Pythagoras’ theorem yet.

· Basic test 3

Single lesson

6. Proportion

· Basic principles

· Change of units

· Comparative costs

· Problem solving

· Inverse proportion

· Science problems

· Revision exercises

2 weeks

· An easy but interesting HW. Students to find cost/litre of everyday items eg bleach, perfume, tippex

· Exchange rate (mental)

· Basic algebra test 2

2 x single lesson

Test Chapters 4 to 6 Approximately January

Investigation

7. Algebra 2

· Equations

· Trial and improvement

· Inequalities

· Circumference of a circle

· Area of a circle

· Pythagoras’ theorem

· The cylinder

· Formulae

· Rearranging formulae

· Revision exercises

2 and 3

4 weeks

· Perimeter problem ws

· Rearranging ws

· Excel

SSM20

· Pencil and paper test

Single lesson

8. Graphs 2

· Basic principles

· Graphs of y = ax

· Graphs of y = ax + b

· Graphs of y = ax²

· Graphs of y = a/x

· Revision exercises

3 weeks

· Graph matching ws

· Omnigraph or other graph package. Compare shapes of graphs by order of equation.

· SSM13,SSM14

· Basic test 4 test

9. Arithmetic 2

· Tolerance

· Percentages

· Wages and salaries

· Taxation

· Interest and loans

· Discount and hire purchase

· Revision exercises

2 weeks

· Additional ws available

· Basic test 5 test

Test Chapters 7 to 9 Approximately: mid May

Investigation

10. Statistics and probability

· Basic principles

· Misuse of statistics

· Scatter diagrams

· Calculating averages

· Frequency distributions

· Probability: single event

· Probability: combined events

· Revision exercises

2 weeks

· Describing correlation ws

· Add in : Finding mean, mode, median from table. Estimating mean, modal, median group from grouped frequency table.

· Cumulative frequency not covered—useful for SAT 6-8 paper

HD9, HD11

HD12

HD10

HD7, HD8

· Pencil and paper test

11. Geometry 2

· Basic principles

· Enlargements

· Loci

· Maps and bearings

· Scale drawing

· Drawing 3-D figures

· Networks

· LOGO

· Revision exercises

SSM9, SSM10

LOGO

· Basic algebra test 3

Revision

· Multiple choice revision

activities

KS3 SAT Exam (before chp9)

Scheme of work for text ‘Key Maths 9 ²’

· H means that various useful worksheets are available in the 9 ² teacher’s file for this chapter

· tü means that the level is being ‘worked towards’

		National Curriculum Level (may be working towards)
		AT	4	5	6	7
Chapter title	Content						No. of weeks	Additional resources / ideas	Comments / feedback from departmental meetings	IT Opportunities
1. Pythagoras	· Pythagorean triples · Finding the hypotenuse · Finding any side	3			ü ü ü	ü ü ü	2	H (some available) Ø Could use a practical method to see if children can ‘discover Pythagoras’ theorem. Ø Use of calc. For sq. rt. & square
2. Formulas	· Using letters to represent variables · Patterns	2		ü ü	ü	ü	1 ½	Ø Squared paper. Ø Multilink cubes may be useful for less able
3. Circles	· Diameter · Area of a circle	3			ü ü		1 ½	H Ø Worksheet method is O.K; could also evaluate an estimate for p.
4. Statistics	· Discrete and continuous data (& histograms) · Averages and range	4	ü	ü ü	ü ü	ü	2	H	Ø Some of these worksheets need thorough explanation. Some are totally unsuitable.	HD8 Quartiles. Averages and range HD11 Looking at data 4 HD12 Estimating the mean
	MA 1 investigation: ‘Frogs’	1					1

		AT	4	5	6	7
Chapter title	Content						No. of weeks	Additional resources / ideas	Comments / feedback from departmental meetings	IT Opportunities
5. Accuracy	· Sensible rounding · Multiplying & dividing by nos. less than 1 · Using a calculator · Error in measurements	2		ü	ü	ü ü ü ü	2
6. Volume	· Units of capacity · Volume of a cuboid · Volumes of prisms and cylinders	3	ü ü	ü ü	ü ü	ü	2 ½	Ø Bring in containers of various volumes to aid understanding. Ø 1 cm cubes available for less able	Ø May fit in with ‘max-box’ investigation later (especially the IT aspect)	Enter the dimensions of cuboids into a spreadsheet and use the formula facility to find the volumes.
7. Number Revision	· Fractions, decimals and percentages · Increase and decrease by a certain percentage · Ratio	2	ü ü	ü ü	ü ü ü	ü ü	2 ½	Ø Counters for less able		NA4 Investigating decimal fractions NA7 Personal finances and percentages
8. Algebra	· Use of brackets · Equations	2			ü ü		3 ½	Ø BODMAS Ø Development of the necessary rigour
9. Statistics	· Scatter diagrams · Pie charts · Misleading diagrams	4		ü ü	ü ü tü	ü	2	Ø Scatter diagram/survey of class hand versus foot sizes.	Ø This worked well. Children used measuring & data collection skills & had an intro. to correlation. Ø Set 4 found the misleading diagrams section challenging.	Could use spreadsheets to input data from a class survey & draw a pie chart using a graphing package EX3 Getting started in EXCEL 3 HD11 Looking at data 4
10. Probability	· Revision of basics · Relative frequency · Listing outcomes · Probability methods	4		ü ü ü	ü ü ü	ü	2	Ø Real spinners work well in conjunction with discussion Ø Real experiments can be conducted using counters in bags and bias die	Ø Practical maths worked very well here	HD10 Probability models

		AT	4	5	6	7
Chapter title	Content						No. of weeks	Additional resources / ideas	Comments / feedback from departmental meetings	IT Opportunities
11. Algebra	· Trial and improvement · Inequalities	2			ü	ü	2 ½		Ø Ideal time after this to complete ‘max box’ investigation	Ø Could be done in conjunction with using a spreadsheet.
	MA 1 investigation: ‘Max – Box’	1					1 ½		Ø See note above Ø Takes 3 doubles if using IT Ø Pupils may need some training on the use of a spreadsheet	Ø Ideally, if this is to be done using IT one needs a block of time or at the very least a double lesson per week.
12. Decimals	· Using a calculator · Mental decimals · Multiplying and dividing decimals	2		ü ü		ü	2	Ø 9 set 4 were especially weak in 1999/2000 with non-calculator skills. Some pupils required much extra individual assistance
13. Angles	· Revision of basic rules · Polygons and tessalations · Transformations	3			ü ü ü	ü	2	Ø Nice opportunity for some practical maths outside (see textbook pg. 255)		Logo is very useful here. See the activity on IT support pages in ‘Key Maths Year 7’. SSM1 Plotting coordinates 1 SSM2 Plotting coordinates 2
14. Further Algebra	· Equation of straight line · Simultaneous equations	2		ü	ü	ü	2			Ø Could use ‘Omnigraph’ to plot graphs and graphical solutions of simultaneous equations. SSM11 Coordinates and straight lines SSM13 Investigating straight lines 1 SSM14 Investigating straight lines 2
15.Loci	· Locus of a point · Constructions	3				ü ü	2	Ø An actual bicycle wheel works well for a demo of page 302 esp. for less able (as do other physical demonstrations)		SSM18 Triangles, bisectors and circles
16. Get in shape	· Symmetry · Nets of solids ~~· Building a shape sorter~~	3			ü ü		1	Ø Multilink cubes and common 3D shapes useful for less able Ø I would question the validity of this. Better to do revision and/or an extra investigation

Notes:

I. Total lesson time: 36 weeks. Timing is approximate Set 4 may take slightly longer than above; Set 3 slightly less time.

II. Contact time above does not include mental arithmatic tests and examinations, chapter tests and revision of topics.

III. General numeracy is integral to the SOW (although not specifically referred to) and departmentally it was agreed that numeracy is ongoing and should be executed regularly (20 – 30 minutes per week) and using a variety of methods. Each lesson should involve a short numeracy task.

Scheme of work for text ‘Key Maths 9 ³

		National Curriculum Level (may be working towards)
		AT	5	6	7	8
Chapter title	Content						No. of weeks	Notes	Comments / feedback from departmental meetings	IT Opportunities
1. Pythagoras	· Pythagorean triples · Finding the hypotenuse · Finding any side	3		ü ü ü	ü ü ü		1	Using calculator Solving problems Exs: 1:1,q2 only 1:2 – 1:5 + Questions
2. Formulas	· Using letters to represent variables · Patterns · Trial and improvement	2	ü		ü ü	ü ü	1	Generalising, finding n^th term of both linear and quadratic sequences. For non linear sequences, try using factors. Exs: 2:1 orally, 2:2, 2:3 hwk, 2:4,2:5 Exs 2:6, 2:7 (eg p. 31 unnecessarily difficult) Give answer to correct degree of accuracy by deciding to round up or down. Ex 2:8 odd nos only Questions		IT Use Excel to solve by Trial and Improvement.
3. Circles	· Diameter · Area of a circle	3			ü ü		1	Finding the circumference of a circle. Not ex 3:1. Exs 3:2 odd nos, 3:3 qs 3,4 Area exs: 3:4 odd nos, 3:5 Mixed ex 3:6 Questions		LOGO

4. Statistics	· Discrete and continuous data (& histograms) · Averages and range · Cumulative frequency	4	ü	ü	ü ü	ü	2 ½	Difference between discrete and continuous data Not ex 4:1 Mean , mode and median. Deciding which is appropriate for given data. Ex 4:2 Range. Ex 4:3 Finding mean, mode and median from grouped data Ex 4:4 + Q4 p77 Cumulative frequency, median, upper and lower quartiles. Ex 4:5 together. Exs 4:6,4:7,4:8+ Questions	Ø Some of these worksheets need thorough explanation. Some are totally unsuitable.
	MA 1 investigation: ‘Frogs’	1					1
5. Accuracy	· Rounding · Error in measurements · Standard form	2	ü		ü ü ü	ü	2	Significant figures, decimal places. Ex5:1 orally Estimating. Ex 5:2 Multiplying and dividing by numbers less than 1. Ex 5:3,5:4 Upper and lower limits Exs 5:5, 5:6 odd nos Numbers greater than and less than 1. Using calculators. Not ex 5:7. Exs 5:8,5:9,5:10. Questions
6. Volume	· Volumes of prisms and cylinders · Another Dimension	3		ü ü	ü	ü	2 ½	Define prism, area of cross-section. Exs 6:1,6:2, 6:3,6:4 Questions 1-4 ex6:5 Dimensions, what units for length, area , volume Exs 6:7, 6:8	Ø May fit in with ‘max-box’ investigation later (especially the IT aspect)	Enter the dimensions of cuboids into a spreadsheet and use the formula facility to find the volumes.

7. Number Revision

· Fractions, decimals and percentages

· Increase and decrease by a certain percentage

· Ratio

2 ½

Re visit percentages, decimals, fractions. Conversions from/to… Exs 7:2, 7:3

Increase and decrease percentages. Unitary method to find original value Exs 7:4, 7:5 qs 7-12 only

ex 7:6 even nos only

Fraction of… ex 7:7 Finding 100%, exs 7:8, 7:9

Dividing in ratio, increase and decrease in ratio.

Exs 7:11, 7:13

Speed ,distance, time Exs 7:14, 7:15 + Questions

8. Algebra

· Use of brackets

· Two brackets

· Equations

Collecting like terms, BODMAS, expanding brackets, factorising. Ex 8:1 orally, 8:2 odd nos, 8:3 even nos, 8:4, 8:5, 8:6q1 only, 8:7, 8:8, 8:9

Directed numbers, expanding brackets with negative numbers, multiplying expressions of the form

(a + b)(c + d). Ex 8:10 orally, 8:11, 8:12, 8:13

Solving equations, Ex 8:14 , 8:15, 8:16 all even nos only. Equations with brackets, Ex 8:17 odd nos

Rearranging formulae Ex 8:18 + Questions

9. Statistics

· Scatter diagrams

· Pie charts

· Misleading diagrams

Lines of best fit, correlation. Ex 9:1

Ex 9:2 orally, 9:3

Ex 9:4 together + Questions

Could use spreadsheets to input data from a class survey & draw a pie chart using a graphing package

IT Use Excel to produce Statistical diagrams

10. Trigonometry	· Introduction · Finding lengths · Finding an angle	4				üüü	3	Ratios between sides in right angled triangles. Labelling sides in relation to a given angle. Using a calculator. Correct mode!	Ø
11. Probability	· Probability and relative frequency · Listing outcomes · Tree Diagrams	4	ü ü	ü ü ü	ü	ü ü ü ü	2	Probability: definition, lies between 0 and 1. P(A') = 1 – P(A). Frequency of an event. Relative frequency giving estimate of the probability. Sample space and diagrams. Independent events, Probability of independent events Tree diagrams as a sample space to show the outcomes of independent events.	Ø Practical maths worked very well here	IT: 10/10 Probability (on Acorns)
12.Loci	· Locus of a point · Constructions	3				ü ü	2	Definition Angle bisector; ,perpendicular bisector	Ø An actual bicycle wheel works well for a demo
	MA 1 investigation: ‘Max – Box’	1					1 ½		Ø See note above Ø Takes 3 doubles if using IT Ø Pupils may need some training on the use of a spreadsheet	Ø Ideally, if this is to be done using IT one needs a block of time or at the very least a double lesson per week.
13. Algebra	· Straight Line Graphs · Simultaneous Equations · Inequalities	2	ü	ü	ü ü	ü	2 ½	Straight line graphs, gradient and intercept, y = mx + c . Simultaneous equations by graph, by elimination method. Shading regions on a graph, when to use continuous or dotted line. Finding regions, graphical inequalities.	Ø Ideal time after this to complete ‘max box’ investigation	Could be done in conjunction with using a spreadsheet. Omnigraph

14. Graphs

· Graphs of calculator buttons

· Sketching graphs

Graphs of y=x², y=x³ etc

Comparison graphs. Gradient of a curve. Interpretation. Graphs of depths in non-uniform containers

Can be covered very briefly if necessary

Mouseplotter

Excel

Omnigraph

15. Transformations

· Transformations

· Combined transformations

· Enlargement

· Similar triangles

üü

Reflection, tranlation, rotation

Scale factor, inc fractional. Centre of rotation

Definition + proof

16. Get in shape

· Polygons

· Symmetry

· Nets of solids

· Building a shape sorter

üüü

1½

Sum of exterior angles; finding interior angle.

Line, order, plane of symmetry

Ø Multilink cubes and common 3D shapes useful

Ø 'Back-to-back' activity

LOGO

Notes:

I. Total lesson time: 32 weeks

II. Contact time above does not include mental arithmetic tests and examinations, chapter tests and revision of topics.

Scheme of work for text Active Maths 3

AT

AT

AT

Scheme of work for text ‘Key Maths 9 3

AT

Scheme of work for text ‘Key Maths 9 ³