sow year 9 higher target levels: 6 8 set 1 only · sow year 9 higher target levels: 6 ... write...

$: SOW Year 9 Higher Target Levels: 6 8 Set 1 only · SOW Year 9 Higher Target Levels: 6 ... Write 0.4545454545 as a fraction in its simplest terms (= 5/11) Level 8 Probing Questions:$
SOW Year 9 Higher Target Levels: 6 – 8 Set 1 only

Date Module Topic Key skills development/ prerequisites/assessment/tests Homework: Written & www.mymaths.co.uk

Other Resources For use in: lessons/IL/hwk /Framework

24th

Jun 2013

1.1

Working with numbers Inverse operations Factors, multiples & primes Ratio & proportion Using a calculator Negative numbers Long multiplication & division FDP

Examples of what pupils should know and be able to do:

Level 7 Probing Questions:

‘Division makes things smaller.’ When is this statement true and when is it false?

How would you justify the idea that dividing by ½ is the same as multiplying by 2? What about

dividing by 1⁄3 and multiplying by 3? What about dividing by 2⁄3 and multiplying by 3⁄2 ? How does this

link to division of fractions?

x & ÷ 10, 100, 1000 tarsia

1st

Jul 2013

1.2

Using algebra Simplifying terms Solving equations Solving problems with equations Factorising – single brackets only

Examples of what pupils should know and be able to do at Level 7:


8th

Jul 1.3

Congruent shapes & construction Congruent triangles



15th

Jul END OF TERM ACTIVITIES WEEK

23td Jul – 6

th

Sept

SUMMER HOLIDAYS

9th

Sept 2013

1.4

Geometrical Reasoning Properties of quadrilaterals Angles in polygons Exterior angles of a polygon


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16th

Sept

1.5 Data Handling Averages & range Frequency distribution Calculating mean – grouped data Frequency polygons Cumulative frequency diagrams



How would you go about making up a set of data with a median of 10 and an interquartile range of 7?

Convince me that the interquartile range for a set of data cannot be greater than the range.

How do you go about finding the interquartile range from a stem and leaf diagram? What is it about a

stem and leaf diagram that helps to find the median and interquartile range?

How would you go about finding the median from a cumulative frequency table?

Why is it easier to find the median from a cumulative frequency graph than from a cumulative frequency table?

Describe two contexts, one in which a

variable/attribute has negative skew and the other in which it

has positive skew.

How can we tell from a box plot that the distribution

has negative skew?

Convince me that the following representations are

from different distributions, e.g.:

What would you expect to be the same/different about the two distributions representing, e.g.: heights of pupils in Years 1 to 6 and heights of pupils only in Year 6.

23rd

Sept

1.6 Multiplying Brackets Solving equations


Multiply out these brackets and simplify the result:

(x + 4)(x – 3) (a + b)2 (p – q)2 (3x + 2)2 (a + b)(a – b)


Show me an expression in the form (x + a)(x + b) which when expanded has:

the x coefficient equal to the constant term

the x coefficient greater than the constant term.


Factorise: x2 + 5x + 6 x2 + x – 6 x2 + 5x

Recognise that: x2 – 9 = (x + 3)(x – 3)

Solve linear equations involving compound algebraic fractions with positive integer denominators, e.g.:

Simplify: (2x – 3)(x – 2) 10 – (15 – x) (3m – 2)2 – (1 – 3m)2

Cancel common factors in a rational expression such as:

Expand the following, giving your answer in the simplest form possible: (2b – 3)2


Talk me through the steps you take when factorising a quadratic expression.

Show me an expression which can be written as the difference of two squares. How can you tell?

Why must 1000 × 998 give the same result as 9992 –1?

Give pupils examples of the steps towards the solution of equations with typical mistakes in them. Ask them to

pinpoint the mistakes and explain how to correct.

Give me three examples of algebraic fractions that can be cancelled and three that cannot be cancelled. How did

you do it?

How is the product of two linear expressions of the form (2a ± b) different from (a ± b)?

30th

Sept

Review 1

7th

Oct

2.1 Using Fractions 4 operation with fractions Solving problems Recurring decimals Algebraic fractions Equations with fractions


Find the area and perimeter of a rectangle measuring 4¾ inches by 6 3/8 inches.

Using

as an approximation for π, estimate the area of a circle with diameter 28mm.

Pupils should be able to understand and use efficient methods to add, subtract, multiply and divide fractions, including mixed numbers and questions that involve more than one operation.


How do you go about adding and subtracting more complex fractions, e.g. 22/5 – 1 7/8?

Give me two fractions which multiply together to give a bigger answer than either of the fractions you

are multiplying. How did you do it?

Give pupils some examples of +, –, × and ÷ with common mistakes in them (including mixed

numbers). Ask them to talk you through the mistakes and how they would correct them.

How would you justify that dividing by ½ is the same as multiplying by 2? What about dividing by 1⁄3 and multiplying by 3? What about dividing by 2⁄3 and multiplying by 3⁄2 ? How does this link to what you know about dividing by a number between 0 and 1?


Decide which of the following fractions are equivalent to terminating decimals: 3⁄5, 3⁄11, 7⁄30, 9⁄22,

9⁄20, 7⁄16

Write 0.4545454545 as a fraction in its simplest terms (= 5/11)


Write some fractions which terminate when converted to decimals. What do you notice about these

fractions? What clues do you look for when deciding if a fraction terminates?

1⁄3 is a recurring decimal. What other fractions related to one-third will also be recurring?

Using the knowledge that 1⁄3 = 0.333333, how would you go about finding the decimal equivalents of

1⁄6, 1⁄30…?

1⁄11 = 0.090909090909. How do you use this fact to express 2⁄11, 3⁄11,…., 12⁄11 in decimal form?

If you were to convert these decimals to fractions: 0.0454545….., 0.454545……, 4.545454……, 45.4545…..

Which of these would be easy/difficult to convert? What makes them easy/difficult to convert?

Can you use the fraction equivalents of 4.54545454545 and 45.4545454545 to prove the second is ten times

greater than the first?

Which of the following statements are true/false?

All terminating decimals can be written as fractions.

All recurring decimals can be written as fractions.

All numbers can be written as a fraction.

14th

Oct 2.2 Working with indices Index laws Solve equations involving indices Graphs of a

x



Convince me that: 37 × 32 = 39 37 ÷ 3-2 = 39 37 × 3-2 = 35

What does the index of ½ represent?

Are the following statements always, sometimes or never true?

Cubing a number makes it bigger.

The square of a number is always positive.

You can find the square root of any number.

You can find the cube root of any number.

If sometimes true, precisely when is the statement true and when is it false?

Which of the following statements are true?

= 82 the length of an A4 piece of paper is 2.97 × 105km

8-3 =

272 = 36 3√7 × 2√7 = 5√7

21st

Oct 2.3 Standard form Standard form ↔ ordinary form Using a calculator Solve problems in Standard


Given the following dimensions: Diameter of the eye of a fly: 8 × 10-4m ; Height of a tall skyscraper: 4 × 102m

& Height of a mountain: 8 × 103m. How many times taller is the mountain than the skyscraper? & How high is

the skyscraper in km?

form Level 8 Probing Questions:

28th

Oct 1

st Nov

OCTOBER HALF TERM

4th

Nov 2.4 Applying maths in contexts 1

11th

Nov 2013

2.5 Scatter graphs Correlation Lines of best fit


Probing Questions:

18th

Nov

2.6 Trial & Improvement Solve equations & problems


Probing Questions:

Review 2

25th

Nov

3.1 Shape & space – mixed problems Finding angles in various shapes Bearings Pythagoras theorem Pythagoras theorem in circles Transformations


Probing Questions:

What do you look for in a problem to decide whether it can be solved using Pythagoras’ theorem?

How can you use Pythagoras’ theorem to tell whether an angle in a triangle is equal to, greater than or

less than 90 degrees?

What is the same/different about a right-angled triangle with sides 5cm, 12cm and an unknown hypotenuse, and a right-angled triangle with sides 5cm, 12cm and an unknown shorter side?

2nd

Dec 3.2 Sequences – finding a rule Sequences, the nth term Quadratics sequences


Find the nth term of the sequence: 6, 15, 28, 45, 66 ...

Find the first ten terms of these sequences: T(n) = n2 ; T(n) = 2n2 + 1 & T(n) = n2 – 2

Know that rules of the form T(n) = an2 + bn + c generate quadratic sequences. Know that the second difference is constant and equal to 2a. Use this result when searching for a quadratic rule.


What do you look for to decide whether a sequence is linear or quadratic?

How can you continue a sequence starting 1, 2,... so that it has a quadratic nth term?

What are the similarities and differences between the way you find the nth term for a linear sequence and the way you find the nth term for a quadratic sequence?

An Investigation: Draw a rectangle of integer length and width. Fill it with squares of side equal to its width, until no more squares will fit. Write down the number of squares. Now attend to the unfilled remainder which is also a rectangle. Fill this similarly and write down the number of squares. Continue this process until there is no remainder.

Figure 1: Filling a rectangle with squares and starting to generate an associated sequence Inspect your sequence. How many terms does it have? How do these terms relate to the dimensions of the original rectangle? Can you choose a starting rectangle to generate a longer sequence? Can you produce a sequence of any length you like? Will the sequence always terminate? Given a sequence, can you find a rectangle that would generate it? With what mathematics are you engaging? Other Investigations leading to linear and quadratic sequences: Jigsaws (easier) and painted cubes (harder)

See IV for these investigations

9th

Dec 3.3 Rounding, errors & estimates Significant figures & decimal places Estimating Errors in measurement Bounds of accuracy


Estimate answers to:

5.16 × 3.14 0.0721 × 0.036 (186.3 × 88.6) / (27.2 × 22.8)


Show me examples of multiplication and division calculations using decimals, with answers that are

approximate to 60.

Why is 6 ÷ 2 a better approximation for 6.59 ÷ 2.47 than 7 ÷ 2?

Why is it useful to be able to estimate the answer to complex calculations?

Explain the difference in meaning between 0.6m and 0.600m. When is it necessary to include the zeros

in measurements?

What range of measured lengths might be represented by the measurement 320cm?

What accuracy is needed to be sure a measurement is accurate to the nearest centimetre?

16th

Dec

3.4 Drawing & Visualising 3D shapes 3D objects using isometric paper Draw side, front & plan views Planes of symmetry



20th

CHRISTMAS HOLIDAYS

Dec – 3

rd Jan

6th

Jan 2014

3.5 Percentage change Reverse percentages


The new model of an MP3 player holds 1⁄6 more music than the previous model. The previous model holds

5000 tracks. How many tracks does the new model hold?

Weekend restaurant waiting staff get a 4% increase. The new hourly rate is £6.50. What was it before the

increase?

My friend has savings of £957.65 after 7% interest has been added. What was the original amount of her savings before the interest was added? Level 7 Probing Questions:

How do you go about finding a multiplier to increase by a given fraction (percentage)? What if it was a fractional

(percentage) decrease?

Why is it important to identify ‘the whole’ when working with problems involving proportional change?


How long would it take to double your investment with an interest rate of 4% per annum?

A ball bounces to 3⁄4 of its previous height each bounce. It is dropped from 8m. How many bounces

will there be before it bounces to approximately 1m above the ground?

Each side of a square is increased by 10%. By what percentage is the area increased?

The length of a rectangle is increased by 15%. The width is decreased by 5%. By what percentage is the area changed?


Talk me through why this calculation will give the solution to this repeated proportional change

problem.

How would the calculation be different if the proportional change was…?

What do you look for in a problem to decide the product that will give the correct answer?

How is compound interest different from simple interest?

Give pupils a set of problems involving repeated proportional changes and a set of calculations. Ask pupils to match the problems to the calculations.

13th

Jan Review 3

20th

Jan 4.1 Transformations Translation Describing transformations Successive transformations


Investigate the standard paper sizes A1, A2, A3, exploring the ratio of the sides of any A-sized paper and the scale factors between different A-sized papers.


How does the position of the centre of enlargement (e.g. inside, on a vertex, on a side, or outside the

(

original shape) affect the image? How this different if the scale factor is between 0 and 1?

27th

Jan 4.2 Reading & interpreting charts & graphs Pie charts & bar charts Interpreting & sketching line graphs Travel graphs



3rd

Feb 4.3 Area & Volume Formulae for: rectangle, triangle, trapezium, circle, prisms, cylinder Finding the radius of a circle Problem solving


The cross section of a skirting board is the shape of a rectangle, with a quadrant (quarter circle) on the

top. The skirting board is 1.5cm thick and 6.5cm high. Lengths totalling 120m are ordered. What

volume of wood is contained in the order?

Probing Questions:

How many different square-based right prisms have a height of 10cm and a volume of 160cm3? Why?

10th

Feb 4.4 Collecting & interpreting data Collecting data Bias



Why is it only possible to estimate the mean (median, range) from grouped data?

Why is it important to use the lowest class value for the first class and the highest class value for the

last class to estimate range? Why not the mid-point?

17th

– 21

st Feb

FEBRUARY HALF TERM

24th

Feb 4.5 Applying maths in context 2

3rd

Mar 4.6 Simultaneous equations What are SE?


Given that x and y satisfy the equation 5x + y = 49 and y= 2x, find the value of x and y using an

Graphical solution of SE Algebraic solution of SE Solving problems with SE

algebraic method.

Solve these simultaneous equations using an algebraic method: 3a + 2b = 16, 5a – b = 18

Solve graphically the simultaneous equations: x + 3y = 11 and 5x – 2y = 4


Is it possible for a pair of simultaneous equations to have two different pairs of solutions or to have

no solution? How do you know?



Review 4

10th

Mar

5.1 Trigonometry Labelling the sides of a triangle Ratio of sides (sin, cos, tan) Finding a side Finding an angle Finding the hypotenuse


Calculate the shortest distance between the • buoy and the harbour and the bearing that the boat sails on. The boat sails in a straight line from the harbour to the buoy. The buoy is 6km to the east and 4km to the north of the harbour.


Is it possible to have a triangle with the angles and lengths shown below?

What’s the minimum information you need about a triangle to be able to calculate all three sides and

all three angles?

How do you decide whether a problem requires use of a trigonometric relationship (sine, cosine or

tangent) or Pythagoras’ theorem to solve it?

17th

Mar

5.2 Inequalities Writing inequalities on number lines Solving inequalities Inequalities in two variables


An integer n satisfies –8 < 2n ≤ 10.List all possible values of n.

Solve these inequalities marking the solution set on a number line.

3n + 4 < 17 and n > 2

2(x – 5) ≤ 0 and x > –2

Regions & inequalities Level 7 Probing Questions:

How do you go about finding the solution set for an inequality?

What are the important conventions when representing the solution set on a number line?

Why does the inequality sign change when you multiply or divide the inequality by a negative number?


This pattern is formed by straight line graphs of equations in the first quadrant.

Write three inequalities to describe fully the shaded region.

The shaded region is bounded by the line y = 2 and the curve


What are the similarities and differences between solving a pair of simultaneous equations and solving

inequalities in two variables?

Convince me that you need a minimum of three linear inequalities to describe a closed region.

24th

Mar

5.3 Probability Relative frequency Working out probabilities Listing possible outcomes Exclusive events



Which of the following statements are true/false?

Experimental probability is more reliable than theoretical probability.

Experimental probability gets closer to the true probability as more trials are carried out.

Relative frequency finds the true probability.


The probability that Nora fails her driving theory test on the first attempt is 0.1. The probability that she passes her practical test on the first attempt is 0.6. Complete a tree diagram based on this information and use it to find the probability that she passes both tests on the first attempt.


Show me an example of:

a problem which could be solved by adding probabilities

a problem which could be solved by multiplying probabilities.

If I throw a coin and roll a dice the probability of a 5 and a head is 1⁄12. This is not 1⁄2 + 1⁄6. Why

not?

Why do the probabilities on each set of branches have to sum to 1?

31st

Mar

5.4 Gradient of a line, y = mx + c Gradients of lines + given 2 points Gradients given an intercept The line y = mx + c Parallel & perpendicular lines



7th

– 22

nd

Apr

EASTER HOLIDAYS

28th

Apr 5.5 Mathematical Reasoning & proof Dots Creating numbers Diamonds & triangles Connect the transformations In search of Proof

Leave until after the may exams

5th

May Review 5

12th

May

Year 9 EXAM WEEK

19th

May

Mark & go through the exams

26th

– 30

th

May

MAY HALF TERM

Jun-Jun 20th

Complete the rest of book 9H

6.1 Drawing & using curved graphs Straight lines Curved graphs


Construct tables of values, including negative values of x, and plot the graphs of these functions:

y = x² y = 3x² + 4 y = 2x2 – x + 1 y = x³


Convince me that there are no coordinates on the graph of y = 3x² + 4 which lie below the x-axis.

Why does a quadratic graph have line symmetry? Why doesn’t a cubic function have line symmetry? How would you describe the symmetry of a cubic function?



Show me an example of an equation of a quadratic curve which does not touch the x-axis. How do

you know?

Show me an example of a function that has a graph that is not continuous, i.e. cannot be drawn

without taking your pencil off the paper. Why is it not continuous?

6.2 Compound measures Speed Other compound measures


Understand that:

Rate is a way of comparing how one quantity changes with another, e.g. a car’s fuel consumption

measured in miles per gallon.

Solve problems such as:

The distance from London to Leeds is 190 miles. An intercity train takes about 2.34 hours to travel from London to Leeds. What is its average speed?

Probing Questions:

Talk me through the reasoning of why travelling a distance of 30 miles in 45 minutes is an average of

40mph.

6.3 Locus Examples of what pupils should know and be able to do at Level 7:

Trace the path of a vertex of a square as it is rolled along a straight line.

Visualise simple paths such as that generated by walking so that you are equidistant from two trees.


What is the same/different about the path traced out by the centre of a circle being rolled along a straight line and the centre of a square being rolled along a straight line?



6.4 Changing the subject of a formula Formulae involving fractions


Find the value of these expressions:

3x2 + 4x – 2 when x = –3, and when x = 0.1

Formulae with negative x terms Formulae involving squares & square roots

Make l or w the subject of the formula: P = 2(l + w)

Make C the subject of the formula: F = 9C/5 + 32

Make r the subject of the formula: A = πr2

Level 7 Probing Questions: What are the similarities and differences between rearranging a formula and solving an equation?


Change the subject of a formula, including cases where the subject occurs twice such as:

y – a = 2(a + 7)

By formulating the area of the shape below in different ways, show that the expressions a2 – b2 and (a

– b)(a + b) are equivalent.

Derive formulae such as:

the area A of an annulus with outer radius r1 and inner radius r2: A = π (r12–r2

2)

the perimeter , p of a semicircle with radius r: p = r (π+2)

Substitute integers and fractions into formulae, including formulae with brackets, powers and roots, e.g.:

p = s + t + (5√(s2 + t2))/3

Work out the value of p when s = 1.7 and t = 0.9.

Clay is used to make this shape, a torus, with radii a = 4.5 and b =7.5

Its volume is ¼ π2 (a + b)(b – a)2 Work out the volume of clay used.


What strategies do you use to rearrange a formula where the subject occurs twice?

How would you help someone to distinguish between the formula for the surface area of a cube and

the volume of a cube?

6.5 Similar shapes


Recognising similar shapes Similar Triangles


Which of these statements are true? Explain your reasoning.

Any two right-angled triangles will be similar.

If you enlarge a shape you get two similar shapes.

All circles are similar

Convince me that:

any two regular polygons with the same number of sides are similar.

alternate angles are equal (using congruent triangles).

Review 6

Summer Term Activities

Jun 2015 CHANGE OF TIMETABLE

NOTES FOR THE TEACHER

This is an ‘Active SOW’ which tells the teacher what to teach and when. It is a working document and notes should be made as required.

Main Textbook: Elmwood Press 9 Higher student book.

Notes: Leave out the Mixed Review exercises until you start doing end of year revision in April. Leave out the Fully Functional & Puzzle pages until after the end of year exams in May.

Resources: Elmwood Press Textbooks 7,8,8: Higher, Core & Support available

Homework: a variety of tasks can be set ranging from short Q&A to extended pieces of investigation work. When you set homework – you MUST mark it and record it. You could also ask students to make summary

notes of each topic to lay foundations for independent study.

Fronter: has been loaded with a wealth of homework practice which students should be directed to by you.

Lesson Planning: When planning lesson have extremely high expectations of all your students at all times.

Overall aims of the new National Curriculum: These aims are that pupils should develop fluency, reason mathematically and be able to solve problems.

Rules for Closing the Gap: Know your students; Plan effectively; Enthuse & Inspire; Engage & Guide; Feedback appropriately & Evaluate together.

Assessment: All Year 9 pupils will sit for their end of Year exams in the 2nd

week of May

Year 9 Higher CONTENTS

NB: Teachers should aim to complete a minimum of 1 unit each

half-term

sow year 9 higher target levels: 6 8 set 1 only · sow year 9 higher target levels: 6 ... write...

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