addressing the three key questions of the qca big picture ... · arranging the learning in year 8...

Arranging the Learning in Year 8

Addressing the three key questions of the QCA Big Picture of the curriculum

Content

The QCA Big picture page 03

Overarching themes page 04

The schemes explained page 05

Millions page 07

History of mathematics page 11

of 16www.nctem.org.uk

A Department for Children, Schools and Families initiative to enhanceprofessional development across mathematics



Use of hooks for learning, probing questions and rich activities will support developing successful learners, confident individuals and responsible citizens.

Enjoyment stems from the creative and investigative aspects of mathematics, and from developing different ways of looking at the world and becoming aware of an increasing range of patterns and aspects of mathematical thinking, such as perspective and patterns in numbers. It helps learners to understand many of the decision-making models used in building and design, and in modern business and industry.

The skills of reasoning with numbers, interpreting graphs and diagrams and communicating mathematical information are vital in enabling individuals to make sound economic decisions in their daily

Having confidence and capability in mathematics allows pupils to develop their ability to contribute to arguments using logic, data and generalisations with increasing precision. This in turn allows pupils to take a greater part in a democratic society. Becoming skilled in mathematical reasoning means that pupils learn to apply a range of mathematical tools in familiar and unfamiliar contexts.

Understanding risk through the study of probability is a key aspect of staying safe and making balanced risk decisions.

Opportunities to develop problem-solving, reasoning and communication skills are an important part of maintaining mental health.

Overarching themes

It’s a kind of magicHistory of mathematicsThe world around usPeople maths

Millions

(More details on next page)

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Explicit references to learning intentions and criteria for success

The QCA Big picure



Overarching themes

Millions

Construct, on paper and using ICT:pie charts for categorical data;bar charts and frequency diagrams for discrete data;simple time graphs for time series;simple scatter graphs;

identify which are most useful in the context of the problem.

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Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids

History of mathematics

Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations

Estimate probabilities from experimental data; understand that:if an experiment is repeated there may be, and usually will be, different outcomes;increasing the number of times an experiment is repeated generally leads to better estimates of probability

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Find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way

Plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c correspond to straight-line graphs

Classify quadrilaterals by their geometric properties

The world around us

Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease

Substitute integers into simple formulae

Transform 2D shapes by simple combinations of rotations, reflections and translations, on paper and using ICT; identify all the symmetries of 2-D shapes

Enlarge 2D shapes, given a centre of enlargement and a positive whole-numberscale factor

It’s a kind of magic

Deduce and use formulae for the area of a triangle, parallelogram and trapezium

Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket

Add, subtract, multiply and divide integers

People maths

Identify alternate angles and corresponding angles; understand a proof that:the sum of the angles of a triangle is 180° and of a quadrilateral is 360°–

Use units of measurement to estimate, calculate and solve problems in everyday contexts involving length, area, volume, capacity, mass, time and angle; know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons)

Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic or graphical form

Use logical argument to establish the truth of a statement



The schemes explained

Page 7 of 35www.nctem.org.uk


Y8It’s a kind of magic Part 1Learning intentions NC Hooks for learning Probing questions Rich activities

Calculate the surface area of cubes and cuboids

Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles

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Show me an example of…

What is wrong with the statement? How can you correct it?

What is the same and what is diff erent about these objects?

How can you change …

Is this always, sometimes or never true? If sometimes, when?

Convince me that…

Derive and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound shapes

Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids

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Curry triangle

Fibonacci’s disappearing squares

What makes you think that you have to multiply the base by the perpendicular height to fi nd the area of a parallelogram?

The area of a triangle is 12 cm². What are the possible lengths of base and height?

Right-angled triangles have half the area of the rectangle with the same base and height. What about non-right-angled triangles?

What other formulae for the area of 2D shapes do you know? Is there a formula for every 2D shape?

Standards UnitSS2 Understanding Perimeter and Area SS4 Evaluating statements about length and area

Use a practical approach for deducing formulae – cutting up rectangles and rearranging

Know the defi nition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by equal divisions of a circle

Know and use the formulae for the circumference and area of a circle

Calculate the surface area and volume of right prisms

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What is the same and what is diff erent about these objects?



Convince me that…

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Hooks for learning

THE STARTING POINT

Hyperlinks (mostly) to activities connected to the highlighted objective linked to the ‘theme’

Unit of work for the theme

The ‘theme’

- broken down into units of work

Rich activities

Examples of other rich activities that can be used to develop mathematical

thinking further

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Probing Questions

This section is populated for the highlighted objective linked to the ‘theme’ including questions from the Secondary National Strategy APP materials

Probing question stems provided for the other objectives – exemplified in the Standards Unit ‘Improving learning in mathematics’ materials and the ATM publication ‘Thinkers’



The schemes explained - continued

Page 8 of 16www.nctem.org.uk


I can... Criteria for success

fi nd the mode and range of the set of numbers here: 15, 17, 8, 9, 15, 7, 21, 6, 12?

fi nd the mean and median of the set of numbers here: 15, 17, 23, 9, 11, 27, 31, 6, 12. show that the mean of the numbers below is 7:

4 9 8

interpret and draw simple conclusions from graphs and diagrams such as:

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understand that pie charts are mainly suitable for categorical data. Draw pie charts using ICT and by hand, usually using a calculator to fi nd angles.

draw compound bar charts with subcategories.

use frequency diagrams for continuous data and know that the divisions between bars should be labelled.

know that it can be appropriate to join points on a line graph in order to compare trends over time.

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design a survey or experiment to capture the necessary data from one or more sources.

determine the sample size and degree of accuracy needed. construct tables for large discrete and continuous sets of raw data, choosing suitable class intervals.

design and use two-way tables.

construct, on paper and using ICT, scatter graphs.

understand correlation such as:

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Further support can be found at: www.standards.dfes.gov.uk/local/progressionmaps/maths/sec_ma_prgrsn_index

Number of children in family

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Criteria for success

Examples of possible outcomes for the bold assessment criteria in each of the ‘All’, ‘Most’, and ‘Some’ sections that could be used as criteria for success including examples from the Secondary National Strategy APP materials

Further support for criteria for success, probing questions and addressing barriers to progress can be found on the ‘Progression

Maps’ produced by the Secondary National Strategies

Recommended reading:- ‘1089 and all that’, David Acheson, first published in 2002.- ‘Why do Buses Come in Threes?’, Rob Eastaway and Jeremy Wyndham, first published in 1998 (esp. chapter 19)

At the end of each theme there is a list of any recommended books

that support the them



Y8Millions Part 1Learning intentions NC Hooks for

learningProbing questions Rich

ActivitiesPlan how to collect and organise small sets of data from surveys and experiments:

design data collection sheets or questionnaires to use in a simple surveyconstruct frequency tables for gathering discrete data, grouped where appropriate in equal class intervals

Calculate statistics for small sets of discrete data:find the mode, median and range, and the modal class for grouped datacalculate the mean, including from a simple frequency table, using a calculator for a larger number of items

Compare two simple distributions using the range and one of the mode, median or mean

Construct, on paper and using ICT, graphs and diagrams to represent data, including:bar-line graphsfrequency diagrams for grouped discrete datasimple pie charts

Interpret diagrams and graphs (including pie charts), and draw simple conclusions based on the shape of graphs and simple statistics for a single distribution

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What is the same and what is different about these objects?

How can you change…?


Convince me that…

Standards UnitS4 Understanding mean, median, mode and range

Discuss a problem that can be addressed by statistical methods and identify related questions to exploreCalculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal classConstruct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: (i) pie charts for categorical data (ii) bar charts and frequency diagrams for discrete and continuous data, (iii) simple line graphs for time series, (iv) simple scatter graphs, (v) stem-and-leaf diagramsMake accurate mathematical diagrams, graphs and constructions on paper and on screen

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The National Lottery

Nice lottery

Millions of sweets

When drawing a pie chart, what information do you need to calculate the size of the angle for each category?What is discrete/continuous data? Give me some examples.How do you go about choosing class intervals when grouping data for a bar chart/frequency diagram? What’s important when choosing the scale for the frequency axis?Is this graphical representation helpful in addressing the hypothesis? If not, what makes you think that and what would you change?When considering a range of graphs representing the same data:Which is the easiest to interpret? What makes you think that?Which is most helpful in addressing the hypothesis? What makes you think that?

Standards UnitS5 Interpreting bar charts, pie charts, box and whisker plotsS6 Interpreting frequency graphs

Lottery Project – as linked in the ‘hooks’ column

Design a survey or experiment to capture the necessary data from one or more sources; design, trial and if necessary refine data collection sheets; construct tables for gathering large discrete and continuous sets of raw data, choosing suitable class intervals; design and use two-way tablesSelect, construct and modify, on paper and using ICT, suitable graphical representations to progress an enquiry and identify key features present in the data. Include:

line graphs for time seriesscatter graphs to develop further understanding of correlation

Review interpretations and results of a statistical enquiry on the basis of discussions; communicate these interpretations and results using selected tables, graphs and diagrams

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http://www.kangaroomaths.com/free_resources/enrichment/lottery_project.doc

http://www.kangaroomaths.com/free_resources/enrichment/nice_lottery.ppt

http://www.kangaroomaths.com/free_resources/ks3/resources/MAP/swillions.pdf




find the mode and range of the set of numbers here: 15, 17, 8, 9, 15, 7, 21, 6, 12?

find the mean and median of the set of numbers here: 15, 17, 23, 9, 11, 27, 31, 6, 12. show that the mean of the numbers below is 7:

4 9 8

interpret and draw simple conclusions from graphs and diagrams such as:

•

•

•

•

understand that pie charts are mainly suitable for categorical data. Draw pie charts using ICT and by hand, usually using a calculator to find angles.

draw compound bar charts with subcategories.

use frequency diagrams for continuous data and know that the divisions between bars should be labelled.

know that it can be appropriate to join points on a line graph in order to compare trends over time.

•

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•

design a survey or experiment to capture the necessary data from one or more sources.

determine the sample size and degree of accuracy needed. construct tables for large discrete and continuous sets of raw data, choosing suitable class intervals.

design and use two-way tables.

construct, on paper and using ICT, scatter graphs.

understand correlation such as:

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Y8Millions Part 2Learning intentions NC Hooks for learning Probing questions Rich activities

Use 2D representations to visualise 3D shapes and deduce some of their properties

Use ruler and protractor to construct simple nets of 3-D shapes, e.g. cuboid, regular tetrahedron, square-based pyramid, triangular prism

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Convince me that…

Know and use geometric properties of cuboids and shapes made from cuboids; begin to use plans and elevations.

Make simple scale drawings

Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids

Evaluate the efficiency of alternative strategies and approaches

Refine own findings and approaches on the basis of discussions with others; recognise efficiency in an approach; relate the current problem and structure to previous situations

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How many grains of rice will fill your classroom?

How do you go about finding the volume of a cuboid? How do you go about finding the surface area of a cuboid?

‘You can build a solid cuboid using any number of interlocking cubes.’ Is this statement always, sometimes or never true? If it is sometimes true, when is it true and when is it false? For what numbers can you only make one cuboid? For what numbers can you make several different cuboids?

The rice problem – as linked in the ‘hooks’ column

Visualise and use 2-D representations of 3-D objects; analyse 3-D shapes through 2-D projections, including plans and elevations

Use and interpret maps, scale drawings.

Calculate the surface area and volume of right prisms.

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Convince me that…

Standards UnitThe rice problem – as linked in the ‘hooks’ column

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http://www.kangaroomaths.com/free_resources/ks3/resources/MAP/class_of_rice.doc

http://www.kangaroomaths.com/free_resources/ks3/resources/MAP/class_of_rice.doc




construct a cube, tetrahedron and octahedron using the nets here:

construct the net of a cuboid measuring 2 by 3 by 4 units.

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find the volume and surface area of the cuboid below:

• draw plans and elevations for solids such as:

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Recommended reading:

- ‘Innumeracy’, John Allen Paulos, latest edition published in 2001

- ‘Thinkers’ – First Published by the ATM in 2004

5cm

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Y8History of Mathematics Part 1Learning Intentions NC Hooks for

learningProbing questions Rich

ActivitiesUnderstand and use decimal notation and place value; multiply and divide integers and decimals by 10, 100 and 1000, and explain the effectRound positive whole numbers to the nearest 10, 100 or 1000 and decimals to the nearest whole number or one decimal placeMultiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbersCarry out calculations with more than one step using brackets and the memory; use the square root and sign change keysUse efficient written methods to add and subtract whole numbers and decimals with up to two placesCheck a result by considering whether it is of the right order of magnitude…… and by working the problem backwardsEnter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures)

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Convince me that…

Standards Unit N3 Rounding numbers

Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01.Order decimalsRound positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal places.Make and justify estimates and approximations of calculations.Use efficient written methods to add and subtract integers and decimals of any size, including numbers with differing numbers of decimal placesUse efficient written methods for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculationsCarry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots and fractions; use brackets and the memoryEnter numbers and interpret the display in different contexts (extend to negative numbers, fractions, time)

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Napier’s bones

The decimal point

Who invented zero?

Russian multiplication

Give pupils written examples of x and � calculations that are incorrect. Ask them to identify and talk through the errors and how they might be corrected.

37 × 64 = 2368. Explain how you can use this fact to devise calculations with answers 23.68, 2.368, 0.2368.

2368 ÷ 64 = 37. Explain how you can use this fact to devise calculations with answers 3.7, 3700, 0.37

3.2 × 23 = 73.6. Explain how you can use this fact to devise other calculations with the same answer.

73.6 ÷ 3.2 = 23. Explain how you can use this fact to devise other calculations with the same answer.

Standards Unit N2 Evaluating statements about number operations

Extend knowledge of integer powers of 10; recognise the equivalence of 0.1,

and 110 _

; and 10-1; multiply and divide by any integer power of 10Use efficient written methods to add and subtract integers and decimals of any size; multiply by decimals; divide by decimals by transforming to division by an integerUse a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation; use the constant, and sign change keys; use the function keys for powers, roots and fractions; use brackets and the memory

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Convince me that…

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http://nrich.maths.org/public/viewer.php?obj_id=1132

http://mathworld.wolfram.com/DecimalPoint.html

http://www.scienceiq.com/ShowFact.cfm?ID=205

http://www.scienceiq.com/ShowFact.cfm?ID=205

http://mathforum.org/dr.math/faq/faq.peasant.html

http://mathforum.org/dr.math/faq/faq.peasant.html




Work out mentally the answers to questions such as: 476 × 1000 = 9000 ÷ 100 = 43 x = 430 4600 ÷ = 46 610 x = 6100 5700 ÷ = 570

Solve problems such as: ¿ ÷ 10 = 800. What does the ¿ represent? 700 ÷ ¿ = 7. What is the missing number?

Place these numbers in order of size, starting with the greatest: 0.206, 0.026, 0.602, 0.620, 0.062

Work out mentally the answers to questions such as: 47.6 × 1000 = 910 ÷ 100 = 4.3 × = 430 4600 ÷ = 4.6 0.61 × = 6100 570 ÷ = 0.57

Solve problems such as: ¿ X 0.2 = 200. What does the ¿ represent? What number do you multiply by 0.6 to get 60?

Calculate: 312 x 43 611 ÷ 13 384.6 x 7 298.2 ÷ 7 374.37 + 46.8 382.7 – 61.3

Check a result by approximating the answer such as: 18 × 39 ≈ 800 (20 × 40)

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Calculate: 347 × 0.23 65.2 × 7.1 115 ÷ 4.6 64.6 ÷ 17 151.8 ÷ 0.06

Calculate: 2.41 x 31 is approximately 3 x 30 = 90, and is equivalent to 2.71 x 100 x 31 x 100 or 271 x 31 x 100 518 ÷ 4.8 is approximately 500 ÷ 5 = 100 and is equivalent to 5180 ÷ 48

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Calculate: 0.63 × 0.01 9.3 x 0.1 0.27÷ 0.1 5.96 ÷ 0.01

Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation, such as: 47.72 × 68.3 2.01 × (9.2 – 3.6)

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Y8History of Mathematics Part 3Learning intentions NC Hooks for learning Probing questions Rich activities

Use vocabulary and ideas of probability, drawing on experience

Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts; identify all the possible mutually exclusive outcomes of a single event

Estimate probabilities by collecting data from a simple experiment and recording it in a frequency table; compare experimental and theoretical probabilities in simple contexts

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Convince me that…

Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable

Compare estimated experimental probabilities with theoretical probabilities, recognising that:

if an experiment is repeated the outcome may, and usually will, be differentincreasing the number of times an experiment is repeated generally leads to better estimates of probability

Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 - p; use diagrams and tables to record in a systematic way all possible mutually exclusive outcomes for single events and for two successive events

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Blaise Pascal

Pascal’s triangle

Pierre Fermat

When you spin a coin, the probability of getting a head

is ½. So if you spin a coin ten times you would get exactly 5 heads. Is this statement true or false? What makes you think that?

You toss a coin 100 times and count the number of times you get a head. A robot is programmed to toss a coin 1000 times. Who is most likely to be closer to getting an equal number of heads and tails? What makes you think that?

Standards UnitS1 Ordering probabilitiesS2 Evaluating probability statementsS3 Playing probability computer games

Link with the Lottery project from earlier in the year

Interpret results involving uncertainty and prediction

Identify all the mutually exclusive outcomes of an experiment; know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems

Compare experimental and theoretical probabilities in a range of contexts; appreciate the difference between mathematical explanation and experimental evidence

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What strategies do you use to make sure you have found all possible mutually exclusive outcomes for two successive events, for example rolling two dice?How do you know you have recorded all the possible outcomes?

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http://www.kangaroomaths.com/free_resources/enrichment/april_pascal.doc

http://www.mathsisfun.com/pascals-triangle.html

http://www.kangaroomaths.com/free_resources/enrichment/january_fermat.doc




give an example of an event which would be placed at ‘0’ on the probability scale below. Give an example of an event that would be placed at ’1’.

solve problems such as: A card is picked from a pack of 52 ordinary playing cards. What is the probability of getting (a) a three, (b) a club, (c) the queen of hearts? Draw an arrow to show the position of each of your answers on the probability scale.

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understand that if an experiment is repeated there may be, and usually will be, different outcomes by explaining problems such as: Marjorie drops a drawing pin 10 times while waiting for the phone to ring. She notices it lands point up on 7 occasions. When Ruth finally calls Marjorie, she is told about the experiment. Ruth says, ‘If you drop the pin 100 times it will land point up 70 times.’ Is Ruth correct?

understand that increasing the number of times that an experiment is repeated generally leads to better estimates of probability.

find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way buy solving problems such as: Two dice are rolled together and the product of the two numbers is found. Construct a sample space diagram and find the probability that the product is a multiple of 3. A greengrocer’s lucky dip contains a large selection of kiwi fruit, kumquats, cauliflower and cabbages. For 75p you get to pick two items. List the different possible selections of ‘fruit ‘n’ veg’ you could get as a result of taking part.

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Solve probability problems such as: The probability that a snooker ball chosen at random is red is 15/21. What is the probability that a ball chosen is a colour other than red? The probability that a certain traffic light shows red as James approaches it is 0.3 and the probability that it is green is 0.65. What is the probability that it is amber? A bag contains a selection of multilink cubes. There are 3 red, 5 yellow, 2 blue and 6 green cubes. A cube is picked at random. What is the probability that a blue or yellow cube is not chosen? The probability that Jonathan’s train is on time is 3/8. The probability that the train is early is 5/15. What is the probability that the train is late?

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Y8History of mathematics Part 3Learning intentions NC Hooks for learning Probing questions Rich activities

Describe integer sequences; generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence)Generate sequences from patterns or practical contexts and describe the general term in simple casesExpress simple functions in words, then using symbols; represent them in mappingsUse conventions and notation for 2D coordinates in all four quadrants; find coordinates of points determined by geometric informationGenerate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of, on paper and using ICT; recognise straight-line graphs parallel to the x -axis or y -axisPlot and interpret the graphs of simple linear functions arising from real-life situations, e.g. conversion graphsUse correctly the vocabulary, notation and labelling conventions for lines, angles and shapes

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Show me an example of…What is wrong with the statement? How can you correct it?What is the same and what is different about these objects?How can you change…? Is this always, sometimes or never true? If sometimes, when?Convince me that…

Generate terms of a linear sequence using term-to-term and position-to-term rules, on paper and using a spreadsheet or graphics calculatorUse linear expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generatedExpress simple functions algebraically and represent them in mappings or on a spreadsheetGenerate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x , on paper and using ICT; recognise that equations of the form y = mx + c correspond to straight-line graphsConstruct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations, e.g. distance–time graphs

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Rene Descartes and the fly

Why ‘m’ and ‘c’?

Class Debate:Is a square a rectangle? Is a parallelogram a trapezium? Is a square a rhombus? Is an oblong a shape? Is a diamond a shape? Is a kite a diamond? Is a rhombus a kite?

How do you go about finding a set of coordinates for a straight line graph, for example y = 2x + 4?How do you decide on the range of numbers to put on the x and y axes?How do you decide on the scale that you are going to use?If you increase/decrease the value of m, what effect does this have on the graph? What about changes to c?What have you noticed about the graphs of functions of the form y = mx + c? What are the similarities and differences?What properties do you need to know about a quadrilateral to be sure it is a kite; a parallelogram; a rhombus; an isosceles trapezium?Can you convince me that a rhombus is a parallelogram but a parallelogram is not necessarily a rhombus?Why can’t a trapezium have three acute angles?Which quadrilateral can have three acute angles?

Link to People maths with Graph aerobicsResearch origins of names of shapes

Standards UnitA7 Interpreting functions, graphs and tablesSS1 Classifying shapes

Generate sequences from practical contexts and write and justify an expression to describe the term of an arithmetic sequenceGenerate terms of a sequence using term-to-term and position-to-term rules, on paper and using ICTFind the inverse of a linear functionGenerate points and plot graphs of linear functions, where is given implicitly in terms of x (e.g. ay + bx =, y + bx + c +), on paper and using ICT; find the gradient of lines given by equations of the form, y = mx + c, given values for m and c Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations, e.g. time series graphsKnow the definition of a circle and the names of its parts

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Show me an example of…What is wrong with the statement? How can you correct it?What is the same and what is different about these objects?How can you change…?Is this always, sometimes or never true? If sometimes, when?Convince me that…

Standards UnitA5 Interpreting distance-time graphs with a computerA6 Interpreting distance-time graphs

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http://www.xycharts.com/descartes.html

http://www.xycharts.com/descartes.html




plot the points (3,11), (5, 7) and (12,7) and write down the coordinates of a fourth point that will make a parallelogram when joined in the correct order.

generate and plot pairs of co-ordinates for y = x + 1 and y = 2x

plot graphs such as y = x, y = 2x, y = x+1 and y = x -2

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plot the graphs of simple linear functions using all four quadrants by generating co-ordinate pairs or a table of values such as: y = 2x - 3 y = 4 - 2x

understand the gradient and intercept in y = mx + c by describing similarities and differences of given straight line graphs such as: Which of these graphs are parallel: y=2x+2, y=x+2, y=2-2x, y=½x+2, y=2x-½, y=½+2x ? Which of these graphs have the same y-intercept: y=2x+2, y=x+2, y=2-2x, y=½x+2, y=2x-½, y=½+2x?

know the properties (equal and/or parallel sides, equal angles, right angles, diagonals bisected and/or at right angles, reflection and rotation symmetry) of:

an isosceles trapeziuma parallelograma rhombusa kitean arrowhead or delta.

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generate the first five terms of a linear sequence such as:

start with 12 and add 5 each timestart with 6 and double each timethe nth term is n + 3the nth term is 2n + 3the nth term is 6 – 3n

use a spreadsheet or graphical calculator to generate tables of values and explore terms of sequences.

find the gradient of lines given by equations of the form y = mx + c such as: y = 3x y = 3x + 4 y = x + 4 y = x – 2 y = 3x – 2 y = -3x + 4

construct linear functions arising from real-life problems, plot their corresponding graphs and discuss and interpret graphs arising from real situations such as writing a commentary for the race shown below:

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Recommended reading:

- ‘Thinkers’ – First Published by the ATM in 2004- ‘Men of Mathematics’, E.T.Bell, first published in 1937

addressing the three key questions of the qca big picture ... · arranging the learning in year 8...

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