CfE Course Plan - Newbattle High School [PDF]

S3 Planet Maths 4th level . ... National 4 Maths: cover all content, plus National 5. Numeracy. Decagon. Beyond 4th leve

4 downloads 21 Views 316KB Size

Recommend Stories


High School COURSE CATALOG
When you talk, you are only repeating what you already know. But if you listen, you may learn something

High School Course Equivalents
Your task is not to seek for love, but merely to seek and find all the barriers within yourself that

High School Course Catalog
Never wish them pain. That's not who you are. If they caused you pain, they must have pain inside. Wish

Grinnell High School Course Guide
Forget safety. Live where you fear to live. Destroy your reputation. Be notorious. Rumi

RONALD REAGAN HIGH SCHOOL – COURSES & CURRICULUM Four-Year Course Plan
Goodbyes are only for those who love with their eyes. Because for those who love with heart and soul

CfE Briefing
Kindness, like a boomerang, always returns. Unknown

Chichester High School Course Guide 2018-19.pdf
The best time to plant a tree was 20 years ago. The second best time is now. Chinese Proverb

Chichester High School Course Guide 2018-19.pdf
Seek knowledge from cradle to the grave. Prophet Muhammad (Peace be upon him)

Senior Course Offerings for Loveland High School
We can't help everyone, but everyone can help someone. Ronald Reagan

Orlando Christian Prep High School Course Guide
You often feel tired, not because you've done too much, but because you've done too little of what sparks

Idea Transcript


INDEX (if viewing this file in MS Word, control+click takes you straight to that section) Index ...................................................................................................................................... 1  Course Aims ......................................................................................................................... 2  Levels of Course ................................................................................................................. 2  Statistics ............................................................................................................................... 3  Measurement ........................................................................................................................ 8  Perimeter, Area and Volume .............................................................................................. 14  Time ..................................................................................................................................... 19  Direction and Scale ............................................................................................................ 23  Angle ................................................................................................................................... 26  Money .................................................................................................................................. 29  Shape (includes Trigonometry) ......................................................................................... 34  S1 Shape Experience ....................................................................................................... 34  S1–S6 Shape and Trigonometry ....................................................................................... 35  Co-ordinates and Symmetry .............................................................................................. 37  Probability and Risk ........................................................................................................... 41  Proportion and Ratio (includes Similarity) ....................................................................... 44  Mathematics – its impact on the world, past, present and future .................................. 48  S1/S2 Planet Maths 3rd level ............................................................................................ 48  S3 Planet Maths 4th level ................................................................................................. 48 

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

COURSE AIMS        



To develop the mathematical skills and confidence of our pupils at a level that is appropriate for them. To give every pupil the opportunity to master mathematical skills at a level that is appropriate for them. To allow for number and algebra to be taught in detail. To promote depth and breadth of learning and understanding by ensuring pupils master the previous level before moving on to the next level of study. To provide appropriate challenge at every level, not just the higher levels. To develop the mathematical skills that pupils will need for everyday life, the world of work and Further/Higher Education. To give pupils all the prerequisite skills they will need to be ready to complete the appropriate SQA qualification in S4. To provide full coverage of all 3rd level outcomes and experiences for (almost) all; and 4th level for those who become secure at 3rd level. To ensure progression in all topics is based on prior understanding of number and algebra.

Levels of Course CfE Level Circle Triangle Pentagon

Work on basic skills across First Level and Second Level Achieve Second Level and begin to develop Third Level Consolidate, then achieve Third Level

Octagon

Achieve Fourth Level and beyond

Decagon

Beyond 4th level

Dodecagon

Beyond 4th level

CfE reporting

National Qualifications Roughly National 2 Applications of Mathematics National 3 Applications of Mathematics: cover all content National 4 Applications of Mathematics: cover all unit content and ready for Added Value once the senior phase starts. Lifeskills Route Maths Route National 4 Maths: cover all National 5 Applications of content, plus National 5 Mathematics cover all content Numeracy start National 5 Mathematics up to grade C standard, including covering all content in the Expressions and Formulae unit Pass National 5 Mathematics exam with an A or B Classes who have enough time to cover dodecagon in full (likely to be those who came through the maths route) ought to be able to pass the exam with an A and be Ready for Higher. Teachers with less able classes (possibly those who came through the Lifeskills route) will not necessarily cover the entire dodecagon course but will still be able to guide classes to an exam pass at National 5.

- Page 2 -

(it is recognised that (e.g.) 3S and 4D are essentially the same level)

Maximum of 2D for number Maximum of 2C for other areas Maximum of 2S for number Maximum of 3D for other areas Maximum of 3S for number Maximum of 4D for other areas Maximum of 4C for all areas. 4S if added value unit is complete. If a pupil is working successfully at decagon, they are 4S for everything

n/a

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

STATISTICS rd

th

3 /4 level CfE Statistics outcomes: I can work collaboratively, making appropriate use of technology, to source information presented in a range of ways, interpret what it conveys and discuss whether I believe the information to be robust, vague or misleading. MNU 3-20a I can evaluate and interpret raw and graphical data using a variety of methods, comment on relationships I observe within the data and communicate my findings to others. MNU 4-20a

When analysing information or collecting data of my own, I can use my understanding of how bias may arise and how sample size can affect precision, to ensure that the data allows for fair conclusions to be drawn MTH 3-20B In order to compare numerical information in real-life contexts, I can find the mean, median, mode and range of sets of numbers, decide which type of average is most appropriate to use and discuss how using an alternative type of average could be misleading. MTH 4-20b

I can display data in a clear way using a suitable scale, by choosing appropriately from an extended range of tables, charts, diagrams and graphs, making effective use of technology. MTH 3-21a I can select appropriately from a wide range of tables, charts, diagrams and graphs when displaying discrete, continuous or grouped data, clearly communicating the significant features of the data. MTH 4-21a

Cross Curricular Links (whole school numeracy record): there is a whole school progression for teaching drawing graphs, and interpretation of graphs. There is a whole school agreement on common standards for graph drawing. Graph drawing is used a lot in science and geography. Interpretation of statistics is required in science and RME. RESOURCES (in addition to topic PROGRESSION SUGGESTIONS FOR ACTIVITIES FOR LEARNING SmartBoard files on server)

Pupils should be aware that surveying and interpreting is part of this process: ASK: Ask questions that can be answered by carrying out a survey or investigation and comparing sets of data. COLLECT: gather and record data from a variety of sources including class surveys, data from internet, books and newspapers. ORGANISE: design and use tables and diagrams DISPLAY: construct graphs, using technology if possible. INTERPRET: draw and communicate conclusions

In general the teaching approach for introducing this topic should be as follows for all year groups. These approaches allow the topic to be set in a relevant context: 1. In their first lesson(s), all classes will complete the department’s Census at School (CaS) questionnaire or gather other data relevant to the class. 2. When constructing graphs there should be a clear focus on drawing axes, writing good titles, and labelling graphs. 3. Ideally pupils should always have an experience of constructing graphs using ICT, although we do not currently always have access to the resources for this. 4. Pupils also need to interpret and explain situations represented in graph forms. Where possible, real-life graphs should be used as non-routine questions. A key skill to develop here is clearly communicating the pupil’s observations. In this outcome, we should be putting pupils in a situation where literacy is a major part of the outcome. We should be developing their ability to interpret graphs or calculated statistics in a written and oral way and to write conclusions in proper sentences.

- Page 3 -

Item Banks of level D/E questions

Smartboard File on literacy in folder

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

STATISTICS (CIRCLE COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements Construct:  Basic Frequency Tables  Straightforward Bar graphs  Pie charts (using pre-printed template)

Using real-life or made up data as appropriate

Active Worksheet Website: Pie Chart Templates Primary O3, Secondary Q7

Describe and compare key features of:  Bar graphs (no decimal numbers at all).  Line graphs (no decimal numbers)  Pictographs  Basic pie charts Conduct a survey on a topic of their choice

ICT Resources: Maths Pack 2 (bar graphs/ /pictographs); supermathsworld.com (games)

Banks of graphs are available in file on server and past 5-14 questions Maths Pack 2: Tally chart, Bar chart, Pictogram

Class should do all of the following: Design questionnaire using ICT, decide who to ask, collect results, create graphs using ICT (not by hand)

- Page 4 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

STATISTICS (TRIANGLE COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements Construct:  (Ungrouped) Frequency Tables, with emphasis on labelling and column headings (to National 3 Standards)  Bar Charts (to National 3 Standards)  Line Graphs (whole numbers only)  Scatter Graphs (no line of best fit)

Real life or made up data as appropriate

Calculate the mean, and compare data set using means, giving answer in a sentence

Likely to be mostly with a calculator at this level, trying to avoid recurring/infinite decimals

Newbattle documents: refer to the whole school common approaches for graph drawing and to the whole school progression for graph drawing. For a confident triangle class, extend bar graphs into compound bar graphs

Include some basic examples along the lines of “the company say there are ___ on average, are they right?”

Smartboard Files containing example graphs to select suitable examples from ICT Resources: Maths Pack 2 (bar graphs/line graphs/pie charts/pictographs)

Dynamic Maths: Statistics-04 Worksheet “Mean Calculate and Compare”

Describe and compare (in sentences) key features of:  Tables (including non-routine)  Bar graphs (including non-routine ones e.g. compound, stacked)  Line graphs (including non-routine ones e.g. multiple lines)  scatter graphs (basic comment only, no best fit line)  pie charts (recognise max/min sectors; o For sectors that are quarters and halves, evaluate frequency when they know population size (basic examples only)

Newbattle documents: refer to the progression document for graph interpretation.

Make basic decisions based on data presented in a graph

 

Discuss examples of misleading conclusions drawn from graphs and examples of misleading graphs. One example should include a very small sample.

At least one lesson must focus on literacy, reasoning, sampling and validity, with class writing answers in full sentences. Every class MUST have experience of:  Identify key words in question and discuss their meaning  Writing multiple sentences in their own words describing what a graph is showing in their  putting sentences up on boards; discussing as a class which sentences were stronger or weaker interpretations of graphs (i.e. identifying when a pupil’s sentence actually doesn’t answer the question; or where a pupils sentence makes no sense to a reader (“Mayfield was most”) ) e.g. temperature graph: what day should he go out to sell most ice creams? e.g. triangle Record of Work question (Sean’s kilt)

Questions that ask pupils to evaluate the validity of the data  e.g. a pie chart showing 10 pupils at Newbattle. 80% of them support Celtic. The chart says that most Newbattle pupils support Celtic. Do you agree? What if the same survey was repeated in London?

- Page 5 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

STATISTICS (PENTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: triangle percentages and fractions Pie Charts  construct from raw data (straightforward examples where the angles work out to be whole numbers, avoiding decimals)  calculate the frequency for a sector when given the percentage or angle and the population size  compare two pie charts (e.g. before and after) and comment on the change. Scatter Graphs  Construct from raw data  Draw line of best fit  Describe trends shown in graph in sentences, including use of word correlation  Use line of best fit to estimate one value given another

Pie charts: link to work on fractions. Pupils may need revision on how to use a protractor e.g. pie chart shows 20% of people voted Labour. If 3500 voted Labour, how many voted altogether? Newbattle documents: refer to progression in drawing graphs; and common standards in graph drawing

Stem and Leaf Diagram  Interpret a stem-and-leaf diagram  Construct from raw data including a key

Smartboard Files containing example graphs to select suitable examples from Active Worksheet Website: Worksheet Secondary D24 Active Worksheet Website: Worksheet Secondary Q9 (draw line of best fit) Active Worksheet Website: Worksheet Secondary Q15

Line Graphs  Construct line graphs, paying attention to scale

Worksheet on server Newbattle documents: refer to progression in drawing graphs;

Mean, median, mode and range:  Calculate  Write two comments comparing two data sets represented by mean/median/mode and range

Ideally, if time allows, also include a lesson on literacy and writing comments (see description in triangle course)

Discuss examples of misleading conclusions drawn from graphs and examples of misleading graphs. Discuss problems of very small or very large sample sizes and how sampling can be done in practice

Dynamic Maths: Statistics-03, 04, 05, 06 Active Worksheet Website: Worksheet Secondary Q12

Bias worksheet on server Rich Task Opportunity: various extended projects on server in real-life situations including Wimbledon Statistics, and Crime Scene Analysis

- Page 6 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

STATISTICS (OCTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements MATHS ROUTE:  revise Pentagon Statistics as required  Describe and compare in sentences key features of graphs, compare graphs, compare data sets using statistics  Discuss whether data is valid and using sampling strategies and making informed choices LIFESKILLS ROUTE ONLY: Revise following pentagon content:  Constructing scatter graphs, drawing line of best fit and estimating  Drawing pie charts from raw data

Consult SQA documentation on the course content for National 5 Applications of Maths (Managing Finance and Statistics unit, outcome 2)

Calculate sample standard deviation (n < 7)

Always calculate standard deviation using the table method represented by

(x  x ) the formula s 

Calculate quartiles and (semi) interquartile range

Dynamic Maths: Statistics-01, 02

2

n 1

Constructing and interpreting boxplots Write comments to compare means/medians/standard deviations/IQR/SIQR for two data sets

(***DEPARTMENT POLICY agreed 30/4/12***)

Rich Task Opportunity: various extended projects on server in real-life situations No content at Decagon

STATISTICS (DODECAGON COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements The content for dodecagon is the same as the content of the Octagon Lifeskills course except:  Added content of determining the equation of a line of best fit and use it to calculate one variable when the value of the other is known  drawing pie charts from raw data is not included for National 5 Mathematics  boxplots are not included for National 5 Mathematics

- Page 7 -

Dynamic Maths: Statistics-01, 02

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

MEASUREMENT rd

th

3 /4 level CfE Measurement outcomes: I can solve practical problems by applying my knowledge of measure, choosing the appropriate units and degree of accuracy for the task. MNU 311a

Having investigated the practical impact of inaccuracy and error, I can use my knowledge of tolerance when choosing the required degree of accuracy to make real life calculations. MNU 4-01a

I can apply my knowledge and understanding of measure to everyday problems and tasks and appreciate the practical importance of accuracy when making calculations. MNU 4-11a

Cross Curricular Links (whole school numeracy record): CDT, HE and PE all make use of measurement of length and/or weight and/or volume and/or time Notes on approaches and activities for RESOURCES (in addition By the end of the topic, pupils should be able to: to topic SmartBoard files on learning server)

MEASUREMENT (CIRCLE COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements Discuss and investigate concepts of length, weight and volume. 

Reading ruler scales in centimetres to nearest whole number; draw lines of a given length. Introduce the idea of reading ruler scales in centimetres using one decimal place. Tolerance ± 5 millimetres

This would be the first occasion that S1 pupils have come across decimal places in maths

Measure lengths of small objects in millimetres Estimate then measure: * length of classroom objects in millimetres or centimetres * lengths around the school in metres. Class discussion on sensible estimates for weights, heights, volumes of everyday objects Equivalences: 100cm = 1 metre, 10mm = 1cm, 1000m = 1km, 1000g =1kg, 1000ml = 1litre Changing between units, whole numbers only:  From metres into centimetres  From centimetres into millimetres  From kilometres into metres  From kilograms into grams  From litres into millilitres

Pupils should be encouraged to choose an appropriate measuring instrument, to choose the most appropriate units, and to decide on an appropriate degree of accuracy. Get pupils to physically hold gram weights and kilogram weights Whole numbers only, no decimals. The experience of measurement at this level should be focussed on practical work. Try to avoid too much emphasis on paper based theoretical conversion exercises. Change units in one direction only (i.e. “how many centimetres in 2 metres, 7 metres, 10 metres…” but not “how many metres in 500 centimetres?”)

- Page 8 -

Dynamic Maths: Measure-01  Teaching Measures: What’s my length  Measurement equipment in Base.  Active Worksheet: Worksheet Primary P2 Measuring worksheets on server Weights in base

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

MEASUREMENT (TRIANGLE COURSE) Prerequisites from Number/Algebra courses and other topics: Triangle decimals will be useful Classes repeating triangle are unlikely to need to cover this again. Pupils should be aware that people in measuring jobs only use millimetres.

 

Read scales on measuring devices to the nearest marked, numbered division

Science SmartBoard file (abc CIRCLE TRIANGLE PENTAGON Measurement Lesson CrossCurricular Science)



Class discussion on making sensible estimates (including choosing sensible units) for:  Long distances in miles/km (using 1km≈½ mile)  Heights of people (3 feet ≈ 1 m), buildings, hills, mountains etc.  Capacity of everyday objects  Weights of everyday objects, including large objects  Temperature in different places under certain weather conditions Equivalences for length: 100cm =1 metre, 10mm = 1cm, 1000m = 1 kilometre, 1000mm = 1 metre

Class discussions are likely to also touch upon commonly used imperial measurements (e.g. feet and inches for height; stone for weight). An in depth treatment would not be required, but pupils should know their existence.

Who Wants to Be a Millionaire PowerPoints/voting handsets

Use a ruler to measure in centimetres (giving answers to one decimal place) and/or millimetres, to a tolerance of ±2mm/0·2cm



Dynamic Maths: Measures-01 Teaching Measures: What’s my length? Teaching Measures: What’s my length, Class Mass, Class Capacity Active Worksheet Website: Worksheet Primary P9, P11 (Reading Scales)

Various “Choosing units DGW” worksheets on server

Class should be told that 1cm³ holds 1ml of water; and that 1ml of water weighs 1 gram.

Other equivalences: 1000g = 1 kilogram, 1000ml = 1 litre, 1ml = 1cm³, 1 litre = 1000cm³ Change mixed units (e.g. m and cm, l and ml) to (e.g.) cm/ml only (i.e. no decimals) Change backwards and forwards between units, (whole numbers and basic halves) Problem solving: Solving problems involving measurement

e.g. 1m 3cm = 103cm, 2m 14cm = 214cm, 10m 5cm = 1005cm Whole numbers and basic halves (e.g. 2½m, 4½kg) and “point fives” e.g. 2·5cm, 4·5m. With more able classes, could extend towards 2·3m, 4·7kg etc. using a calculator. e.g. A 1 metre piece of wood has 20cm cut off it. What is the length of the wood?

- Page 9 -

Dynamic Maths: Measure-02, 04 Teaching Measures: Measure Match, Conversion Tables (and worksheets)

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

MEASUREMENT (PENTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: pentagon decimals Read scales on measuring devices to the nearest marked, unnumbered division

Know all equivalences from triangle, plus 1000kg = 1 tonne, 1000cm³ = 1 litre Changing between all units, emphasising decimals.

Science SmartBoard file (abc CIRCLE TRIANGLE PENTAGON Measurement Lesson Cross-Curricular Science)

*** NUNP: check whether the class has covered multiplying or dividing decimal by 10, 100 or 1000. If they haven’t, take this into account when choosing examples.

Changing between mixed units (e.g. m&cm to cm or to m (with a point)) e.g. 2·04kg = 2kg___g e.g. write 1m 3cm as a decimal, write 10 litres 5 ml as a decimal

Active Worksheet Website: Worksheet Primary P9, P11 (Reading Scales) Teaching Measures: What’s my length, Class Mass, Class Capacity Dynamic Maths: Measure02, 03, 04 Teaching Measures: Measure Match, Conversion Tables (and worksheets)

Activity: Class measure various items (e.g. width of a protractor in mm, width of a desk in cm, length of jotter in mm). Discuss range of values measured by class and how this can be expressed. Understand the meaning of tolerance (±) notation in the context of measurement

e.g. the temperature is allowed to be 40°C ± 2°C e.g. the height of a box is 1.5m ± 0.1m

Dynamic Maths: Measures05, 06

Identifying maximum and minimum values from tolerance notation. Identify the range of values which are acceptable.

e.g. in the example above, could the temperature be 39°, could it be 45°? Write five values that the height of the box in the second example could take

See National 4 Lifeskills AVU for examples of the style of question

Identify which measurements are/are not acceptable given a particular tolerance requirement . Problem solving: Non-routine questions, discussing methods, e.g. questions where units are mixed (e.g. one length in cm, the other in mm) Work out how many uniform sized items can fit into a given space e.g. books are 3cm wide, how many books can fit on a shelf 90cm wide? 91cm wide? 89cm wide?

- Page 10 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) Be aware of the need to round decimal answers up or down to the nearest whole number as the context requires

The remaining topics should be done with S3 (or beyond) only: Work out how many uniform sized items can fit onto a given shelf by considering two dimensions

Pack differently-sized items into uniform containers in the most efficient way (based on order of arrival) using a first-fit algorithm

e.g. how many 30cm boxes can fit onto a 2 metre long shelf? e.g. how many 60 seater buses are needed to transport 347 pupils?

e.g. boxes are 20cm wide and 30cm tall, how many can fit onto a shelf that is 90cm wide and 50cm tall? What if the boxes were turned around the other direction?

Brechin worksheet on server

Suggested one lesson maximum on this, although could do more if time was available

DGW Octagon Measures file Worksheets on server:  Education Scotland Container Packing First Fit worksheets on server  Ferry packing  Files on computer discs

- Page 11 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

MEASUREMENT (OCTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements MATHS ROUTE AND LIFESKILLS ROUTE Read scales on measuring devices to the nearest marked, minor unnumbered division

Science SmartBoard file (abc CIRCLE TRIANGLE PENTAGON Measurement Lesson Cross-Curricular Science)

Convert between all units previously encountered (100cm =1 metre, 10mm = 1 centimetre, 1000m = 1 kilometre, 1000mm = 1 metre, 1000g = 1 kilogram, 1000ml = 1 litre, 1ml = 1cm³, 1 litre = 1000cm³, 1000kg = 1 tonne, 1000cm³ = 1 litre) Understand the meaning of tolerance (±) notation in the context of measurement, where units may be mixed or the tolerance may be expressed as a percentage. Identifying maximum and minimum values. Identify the range of values which are acceptable. Rich task opportunity: Be aware of the range of possible “real” values of a given rounded measurement

Problem solving: Apply knowledge of tolerance to solve problems

Pack differently-sized items into uniform containers in an efficient way, subject to various conditions

Dynamic Maths: Measure 02, 03, 04

i.e. tolerance of 17cm ± 2mm, 70 tonnes ± 50kg, 12·8km ± 10%

Dynamic Maths: Measure05, 06

Factory requires screws of length 2·5cm ± 2mm. Which of following would be rejected? 21mm, 25mm, 26mm, 29mm, 24·5mm, ... e.g. the length of a pencil is 12·7cm (1d.p.). Identify the maximum and minimum possible lengths of the pencil (12·75cm and 12·65cm). e.g. The Great Wall of China is 6700km long to the nearest hundred km. What is the maximum possible length? e.g. a box has height 50cm ± 10mm. Four identical boxes are stacked on top of each other. What is the minimum height of the stack? Would the boxes fit into a room 2 metres tall? Perimeter/area/volume questions where length(s) are expressed with a tolerance. What is the max/min perimeter/area/volume? Suggested one lesson maximum on this, although could do more if time was available

- Page 12 -

Worksheets on server: Education Scotland Container Packing worksheets on server Ferry packing Files on computer discs

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) S3 CLASSES (and older) ONLY: Identify the maximum number of uniform cuboids that can be packed upright into a larger cuboid by considering the two possible orientations.

See National 5 Applications of Maths unit assessments and past exam questions to get the idea of the type of questions that might be asked

Identify the maximum number of uniform cuboids or cylinders that can be packed in any orientation by considering the six (or three) possible orientations No content at decagon No content at dodecagon

- Page 13 -

Container packing DGW worksheets on server

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

PERIMETER, AREA AND VOLUME rd

th

3 /4 level CfE Perimeter Area Volume outcomes: I can solve practical problems by applying my knowledge of measure, choosing the appropriate units and degree of accuracy for the task and using a formula to calculate area or volume when required. MNU 311a

Having investigated different routes to a solution, I can find the area of compound 2D shapes and the volume of compound 3D objects, applying my knowledge to solve practical problems.MTH 3-11b

Having investigated the relationships between the radius, diameter, circumference and area of a circle, I can apply my knowledge to solve related problems. MTH 4-16b

Through investigating real life problems involving the surface area of simple 3D shapes, I can explore ways to make the most efficient use of materials and carry out the necessary calculations to solve related problems. MTH 4-11b

I have explored with others the practicalities of the use of 3D objects in everyday life and can solve problems involving the volume of a prism, using a formula to make related calculations when required. MTH 4-11c

Cross Curricular Links (whole school numeracy record): none have been identified yet (will be added later as required) RESOURCES (in Notes on approaches and addition to topic By the end of the topic, pupils should be able to: SmartBoard files on activities for learning server)

PERIMETER, AREA AND VOLUME (CIRCLE COURSE) Prerequisites from Number/Algebra courses and other topics: circle measurement Perimeters:  simple straight-sided shapes, all lengths given Areas:  Units for area: cm², m², …  Area of straight sided shapes drawn on squared paper by counting squares  Area of straight sided shapes by counting squares and half squares  Draw shapes with a given area  

Area of curved sided shapes by considering full squares and part squares Area of rectangles with cm² grid showing; leading to multiplying instead of counting

Volume  Units for volume: cm³/m³, … (at this level it is probably best not to refer back to ml/litres at this stage)  Volume of objects by counting cubes  Volume of cuboids by counting cubes  Make shapes with a given volume using interlocking cubes

Most pupils at this level will require practice at counting up in halves and in expressing answers as a mixed number

TJ Counting Squares Worksheets on server Maths Pack 3: Area Active Worksheets pP13, sP11/19/13/21

using rule by words and not using formula

Show pupils a physical cubic centimetre and a metre cube

Cubes in base; construction kit for metre cube

Not leading to multiplying at this level, but will at triangle

Plastic interlocking multilink cubes

- Page 14 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

RESOURCES (in

Notes on approaches and activities for learning

addition to topic SmartBoard files on server)

PERIMETER, AREA AND VOLUME (TRIANGLE COURSE) Prerequisites from Number/Algebra courses and other topics: triangle measurement, triangle formulae Perimeters:  Find a missing length in a square, rectangle or triangle or composite shape when given the perimeter  Perimeter of simple straight sided shapes where some sides are not marked  Application to real-life context involving cost of materials Areas, briefly with counting squares, then leading to a formula (but only if class have done triangle algebra, otherwise use this topic to introduce and teach the concept of a formula):  Units for area: cm², m² etc.  Area and perimeter of rectangles and squares; for area using the formula A=LB (or A=L×B if needed) 

Right-angled triangles as half a rectangle, leading to formula.



Application in real-life context involving: o cost of materials o how many smaller objects can be cut from a larger one

Volumes:  Units for volumes: ml/l as well as cm³/m³ etc,

 

Volume of cuboids, first by counting cubes, leading to formula V=LBH (or V=L×B×H if needed) Application to real-life contexts involving o cost of materials o how many smaller objects can be filled from a larger one

e.g., ribbon costs 30p a cm, how much will ribbon cost to go around the outside of this shape? Fences around fields etc.

(do not use the term “squaring” when doing squares as the concept of ‘squaring a number’ is not taught until pentagon) At triangle, the formula should be A=½LB (explained as “half OF length times breadth”; and not “½ × length times breadth”), not A=½BH and definitely not A=LB/2. *** DEPARTMENTAL POLICY agreed 9/3/12 ***

Active Worksheet Website: Worksheet pri P13 , sec P11(Area/ Perimeter of rectangles) Worksheets on server Maths Pack 3: Area & Perimeter Worksheets on server

e.g. carpet costs £5 per m², how much will it cost to carpet this room? painting a wall, turf for a garden etc. Old SG Foundation coursework task: Laying Carpets, Mirror Tiles discuss with class where they have come across this word in science, and what it means to them remind class of the links between cm³/ml covered in the measurement topic

Investigation using cubes (M1) Harder counting cubes worksheet on server Active Worksheet Website: Secondary P21a

e.g. the volume of a drinks carton is 3×2×7. How many cartons could you fill from 420ml of juice?

- Page 15 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

PERIMETER, AREA AND VOLUME (PENTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: pentagon multiply, measurement, formulae Perimeter:  Find the missing side and then calculate perimeter in more complex shapes  Application to real-life contexts involving o cost of materials o how many smaller objects are needed to go around a larger one Areas using formulae      

Units for area: cm², m² etc. Reinforce the formula A=LB for area of a rectangle and A=L² for area of a square Area of triangles: revise right-angled triangles, adapting the formula learnt at triangle level (A=½LB), to become A=½BH Area of any triangle when given base and perpendicular height. Area of composite shapes involving two or more rectangles or a rectangle and right-angled triangles; including examples involving area of walls/doors/windows to match N4 Lifeskills Geometry assessment Application in real-life context involving: o cost of materials o how many smaller objects can be cut from a larger one

Volume of cuboids:  Units for volumes (cm³, m³, ml, litres and the link between them)  Reinforce the formula V=LBH for volume of a cuboid  Application in real-life context involving: o cost of materials o how many smaller objects can fill a larger one (cuboids only) Circles:  Briefly revise link between diameter and radius  Practical Activity: Discover pi by measuring circumference and diameter of real circles  Circumference of circles when given diameter or radius using formula, basic examples.  Area of circles and half-circles when given diameter or radius using formula, basic examples  Area of Basic composite shapes with semicircles

- Page 16 -

See National 4 Lifeskills Added Value Unit for style of questions Old SG Foundation coursework task: Laying Carpets, Mirror Tiles Worksheet “WS Volume Problem Solving Litres Millilitres”

Introduce pi initially through a practical activity (see spreadsheet on server)

Active Worksheet Website: Worksheet Secondary P1, P20, P25 Worksheets on server

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) Notes on approaches and activities for learning

By the end of the topic, pupils should be able to:

RESOURCES (in addition to topic SmartBoard files on server)

PERIMETER, AREA AND VOLUME (OCTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: octagon measurement, octagon formulae MATHS ROUTE AND LIFESKILLS ROUTE: Circles:  Revise area and circumference of any circle, including basic fractions of circles. Areas:  Area of composite shapes including: o Areas of composite shapes involving basic fractions of circles o Revision of areas of kites, parallelograms, trapeziums by splitting into triangles and using a composite shape approach.

o 

Intermediate 1 and General item bank Worksheet “WS Quadrilateral Areas DGW”

Pupils covered areas of composite shapes using rectangles/triangles in pentagon; so the approach here should be brief.

Surface areas of a cuboid or basic triangular prism from a 3d sketch.

Intermediate 1 and General and Intermediate 1 with Applications item bank Surface Area Worksheet on server

Application in real-life context involving: o cost of materials o questions involving a mixture of units o how many smaller objects can be made from a larger one o calculating a length when given the area

Volumes:  Volume of prisms where the cross-section is a 2-d composite shape made from rectangles, triangles and/or fractions of circles.  Volume of cylinder using formula.  Volume of basic pyramid, cone, sphere using formulae.  Volume of basic composite solids. 

e.g. three-quarters of a circle, a circle with 120° marked, but not a circle with 125° marked

Application in real-life context involving: o cost of materials o questions involving a mixture of units o how many smaller objects can be made/filled from a larger one o calculating a length when given the volume

Pupils should be taught “changing the subject of a formula” from octagon formulae as an approach here, although they may choose to use other methods

Old Standard Grade General coursework tasks: Glass Greenhouse, Which Container, Wooden Display Boxes

For classes taking the maths route

Prisms group work task (laminated cards) M5

Including hemisphere

Worksheets on server See Intermediate 2 item bank questions

Pupils should be taught “changing the subject of a formula” from octagon formulae as an approach here, although they may choose to use other methods

- Page 17 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) Notes on approaches and activities for learning

By the end of the topic, pupils should be able to:

RESOURCES (in addition to topic SmartBoard files on server)

PERIMETER, AREA AND VOLUME (DECAGON COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements Areas:  Area of any triangle using ½ ab sin C – routine examples only Volumes:  Revise volumes of sphere, cones, pyramids, cylinders briefly  Volumes of composite shapes

Intermediate 2 item bank questions

Circles:  Arc length and area of any sector – routine examples only

Active Worksheet Website: Worksheet Secondary P26

PERIMETER, AREA AND VOLUME (DODECAGON COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements Areas and Perimeters:  Area of composite shapes using A = ½ab sin C  Areas of segments of sectors of circles (i.e. sector area minus triangle area)  Calculate the angle, given the sector area or arc length.

Volumes:  Going backwards with all volume formulae  Volumes of prisms where the cross-sectional area requires use of ½ ab sin C or area of a sector of a circle

The focus of this topic should be practising exam style questions by working through Item Banks

The focus of this topic should be practising exam style questions by working through Item Banks

- Page 18 -

Intermediate 2 and Credit Item Bank questions

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

TIME rd

th

3 /4 level CfE Time outcomes: Using simple time periods, I can work out how long a journey will take, the speed travelled at or distance covered, using my knowledge of the link between time, speed and distance. MNU 3-10a

I can research, compare and contrast aspects of time and time management as they impact on me. MNU 4-10a

I can use the link between time, speed and distance to carry out related calculations. MNU 4-10b

(our interpretation is this means timetables, “being on time” etc)

Cross Curricular Links (whole school numeracy record): pupils need to read and tell time in Modern Languages

TIME (CIRCLE COURSE) By the end of the topic, pupils should be able to:

RESOURCES (in Notes on approaches and activities for learning

addition to topic SmartBoard files on server)

Prerequisites from Number/Algebra courses and other topics: no specific requirements Know the facts:  60 seconds in a minute  60 minutes in an hour  24 hours in a day  7 days in a week  52 weeks in a year  365 days in a year  The names of the days of the week  The names of the months of the year  The number of days in each month (S1 only) Read time from analogue clocks

Teaching Time: Class Clock, worksheets Maths Pack 1: Clock

Understand digital time

Teachers should use their discretion as to how much time to spend on analogue time. Past experience has shown that continuing to do lots of examples in class, without more individual support, does not usually result in much further improvement. Teachers should note that pupils who are finding it difficult to make progress with reading analogue time and consult with Pupil Support in order to have this noted as an Additional Support Need for other staff to be aware of. e.g. quarter to six = 5.45, half past twelve = 12.30

Understand use of am and pm

e.g. quarter to six in the morning = 5:45am

Understand and convert 24 hour times used in context

The bus arrives at 14.30. What time is that?

- Page 19 -

Dynamic Maths: Time-02 TJ Worksheets on server

Active Worksheet Website: Worksheet Primary P19, P20, P23, P27, P28 (Digital/Analogue)

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) RESOURCES (in

By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

addition to topic SmartBoard files on server)

TIME (TRIANGLE COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements All pupils should be confident in telling the time in analogue and digital and 24 hours.

Active Worksheet Website: Worksheet Primary P19, P20, P23, P27, P28 Teaching Time, Maths Pack 1 Class Clock

Use the six basic facts to convert between units of time  60 seconds in a minute  60 minutes in an hour  24 hours in a day  7 days in a week  52 weeks in a year  365 days in a year

e.g. how many seconds are in 4 minutes? How many hours in 2 days? How many months in 3 years? How many minutes in 2½ hours? How many minutes in 3 hours 20 minutes? How many hours and minutes in 200 minutes?

Dynamic Maths: Time04

Convert between 12 and 24-hour time

Class discussion, worksheets

Dynamic Maths: Time02

Calculate time intervals (12 and 24 hour time) (multiples of 5 minutes)

Whiteboards; splitting time interval into smaller intervals and adding. “A film starts at 7.35pm and finishes at 10.20pm – how long does it last?

Dynamic Maths: Time01

Interpret and solve problems using bus and train timetables



Lothian Bus Number 3/29 timetable, worksheets and group activity (M5)



Smartboard file – class discussions/whiteboards: if I get the 8am train from Edinburgh, when will I arrive at Glasgow? if I need to be in London by 11am which is the last train I can get from Edinburgh? If I am at Dundee station at 7.15am, how long do I have to wait for the next train? Worksheets and group activities on reading the number 3 and number 29 bus timetables (M5).

- Page 20 -

Timings in a Hair Salon worksheet (on server)

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

RESOURCES (in Notes on approaches and activities for learning

addition to topic SmartBoard files on server)

TIME (PENTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: triangle fractions/decimals, triangle formulae Calculate time intervals, including over midnight

I go to sleep at 2148 and wake up at 0824. How long did I sleep for?

Calculate ending (or start) time given the time interval, including over midnight

I go to sleep at 2148 and sleep for 10 hours 36 minutes. What time do I wake up? I wake up at 0824 having slept for 10 hours 36 minutes. What time did I go to sleep?

Use knowledge from number course to convert hours and minutes (15 minutes, 30 minutes, 45 minutes) into hours as a decimal

e.g. 3 hours 45 minutes = 3·75 hours

Meaning of speed and units used for it

Class discussion: km/h, mph, m/s etc. What does it mean to say a car is travelling at 30mph?

Dynamic Maths: Time-01 Active Maths Worksheet sP24 Smartboard file, Standard Grade/Int 1 Item Banks Extended task: Catch me if you can (on server) Dynamic Maths: Time-04 AW sJ25 option 1

Worksheets on server

Know the formulae for speed, distance and time Active Worksheet Website: Worksheet Secondary J25

Use knowledge of how to use algebraic formula to calculate speed, distance or time taken in routine problems

Dynamic Maths: Time-03

- Page 21 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

TIME (OCTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: pentagon fractions/decimals, pentagon formulae MATHS AND LIFESKILLS ROUTES: Convert hours and minutes (or minutes and seconds) into a decimal

Starting with multiples of six minutes (e.g. 5 hours 24 minutes), but work towards any number of minutes (e.g. 5 hours 26 minutes), with rounding (to at least two decimal places). Pupils should be aware of the effect on accuracy of rounding too much.

AW sJ25 option 2 Dynamic Maths: Time-03, 05, 06 Past Intermediate 1/Standard Grade questions AW sK28

Convert hours (as a decimal) into hours and minutes; or minutes into minutes and seconds

What is 5·4 hours in hours and minutes? What is 6·29 minutes in minutes and seconds?

Be aware of terms GMT, BST, UTC, “+1”, “–6” etc. (in context of time zones)

Brief discussion

Time Zone Worksheets on server (M5)

Convert times from one time zone to another

Cross-curricular link: class could use time zone map to find place on map and identify its time zone

Paralympic Time Zones worksheet

Solve problems involving speed, time (decimals) and distance

Class should experience questions including:  Calculating time taken, then converting to hours and minutes (or minutes/seconds) and then adding on to (or taking away from) a start (or finish) time. e.g. a train leaves at 1048 and travels 550km at an average speed of 98km/h. What time does it arrive?  As above but also moving from one time zone to another  Interpreting information (e.g. what time do I need to leave the house to get to the airport on time? Which of the trains on this timetable should I take to be at work by 8.30am?)

The remaining topics are for S3 and above only: Interpret an activity network.

Including identifying the minimum total time required (i.e. the critical path, although pupils do not need to use this vocabulary)

See Intermediate 1/Standard Grade General item bank National 5 Applications of Maths practice questions Extended task: Catch me if you can

Angus precedence tables worksheet National 5 Applications of Maths Measures Smartboard file

Understand the meaning of a precedence table and of prerequisite tasks and identify prerequisite tasks in a real life context

Extended task: House renovation on server

Construct a precedence table for an activity and use a precedence table to construct an activity network No content at decagon No content at dodecagon

- Page 22 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

DIRECTION AND SCALE rd

th

3 /4 level CfE Direction and Scale outcomes: Having investigated navigation in the world, I can apply my understanding of bearings and scale to interpret maps and plans and create accurate plans, and scale drawings of routes and journeys. MTH 3-17b

I can apply my understanding of scale when enlarging or reducing pictures and shapes, using different methods, including technology. MTH 3-17c

I can apply my understanding of the properties of similar figures to solve problems involving length and area. MTH 4-17b

Cross Curricular Links (whole school numeracy record): none have been identified yet (will be added later as required) RESOURCES (in addition to topic By the end of the topic, pupils should be able to: Notes on approaches and activities for learning SmartBoard files on server)

DIRECTION AND SCALE (CIRCLE COURSE) Prerequisites from Number/Algebra courses and other topics: circle measurement Use an 8 point compass diagram.

“Never Eat Shredded Wheat” “Naughty Elephants Squirt Water”

Give directions for a very simple journey.

Practical Split class into groups; each group has to choose somewhere in the school and give accurate directions from maths classroom to that place (move around school). Groups then swap directions and try to follow them. Class discussion on good and bad ways of phrasing instructions (literacy).

Follow paths described by instructions such as:  Straight ahead, second on left, first on right  (if appropriate) Logo or turtle (or other more modern equivalent!) Giving directions to others

Use plan of classrooms in school or maps of local area to describe journeys from one classroom to another

World Tour worksheet: crosscurricular Geography; atlases Electronic LOGO  ICT Services have a “turtle” that can be lent to schools Maps of classrooms (on Intranet)

Investigate scale drawings, maps and plans of the school and its local area, and who uses them.

Look at a variety of scale drawings, maps, etc.

Draw a diagram of a room using the scale 1cm = 1m

e.g. class measure the classroom (Bite Site, corridor, car park, football pitch…) and then draw scale drawing

Enlarge or reduce basic shapes by either doubling or halving

No diagonal lines

- Page 23 -

Electronic school map (on server) Street maps of local communities

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

DIRECTION AND SCALE (TRIANGLE COURSE) Prerequisites from Number/Algebra courses and other topics: triangle angle Understand and measure 3 figure bearings

Class need to understand the words “to” and “from” in the context of bearings

Convert the eight compass points into bearings Use a scale drawing or map to calculate real life distance

Where the scale is expressed in the form 1cm = 1m, 1cm = 2m, 1cm = 10m, 1cm = 5m

Enlarge or reduce a simple shape on squared paper by a scale factor of 2, 3 or ½

Shapes can include some basic diagonal lines (i.e. gradient 1 or –1)

Follow or give more complicated directions (e.g. from a street map) involving three or more steps

e.g. old Access 3 questions

Worksheets “Bearings real-life maps” (server) Worksheets in context: U Boat Attack/AirCraft diagram worksheets on server Midlothian maps worksheets (server) Class set of orienteering compasses (Base) Enlargement Worksheets (server)

DIRECTION AND SCALE (PENTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: pentagon angle Briefly introduce the idea of scale as a ratio Revise meaning of bearings from triangle Solve a problem by creating a simple scale drawing and/or navigation course including an angle and three-figure bearing

e.g. 1:3 is another way of writing 1cm = 3cm (remember that a scale of 1cm = 3metres is not 1:3, but is 1:300. Class do not need to know this.) Pupils will be told which scale to use  e.g. draw a right-angled triangle with base 24m and angle 30° to a scale of 1cm = 4m, and then use it to calculate the real-life height of the triangle.  e.g. navigation course: 5km on bearing 045°, then 7km on bearing of 240° using scale of 1cm = 1km. How far is it back to the starting point? Class need to understand the words “to” and “from” in the context of bearings

- Page 24 -

Old Standard Grade coursework task: Television cabinet, Sports field, (harder) James Bond Scale Drawing Perth Academy worksheets on server

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra) By the end of the topic, pupils should be able to:

RESOURCES (in addition Notes on approaches and activities for learning

to topic SmartBoard files on server)

DIRECTION AND SCALE (OCTAGON COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements MATHS ROUTE No content at octagon (fractional scale factors is covered in the proportion topic and bearings is covered in the angle topic) LIFESKILLS ROUTE: Create scale drawings where the pupil must choose the scale.

Perth Academy worksheets on server

Solve a problem by creating a more complex navigation course including three-figure bearings.

James Bond Scale Drawing task

No content at decagon Be aware that pupils who came via Lifeskills route will have missed back bearings at octagon No content at dodecagon (covered in shape, and proportion topics instead)

- Page 25 -

Newbattle High School Maths Department CfE Course Planner: TOPICS (everything except number/algebra)

ANGLE 3rd/4th level CfE Angles outcomes: I can name angles and find their sizes using my knowledge of the properties of a range of 2D shapes and the angle properties associated with intersecting and parallel lines. MTH 3-17a

Having investigated the relationship between a radius and a tangent and explored the size of the angle in a semi-circle, I can use the facts I have established to solve related problems. MTH 4-17a

Cross Curricular Links (whole school numeracy record): none have been identified yet (will be added later as required) By the end of the topic, pupils should be able to:

Notes on approaches and activities for learning

RESOURCES (in addition to topic SmartBoard files on server)

ANGLE (CIRCLE COURSE) Prerequisites from Number/Algebra courses and other topics: no specific requirements Recognise right, acute and obtuse angles Draw angles in degrees using a protractor to within 5° Measure angles in degrees using a protractor to within 5° Identify and know:  Right angle = 90º  Acute angles90º and

Smile Life

When life gives you a hundred reasons to cry, show life that you have a thousand reasons to smile

Get in touch

© Copyright 2015 - 2024 PDFFOX.COM - All rights reserved.