Canning Vale College YEAR 11. Mathematics: Essentials Units 1 & 2 Course Outline 2018

Transcription

1 Canning Vale College YEAR 11 Mathematics: Essentials Units 1 & 2 Course Outline 2018

2 Introduction Welcome to Mathematics: Essentials! Please see Connect for access to important course information and resources. Assessments Assessment weightings for the year are shown below. The final year result and grade will be recorded for both units 1 and 2. UNIT 1 UNIT 2 Assessment Tests (3 Tests per semester ) Quiz (1 Quiz per semester) Investigations ( 1 Investigation & 1 Application) Weighting 24% (8% each) 4% 20% (10 % each) 48% Assessment Tests (3 Tests per semester) Quizzes (2 Quizzes per semester) Investigations (1 Investigation & 1 Application) TOTAL 100 % Weighting 24%(8% each) 8% (4% each) 20% (10% each) 52%

3 Resources Text Books: Essential Mathematics Units 1 and 2 () Buckley, Callaway & Ostberg (MAWA) Nelson Senior Maths Essentials Unit 1 & 2 On-line: Calculators: Mathletics Casio Scientific FX-82AU Plus II (or similar instruments) A copy of the Syllabus statement is available via Connect, or on the School Curriculum and Standards Authority website (

4 Mathematics: Essentials UNIT 1 Program 2018 TERM1 WEEK CONTENT TEXT REF/RESOURCES ASSESSMENTS 1-2 Skills review Number Operations: Calculations MAWA Unit1 1 Skills Review use leading digit approximation to obtain estimates of calculations Nelson Unit 1 check results of calculations for accuracy understand the meaning and magnitude of numbers involved, including fractions, percentages and the significance of place value after the decimal point Chapters 1 &2 ascertain the reasonableness of answers, in terms of context, to arithmetic calculations round up or round down answers to the accuracy required, including to the required number of decimal places choose and use addition, subtraction, multiplication and division, or combinations of these operations, to solve practical problems apply arithmetic operations according to their correct order convert between fractions, decimals and percentages, using a calculator when appropriate evaluate fractions and decimals of quantities to the required number of decimal places; for example, 3 4 of 250 ml, 0.4 of 3kg apply approximation strategies for calculations if appropriate use a calculator appropriately and efficiently for multi-step calculations calculate a percentage of a given amount, using mental/written strategies or technology when appropriate determine one amount expressed as a percentage of another apply percentage increases and decreases in situations, for example, mark-ups and discounts and GST 2 Introduction to the Mathematical Thinking Process involving applications of unit 1 content (percentages, area, money ) MAWA Unit1 Chapter 2 Nelson Unit 1 Chapters 1 & 2 Chapters 1 &2

5 3-4 Measurement: ascertain the reasonableness of answers, in terms of context, to arithmetic calculations choose and use addition, subtraction, multiplication and division, or combinations of these operations, to solve practical problems apply approximation strategies for calculations if appropriate evaluate fractions and decimals of quantities to the required number of decimal places; for example, 3 of 250 ml, 0.4 of 3kg identify common usage of rates, such as: km/h as a rate to describe speed or beats/minute as a rate describing pulse rate convert units of rates occurring in practical situations to solve problems. For example, 1 tablespoon (tbsp) = 4 teaspoons (tsp) or 1 tbsp = 20 ml (Australia) or 15 ml (US and UK) use rates to make comparisons substitute values for the variables in a mathematical formula in given form to calculate the value of the subject of the formula choose and use appropriate metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy, such as mm for building and other trade contexts, cm for textiles estimate lengths convert between metric units of length and other length units for simple practical purposes, for example, 1 inch 2.54cm calculate perimeters of familiar shapes, including: triangles, squares, rectangles and composites of these choose and use appropriate metric units of mass, their between them estimate the mass of different objects Examples in context Mass: abbreviations and conversions comparing and discussing the components of different food types for the components of MAWA Unit1 Chapter 3,4, 5, 6 Nelson Unit 1 Chapter 3,6,7 Chapter Quiz 1 Non calculator based (Teachers to announce the topics in the class) Week 3: Lesson 3/4

6 packaged food expressed as grams calculating and interpreting dosages for children from adults medication using various formulas (Fried, Young, Clark) in milligram 5 TEST in Basic Calculations Units of length, mass, capacity and rates; Formulae 5-7 Nutrition and health Practical Applications involving linear measurement, mass, volume and capacity, rates and practical formulas and interpreting information present in tables Units of energy use units of energy to describe consumption of electricity, such as kilowatt hours use units of energy used for foods, including kilojoules and calories use units of energy to describe the amount of energy expended during activity convert from one unit of energy to another, such as calories/kilojoules interpret information presented in two-way tables discuss and interpret graphs found in the media and in factual texts check results of calculations for accuracy understand the meaning and magnitude of numbers involved, including fractions, percentages and the significance of place value after the decimal point ascertain the reasonableness of answers, in terms of context, to arithmetic calculations round up or round down answers to the accuracy required, including to the required number of decimal places choose and use addition, subtraction, multiplication and division, or combinations of these operations, to solve practical problems apply arithmetic operations according to their correct order convert between fractions, decimals and percentages, using a calculator when appropriate evaluate fractions and decimals of quantities to the required number of decimal places; for MAWA Unit 1 Chapters 1-6 MAWA Unit 1 Chapters 7-9 Nelson Unit 1 Chapter 3,6,7 TEST 1 Lesson 1 or 2

7 example, 3 of 250 ml, 0.4 of 3kg 4 apply approximation strategies for calculations if appropriate use a calculator appropriately and efficiently for multi-step calculations calculate a percentage of a given amount, using mental/written strategies or technology when appropriate determine one amount expressed as a percentage of another identify common usage of rates, such as: km/h as a rate to describe speed or beats/minute as a rate describing pulse rate convert units of rates occurring in practical situations to solve problems. For example, 1 tablespoon (tbsp) = 4 teaspoons (tsp) or 1 tbsp = 20 ml (Australia) or 15 ml (US and UK) use rates to make comparisons choose and use appropriate metric units of mass, their abbreviations and conversions between them estimate the mass of different objects Examples in context Mass: comparing and discussing the components of different food types for the components of packaged food expressed as grams calculating and interpreting dosages for children from adults medication using various formulas (Fried, Young, Clark) in milligrams Volume and capacity (Reference only) choose and use appropriate metric units of volume, their abbreviations, and conversions between them understand the relationship between volume and capacity, recognising that 1 cm 3 = 1 ml and 1 m 3 = 1 kl estimate volume and capacity of various objects calculate the volume and capacity of cubes and rectangular and triangular prisms Examples in context Volume and capacity:

8 determining the volume of water collected from a roof under different conditions materials for applications, such as fertiliser, pool chemicals, paint calculating and interpreting dosages for children from adults medication using various formulas (Fried, Young, Clark) in millilitres Identify common use of formulas to describe practical relationships between quantities substitute values for the variables in a mathematical formula in given form to calculate the value of the subject of the formula choose and use appropriate metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy, such as mm for building and other trade contexts, cm for textiles estimate lengths convert between metric units of length and other length units for simple practical purposes, for example, 1 inch 2.54cm 7-8 Practical applications of area, volume and capacity. Units of measurement conversions (optional) choose and use appropriate metric units of area, their abbreviations and conversions between them estimate the areas of different shapes convert between metric units of area and other area units calculate areas of rectangles and triangles, and composites of these shapes choose and use appropriate metric units of volume, their abbreviations, and conversions between them understand the relationship between volume and capacity, recognising that 1 cm 3 = 1 ml and 1 m 3 = 1 kl estimate volume and capacity of various objects MAWA Unit 1 Chapters Nelson Unit 1 Chapter 6, 7 Week 7 Lesson 2 Investigation 1- Take home part - Out

9 calculate the volume and capacity of cubes and rectangular and triangular prisms 9-10 Earning Money Rates of pay (weekly, fortnightly, annual income, quotes, career research/incomes) Applications of basic calculations percentages, rates and their use of formulae. More applications in measurement choose and use appropriate metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy, such as mm for building and other trade contexts, cm for textiles estimate lengths convert between metric units of length and other length units for simple practical purposes, for example, 1 inch 2.54cm calculate perimeters of familiar shapes, including: triangles, squares, rectangles and composites of these Examples in context Linear measure: MAWA Unit 1 Chapters Nelson Unit1 Chapter 4.03 Chapter 4 Investigation 1 Week 8 Inclass validation Lesson 2 determining the dimensions/measurements of food packaging determining the length of the lines on a sporting field to calculate the cost of marking it choose and use appropriate metric units of area, their abbreviations and conversions between them estimate the areas of different shapes convert between metric units of area and other area units calculate areas of rectangles and triangles, and composites of these shapes choose and use appropriate metric units of volume, their abbreviations, and conversions between them understand the relationship between volume and capacity, recognising that 1 cm 3 = 1 ml and 1 m 3 = 1 kl estimate volume and capacity of various objects

10 TEST in Measurement and its applications Basic applications of earning money MAWA Unit 1 Chapters Nelson Unit 1 Chapter 3,6,7 TEST 2 In Measurement Week 10 last lesson 11 Earning Money 1- Revise Percentage, rate, fraction, decimal, rounding skills applies Percentage, rate, fraction, decimal, rounding skills applies apply approximation strategies for calculations if appropriate use mental and/or flexible written strategies when appropriate use a calculator appropriately and efficiently for multi-step calculations Examples in context Basic calculations: creating a budget for living at home and for living independently using timesheets, which include overtime, to calculate weekly wages using and interpreting tax tables converting between weekly, fortnightly and yearly incomes converting a recipe for a larger or smaller number of servings determining how much money is spent in the school canteen each day MAWA UNIT 1 Chapters 16 Plus Miscellaneous exercises TERM1 BREAK

11 TERM 2 WEEK CONTENT TEXT REF/RESOURCES ASSESSMENTS 1-2 Earning money continues Earning Money 2- Superannuation, Commission, Income tax Percentage, rate, fraction, decimal, rounding skills applies MAWA UNIT 1 Chapters Plus Miscellaneous exercises apply approximation strategies for calculations if appropriate use mental and/or flexible written strategies when appropriate use a calculator appropriately and efficiently for multi-step calculations Examples in context Basic calculations: creating a budget for living at home and for living independently using timesheets, which include overtime, to calculate weekly wages using and interpreting tax tables converting between weekly, fortnightly and yearly incomes converting a recipe for a larger or smaller number of servings determining how much money is spent in the school canteen each day Nelson Unit1 Chapter 1.08, 2.06 Ellery Strickland Chapters 1 and 2 Excel spread sheets ABS website Week 2 Lesson 1 Practical Application 1 take home out Data interpretation skills like reading tables, interpret two-way tables, discuss the factual texts 3 Managing Money Bank accounts, percentages, using formulas calculate a percentage of a given amount, using mental/written strategies or technology when appropriate determine one amount expressed as a percentage of another apply percentage increases and decreases in situations, for example, mark-ups and discounts and GST 3-4 Spending money Discounts, best buys, budgets, using data to make decisions Parts of Nelson Unit1 Chapters 1-10 Excel spread sheets ABS website MAWA UNIT 1 Chapters Week 3 Lesson 1 Practical application 1 in-class validation

12 choose and use appropriate metric units of mass, their abbreviations and conversions between them estimate the mass of different objects Examples in context Mass: comparing and discussing the components of different food types for the components of packaged food expressed as grams calculating and interpreting dosages for children from adults medication using various formulas (Fried, Young, Clark) in milligrams Volume and capacity choose and use appropriate metric units of volume, their abbreviations, and conversions between them understand the relationship between volume and capacity, recognising that 1 cm 3 = 1 ml and 1 m 3 = 1 kl estimate volume and capacity of various objects Data interpretation information from the tables 5-6 Work Experience Exam Break 7 UNIT 2 BEGINS Nelson Unit 1 Chapter 10 Ellery Strickland Chapters 1 and 2 Excel spread sheets activities ABS website Test 3 : 8% Week 4 Lesson 2 or 3

13 TERM 2 WEEK DESCRIPTION/ SYLLABUS REFERENCE TEXT REFERENCE/RESOURCE ASSESSMENT Classifying data: identify examples of categorical data, identify examples of numerical data, compare the suitability of different methods of data presentation in real-world contexts identify the mode and calculate other measures of central tendency, the arithmetic mean and the median, using technology when appropriate investigate the suitability of measures of central tendency in various real-world contexts investigate the effect of outliers on the mean and the median **Data collection, data representation, types of data, categorical, numeric, continuous, discrete, measurement of location Data presentation and interpretation: display categorical data in tables and column graphs display numerical data as frequency distributions, dot plots, stem and leaf plots and histograms recognise and identify outliers identify the mode and calculate other measures of central tendency, the arithmetic mean and the median, using technology when appropriate investigate the suitability of measures of central tendency in various real-world contexts use informal ways of describing spread, such as: spread out/dispersed, tightly packed, clusters, gaps, more/less dense regions, outliers interpret statistical measures of spread, such as: the range, interquartile range and standard deviation. Ch26, Ch27 and Ch28 Ch 8 Ch 6 & 7 Ch29, Ch30 and Ch31 Ch 8 & 11 Ch 5 Week 9 Quiz 2 Lesson 2 or 3 Term 2 Break

14 TERM 3 WEEK DESCRIPTION & SYLLABUS REFERENCE TEXT REFERENCE/ RESOURCES ASSESSMENTS 1 2 Data presentation and interpretation: display numerical data as frequency distributions, dot plots, stem and leaf plots and histograms recognise and identify outliers identify the mode and calculate other measures of central tendency, the arithmetic mean and the median, using technology when appropriate investigate the effect of outliers on the mean and the median use informal ways of describing spread, such as: spread out/dispersed, tightly packed, clusters, gaps, more/less dense regions, outliers compare back to back stem plots for different data sets compare the characteristics of the shape of histograms using symmetry, skewness and bimodality Summarising and interpreting data: identify the mode and calculate other measures of central tendency, the arithmetic mean and the median, using technology when appropriate calculate and interpret quartiles complete a five number summary for different data sets construct and interpret box plots using a five number summary Ch32 and Ch33 Ch 11 Ch 6 & 7 Ch34 and Ch35 Ch 11 3 Data presentation and interpretation: display categorical data in tables and column graphs display numerical data as frequency distributions, dot plots, stem and leaf plots and histograms compare the suitability of different methods of data Ch36 and Ch37 Ch 11 & 14

15 presentation in real-world contexts identify the mode and calculate other measures of central tendency, the arithmetic mean and the median, using technology when appropriate investigate the suitability of measures of central tendency in various real-world contexts investigate real-world examples from the media illustrating inappropriate uses, of measures of central tendency and spread 4 Percentage Fraction Skills Review: convert between fractions, decimals and percentages, using a calculator when appropriate calculate a percentage of a given amount, using mental/written strategies or technology when appropriate determine one amount expressed as a percentage of another apply percentage increases and decreases in situations, for example, mark-ups and discounts and GST Revise percentage fundamentals Ch 2 & 10 Ch 2 Test 4 Representing and comparing data Lesson 1/2 5 6 Percentage calculations: review calculating a percentage of a given amount review one amount expressed as a percentage of another Applications of percentages: determine the overall change in a quantity following repeated percentage changes; for example, an increase of 10% followed by a decrease of 10% calculate simple interest Ratios: identify common use of ratios to express comparisons of quantities in practical situations use diagrams or concrete materials to show simple ratios, such as 1 to 4, 1:1: understand the relationship between simple fractions, percentages and ratio, for example, a ratio of 1:4 is the same as 20% to 80% or 1/5 to 4/5 Ch41 Ch 10 Ch 8 Ch38 Ch 12 Ch 9 Quiz 3 Lesson 3 or 4

16 2.3.4 express a ratio in simplest form determine the ratio of two quantities in context divide a quantity in a given ratio, for example, share $12 in the ratio 1 to use ratio to describe simple scales 7 Ratios: identify common use of ratios to express comparisons of quantities in practical situations use diagrams or concrete materials to show simple ratios, such as 1 to 4, 1:1: understand the relationship between simple fractions, percentages and ratio, for example, a ratio of 1:4 is the same as 20% to 80% or 1/5 to 4/ express a ratio in simplest form determine the ratio of two quantities in context divide a quantity in a given ratio, for example, share $12 in the ratio 1 to use ratio to describe simple scales 8 Rates: review identifying common usage of rates, such as km/h convert units for rate; for example, km/h to m/s, ml/min to L/h complete calculations with rates, including solving problems involving direct proportion in terms of rate use rates to make comparisons use rates to determine costs 9 Time: use of units of time, conversions between units, fractional, digital and decimal representations represent time using 12 hour and 24 hour clocks calculate time intervals, for example, time between, time ahead, time behind Ch39 Ch 12 Ch40 Ch 6 Ch 9 Ch42 and Ch43 Ch 9 Ch 10 Statistical Investigation 2 Take home - out Statistical Investigation 2 In-class validation- Due

17 10 Time: interpret timetables, such as bus, train and ferry timetables use several timetables and electronic technologies to plan the most time-efficient routes Chapter 44 Test 5 Percentages Rates and Ratio Lesson 2 or 3 TERM 3 BREAK TERM 4 DESCRIPTION & SYLLABUS REFERENCE RESOURCES ASSESSMENTS 1 2 Time: (Revise) interpret timetables, such as bus, train and ferry timetables use several timetables and electronic technologies to plan the most time-efficient routes interpret complex timetables, such as tide charts, sunrise charts and moon phases compare the time taken to travel a specific distance with various modes of transport Speed: identify the appropriate units for different activities, such as walking, running, swimming and flying calculate speed, distance or time using the formula speed = distance/time calculate the time or costs for a journey from distances estimated from maps interpret distance versus time graphs calculate and interpret the average speed Ch44 and Ch45 Ch 9 Ch46 and Ch47 Ch 9 Ch 10 Practical Application 2 Take home -Out Practical Application 2 In-class Validation -Due

18 3-4 Distance and Length: use scales to calculate distances and lengths on plans, maps and charts plan routes for practical purposes, accounting for local Distance and Length: use scales to calculate distances and lengths on plans, maps and charts plan routes for practical purposes, accounting for local Ch48-50 Ch 13 Ch 10 Networks: Practical applications of Time, distance, speed in networks. Traversability Shortest paths Revise Unit 2 Chapters Test 6 Time and Motion (Lesson 2 or 3) Test 5-6 END OF YEAR 11 ESSENTIALS UNIT 1 & UNIT 2 COURSE