Topic Lesson Widget HOTsheet

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Miles Arnold
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1 Table of Contents Middle Secondary Topic Lesson Widget HOTsheet Number notations Significant figures & rounding Rounding to significant figures How accurate is it? Scientific notation Writing in scientific notation From scientific notation into basic numerals Comparing numbers in scientific notation Large and small units Exploring recurring decimals Exploring recurring decimals Patterns in recurring decimals Converting rates Racing cars Common conversions Earning money Wages & salaries Understanding job advertisements Extra earnings Part-time work Relying on commission for income Timesheets Spreadsheets and timesheets Tax & other deductions Using a tax table Understanding tax brackets from tables Gains from superannuation Budgeting Buying, borrowing, investing Best buys, discounts, sales tax Comparing discounts Best buys GST Buying on credit Living away from home Credit card payments and balances Simple interest Simple interest formula Spreadsheets and simple interest tables Savings accounts Compound interest Simple vs compound interest The effect of compounding interest Comparing compound and simple interest Compound interest formula Comparing compound interest periods Deriving the compound interest formula Depreciation The effect of depreciation Exploring depreciation Loans Exploring a variable interest home loan Home loan repayments Indices Multiply and divide terms with powers Multiplying and dividing with indices Developing the index law for multiplication Developing the index law for division Investigating the zeroth power Powers upon powers Negative indices & reciprocals Checking solutions using index rules Squaresaw puzzle: Combining the laws What do negative indices mean? Index laws and negative indices Testing for equivalent expressions Fractional indices & roots The meaning of fractional indices Exploring fractional indices Squaresaws with fractional indices 1

2 Algebraic expressions Add & subtract algebraic fractions Adding and subtracting algebraic fractions Which common denominator? What was the question? Multiply & divide algebraic fractions Multiplying algebraic fractions Missing bits Expanding & simplifying Factorising Extending algebraic fractions Using algebra Expanding with negatives Expanding and simplifying algebraic expressions Factor numbers Factor numbers and pronumerals Add mixed algebraic fractions Numerators with two terms Combine tricky algebraic fractions Checking and practical applications Checking your factorisation Numerators with two terms Algebra from statements Algebra and spreadsheets Linear equations & inequalities Solving linear equations Guessing and checking Checking solutions to linear equations Equations with brackets Solving equations with brackets Using spreadsheets to solve linear equations Techniques in solving linear equations Equations with fractions Equations with one fraction Equations with two fractions What went wrong? Equations with algebraic denominators Problems & formulas Using formulas in a light circuit Finding values of pronumerals in formulas Use an equation to solve a problem Inequalities Solving inequalities Inequalities in different forms Extending inequalities Checking solutions to inequalities Compare methods of solving inequalities Using inequalities for solving problems Simultaneous equations Graphs, tables or guess and check Discovering where lines cross Guess and check simultaneous equations Investigating simultaneous equations Using the substitution method Sample solutions Solving by substitution Using the elimination method Solving problems simultaneously Elimination of a common term Elimination without a common term Solving by elimination Creating a common term Choosing your method Creating equations to solve problems Surds Reals, rationals and surds Surds on the number line Surds and your calculator Operations with surds Testing surd operations Adding and subtracting surds Rewriting surds Simplifying surds Entire surds Rationalising and simplifying Binomial surds Product of binomial surds Multiplying conjugates 2

3 Quadratic expressions Expanding binomial products Expanding using two separate brackets Expanding a term at a time Describing a pattern Analysing expansions Factorising monic quadratics Decisions when factorising Examining factors Factorising non-monic quadratics The cross method Procedure for factoring non-monics Let me count the ways A search for psi and omega Special products and factors Creating perfect squares The difference of squares Perfect squares Other factorizations Puzzling common factors Combining skills Simplifying using factors Fiddling with fractions Quadratic equations How many solutions? Locating solutions Examining solutions Solving using factors Factorise and solve Exploring solutions and factors Problematic Completing the square Solving by completing the square Using perfect squares Triangular number formula The quadratic formula Deriving the formula Exploring the quadratic formula Comparing methods Simultaneous solutions Guess and graph solutions Reading solutions from graphs Visual vs symbolic Number plane: Calculations Midpoint Locating the midpoint Extending understanding of the midpoint Distance using graphs Calculating distances Calculating the distance between two points Gradient using graphs Calculating gradient Exploring gradient Distance formula Distance using the formula Using the distance formula Investigating distance Gradient formula Gradient using the formula Using the gradient formula Number plane: Straight lines Slopes & intercepts Describing slope Special lines Tables to graph lines Graphing a line Where is the point? Equation/graph match-up Download costs Reading the equation Comparing lines and equations Line it up Mix and match equations and graphs Gradient intercept graphs Graphing using the gradient Rearranging linear equations Graphing lines using rise and run Rearrange and graph equations Linear quotations from graphs Equation of line from the graph What is the equation Number plane: Curves Plotting curves Graphing a curve Exploring types of curve Square grid paper Parabolas Graphing parabolas Investigating parabolas Parabola match-up Hyperbolas Graphing hyperbolas Comparing hyperbolas Graphing a basic hyperbola Matching graphs 3

4 Perimeter & area Perimeter & arcs Calculating the length of an arc Arc length and subtended angle Area of a kite & a rhombus Determining the area of a kite Deriving the area of a kite Area of a trapezium Determining the area of a trapezium Investigating the area of a trapezium Areas of parts of circles Areas of sectors Exploring areas of sectors Volume Volumes of prisms & cylinders Finding the volume of any prism Reviewing area and calculating volumes Comparing volumes Volumes of pyramids How pyramids relate to prisms Comparing volumes of prisms and pyramids Calculating pyramid volumes Old and new mathematics Volumes of cones How many cones to the cylinder? Comparing right and oblique cones Constructing cones Investigating cones Volumes of spheres Calculating the volume of a sphere The relationship of volume and radius The sphere and the cube Surface area Surface area of Prisms Surface area of a triangular prism Surface area of a pentagonal prism Nets of prisms and areas of faces Does this formula work? Surface area of Cylinders Surface area of a cylinder Derive the formula Surface area of familiar cylinders Surface area of Pyramids Surface area of a rectangular pyramid Surface area from nets Surface area of Cones & spheres Calculations with cones Calculating surface area of cones The sphere and the cylinder Trigonometry: Introduction Naming the sides Naming sides in right-angled triangles Find-a-Word The tangent ratio Exploring the tangent ratio Investigating the tangent ratio Using the tangent ratio Finding the length of the opposite side Finding the length of the adjacent side Does trigonometry really work The sine & cosine ratios Exploring the sine and cosine ratios Investigating the sine and cosine ratios Side lengths using any ratio Selecting a trig ratio Which ratio? Calculating angles Comparing tangent ratio and angle size Predicting the angle Ratio reckoning Applying trigonometry Plane table surveying Using a clinometer Clinometer Trig: Minutes & bearings Splitting the degree Why 360 degrees? Sides & angles What are bearings? Estimating compass bearings Getting your bearings in New South Wales Diagrams and problem solving Reading the compass rose Bearings in New South Wales 360 degree compass for overhead projector Compass and three-figure bearings Using bearings X marks the spot Using bearings and trigonometry Using bearings to calculate distances Calculating bearings 4

5 Trigonometry beyond right triangles The unit circle Plotting sine and cosine curves Trig curves from unit circle Related ratios Related angles Exact ratios Estimating sine and cosine Graphs of trig equations Trig relationships Proof of sin cos 2 0 = 1 Linking sine, cosine and tangent Comparing gradient and tangent ratios Area using trig Determining the area formula The formula in right triangles Finding the angle Sine rule Proving the sine rule Testing the sine rule Exploring the sine rule Sine rule applications Cosine rule Proving the cosine rule Exploring the cosine rule Combining trigonometric rules Reasoning in geometry Angles in polygons Polygon slices Turtle walk Exterior angles of polygons Angle sum Round the window Tests for congruent triangles Constructing triangles Straw triangles Making a triangular window Writing reasons Geometry with reasoning Mix and match reasoning Completing an argument Similar triangles Similar triangle calculator Family portrait Measuring the immeasurable The pentagram Probability Relative frequency Laughing clown Calculating relative frequencies The clown game Using relative frequency Calculating probability Marble mania Fishing for data The spinner tree Collecting random colours The marble game Gone fishing Hidden counters Theory vs experiment Can you predict what you will get? Data collection Cumulative frequency Completing the cumulative frequency column Organising and analyzing Cumulative frequency histograms Creating cumulative frequency histograms Tables, histograms and ogives Histograms for grouped data Changing class intervals Comparing class intervals Using a spreadsheet with class intervals Data analysis Centres for grouped data Mean of grouped data Which mobile phone plan? Box-and-whisker plots Box-and-whisker plot Creating boxplots Comparing data Standard deviation & distribution Measures of spread Statistical spreads Match, rank and classify 5

6 Bivariate Data Distance/time graphs Graphing the burger run Replicating the journey Graphing the story Telling the story Other line graphs Dunking machine Dunking machine stories Sketch and match Graphs with curves Graphs of filling/emptying containers Match graphs and vessels Pendulum Drawing graphs from scenarios 6

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