DE LA SALLE SCHOOL LEARNING PROGRAMME. YEAR 8 Pi Pathway. Half Term 1a

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1 Pi Pathway Half Term 1a Weeks 1 and 2: Adding and subtracting larger numbers More calculations Negative numbers Why is it important that I can do simple calculations in the real world? integer negative Weeks 3, 4 and 5: STEM: Writing ratios Using ratios Multiplicative reasoning 3D solids Nets of 3D solids Does sharing out mean always in equal amounts? By understanding ratio can I understand better world wealth and poverty? integer equivalent simplify ratio proportion Weeks 6 and 7: Surface Area Volume Working with measures Length, area and capacity Converting between cubic cm and litres When do I use formulae in real life? cube cuboid cone sphere pyramid prism edge face vertex/vertices area volume capacity convert formula

2 Theta Pathway Half Term 1a Weeks 1 and 2: Calculations (written and mental) Calculating with negative integers Powers, roots and brackets Why is it important that I can do simple calculations in the real world? integer negative index/indices estimate substitute Weeks 3, 4 and 5: Substituting into expressions Multiples and factors Prime factor decomposition Area of a triangle Area of a parallelogram Area of a trapezium When is maths practically useful in the real world? integer substitute index notation factor multiple prime factor decomposition HCF LCM formula/formulae compound shapes Weeks 6 and 7: Volume of cubes and cuboids Nets of 3D shapes Surface area of cubes and cuboids Problems solving (volume and surface area) When do I use formulae in real life? cube cuboid edge face vertex/vertices area volume capacity convert formula

3 Delta Pathway Half Term 1a Weeks 1 and 2: Prime factor decomposition Laws of indices STEM: Powers of 10 How do prime numbers make sure online financial transactions are secure? integer negative decomposition index/indices significant Weeks 3, 4 and 5: Calculating and estimating Simplifying expressions Expanding and simplifying Why is algebra useful? integer expressions powers algebraic Weeks 6 and 7: Factorising Substituting into expressions What equations have changed the world? substitute solve solution Constructing and solving equations

4 PI Pathway Half Term 1b Weeks 1, 2 and 3: Planning a survey Data collection sheets Interpreting bar charts Drawing bar charts be asking Can graphs be used to influence peoples opinions? Modal class Class intervals Grouped frequency Dual bar chart and resources that Compound bar chart Axes Weeks 4 and 5: STEM: Pie charts Simplifying expressions Why is algebra useful? Sectors Fraction Functions Proportion Percentage Equivalent Like terms Input/output Inverse Weeks 6, 7 and 8: Solving equations Using brackets What equations have changed the world? Equation Expression Expand

5 THETA Pathway Half Term 1b Weeks 1, 2 and 3: Algebraic powers Expressions and brackets Factorising expressions be asking Why is algebra useful? Products Index notation Expand Common factor and resources that Weeks 4 and 5: One step equations Two step equations The balancing method Conversion graphs What equations have changed the world? Operation Inverse Balancing method Axes Weeks 6, 7 and 8: Conversion graphs Distance time graphs Line graphs STEM; Graphs of functions When will I used conversion graphs in real life? When do I use formulae in real life? Axes Estimate Formula How can the graph help me understand relationships between quantities?

6 DELTA Pathway Half Term 1b Weeks 1, 2 and 3: Plans and elevations Surface area of prisms Volume of prisms Circumference of a circle be asking What profession will these skills be used in? Net Isometric paper Front elevation Side elevation Plan Cross section Radius Diameter and resources that Weeks 4 and 5: Area of a circle Volume and surface area of cylinders Pythagoras Theorem Direct proportion Geologists can use Pythagoras Theorem to find the epicentre of an Earthquake, how? Radius Diameter Hypotenuse Can you think of any bills that are in direct proportion? Weeks 6, 7 and 8: FINANCE: Interpreting financial graphs Distance time graphs Rates of change Misleading graphs Why do we take an overview and not look at specific points with financial graphs? Profit Trend Compound measures Linear relationship Non linear Why might graphs be misleading? What are the benefits?

7 Pi Pathway Half Term 2a Weeks 1 and 2 Decimal calculations Adding and subtracting decimals Multiplying decimals Ordering and rounding decimals Why is being proficient at calculating a desirable skill in most jobs? Decimal Place value Ordering Ascending Descending Weeks 3 and 4 STEM: Problem solving with decimals Measuring and drawing angles Vertically opposite angles What profession will these skills be used in? Protractor Isosceles Equilateral scalene Angles in triangles Interior angles Vertically opposite Weeks 5 and 6 Work out the size of unknown angles in a triangle. Accurately draw triangles using a ruler and protractor. How are angles linked to navigation? Net Dimensions Hypotenuse Accurately draw a net of a 3D shape. Investigate the sides of a right angled triangle.

8 THETA Pathway Half Term 2a Weeks 1 and 2 Ordering decimals and rounding Place value calculations Decimal places Multiplying decimals with up to two decimal places. Multiplying any number by 0.1 and Why is being proficient at calculating a desirable skill in most jobs? Calculations with decimals Adding and subtracting decimals of any size. Multiplying and dividing by decimals. Dividing by 0.1 and Weeks 3 and 4 Ratio and proportion with decimals STEM: Using ratios Solving engineering problems using ratio and proportion. Quadrilaterals How does maths in the classroom reflect maths in the real world? Ratio Proportion Engineering Quadrilaterals Using known facts about quadrilaterals to solve problems. Weeks 5 and 6 Alternate angles and proof Geometrical problems Identifying corresponding angles. Solving problems using properties of angles in parallel and intersecting Which professions need to understand about angles and the properties of triangles and quadrilaterals? Alternate angles Corresponding angles Parallel lines. Calculating the sum of the interior and exterior angles of a polygon. Interior angles Exterior angles Solving geometric problems

9 DELTA Pathway Half Term 2a Weeks 1 and 2 Describe and carry out translations. Describe and carry out reflections. Describe and carry out rotations. Enlarge a shape. How does maths in the classroom reflect maths in the real world? Transformations Reflection Rotation Translation Describe an enlargement. Vector Enlarge a shape using negative and Enlargement fractional scale factors. Scale factor Weeks 3 and 4 STEM: Combining transformations Identify planes of reflection symmetry in 3D solids. Find the perimeter and area of 2D In what jobs are transformations useful? Plane of symmetry Reflection symmetry Scale factor Area scale factor Volume scale factor shapes after enlargement. Find the volume of 3D solids after enlargements. Weeks 5 and 6 Recognise fractional equivalents to important recurring decimals. Recognise which denominators of simple fractions produce recurring decimals. World debt is a huge problem how can maths help solve this social issue? Equivalent Recurring Denominators Repeated percentage change Compound interest Change a recurring decimal into a fraction. Using percentages FINANCE: Repeated percentage change.

10 PI Pathway Half Term 2b Weeks 1 and 2 Calculate squares and square roots, mentally and using a calculator. Calculate cubes and cube roots, mentally and using a calculator. What is a sensible answer? Square Powers Index Indices Square root Calculating with brackets and indices Cube Cube root Weeks 3 and 4 Carry out calculations involving brackets and square numbers. Use the brackets keys on a calculator. Use index notation. Is guessing a legitimate mathematical process? Brackets BIDMAS Index Indices Weeks 5 and 6 Find the factor pairs of any whole number Factor Factor pairs Use the lowest common multiple Multiple (LCM) and highest common factor (HCF) to solve problems. Find the prime factor decomposition How does maths in the classroom reflect maths in the real world? LCM HCF Prime factor of a number less than 100 Use the lowest common multiple (LCM) and highest common factor (HCF) to solve problems.

11 THETA Pathway Half Term 2b Weeks 1 and 2 Adding and subtracting fractions with any size denominator. Multiply integers and fractions by a fraction. Use appropriate methods for Why is being proficient at calculating a desirable skill in most jobs? Denominator Common denominator LCM Integer multiplying fractions. Weeks 3 and 4 Convert fractions to decimals. Write one amount as a fraction of another. What profession will these skills be used in? Convert Reciprocal Find the reciprocal of a number. Weeks 5 and 6 Divide integers and fractions by a fraction. Use strategies for dividing fractions. Use the four operations with mixed numbers. World debt is a huge problem how can maths help solve this social issue? Integer Operation Order of operations

12 DELTA Pathway Half Term 2b Weeks 1 and 2 Draw triangles accurately using a ruler and protractor. Draw diagrams to scale. Draw accurate nets of 3D solids. Why does a chartered surveyor need to understand accurate drawing to make sense of buildings? Construct Sketch Accurate Scales Nets Protractor Weeks 3 and 4 Construct triangles using a ruler and compasses. Construct nets of 3D solids using a ruler and compasses. Bisect a line using a ruler and Which professions must be aware of accurate diagrams and how to understand them? Construct Accurate Bisect Perpendicular compasses. Construct perpendicular lines using a ruler and compasses. Weeks 5 and 6 Bisect angles using a ruler and compasses. Draw accurate diagrams to solve problems. Draw a locus. How can we ensure, that by using loci, mobile phone coverage is at its most effective? Construct Bisect Locus Loci Use loci to solve problems.

13 PI Pathway Half Term 3a Weeks 1 and 2 Generating sequences Extending sequences Special sequences Where did algebra come from? Pattern Sequence Term Generate Generate terms of a sequence using Position to term rule the position to term rule. Nth term Find the nth term of a simple sequence. Weeks 3 Compare fractions. Simplify fractions. Identify equivalent fractions. Fractions of amounts Adding and subtracting fractions Why is being proficient at calculating a desirable skill in most jobs? Compare Numerator Denominator Simplify Cancel Weeks 4 and 5 Fractions and percentages Write a number as a fraction of Percentage Proportion another number. Change between fractions and percentages. Is guessing a legitimate mathematical process? Calculate percentages. STEM: Percentages and proportion

14 THETA Pathway Half Term 3a Weeks 1 and 2 Direct proportion on graphs Plot a straight line graph and work out its gradient. Equations of straight lines How can the graph help me to understand relationships between quantities? Direct proportion Linear Gradient Intercept Write the equations of straight line Equation graphs in the form y = mx + c Weeks 3 STEM: Direct proportion problems Identify and describe practical examples of direct proportion. Solve problems involving direct Can you think of any bills that are in direct proportion? Equivalent Proportion Recurring Terminating proportion with or without a graph Use different methods to find equivalent fractions, decimals and percentages. Weeks 4 and 5 Working out one number as a percentage of another. Working out percentage increase and decrease. Are percentages the only maths used in the financial sector? Percentage Increase Interest VAT Percentages of amounts Decrease Use a multiplier to calculate Depreciates percentage increase and decrease. Reduce Use the unitary method to solve percentage problems. FINANCE: Solving problems

15 DELTA Pathway Half Term 3a Weeks 1 and 2 Calculate and compare probabilities. Decide if a game is fair. Mutually exclusive events Estimating probability Did you know probability is a large area of maths? Probabilities Chance Estimate Relative frequency Use relative frequency to estimate Expected frequency the probability of an event. Use estimated probability to calculate expected frequencies. Weeks 3 Carry out a probability experiment. Work out the expected results when an experiment is repeated. List all the possible outcomes of one or two events in sample space Did you know probability developed out of trying to understand gambling? Experiment Outcomes Possibility Venn diagram Tree diagram diagrams or Venn diagrams. Use tree diagrams to find the probabilities of two or more events. Weeks 4 and 5 Maps and scales Bearings Scales and ratio Congruent and similar shapes Solving geometry problems Cartography, map drawing, is a specialised area of maths. Do you know how ancient mariners used maths to help navigate the seas and oceans? Scales Bearings Ratio Congruent Similar

16 PI Pathway Half Term 3b Weeks 1, 2 and 4 Fractions, decimals and percentages Solve problems by adding and subtracting. Add and subtract decimal numbers. Are percentages the only maths you use in the financial sector? Denominator Numerator Common denominator Weeks 4 and 5 Multiply numbers including decimals. Divide by a decimal number. What is a sensible answer? Decimal Place value Estimate Multiply and divide with negative numbers. Weeks 6, 7 and 8 Squares, cubes and roots Work out calculations involving brackets, squares, cubes and square roots. Estimate answers. How did we as a species start understanding complex things like square numbers...and why? Square Cube Root Estimation Recurring decimal Write recurring decimals as fractions.

17 THETA Pathway Half Term 3b Weeks 1, 2 and 3 Planning a survey Identify factors that may affect data collection and plan to reduce bias. Collecting data World debt is a huge problem how can maths help solve this social issue? Survey Questionnaire Data Sample Design and use data collection sheets Pie charts and tables. Interpret Interpret simple pie charts. Weeks 4 and 5 Calculate angles and draw pie charts. Using tables Drawing and interpreting two way tables. Why might graphs and diagrams be misleading? Angles Two way tables Mean Medium Calculating the mean from a simple Mode frequency table. Range Stem and leaf diagrams Frequency Finding mode, median and range Stem and leaf from stem and leaf diagrams, and comparing them for different data sets. Weeks 6, 7 and 8 Scatter graphs Draw scatter graphs. Describe types of correlation. Draw a line of best fit by eye on a scatter graph. How can graphs help me to understand the relationship between quantities? Correlation Line of best fit Scatter Relationship FINANCE: Misleading graphs Identify graphs and charts that are misleading because of the scales used and missing axis labels, mainly in financial contexts.

18 DELTA Pathway Half Term 3b Weeks 1, 2 and 3 Plot straight line graphs. Find the y intercept of a straight line graph. How are linear graphs used in the real world? Intercept Gradient Linear Coordinate Find the gradient of a straight line Quadrant graph. Weeks 4 and 5 Plot graphs using the gradient and y intercept. Use y = mx + c Find the equation of a straight line graph. Does understanding relationships between different variables help us make sense of the world? Equation Gradient Linear Weeks 6, 7 and 8 Identify parallel and perpendicular lines. Find the inverse of a linear function. Plot and use non linear graphs. Can graphs influence people s opinions? Parallel Perpendicular Reciprocal Negative Quadratic Cubic Inverse Function