DE LA SALLE SCHOOL LEARNING PROGRAMME. YEAR 9 Foundation. Half Term 1a

Transcription

1 YEAR 9 Foundation Half Term 1a Calculations Use priority of operations with positive and negative numbers. Simplify calculations by cancelling. Use inverse operations. Decimal numbers Place value Factors and multiples Why do I need to be able to calculate when I have a calculator on my phone? Understanding big numbers. How much is a trillion dollars? Integer Positive Negative Inequality Prime Convert Metric Factor Multiple Maths How big is world debt? Weeks 3, 4 and 5: Squares, cubes and roots Recognise powers of 2, 3, 4 and 5. Understand surd notation on a calculator. Index notation Prime factors Algebraic expressions How do prime numbers keep my information safe on the internet? Accuracy Significant Evaluate Prime Powers Indices Term Expression Simplify Maths Simplifying expressions Weeks 6 and 7: Formulae Factorising Factorise algebraic expressions. Using expressions and formulae Write expressions and simple Is algebra useful? Factorise Formula Formulae Expression Solve Algebra Maths formulae to solve problems. Use maths and science formulae.

2 YEAR 9 Higher Half Term 1a Number problems and reasoning Place value and estimating HCF and LCM Calculating with powers (indices) Why do I need to be able to estimate calculations in the real world? How do prime numbers keep my information safe on the internet? Integer Estimation Significant figure Factor Prime Multiple Accuracy Weeks 3, 4 and 5: Zero, negative and fractional indices Powers of 10 and standard form Surds Understand the difference between Why use standard form to write large and small numbers? Index Indices Standard form rational and irrational numbers. Rationalise a denominator. Algebraic indices Expanding and factorising Understanding big numbers. How much is a trillion dollars? How big is world debt? Weeks 6 and 7: Equations Formulae Distinguish between expressions, equations, formulae and identities. Linear sequences Non linear sequences More expanding and factorising Why is algebra useful? Surds Inverse operation Linear Sequence Pattern Expand Factorise Formulae Equation Identities

3 YEAR 9 Foundation Half Term 1b Weeks 1, 2 and 3: Frequency tables Collecting data Two way tables Why does the government collect data? Frequency Grouped data Data Discrete Continuous Graph Corbett Maths Representing data Weeks 4 and 5: Statistical diagrams Time series Stem and leaf diagrams Pie charts How does maths in the classroom reflect maths in the real world? Stem and leaf Range Mode Median Range Angle Sector Pie chart Corbett Maths Weeks 6, 7 and 8: Scatter graphs Plot and interpret scatter graphs. Determine whether or not there is a relationship between sets of data. Draw a line of best fit on a scatter How can graphs help me understand relationships between quantities? Interpret Compare Correlation Estimate Corbett Maths graph. Use the line of best fit to predict values.

4 YEAR 9 Higher Half Term 1b Weeks 1, 2 and 3: Construct and use back to back stem and leaf diagrams. Construct and use frequency polygons and pie charts. Why might graphs be misleading? What are the benefits? Frequency polygon Pie chart Time series Predict Interpret Plot and interpret time series graphs. Use trends to predict what might happen in the future. Weeks 4 and 5: Plot and interpret scatter graphs. Determine whether or not there is a linear relationship between two variables. Draw a line of best fit on a scatter graph. How can the graph help me understand relationships between quantities? Linear relationship Correlation Line of best fit Scatter graph Use the line of best fit to predict values. Weeks 6, 7 and 8: Decide which average is best for a set of data. Estimate the mean and range from a grouped frequency table. Find the modal class and the group containing the median. Why does the government collect data? Mode Median Mean Range Estimate Modal class Class interval Data Construct and use two way tables. Choose appropriate diagrams to display data. Recognise misleading graphs.

5 YEAR 9 Foundation Half Term 2a Working with fractions Operations with fractions Multiplying and dividing fractions Fractions and decimals Fractions and percentages Why is being proficient at calculating a desirable skill in most jobs? Numerator Denominator Reciprocal Percentage Decimal Equivalent Calculating percentages Weeks 3 and 4: Solving equations 1 Solving equations 2 Solving equations with brackets Introducing inequalities More inequalities What do I need algebra for? Equation Term Variable Inequality sign Bracket Expand Inverse Balance Weeks 5 and 6: More formulae Sequences Recognise and extend sequences. Generating sequences Using the nth term of a sequence When do I use formulae in real life? Substitution Rearrange Sequence Pattern Nth term General rule Linear Geometric

6 YEAR 9 Higher Half Term 2a Working with fractions Four operations with fractions Find the reciprocal of an integer, decimal or fraction. Ratio Write ratios in the form 1 : n or n : 1. Compare ratios. Find quantities using ratios. Solve problems involving ratios. Sharing out should be equal or should it? Numerator Denominator Reciprocal Percentage Decimal Equivalent Unitary method Currency Convert Exchange rate Direct proportion Inverse proportion Indirect proportion Convert between currencies and measures. Recognise and use direct proportion. Percentages Work out percentage increases and decreases. Weeks 3 and 4: Angle properties of triangles and quadrilaterals Interior and exterior angles of a polygon Which professions need to understand about angles and the properties of triangles and quadrilaterals? Interior angle Exterior angle Polygon Weeks 5 and 6: Trigonometry Use trigonometric ratios to find lengths in a right angled triangle. Use trigonometric ratios to find angles in a right angled triangle. What profession will these skills be used in? Trigonometry Trigonometric ratios Sine Cosine Tangent Inverse function Hypotenuse Use trigonometric ratios to solve problems. Know the exact values of the sine, cosine and tangent of some angles.

7 YEAR 9 Foundation Half Term 2b Properties of shapes Solve geometric problems using side and angle properties of quadrilaterals. How does maths in the classroom reflect maths in the real world? Geometric Properties Congruent Parallel Alternate Corresponding resources that can be used Identify congruent shapes. Angles in parallel lines Weeks 3 and 4: Understand and use the angle properties of parallel lines. Find missing angles using corresponding and alternate angles. Angles in triangles Which professions must be aware of accurate diagrams and how to understand them? Parallel Alternate Corresponding Isosceles Equilateral Scalene Right angle Weeks 5 and 6: Calculate the interior and exterior angles of regular polygons. Calculate the interior and exterior angles of polygons. Solve angle problems using equations. Which professions need to understand about angles and the properties of triangles and quadrilaterals? Polygons Regular Interior Exterior Geometrical Solve geometrical problems showing reasoning.

8 YEAR 9 Higher Half Term 2b Linear graphs Find the gradient and y intercept from a linear equation. Plot graphs with equations ax + by = c. Sketch graphs using the gradient and How can a graph show relationships between quantities? Linear Gradient Intercept Sketch Coordinates resources that can be used intercepts. Find the equation of a line, given its gradient and one point on the line. Find the gradient of a line through two points. Weeks 3 and 4: Draw and interpret distance time graphs. Calculate average speed from a distance time graph. Understand velocity time graphs. Find acceleration and distance from velocity Why use one unit instead of another? Distance Time Speed Velocity Acceleration Gradient Intercept Area time graphs. Weeks 5 and 6: Line segments Find the equations of lines parallel or perpendicular to a given line. Draw quadratic graphs. Solve quadratic equations using graphs. Identify the line of symmetry of a quadratic graph. Why is being proficient at mathematics a desirable skill in most jobs? Midpoint Parallel Perpendicular Quadratic Symmetry Cubic Reciprocal Linear Non linear Cubic and reciprocal graphs Recognise a graph from its shape. Interpret linear and non linear real life graphs. Draw the graph of a circle.

9 LEARNING PROGRAMME YEAR 9 Foundation Half Term 3a Averages and range Mean and range Mode, median and range Types of average Estimating the mean questions that we will be Which professions will these skills be used in? Average Mean Median Mode Range Estimate Mid point Class interval resources that can be used Sampling Weeks 3: Calculate the perimeter and area of rectangles, parallelograms and triangles. Calculate a missing length, given the area. Trapezia and changing units Calculate the area and perimeter of trapezia Which professions need to understand about angles and the properties of triangles and quadrilaterals? Perimeter Area Trapezium trapezia Calculate the perimeter and area of shapes made from triangles and rectangles. Convert between area measures. Weeks 4 and 5: Surface area of 3D solids Volume of prisms Calculate the volume of a cuboid. Calculate the volume of a prism. More volume and surface area Solve problems involving surface area and volume. Why use one unit instead of another? There are many different units to measure volume. Why is this? Surface area Volume Prism Cuboid Cylinder Cube

10 LEARNING PROGRAMME YEAR 9 Higher Half Term 3a Area and volume Find the perimeter and area of compound shapes. Recall and use the formula for the area of a trapezium. questions that we will be There are many different units to measure volume. Why is this? Area Volume Trapezium Trapezia Upper bound Lower bound Error interval resources that can be used Convert between metric units of area. Calculate the maximum and minimum possible values of a measurement. Weeks 3 and 4: Calculate volumes and surface areas of prisms. Convert between metric units of volume. Calculate the area and circumference of a circle. Calculate the perimeter and area of semicircles and quarter circles. Calculate arc lengths, angles and areas of sectors of circles. When do I use formulae in real life? Volume Surface area Prism Area Circumference Pi Sector Arc Radius Radii Diameter Weeks 5 and 6: Calculate volume and surface area of a cylinder and a sphere. Why use one unit instead of another? Cylinder Sphere Pyramid Cone Calculate volume and surface area of pyramids and cones. Solve problems involving volumes and surface areas.

11 YEAR 9 Foundation Half Term 3b Weeks 1, 2 and 3: Coordinates Linear graphs Gradient y = mx + c How can a graph help me understand relationships between variables? Linear Gradient Intercept Weeks 4 and 5: Real life graphs Distance time graphs Understand and use the relationship between distance, average speed Why use one unit instead of another? Distance Speed Velocity Time Average Constant and time. Weeks 6, 7 and 8: More real life graphs Recall the definitions of positive, negative and no correlation. How does maths in the classroom reflect maths in the real world? Conversion Exchange rates Correlation Equation of a line Find the equation of a line.

12 LEARNING PROGRAMME YEAR 9 Higher Half Term 3b Weeks 1, 2 and 3: Draw plans and elevations of 3D solids. Reflect a 2D shape in a mirror line. Rotate a 2D shape about a centre of rotation. Describe reflections and rotations. Enlarge shapes by fractional and negative scale questions that we will be In what jobs are transformations useful? Plan Elevation Reflect Rotate Enlarge Vector Translation Transformation resources that can be used factors about a centre of enlargement. Translate a shape using a vector. Carry out and describe combinations of transformations. Weeks 4 and 5: Bearings and scale drawings Constructions Construct triangles using a ruler and compasses. Construct the perpendicular bisector of a line. Construct the shortest distance from a point to a Why does a chartered surveyor need to understand accurate drawing to make sense of buildings? Bearing Scale drawing Construct Sketch Perpendicular Bisect line using a ruler and compasses. Weeks 6, 7 and 8: Bisect an angle using a ruler and compasses. Construct angles using a ruler and compasses. Construct shapes made from triangles using a ruler and compasses. Draw a locus. Use loci to solve problems. Which professions must be aware of accurate diagrams and how to understand them? Construct Bisect Locus Loci