Year 11 2009-2010 SOW

GCSE Module 5 Foundation

  1. Angles
  2. Properties of Triangles
  3. Use of symbols
  4. Perimeter and Area
  5. Properties of Polygons
  6. Sequences
  7. Co-ordinates
  8. Area & Volume
  9. Equations
  10. Reflections & Rotations
  11. Trial & Improvement
  12. Translation & Enlargement
  13. Measures
  14. Real-life graphs
  15. Formulae
  16. Construction
  17. Graphs of linear functions
  18. Pythagoras

Angles

  • Recognise acute, obtuse, reflex and right angles.
  • Estimate angles and measure them accurately.
  • Angle properties at a point & on a straight line.
  • Understand terms ‘perpendicular’ and ‘parallel’. (F)
  • Recognise corresponding angles & alternate angles.
  • Understand & use three-figure bearings. (D)

Properties of Triangles

  • Identify the various types of triangle.
  • Use the word ‘congruent’ for identical triangles. (G)
  • Show that angles in a triangle total 180° & use this
  • Show that the exterior angle of a triangle is equal to the sum of the interior opposite angles.
  • Use angle properties of triangles. (E)

Use of symbols

  • Simplify expressions with one variable. (F)
  • Simplify expressions with more than one variable. (E)
  • Multiply out expressions with brackets
  • Factorise simple expressions such as 6a + 8 (D)
  • Expand and simplify harder expressions. (C)

Perimeter and Area

  • Find the perimeter and area of a shape by counting squares.
  • Estimate the area of an irregular shape
  • Name the parts of a circle (G)
  • Work out the area and perimeter of a simple rectangle. (F)
  • Work out the area & perimeter of a harder rectangle. (E)
  • Find the area of a triangle, parallelogram, kite and trapezium
  • Find the area and perimeter of compound shapes
  • Calculate the circumference and area of a circle. (D)
  • Find the perimeter and area of a semi-circle. (C)

Properties of Polygons

  • Recognise and name shapes such as isosceles triangle, parallelogram, rhombus, trapezium and hexagon. (G)
  • Calculate interior and exterior angles of a quadrilateral.
  • Be able to tessellate shapes. (E)
    Classify a quadrilateral by geometric properties
  • Calculate interior and exterior angles of a regular polygon. (C)

Sequences

  • Continue a sequence of numbers or diagrams
  • Write the terms of a simple sequence. (G)
  • Find a particular term in a sequence involving positive numbers
  • Write the term-to-term rule in a sequence involving positive numbers. (F)
  • Find a particular term in a sequence involving negative or fractional numbers
  • Write the term-to-term rule involving negative or fractional numbers. (E)
  • Write the terms of a sequence or a series of diagrams given the nth term. (D)
  • Write the nth term of a sequence or a series of diagrams. (C)

Co-ordinates

  • Use coordinates in the first quadrant. (G)
  • Use coordinates in all four quadrants. (F)
  • Draw line such as x = 3 and y = x + 2 (E)
  • Solve problems involving straight lines
  • Draw lines such as y = 2x + 3 (D)
  • Find the midpoint of a line segment
  • Use and understand coordinates in three dimensions (C)

Area & Volume

  • Find the volume of a solid by counting cubes and state the correct units. (G)
  • Find the volume of a cube or cuboid
  • Find the height of a cuboid if given other dimensions (E)
  • Change between area measures, such as m2 to cm2 (D)
  • Calculate the surface area and volumes of prisms and cylinders
  • Calculate volumes of prisms and cylinders
  • Change between volume measures. (C)

Equations

  • Solve simple one-step equations such as 3x = 12 (F)
  • Solve two-step equations such as 3x – 1 = 9 (E)
  • Solve equations with brackets such as 2 (5x + 1) = 28
  • Solve equations where the letter appears twice (D)
  • Solve more complex equations combining several of the above such as brackets and letter appearing twice
  • Solve inequalities such as 3x < 9 and 12 = 3n < 20
  • Solve linear inequalities such as 4x – 3 < 10
  • Represent sets of solutions on a number line (C)

Reflections & Rotations

  • Draw a line of symmetry on a 2D shape
  • Draw the reflection of a shape in a mirror line (G)
  • Draw ALL the lines of symmetry on a 2D shape
  • Draw the line of reflection for two shapes
  • Give the order of rotation of a 2D shape
  • Name, draw or complete 2D shapes from information about their symmetry (F)
  • Reflect shapes in the axes of a graph (E)
  • Reflect shapes in lines parallel to the axes, such as x = 2 and y = -1
  • Rotate shapes about the origin
  • Describe fully reflections in a line and rotations about the origin
  • Identify reflection symmetry in 3D solids (D)
  • Reflect shapes in lines such as y = x and y = – x
  • Rotate shapes about any point
  • Describe fully reflections in any line and rotations about any point
  • Find the centre of a rotation and describe it fully
  • Combine reflections and rotations (C)

Trial & Improvement

  • Form and solve equations such as x3 + x = 12 using trial and improvement (C)

Translation & Enlargement

  • Give a scale factor of an enlarged shape (F)
  • Enlarge a shape by a positive scale factor
  • Find the measurements of the dimensions of an enlarged shape
  • Use map scales to find distance (E)
  • Enlarge a shape by a positive scale factor from a given centre
  • Translate a shape using a description such as 4 units right and 3 units down
  • Compare the area of an enlarged shape with the original shape (D)
  • Enlarge a shape by a fractional scale factor
  • Translate a shape by a vector
  • Transform shapes by a combination of translation, rotation, and reflection (C)

Measures

  • Decide which metric unit to use in everyday situations (G)
  • Convert between metric and imperial units
  • Make sensible estimates of a range of measures
  • Know simple rough metric equivalents for imperial units (F)
  • Solve simple speed problems (E)
  • Solve more difficult speed problems (C)

Real-life graphs

  • Plot points of a conversion graph & read off values (F)
  • Interpret distance – time graphs (E)
  • Calculate simple speeds from distance – time graphs (D)
  • Calculate complex average speeds from d-t graphs (C)

Formulae

  • Use a formula written in words (G)
  • Use a simple formula with positive numbers (F)
  • Write an expression from a problem
  • Substitute negative numbers into simple formula (E)
  • Substitute numbers into more complicated formulas (D)
  • Solve a problem by forming & solving an equation
  • Rearrange simple linear formulae (C)

Construction

  • Measure a line accurately to the nearest millimetre
  • Recognise the net of a simple solid such as a cuboid (G)
  • Measure & draw angles accurately to the nearest degree
  • Draw the net of a simple solid such as a cuboid (F)
  • Draw a triangle from various measurements (E)
  • Draw a quadrilateral such as a kite or a parallelogram with given measurements
  • Construct and recognise the nets of 3D solids such as pyramids and triangular prisms (D)
  • Construct the perpendicular bisector of a line
  • Construct the perpendicular from a point to a line
  • Construct the perpendicular from a point on a line
  • Construct angles of 60° and 90°
  • Construct the bisector of an angle (C)

Graphs of linear functions

  • Plot the graphs of straight lines such as x = 3 and y = 4
  • Complete a table of values for equations such as
  • y = 2x + 3 and draw the graph (E)
  • Solve problems involving graphs, such as finding where the
    line y = x + 2 crosses the line y = 1 (D)
  • Recognise the equations of straight line graphs
  • Find the gradients of straight line graphs (C)

Pythagoras

  • Use Pythagoras theorem to find:
    • the hypotenuse of a right-angled triangle
    • any side of a right-angled triangle
    • the height of an isosceles triangle (C)