Solving Problems
Shape, Space and Measures 14
All should be able to
Use 2-D representations to visualise 3-D shapes and deduce some of their properties.
Use ruler and protractor to construct simple nets of 3-D shapes, e.g. cuboid, regular tetrahedron, square-based pyramid, triangular prism. Use conventions and notation for 2-D coordinates in all four quadrants; find coordinates of points determined by geometric information.
Use a ruler and protractor to:
measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree; construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA); explore these constructions using ICT.
Calculate the surface area of cubes and cuboids.
Most should be able to
Know and use geometric properties of cuboids and shapes made from cuboids; begin to use plans and elevations. Make simple scale drawings. Given the coordinates of points A and B, find the mid-point of the line segment AB. Use straight edge and compasses to construct:
-a triangle, given three sides (SSS); use ICT to explore this construction.
Find simple loci, both by reasoning and by using ICT, to produce shapes and paths, e.g. an equilateral triangle. Use bearings to specify direction. Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids.
Some should be able to
Visualise and use 2-D representations of 3-D objects; analyse 3-D shapes through 2-D projections, including plans and elevations.
Use and interpret maps, scale drawings.
Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS). Calculate the surface area and volume of right prisms.
Represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.
Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT. Understand the significance of a counter-example. Understand the relationship between ratio and proportion; solve simple problems about ratio and proportion using informal strategies.
Solve more demanding problems and investigate in a range of contexts: number and measures. Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic or graphical form, using correct notation. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation. Use logical argument to establish the truth of a statement; give solutions to an appropriate degree of accuracy in the context of the problem. Suggest extensions to problems, conjecture and generalise; identify exceptional cases or counter-examples. Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.
Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts.
Present a concise, reasoned argument, using symbols, diagrams and graphs and related explanatory text. Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole; compare two ratios; interpret and use ratio in a range of contexts, including solving word problems.