Standards Units
51 classroom activities for active learning through group work, discussion and open questioning.
How Standards Units work
Each unit is a complete lesson. The PDF has the teacher notes, followed by card sets and worksheets to print for the class.
Students work in pairs or small groups, sorting, matching and discussing the cards. Many units also come with a PowerPoint.
Classroom-ready versions by Mature_Maths_Trainee.
Five types of activity
Most units are built around one of these. In each, the discussion between students matters more than the answer.
- 1
Classifying
Sort shapes, numbers or expressions by their properties, and explain how the groups were chosen.e.g. SS1, N13
- 2
Interpreting representations
Match cards that show the same idea in different ways: words, symbols, tables, graphs and diagrams.e.g. N1, A1, A7
- 3
Evaluating statements
Decide whether statements are always, sometimes or never true, and back it up with examples.e.g. N2, A4, S2
- 4
Creating problems
Make up questions for someone else to solve, including your own exam questions.e.g. A2, N10, S7
- 5
Analysing reasoning
Compare methods, and find and fix the errors in worked solutions.e.g. A3, A14
No Standards Units match
Try fewer words, or a different word for the same thing.
Number
Decide whether statements about the four operations are always, sometimes or never true.
Match calculations to words and area diagrams, focusing on the order of operations.
Work out missing temperatures and temperature changes between cities.
Test generalisations about calculating with negative numbers, and find examples and counterexamples.
- Rounding numbersKS2KS3
Place numbers on a number line and round them to the nearest 10, 100 or 1000.
- Dissecting a squareKS2KS3
Work out what fraction of a square each piece is, then design your own dissection.
Also in: Fraction, decimal, percentage equivalence, Perimeter and area
Match percentage changes to decimal multipliers, and see why an increase and a decrease do not cancel out.
Solve proportion problems such as recipes, then make up your own versions.
Also in: Ratio
Compare two van hire deals, then write your own exam question in the same style.
Also in: Straight-line graphs
Estimate the lengths of objects from a fly to a galaxy, and write them in standard form.
Also in: Measures and units
Decide whether statements about surds are true or false, and match equivalent surds.
Algebra
Match algebraic expressions to words, tables and area diagrams.
Also in: Brackets
Decide whether equations and identities are always, sometimes or never true.
Also in: Linear equations
Generalise growing cross patterns, then write your own exam question.
- Analysing sequencesGCSEA Level
Sort sequences into arithmetic and geometric progressions, and define them by their nth term.
Build equations step by step, then swap and solve each other's.
Create and solve equations with the unknown on both sides, and compare methods.
Sort equations of lines by gradient and find the perpendicular pairs.
Use a traffic simulation to make sense of distance–time graphs.
Match distance–time graphs to stories and descriptions, then create your own.
Match functions to their graphs, tables and descriptions in words.
Also in: Straight-line graphs
Match quadratic functions in different forms to their graphs and properties.
Also in: Quadratic equations
- Performing number magicKS3GCSE
Use algebra to explain how number tricks work, then invent your own.
Also in: Introduction to algebra, Brackets
Geometry
- Classifying shapesKS2KS3
Sort shapes by their properties, and explain why some combinations are impossible.
Investigate rectangles with a fixed perimeter or a fixed area, with a spreadsheet to help.
Decide whether statements about length and area are always, sometimes or never true.
- Transforming shapesKS3GCSE
Match pairs of shapes to the transformations that map one onto the other.
Describe transformations of a triangle, then write your own exam question.
Explore what happens to perimeter and area when a shape is enlarged.
Also in: Transformations
Statistics & Probability
Match bar charts to pie charts, and to box and whisker plots.
Also in: Averages and spread
Match frequency graphs, cumulative frequency graphs and box plots for large samples.
Also in: Averages and spread
Match bar charts to their mean, median, mode and range.
Also in: Representing data
- Ordering probabilitiesKS2KS3
Place events on a probability scale from 0 to 1 and justify the order.
Decide whether statements about probability are true, false or unsure, and explain why.
Predict, then simulate, coin and dice races to compare theory with what happens.
Answer a question about two spinners, then write your own exam question.
A Level
A Level Pure
4Match trigonometrical equations to their graphs, exploring translations and stretches.
Also in: Trigonometry
Use the laws of logarithms to match equivalent expressions in a jigsaw.
Match parametric equations to their graphs, and find the errors in worked solutions.
A Level Calculus
4Sketch functions with fractional and negative powers, finding stationary points and intercepts.
Match quadratic functions to their derivatives and to their values at given points.
Rewrite functions in index form, then differentiate and integrate them.
Find and classify the stationary points of cubic functions.
A Level Statistics
1- Using binomial probabilitiesA Level
Match events to binomial probability expressions and their values.
A Level Mechanics
2Solve a constant acceleration exam question, then generalise it and write your own.
Apply Newton's second law to a range of problems, linking each stage of the solution.
A Level Decision
1Sort graphs into Eulerian, semi-Eulerian and neither, then solve route inspection problems.
Classroom-ready versions by Mature_Maths_Trainee.