Developing an Exam Question: Number N10
In this resource from the DfE Standards Unit students learn to use past examination questions creatively by selecting and using appropriate techniques and strategies to solve problems involving numerical, graphical and algebraic manipulation. Most students will have solved problems such as these arithmetically, but they may not…
Using Probability Computer Games S3
In this resource from the DfE Standards Unit, students confront and overcome common misconceptions about probability, count equally likely outcomes using diagrams, discuss relationships between theoretical probabilities, observed outcomes and sample sizes and calculate probabilities of dependent and independent events. Students will…
5/5- Publication year: 2000 - 2009
- Group work
Interpreting Bar Charts, Pie Charts, Box and Whisker Plots S5
In this resource from the DfE Standards Unit, students will learn to understand and interpret bar charts, pie charts, and box and whisker plots. This session is in two linked parts. The first is matching pie charts to bar charts and secondly matching box and whisker plots to bar charts. Each part of the session starts with a whole…
- 5/5
- Publication year: 2000 - 2009
- Group work
Representing 3D Shapes SS6
In this resource from the DfE Standards Unit, students interpret 2D representations of 3D shapes, analyse 3D shapes using plans, elevations, and isometric drawings and develop their reasoning ability in spatial contexts. Many students may have met these ideas before, but they may still experience difficulties in this area. In this…
Understanding Mean, Median, Mode and Range S4
In this DfE Standards Unit resource, students learn to understand the terms: mean, median, mode, range and explore the relationships between these measures and their relationship to the shape of a distribution. Students will have met the terms mean, median, mode and range but they may not have a clear understanding of their meaning…
- 5/5
- Publication year: 2000 - 2009
- Group work
Interpreting Frequency Graphs, Cumulative Frequency Graphs, Box and Whisker Plots S6
In this resource from the DfE Standards Unit, students interpret frequency graphs, cumulative frequency graphs, and box and whisker plots, all for large samples, and then see how a large number of data points can result in the graph being approximated by a continuous distribution (GCSE Grades A - D)
Performing Number Magic A9
In this resource from the DfE Standards Unit, students analyse simple number 'tricks', and explain how they work, using algebra. They then try to create their own variants of the trick, making it more impressive. Students will: develop an understanding of linear expressions and equations; make simple conjectures and generalisations;…
Ordering Fractions and Decimals N1
In this resource from the DfE Standards Unit, students learn to interpret decimals and fractions using scales and areas, find equivalent fractions, order and relate fractions and decimals and to reflect on and discuss these processes. Students will have met these concepts before. Many, however, may still have misconceptions and…
Manipulating Surds N11
In this resource from the DfE Standards Unit students identify equivalent surds and develop their ability to simplify expressions involving surds. Students should understand what a square root is and be able to remove brackets correctly. (GCSE grades A-D; AS and A2 level)
- 5/5
- Publication year: 2000 - 2009
- Group work
Interpreting Algebraic Expressions A1
In this resource from the DfES Standards Unit, students learn to translate between words, symbols, tables, and area representations of algebraic expressions, recognise the order of operations, recognise equivalent expressions and understand the distributive laws of multiplication and division over addition (expansion of brackets).…
- 5/5
- Publication year: 2000 - 2009
- Group work
Transforming Shapes SS7
In this DfE Standards Unit resource, students learn to recognise and visualise transformations of 2D shapes and translate, rotate, reflect and combine these transformations. Students unfamiliar with the terms ‘rotation’, ‘reflection’ and ‘translation’ will need some introduction to these. The session…
- 5/5
- Publication year: 2000 - 2009
- Group work
Interpreting Distance-Time Graphs with a Computer A5
In this DfE Standards Unit resource, students interpret linear and non-linear distance-time graphs using the computer programme Traffic. This program provides a simple yet powerful way of helping learners to visualise distance–time graphs from first principles. The program generates situations involving traffic moving up and…
- 5/5
- Publication year: 2000 - 2009
- Group work
Classifying Shapes SS1
In this resource from the DfE Standards Unit, students learn to name and classify polygons according to their properties, develop mathematical language to describe the similarities and differences between shapes and develop convincing explanations as to why combinations of particular properties are impossible. (GCSE Grades D-F)
Evaluating Algebraic Expressions A4
In this resource from the DfE Standards Unit, students learn to distinguish between and interpret equations, inequations and identities and substitute into algebraic statements in order to test their validity in special cases. Students often use letters in algebra without understanding what they mean. Common misconceptions include…
- 5/5
- Publication year: 2000 - 2009
- Group work
Using Indices N12
In this resource from the DfE Standards Unit students are introduced to fractional and negative indices to enable them to evaluate numerical expressions using negative and fractional indices and use the rules of indices with integer and fractional powers of variables. Students should have some knowledge of the rules of indices for…
Evaluating Probability Statements S2
In this resource from the DfE Standards Unit, students discuss and clarify some common misconceptions about probability. This involves discussing the concepts of equally likely events, randomness and sample sizes. They will also learn to reason and explain. This session assumes that learners have encountered probability before. It…
- 5/5
- Publication year: 2000 - 2009
- Group work
Creating and Solving Equations A2
In this resource from the DfE Standards Unit, students learn to create and solve their own equations, where the unknown appears once. Most students will have been taught rules for solving equations such as ‘change the side, change the sign’ or ‘you always do the same to both sides’. When used without understanding,…
- 3/5
- Publication year: 2000 - 2009
- Group work
Understanding the Laws of Arithmetic N5
In this resource from the DfE Standards Unit, students learn to interpret numerical expressions using words and area representations, recognise the order of operations and equivalent expressions and understand the distributive laws of multiplication and division over addition (the expansion of brackets). Most students will have…
Developing Proportional Reasoning N6
In this resource from the DfE Standards Unit, students reflect on the reasoning they currently use when solving proportion problems, examine proportion problems and appreciate their multiplicative structure and create their own variants of proportion problems. Proportional reasoning is notoriously difficult for many students and…
Evaluating Statements about Number Operations N2
In this resource from the DfE Standards Unit, students learn to understand the properties of number operations, substitute integers, fractions, decimals and negative numbers into statements and equations in order to test their validity and address common misconceptions about the effect of addition, subtraction, multiplication, division,…
Using Percentages to Increase Quantities N7
In this resource from the DfE Standards Unit, students make links between percentages, decimals and fractions, represent percentage increase and decrease as multiplication and recognise the inverse relationship between increases and decreases. Most students will have met these concepts before, however, many will have been introduced…
Interpreting Distance – Time Graphs A6
In this DfE Standards Unit resource students learn to interpret and construct distance–time graphs; relating speeds to gradients of the graphs and accelerations to changes in these speeds. Students have often constructed distance–time graphs before. However, experience shows that many still interpret them as if they are…
- 5/5
- Publication year: 2000 - 2009
- Group work
Evaluating Statements about Enlargements SS5
In this DfE Standards Unit resource, students explore the relationship between linear and area enlargement, substitute into algebraic statements and discuss some common misconceptions about enlargement. Students will have covered some aspects of enlarging shapes before, but they may not have explored the relationships between linear,…
- 5/5
- Publication year: 2000 - 2009
- Group work
Evaluating Directed Number Statements N9
In this resource from the DfE Standards Unit students learn to make valid generalisations about the effect of operations on directed numbers. It is helpful if students have already attempted to use directed quantities in contexts (e.g. money or temperature) before attempting this session. In this session, students are provided with…
- 5/5
- Publication year: 2000 - 2009
- Group work
Interpreting Functions, Graphs and Tables A7
In this DfE Standards Unit resource, students learn to understand the relationship between graphical, algebraic and tabular representations of functions, the nature of proportional, linear, quadratic and inverse functions and doubling and squaring. Students should already be familiar with algebraic symbols such as those representing…
Using Directed Numbers in Context N8
In this resource from the DfE Standards Unit students learn to understand and use directed numbers in the context of temperatures. This session requires no prior knowledge.Students are provided with the temperatures in four cities, temperature differences between these and four other cities are also given. Students are asked to find…
Estimating Length Using Standard Form N4
In this resource from the DfE Standards Unit, students learn to interpret decimals using metric units, estimate lengths of real life objects and interpret standard form.They will also discuss and understand these processes. Some students will have encountered decimals and standard form before. The opening discussion is used to recall…
- 5/5
- Publication year: 2000 - 2009
- Group work
Understanding Perimeter and Area SS2
In this DfE Standards Unit resource, students learn to understand the difference between perimeter and area. Students get practice in calculating the areas and the perimeters of rectangular shapes. Students may have had some previous experience of calculating perimeter and area. (GCSE Grades D - G)
Dissecting a Square SS3
In this resource from the DfE Standards Unit, students learn to express a part or whole diagram in fractions or percentages, convert a fraction to a percentage (using a calculator), calculate areas of rectangles, triangles, circles and parts of circles and add, subtract and multiply fractions. This session builds on students’…
Developing an Exam Question: Transformations SS8
In this resource from the DfE Standards Unit, students learn to use past examination papers creatively, recognise and visualise transformations of 2D shapes, transform triangles and other 2D shapes by translation, rotation and reflection and combinations of these. They develop their ability to generalise and explore their own questions…
- 5/5
- Publication year: 2000 - 2009
- Group work
Creating and Solving Harder Equations A3
In this resource from the DfE Standards Unit, students create and solve their own equations where the unknown appears more than once and learn that there may be more than one way of solving such equations. Before doing this activity students should be able to solve equations where the unknown appears only once. This activity uses…
Connecting Perpendicular Lines A10
In this resource from the DfE Standards Unit, students will identify perpendicular gradients and lines that are perpendicular, learn to relate their learning about perpendicular lines to their previous learning about straight lines and explain the reasons why lines are parallel and perpendicular. Students should have some knowledge…
- 4/5
- Publication year: 2000 - 2009
- Group work