Developing a generalised statement
The standard hundred square is a powerful visual representation of the number system that is used throughout Key Stages 1 and 2. By the end of Key Stage 2, pupils are familiar and comfortable with this representation, and it can be used to further develop other themes within mathematics. This lesson uses the regular layout of the hundred square to explore relationships and patterns within the square, and to express these relationships algebraically. Throughout the lesson, pupils are encouraged to reason mathematically, and communicate that reasoning both verbally and in writing, in precise mathematical language.
Download plan for lesson 1 here
Interpreting marathon data
This lesson aims to provide pupils with opportunities to analyse and interpret data, to use real data to pose their own questions and to solve a specific problem or question. The scenario is the marathon; pupils can analyse and interpret data presented in a range of ways, including a bar chart, pie chart, line graph and table. They can use the data to frame responses to lines of enquiry, such as planning a post-race diet for an athlete, or discussing the point in time when a woman might run a marathon faster than a man. The lessons also lend themselves to providing opportunities for pupils to practice skills such as converting units of time, calculating mean, mode and median and discussing the merits of each as a measure of average.
Download plan for lesson 2 here
Marathon facts sheet
Marathon powerpoint presentation
Constructing the frustrum of a tetrahedron
Throughout Key Stages 1 and 2, pupils learn the names and properties of 2 and 3 dimensional shapes - this lesson builds on that knowledge. Pupils use their knowledge of the properties of shapes to discuss and establish the precise names, angle sizes, side lengths, areas and volumes of shapes using geometric reasoning, rather than protractors and rulers.
Download plan for lesson 3 here
Truncated tetrahedron powerpoint presentation
Investigating a general statement
In Key Stages 1 and 2, pupils develop mathematical proof by finding examples that fit given mathematical statements. Commonly, pupils investigate statements that are true. In this lesson, pupils are presented with a statement for which it is possible to find examples that agree, examples that disagree, and examples that require some discussion about the precise meaning of the original statement. In calculating the counter-examples, pupils have opportunities to practice multiplying by decimal fractions using appropriate pencil and paper methods. The lesson provides further opportunities for pupils to reason and communicate their reasoning, in both verbal and written formats.
Download plan for lesson 4 here
Problem solving and reasoning using a spreadsheet
In Key Stage 1, children’s understanding of the properties of numbers begins to focus on odd and even numbers. The use of odd and even numbers and other properties of numbers can be a powerful tool in problem solving. This is a theme that pupils can make more use of when using and applying mathematics. In this lesson pupils solve problems using ICT as a tool to support their calculation and thinking. The focus is on developing efficient strategies for problem solving and recording findings, whilst using the spreadsheet as a calculation tool. Pupils are supported in using their understanding of the properties of numbers and thinking systematically.
Download plan for lesson 5 here
Number Generator PowerPoint
Bricks in the Wall Excel file
Solve the cipher
This lesson delves into the real life application of mathematics to encode and decode messages – cryptography. Cryptography played its part in key moments of history, including World War 2 and the downfall of Mary Queen of Scots. Pupils work with early coding systems, understanding the mathematics involved and realising how the limitations of each led to the need to develop the next.
Download plan for lesson 6 here
Constructing flags using ratio
In this lesson, pupils explore the construction of flags using their understanding of ratio.
Download plan for lesson 7 here