# Maths in physics

### Teaching Mental Mathematics From Level Five: Algebra

A National Strategies booklet describing teaching approaches that can be used to develop mental mathematics in its broadest sense beyond National Curriculum level five. Each area is covered by looking at teaching strategies, activities, progression and addresses typical algebraic misconceptions.

The booklet covers:

• algebraic conventions

• solving linear equations

• sequences

• functions and graphs.

There are more clouding the picture activities on page 21 of the pdf document.

### Constructing and Solving Linear Equations

School packs on constructing and solving linear equations for Years Seven, Eight and Nine were developed by the National Strategies. They contained booklets which were part of continuining professional development courses.

The year 7 booklet has more examples for solving equations and using pyramids to create equations.

### Algebra Study Units

Unit 2: Transforming expressions and equations - This unit discusses ways of helping students to form equivalent expressions through 'clouding the picture' activities. It also considers two of the teaching principles that help students to use and apply algebra with confidence: providing opportunities for students to express generality asking students to 'find as many ways as you can'. This contains the clouding the picture, transforming equations activity.

Unit 6: Applying skills in the context of ‘pyramids’ - This unit explores how students can use and apply their algebraic skills in the context of 'pyramid puzzles'. The work is developed in four stages: understanding the structure of a pyramid by using numbers collecting like terms constructing and solving equations intuitively constructing and solving equations more formally. This unit contains the informal methods of solving equations activity

### 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 squares, square roots and fractions.

This resource contains matching exercises linking graphs, equations, coordinates and tables of values.

### Interpreting Distance – Time Graphs A6 *suitable for home teaching*

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.

This resource contains the matching exercises used in the session.

### Joined-up thinking

**Case Study: Exploring common content and coordinated teaching of mathematics and physics across KS3, KS4 and KS5 **

Students often feel confused as they are told something in one lesson only for it to be contradicted, or at least not supported, in another lesson. These were the findings of the STEM Knowledge Network at St Thomas More High School. Project Coordinator Jonathan Powell describes how the school is tackling these inconsistencies between the mathematics and physics departments and developing a more coordinated approach to teaching.

### Bridges to learning

**Case Study: Building interdisciplinary links between science and mathematics as part of the ‘Compass’ project.**

Hyde Technology College is focusing on the use of science and mathematics topics with a bridging concept to link the separate disciplines, while keeping to the existing timetable of subjects taught in separate lessons. Andrew Gilday reports on how Hyde’s STEM Knowledge Network is helping to achieve this in collaboration with the University of Manchester.

### Mathematics and science departments working collaboratively.

**Case Study: Mathematics and science departments working collaboratively. It’s not rocket science, or is it?**

Cross-curricular work can be incredibly powerful, both in terms of student outcomes and staff Continuing Professional Development (CPD). However, it is easy to contemplate, but far more difficult to deliver. Effective planning is the key. At King James’s School, near Huddersfield, members of the mathematics and science departments worked collaboratively to prepare a ‘rockets’ project which was delivered jointly on one of the school’s cross-curricular days, and followed up in subsequent mathematics lessons to provide a high quality and enjoyable learning experience for staff and students alike.