 Author # Colin Foster

Assistant Professor in mathematics education in the School of Education at the University of Nottingham

#### Articles by Colin Foster

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###### 15 of the Best KS4 Maths Lesson Plans by Colin Foster

Whether it's mean and median, highest common factor or lowest common multiple, Colin Foster has you covered with his free Key Stage 4 maths lesson plans

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###### KS4 Maths Lesson Plan – Using Number Patterns To Understand Integers

Calculations involving multiplication of whole numbers don’t have to be boring if the answers contain surprising patterns

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###### 44 Free Maths Lesson Plans for KS3 and KS4 by Colin Foster

We've got everything you need for your secondary maths classroom from algebra and geometry to improving number sense and mathematical fluency

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###### KS3 Maths Lesson Plan: Exploring Number Patterns And Where They Appear In The Real World

The way in which the pages are numbered in a newspaper gives opportunities for students to explore number patterns and structure

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###### Sometimes in Maths ‘I Don’t Know’ is Exactly the Right Answer

Colin Foster explains why the guessing game isn't necessarily a bad thing

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###### Your natural teaching style might not be best for your pupils

Just because a particular way of teaching comes instinctively to you, that doesn’t necessarily make it the most effective for your students, warns Colin Foster...

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###### KS4 Maths Lesson Plan – A Simple But Competitive Dice Game Can Really Put Probability Into Context

Uncertainty is all around us in the world. Understanding probability helps us make better decisions about risk.

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###### KS3 Maths Lesson Plan – Explore How Proportions Work By Mixing Paints

Thinking proportionally helps to make sense of lots of different real-life situations

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###### 13 of the Best Colin Foster Geometry and Measures Lesson Plans for KS3/4 Maths

These lesson plans come in all shapes and sizes and cover every angle of secondary geometry you could wish for

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###### 12 of the Best KS3 Maths Lesson Plans by Colin Foster

Improve your secondary students' mathematical fluency, confidence and reasoning with these free maths lessons

#### Resources by Colin Foster

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###### KS3 Maths Lesson Plan – Use Puzzles to Show Students that Algebra is a Powerful Mathematical Tool

Instead of treating algebra as a foreboding, abstract topic to be feared, says Colin Foster students ought to see it as...

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###### KS3 Maths Lesson Plan – Explore Proportions By Mixing Paints

In this lesson, students work on a task about pink paint, which is made from a mixture of red paint and...

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###### KS4 Maths Lesson Plan – Link Maths To Real Life In This Problem Solving Lesson About Money

Mathematical questions about a photo in a carpark gives a real-life context to this maths lesson. Students will devise their own...

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###### KS4 Maths Lesson Plan – Devise Ways to Make Different Numbers To Help Make Sense of Mathematical Operations

Combining four numbers in a multitude of ways shows the creative power of mathematics and allows students to develop their facility...

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###### KS4 Maths Lesson Plan – Use Distance-Time Graphs to Solve Problems about Motion

In this lesson, students explore a scenario involving two robots, each moving at a (different) constant speed along the same straight...

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###### KS4 Maths Lesson Plan – Understand Distance and Movement in 3D

Understanding distances and movements in 3 dimensions is vital for living in a 3D world, says Colin Foster… In this lesson, students...

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###### KS3 Maths Lesson Plan – Develop an Understanding of Numbers by Exploring What Makes Prime Numbers Special

Prime numbers are all around us, and they’re important, yet some are more important than others. Help your pupils discover how...

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###### KS4 Maths Lesson Plan – Quadratic Equations Bring Together A Host Of Different Mathematical Ideas And Techniques.

Quadratic expressions are considerably more complicated to work with than linear expressions, and students often find them hard to handle. Students may...

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###### KS3 Maths Lesson Plan – Use The Page Numbers In A Newspaper To Explore Number Patterns

Patterns in numbers arise in many different circumstances in the world around us. Making sense of these with mathematics allows students...

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###### KS3 Maths Lesson Plan – Teach Trigonometry Without Tears

Using a unit circle can help develop a deeper understanding of working with right-angled triangles. In this lesson, students explore the behaviour...

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###### KS3 Maths Lesson Plan – Investigate Patterns using Sequences of Decimals

In this lesson, students explore decreasing arithmetic sequences in which the common difference is a decimal number. The task is to investigate...

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###### Calculating voucher discounts – KS3 maths lesson plan and resources

Making sound decisions about purchases is an essential use of mathematical thinking… In this lesson, students consider pairs of alternative discount vouchers...

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###### KS4 Maths Lesson Plan – Use Spatial Reasoning in Geometry to Understand How Shapes Move when Broken Down into Points and Lines

In geometry students need to use their spatial reasoning and visualisation skills to understand the shapes and how they will move...

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###### KS4 Maths Lesson Plan – Help Students Understand When One Integer Will Divide Exactly Into Another

Understanding when one integer will divide exactly into another helps students to ‘make friends’ with the integers and feel more secure...

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###### KS4 Maths Lesson Plan – Use Ratio to Work out How to Carry Enough Food to Stay Alive in the Desert

Working out how to carry enough food to stay alive in a challenging environment poses interesting problems. In this lesson, students use...

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###### KS4 Maths Lesson Plan – Explore Simultaneous Equations that have Integer Solutions

In this lesson, students explore a set of two-variable linear equations, constructed so that when you solve any pair of them...

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###### KS3 Maths Lesson Plan – Improve Mathematical Reasoning with a Real-Life Problem: How Many Sweets Can I Buy?

Working out how many large and small bags of doughnuts to buy so as to get your treats as cheaply as...

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###### KS3 Maths Lesson Plan – Work Out The Topic Area By Finding The Three Angles Of A Triangle

Learners are often asked to practise finding the third angle of a triangle when the other two are given. In this...

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###### KS3 Maths Lesson Plan – Help Learners Understand Adding And Subtracting Directed Numbers By Linking To The Topic Of Electricity

Lots of learners have heard that ‘two minuses make a plus’ but may not apply this rule correctly or have much...

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###### KS4 Maths Lesson Plan – Asking Mathematical Questions about Real-World Money Problems Helps Develop Valuable Thinking Skills

Mathematics teachers often say that ‘maths is all around us’, but how often does the stimulus for a mathematics lesson come...

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###### KS3 Maths Lesson Plan – Can Students Carry Out A Probability Experiment And Explain The Results?

If you choose which student will answer a question by drawing lolly sticks bearing their names from a cup, how many...

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###### KS3 Maths Lesson Plan – The Importance of Decimal Point Placement

In this lesson, students are asked to create and solve some puzzles involving decimal calculations where the decimal points have been...

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###### Angles of Triangles – KS4 Maths Lesson Plan

Get them exploring this important method for solving triangles, says Colin Foster… In this lesson, students will explore how the sine rule...

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###### KS4 Maths Lesson Plan – Embed Adding and Subtracting Fractions into a Richer Problem to get the Technique to Stick

They’ve been taught the technique a dozen times or more…but through embedding it within a richer problem, ‘adding and subtracting fractions’...

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###### KS4 Maths Lesson Plan – Explore Probability by Playing Dice Games

In many everyday scenarios, we cannot calculate a theoretical probability of something happening. Even some simple-sounding games involving dice are complicated to...

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###### KS4 Maths Lesson Plan – Use Pythagoras’ Theorem To Find Accurate Values For Triangle Perimeters

In this lesson, students use Pythagoras’ theorem to find accurate values for the perimeters of some triangles. Although the values of...

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###### KS3 Maths Lesson Plan – Find The Centre Of Enlargement For A Given Shape

In this lesson, students are asked to decide where the centre of enlargement can go for a given shape with a...

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###### KS4 Maths Lesson Plan – Use Algebra To Find Out Why A Number Trick Works

In this lesson, algebra is used to make sense of a number trick that the teacher performs. Students are asked to explore...

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###### KS3 Maths Lesson Plan – Investigate Place Value by Moving Around the Digits in Two Numbers

Multiplication is an essential part of any student’s understanding of mathematics. Getting a sense of place value enables students to estimate...

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###### KS3 Maths Lesson Plan – Develop Students’ Algebra Skills with a Problem that Requires Integer Solutions

In this lesson, students have to find a solution to a problem where the unknowns must be non-negative integers. This constraint means...

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###### KS4 Maths Lesson Plan – Help Students Understand How to Work Out What a Statistical Chart Means

In this lesson, students examine two box plots showing marks obtained by two classes. First, they have to interpret the box plots,...

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###### KS3 Maths Lesson Plan – Gain Essential Skills in Simplifying Algebraic Expressions without Repetitious Drills

‘Simplifying Expressions’ lesson plan and accompanying task sheet (originally published in volume 5, issue 2 of Teach Secondary magazine). Exercises are...

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###### KS3 Maths Lesson Plan – Use Creative Approaches to Calculating Angles of Overlapping Polygons to Deepen Mathematical Understanding

The angles created by overlapping regular polygons can be easy or difficult to calculate, depending on what information you are given....

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###### KS3 Maths Lesson Plan – Explore Probability by Experimenting with the Rolls of Dice

People frequently vastly overestimate or underestimate many everyday risks, which can lead to poor decision making. One way to estimate the probability...

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###### KS3 Maths Lesson Plan – Practise Estimating By Converting One Million Pounds Into Coins

A million pounds sounds like a lot of cash, but exactly how much is it really? Converting a vague notion of...

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###### KS4 Maths Lesson Plan – Use Flowcharts To Set Up Rules About Iterative Operations

Flowcharts are a highly visual way of communicating information and are used in this lesson to set up rules about operations...

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###### KS3 Maths Lesson Plan – Use Leaning Ladders to Explore Triangles

Ladders leaning against walls is a classic scenario for mathematics problems and is often used to address topics such as Pythagoras’...

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###### KS3 Maths Lesson Plan – Practice Geometry Skills by Working out Which Sides and Angles can go Together with ‘Five Triangles’

In this lesson, students are given 15 angles and 15 lengths and have to work out how they can be placed...

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###### KS4 Maths Lesson Plan – Teach Students How, When and Why Not Using a Calculator can be the Best Option

Sometimes a technological approach is neither the best nor the easiest way to tackle calculations, says Colin Foster. In this lesson, students...

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###### KS3 Maths Lesson Plan – Explore Ways of Calculating the Area of Quadrilaterals

Students need to understand the reasons behind the formulae for the area of different quadrilaterals, says Colin Foster… In this lesson, students...

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###### KS4 Maths Lesson Plan – Calculating Rate and Time by Exploring How Long it Takes Multiple People to Paint a Wall

This lesson is about calculating how long it will take to paint a wall if several people work at it at...

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###### KS4 Maths Lesson Plan – Use Perimeters And Pythagoras’ Theorem to Calculate the Shortest Route on a Map

Applying their knowledge of scale and Pythagoras’ Theorem, students are tasked with calculating the shortest route between two destinations on a...

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###### KS4 Maths Lesson Plan – Develop Spatial Awareness and Problem-Solving Skills by Exploring Two Successive Geometrical Transformations

Traditionally, pupils are taught geometrical transformations by learning a set of skills they can apply to reflecting, rotating and enlarging shapes...

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###### KS3 Maths Lesson Plan – Explore The Properties Of Triangles And Spot Patterns In A Sequence

In this open ended lesson, learners explore a sequence of gradually larger shapes and consider what mathematical questions they can ask...

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###### KS3 Maths Lesson Plan – Boost 3D Shape Understanding By Making A Children’s Toy

Can you make a shape sorter, with at least four different shapes and holes, so that each shape will go through...

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###### KS3 Maths Lesson Plan – Teach Probability by Considering the Outcomes of a Simple Spinner Game

In this lesson, students have to find the possible total scores when spinning two different spinners. Spinners are quick and easy to...

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###### KS3 Maths Lesson Plan – Understand the Formulae to Work Out the Area of Quadrilaterals

Students need to understand the reasons behind the formulae for the area of different quadrilaterals, says Colin Foster… In this lesson, students...

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###### KS3 Maths Lesson Plan – Use Puzzles to Show Students what Changes in Percentages Really Mean

Percentages are commonplace in everyday life, but can be sometimes be confusing and difficult to interpret. In this lesson plan by...

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###### KS4 Maths Lesson Plan – Show Students the Importance of Histograms by Illustrating the Limitations of Bar Charts

If your maths students are struggling to see the point of why we have histograms, this lesson devised by Colin Foster...

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###### KS3 Maths Lesson Plan – Use Geometry to Define the Attributes of the Shapes Around Us, Like Parallelograms and Rhombuses

Remind your students that maths isn’t just about numbers with this detailed lesson from Colin Foster that encourages pupils to take...

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###### KS4 Maths Lesson Plan – Interpret and Use Bearings

Bearings are a precise way to describe one location relative to another, and have widespread uses. They can be a useful...

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###### KS3 Maths Lesson Plan – Develop Algebra Skills with an Integer Problem

In this lesson, students have to find a solution to a problem where the unknowns must be non-negative integers. This constraint...

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###### KS4 Maths Lesson Plan – Spotting Number Sequences

The most obvious patterns are not always the ones we should be looking for. In this lesson, students will explore a situation...