Enlarging Shapes by a Negative Scale Factor

Enlarging Shapes by a Negative Scale Factor Learning Objectives

  • All students should be able to enlarge an object by a negative integer scale factor and centre.
  • Most students should be able to enlarge an object by a negative scale factor and centre.
  • Some students should be able to perform and describe enlargements using a negative scale factor.


Enlarging Shapes by a Negative Scale Factor

At the start of the lesson students recap enlarging shapes to a positive scale factor by matching a description with the correct enlargement.  To save time I provide handouts for the class so students can draw rays to find the centre. This typically takes about 5 minutes. I then feedback the matching pairs to address any misconceptions.

Enlarging Shapes by a Negative Scale Factor

Recent examiner reports by Edexcel and AQA show there are two common misconceptions when students are asked to enlarge objects to a negative scale.

  1. When asked to enlarge to a negative scale factor, students often enlarge to a positive scale factor. For instance, a scale factor of -2 drawn as +2.
  2. Rays are often drawn in the wrong direction, i.e., from the centre through the object, which leads to an incorrect enlargement.

To address these misconceptions I explain that a negative scale factor changes the direction of the ray so it travels from the vertices on the object through the centre.

I use the interactive Geogebra applet to help students visualise the difference between a positive and negative scale factor.

Next, I demonstrate how to perform a negative scale factor enlargement using rays drawn from the object through the centre.

Click here to watch the video on YouTube.

When students are ready to work independently I ask them to complete the enlargements shown below. This is printed on the back of the handout the class received for the starter.

Enlarging Shapes by a Negative Scale Factor

As the lesson progresses I use mini-plenaries to feedback the enlargements. When this is completed students attempt more challenging questions from the worksheet.


Enlarging Shapes by a Negative Scale Factor

The final activity challenges students to describe two enlargements by a negative scale factor. The first enlargement involves a scale factor of -0.5 and the second -2.

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About Mr Mathematics

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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