Transformations KS3 - KS5 (NJT)

Nicola Trubridge, Dec 15, 2014

Welcome to a collection of resources designed to support developing progression in teaching transformations

Table of Contents

  1. Enlargement
    1. Enlargement Positive integer SF (NJT)
    2. Enlargement: Find the centre 1(NJT)
    3. Enlargement: Find the centre 2(NJT)
    4. Enlargement: Find the centre 3 (NJT)
    5. Are they similar? (1)
    6. Exploring Congruent Shapes
    7. Spreadsheet and Similarity
  2. Rotation
    1. Rotation of 0-360 degrees around a centre (NJT)
    2. Rotation: Find the centre task 1 (NJT)
    3. Rotation: Find the centre task 2 (NJT)
    4. Rotation: Find the centre task 3 (NJT)
  3. Reflection
    1. Reflection in the x axis
    2. Reflection in the y axis
    3. Reflection in the line y=x
    4. EXTENSION: Reflection in y=mx (NJT)
    5. Reflection: Find the mirror line (NJT)
    6. Reflection: Find the mirror line task 2 (NJT)
  4. Translation
    1. Translation 1 (NJT)
    2. Translation 2 (NJT)
  5. Core 1
    1. Translation 3 (NJT)
    2. Transformation of f(x) = x^2
  6. Core 2
    1. Function Transformations
  7. Further Pure 1
    1. 2x2 Matrix Transformation
    2. Matrix Transformations
    3. Transformation matrix: images of (1,0) and (0,1)
  8. Further Pure 4
    1. Linear Transformations
    2. Linear transformations and eigenvectors in 2D
    3. Exploring Eigenvectors and Eigenvalues Visually
    4. Find The Eigenvectors and Eigenvalues
    5. Linear transformations
    6. Matrix transformations and eigenvalues

1.

Enlargement

  • 1. Enlargement Positive integer SF (NJT)
  • 2. Enlargement: Find the centre 1(NJT)
  • 3. Enlargement: Find the centre 2(NJT)
  • 4. Enlargement: Find the centre 3 (NJT)
  • 5. Are they similar? (1)
  • 6. Exploring Congruent Shapes
  • 7. Spreadsheet and Similarity

1.1.

Enlargement Positive integer SF (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move[br][list][br][*]the SF slider[br][*]the centre[br][*]the vertices A,B and C?[br][/list][br]Are there any points that do not move under this transformation?
[color=#0a971e]Created by N.Trubridge[/color]
– Nicola Trubridge

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Rotation

  • 1. Rotation of 0-360 degrees around a centre (NJT)
  • 2. Rotation: Find the centre task 1 (NJT)
  • 3. Rotation: Find the centre task 2 (NJT)
  • 4. Rotation: Find the centre task 3 (NJT)

2.1.

Rotation of 0-360 degrees around a centre (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move [list] [*]the slider? [*]the vertices B,C and D? [*]the centre of rotation? [/list] Are there any points that do not move under this transformation?

[color=#0a971e]Created by N.Trubridge[/color]
– Nicola Trubridge

2.2.

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2.3.

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2.4.

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3.

Reflection

  • 1. Reflection in the x axis
  • 2. Reflection in the y axis
  • 3. Reflection in the line y=x
  • 4. EXTENSION: Reflection in y=mx (NJT)
  • 5. Reflection: Find the mirror line (NJT)
  • 6. Reflection: Find the mirror line task 2 (NJT)

3.1.

Reflection in the x axis

What stays the [b]same[/b] and what [b]changes[/b] as you move the points around?[br]Are there any points that do not move under this transformation?[br]Where would the co-ordinate (x,y) map to?
[color=#0a971e]Created by N.Trubridge[/color]
What happens
– Nicola Trubridge

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Translation

  • 1. Translation 1 (NJT)
  • 2. Translation 2 (NJT)

4.1.

Translation 1 (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move [list] [*]the vertices of the polygons? [*]the polygons? [*]the vector? [*]the ends of the vector? [/list] Do any points stay in the same place after this transformation?

[color=#0a971e]Created by N.Trubridge[/color]
– Nicola Trubridge

4.2.

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5.

Core 1

  • 1. Translation 3 (NJT)
  • 2. Transformation of f(x) = x^2

5.1.

Translation 3 (NJT)

What stays the [b]same[/b] and what [b]changes[/b] when you move [list] [*]the vector? [*]the ends of the vector? [*]the original function? [/list] Do any points stay in the same place after this transformation?

[color=#0a971e]Created by N.Trubridge[/color]
– Nicola Trubridge

5.2.

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6.

Core 2

  • 1. Function Transformations

6.1.

Function Transformations

This applet illustrates basic function transformations.
Function Transformations
– abulawa

7.

Further Pure 1

  • 1. 2x2 Matrix Transformation
  • 2. Matrix Transformations
  • 3. Transformation matrix: images of (1,0) and (0,1)

7.1.

2x2 Matrix Transformation

Experiment by altering the values of the matrix elements
– Mark Dabbs

7.2.

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7.3.

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8.

Further Pure 4

  • 1. Linear Transformations
  • 2. Linear transformations and eigenvectors in 2D
  • 3. Exploring Eigenvectors and Eigenvalues Visually
  • 4. Find The Eigenvectors and Eigenvalues
  • 5. Linear transformations
  • 6. Matrix transformations and eigenvalues

8.1.

Linear Transformations

Explore the effect of varying the elements of a linear transformation matrix. Press the animation button to let the computer take over.
Linear Transformations
– rm11821

8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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