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GM3-6: Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another.

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Elaboration on this Achievement Objective

This means students will explore and describe transformations. “Transformation” is a generic term used to describe actions on shapes that result in some form of pattern, usually symmetric. A reflection is the image of a shape as seen through a mirror line either inside or outside the shape, sometimes called a “flip”. A rotation is the image of the shape turned about a point either inside or outside the shape. A translation is the image of a shift of the shape along a line, and an enlargement is the image of the shape made bigger or smaller by some scale factor. At Level Three students should be able to compare the image of a shape with the original and describe the transformation. This can include a sequence of two transformations. For example:

 

 rotational hearts.

reflection circles.          

 translation big arrows.

A' is the image of A
after a half turn.

B' is the image of B
after a reflection in
the mirror line.

C' is the image of C
after a translation.

 

Teaching resources for this Achievement Objective
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A case for a new phone

Level Three
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage the student in using a description of transformations to solve a problem.
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A cloak for the dreamer

Level Three
Geometry and Measurement
Picture book activities
This is an activity based on the picture book A cloak for the dreamer
  • Students will be able to demonstrate an understanding of tessellation through creating a design that uses more than one shape in a tessellated pattern.
  • Students will be able to explain how the characteristics of the shapes enabled their ability to tessellate the pattern.
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Back to Back

Level Three
Integrated
Figure It Out activities
These are level 3 algebra, geometry and number problems from the Figure It Out series. A PDF of the student activity is included.

explore patterns (Problem 1)

solve problems involving transformations (Problem 2)

use addition skills to solve problems relating to distances (Problem 3)

solve problems using addition (Problem 4)

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Changing Shapes

Level Three
Geometry and Measurement
Figure It Out activities
This is a level 3 geometry strand activity from the Figure it Out series. A PDF of the student activity is included.

explore symmetry and tessellations

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Chessboard Challenges

Level Three
Geometry and Measurement
Figure It Out activities
This is a level 3 link geometry activity from the Figure It Out series.

use symmetry to solve problems

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Circle Power

Level Three
Geometry and Measurement
Figure It Out activities
This is a Level 3 Geometry activity from the Figure It Out Series. A PDF of the student activity is included.
  • Design and make a pattern using reflection, rotation or translation.
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Copycats

Level Three
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Tessellate using squares and triangles.
  • Describe the properties of tessellating shapes.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
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Creases and Cuts

Level Three
Integrated
Figure It Out activities
These are level 3 number, and geometry problems from the Figure It Out series. A PDF of the student activity is included.

use addition and multiplication to solve problems (Problems 1 and 4)

explore different two dimensional shapes (Problem 2)

explore reflections with paper folding (Problem 3)

 

 

 

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Cut It Out!

Level Three
Geometry and Measurement
Figure It Out activities
This is a level 3 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

explore symmetry and transformations

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Dates and Shapes

Level Three
Integrated
Figure It Out activities
These are level 3 number, measurement, and geometry problems from the Figure It Out series. A PDF of the student activity is included.

use addition and a systematic approach to solve problems (Problem 1)

use addition strategies in the context of calendar problems (Problem 2)

use transformations to make triominoes (Problem 3)

use addition facts to solve capacity problems (Problem 4)

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Digit Detail

Level Three
Integrated
Figure It Out activities
These are level 3 number and geometry problems from the Figure It Out series. A PDF of the student activity is included.

use addition and a systematic approach to solve problems (Problems 1 and 2)

explore features of two dimensional shapes (Problem 3)

explore symmetry (Problem 4)

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Eye Antics

Level Three
Integrated
Figure It Out activities
These are level 3 algebra and geometry problems from the Figure It Out series. A PDF of the student activity is included.

explore tessellations with shapes (Problem 2)

use operation signs to make equations (Problem 3)

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Grace's kitchen floor

Level Three
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Create a pattern that involves reflection and rotation.
  • Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
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Growing Changes

Level Three
Geometry and Measurement
Figure It Out activities
This is a Level 3 Geometry activity from the Figure It Out Series. A PDF of the student activity is included.
  • Recognise changes in properties with enlargement.
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Growing in Water

Level Three
Level Four
Geometry and Measurement
Figure It Out activities
This is a level 4 measurement activity from the Figure it Out series. It also has a Level 3 Transformation achievement objective. A PDF of the student activity is included.

explore enlargements

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I Spy Symmetry!

Level Three
Geometry and Measurement
Figure It Out activities
This is a level 3 activity from the Figure It Out series. A PDF of the student activity is included.
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Keeping in Shape

Level Three
Geometry and Measurement
Units of Work
This unit examines tessellations, that is, ways of covering the plane (a two-dimensional surface) with copies of the same shape without any gaps or overlaps. Students will investigate what properties shapes must have in order to tessellate. The tessellations investigated involve both non-regular and...
  • Demonstrate why a given tessellation will cover the plane.
  • Create regular tessellations.
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Layer upon layer

Level Three
Integrated
Figure It Out activities
These are level 3 number, algebra, and geometry problems from the Figure It Out series. A PDF of the student activity is included.

solve problems involving sequential patterns (Problems 1 and 4)

use simple multiplicative strategies to solve problems (Problem 2)

solve problems involving enlargements (Problem 3)

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Learning by Braille

Level Three
Integrated
Figure It Out activities
This is a level 3 activity from the Figure It Out series. A PDF of the student activity is included.
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Logo Licenses

Level Three
Geometry and Measurement
Units of Work
This unit examines the use of reflective, rotational, and translational symmetry in the design of logos. Logos are designs associated with a particular trade name or company and usually involve symmetry to make them aesthetically pleasing as well as functional.
  • Find all the lines of reflection symmetry in a given shape.
  • Identify the order of rotational symmetry of a given shape (how many times it "maps" onto itself in a full turn).
  • Create designs which have reflection symmetry, rotational symmetry (orders 2, 3, 4, 6) and translational symmetry.
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Looking Good

Level Three
Geometry and Measurement
Figure It Out activities
This is a level 3 geometry activity from the Figure It Out series. A PDF of the student activity is included.

identify transformations as translations, reflections or rotations

design patterns that show translations, reflections and rotations

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Measure Up

Level Three
Geometry and Measurement
Figure It Out activities
This is a level 3 measurement and transformation activity from the Figure It Out theme series. A PDF of the student activity is included.

estimate and measure lengths using rulers

compare lengths using estimation and multiplication

explore the relationship between length and area under enlargement (Q5)

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Moa Mystery

Level Three
Geometry and Measurement
Figure It Out activities
This is a level 3 geometry activity from the Figure It Out theme series. A PDF of the student activity is included.

use scale factors from a diagram to calculate length

draw an enlargement

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Money and More

Level Three
Integrated
Figure It Out activities
These are level 3 geometry, and algebra problems from the Figure It Out series.

interpret three dimensional drawings (Problem 2)

use algebraic thinking to solve problems (Problem 3)

predict the results of paper folding reflections (Problem 4)

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Mystery Amounts

Level Three
Integrated
Figure It Out activities
These are level 3 algebra and geometry problems from the Figure It Out series. A PDF of the student activity is included.

use logic to solve equations (Problem 1)

explore tessellations with rectangles (Problem 2)

solve problems using algebraic thinking (Problems 3 and 4)