Making Patterns

Purpose

In this unit students explore patterns involving transformations of shapes. Students make and identify patterns that involve translation, reflection, and rotation. They make their own patterns and pictures to show the transformations, and discuss with others how they included the different transformation elements.

Achievement Objectives
GM1-5: Communicate and record the results of translations, reflections, and rotations on plane shapes.
Specific Learning Outcomes
  • Make patterns that involve translations, reflections, and rotations.
  • Identify translations, reflections, or rotations in patterns.
Description of Mathematics

Translations, reflections, and rotations are explored in this unit. Translations are shifts of a shape along a line, for example repeating a stamp pattern across the top of a page. Reflections are images of a shape as though it is reflected in a mirror. The idea of reflection is covered more extensively in the unit Pattern Matching. Rotations are turns, so when an object is turned about a point, either inside or outside of itself, the image is a rotation of the original shape. In this unit we use examples where the rotation happens around a centre point.

Required Resource Materials
  • Wallpaper or wrapping paper with translation pattern
  • Stamps and inkpad
  • White and blue A4 paper
  • Pictures that show reflection patterns
  • Mirror
  • Scissors, glue, crayons
  • Copymaster
Activity

Session 1

In this session students make patterns that show translations.

  1. Show the students a piece of wallpaper, wall frieze or wrapping paper that shows a translation pattern.
  2. Ask the students: what picture is repeated on the paper to make a pattern?
    Are the pictures the same each time? (Yes)
    How are the pictures the same? (shape, size, orientation, colour)
  3. Using A4 paper and stamps students are to make their own translation pattern on the page. Ensure that the students keep the stamp orientated the same way as they make repeated stamps on the page.

Session 2

In this session students make patterns that show reflections.

  1. Show the students pictures that show reflections, for example scenery reflections in lakes, butterfly wings.
  2. Explain to the students that a reflection picture looks like it could be folded in half so the two sides match. Using a mirror on the fold to show students that the reflection is the same as the other side.
  3. Colouring pictures of butterflies so the wings show a reflection pattern is a common and popular activity. Another idea is to make a reflection patterns on the wings of paper planes.

Session 3

In this session students make patterns that show rotations.

  1. Show the students pictures that show rotations, for example, star fish arms, flower petals, windmill blades, propeller blades, bike spokes.
  2. Explain to the students that in these types of examples part of the object has been turned around a centre point. Ask them to identify the part that has been rotated. For example, if you take one spoke on the bike wheel, leave one end at the centre and turn the other end it will rotate on to the position of the next spoke.
  3. Show the students pictures where the object itself has been rotated, for example:
    4 shot slide with a car rotating
  4. Using the stamps and inkpads students can show a rotation pattern where the whole object is rotated.
  5. Students can make patterns where part of the object is rotated. For example, drawing a flower by cutting out multiple petal shapes and gluing them around the centre or an aircraft with nose and wing propellers that show blade rotation.

Sessions 4 and 5

In these sessions students make an underwater sea picture that shows translation, reflection and rotation.

  1. Discuss with students the patterns they have been making over the last 3 sessions. Explain that they will be making a picture that shows all 3 transformations.
  2. Give the students the picture page. Explain that they will need to make the other half of the octopus. Name the animals in the picture and explain that sea stars (or star fish) are usually found at the bottom of the sea. They will need to cut out the pictures but they don’t need to use them all in their underwater sea picture.
  3. Ask the students:
    Which animal shows reflection? (Octopus)
    How else could you show reflection in your picture? (Put two fish nose to nose.)
    How could you show translation in your picture? (Use 2 or more of the same animal and orientate them the same way.)
    How could you show rotation in your picture? (Use 2 of more sea stars and rotate each one.)
  4. Help the students complete the octopus. Ask the students to cut around the box, fold it in half on the dots, cut around the shape, and open it out.
  5. Students cut out the other animals, colour them and glue them on to blue paper. Remind the students the finished picture needs to show translation, reflection, and rotation.
  6. Students share their pictures with each other. Individuals look for the translation, reflection and rotation elements in each others’ pictures.
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