# Transformations and Tessellations (Year 7)

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This last week of Term 2 we will be doing some transformations and tessellations. Our learning intention is to understand and describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates and to identify line and rotational symmetries.

Your first task is to use the letters of your name, on a poster, to demonstrate your understanding of translation (slide), rotation (turn), reflection (flip) and dilation (increase in size).

Your second task is to use a shape that tessellates (fits together with no gaps or spaces) to create an artwork, similar to the ones in these YouTube videos:

# Euler’s Formula with jubes and toothpicks

Learning Intention: To distinguish between prisms and other three-dimensional shapes and to work out the relationship between vertices, edges and faces (Euler’s Formula).

These two Year 7 students are making three-dimensional models with jubes and toothpicks (or satay sticks) to record vertices, edges and faces. Start with simple shapes, such as triangular pyramids, cubes and square pyramids, distinguishing between shapes that are prisms and those that are not. When students have made at least six or more shapes ask them to see if they can find a relationship between V (vertices); E (edges) and F (faces). I usually give a clue that they only need to use addition and subtraction (not multiplication or division).

# Year 7 – Measurement and Geometry

National Curriculum Standard: “Students use formulas for the area and perimeter of rectangles.”

The perimeter of a rectangle is calculated by adding the four sides. The area of a rectangle is calculated by multiplying the length by the width.

Perimeter =2 x (L+W) = 2L + 2W

Area = Length x Width = LW

Find at least three rectangles around the classroom and measure the length and width. Draw a sketch showing the object and the measurements, including the units (millimetres, centimetres or metres). Calculate the perimeter and the area of the object using the formulae above.

For example; your laptop, the table top, your maths book, a window pane, the door, the whiteboard, the front of the heater, the noticeboard etc.

The perimeter of the locker door will be:

(2 x 35) + (2 x 59) = 70 + 118 = 188 cm

The area of the locker door will be:

35 x 59 = 2065 cm^2 (square centimetres)

# Welcome Back for Term 2!

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This term we will be studying Measurement and Geometry.

Year 7 Maths (JacPlus Chapter 9 – Measurement and Chapter 5 – Geometry)

By the end of this term I hope you will be able to:

• Use appropriate units of measurement
• Calculate the perimeter of 2D shapes
• Calculate the area of triangles, quadrilaterals and composite shapes.
• Identify types of polygons (different triangles and quadrilaterals)
• Estimate, measure and draw angles between 0 and 360 degrees.
• Identify the properties of parallel and perpendicular lines and the angles that form between them.
• Calculate the missing angles in polygons, knowing that the internal angles of a triangle add to 180 degrees.
• Recognise various transformations (translations, reflections, rotations and dilations)

Year 8 Maths (JacPlus Chapter 7 – Congruence and Chapter 10 – Measurement)

By the end of this term I hope you will be able to:

• Use and convert units of measurement for perimeter, area and volume
• Calculate the area of various quadrilaterals.
• Calculate the area and perimeter of circles.
• Calculate the volume of various prisms using formulae.
• Identify congruent shapes
• Transform various shapes (translate, dilate, rotate and reflect).
• Solve geometric problems using congruence.
• Work out problems around different time zones using the 24 hour clock.

# MInecraft Maths – Surface Area and Volume

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Games based learning has been a hot topic in the last year or so and one of the most popular games in educational use has been Minecraft. Although there has been some debate about the value of learning outcomes, many students would agree that Minecraft is a fun way to learn about surface area and volume. This YouTube video, “Minecraft Math – Surface Area and Volume” describes how to calculate the surface area of rectangular prisms and challenges the viewer to calculate the surface area and volume of a huge tower of TNT blocks! Another YouTube video, from the same user, demonstrates the “Volume of Prisms and Pyramids” in Minecraft and offers a challenge to calculate the area of a prism with a pyramid on top.

We spent last lesson looking at the volume and surface areas of various patterns of ‘minecraft’ blocks. Our assumption is that each Minecraft block is 1m x 1m x 1m – a cubic metre. Next lesson I would like you to create your name in Minecraft blocks and measure the volume and the surface area of your construction. Start by using the first letter of your first name. It should be a minimum of five blocks high and three blocks wide. Make sure you take a screenshot of your construction and send it to me by email.

# Euler’s Formula

Learning Intention: Students will investigate Euler’s rule that describes the relationship between the number of faces, the number of edges and the number of vertices of 3D objects.

Success Criteria: Students will create 3D shapes using toothpicks and jelly-lollies to represent edges and vertices. They will then count and record in a table the faces, edges and vertices of the shapes and investigate Euler’s Rule.

Today we are going to learn more about 3D shapes and investigate a special relationship between the number of vertices, edges and faces of such shapes. Create the following shapes using toothpicks and jubes:

1. tetrahedron
2. triangular prism
3. square base pyramid
4. cube
5. pentagonal pyramid
6. pentagonal prism
7. hexagonal pyramid
8. hexagonal prism

Now draw a table with six columns that records the name of the polyhedron, the name of the base shape, the number of sides on the base shape, the number of faces, number of vertices and number of edges. Complete the table for each of the 8 shapes listed above. Now see if you can work out any relationship between the values in your table.

# Tessellations

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Learning Intention: “Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries.” “Define congruence of plane shapes using transformations.”

Success criteria: Students will create a design that shows various transformations of a 2D geometric shape and be able to describe the translations, reflections and rotations that have taken place to form a tessellation.

Tessellations have been popular decorations for hundreds of years, as this tiled ceiling of the Sheikh Lotfollah Mosque in Iran (1602-1619) shows. Any shape or shapes that can be repeated to fill a 2D plane can be considered tessellations; so, equilateral triangles, squares, rectangles and hexagons are all simple shapes that can be tessellated.

Maurits Cornelis Escher (1898-1972) is one of the world’s most famous graphic artists. His art has been reproduced extensively, especially his ‘impossible structures’ and his tessellations. You may have seen some of his work in your art classes. This YouTube video, Escher’s Tessellations,  showcases some of his work.

We are going to create our own tessellations using one of the following methods.

1. Create a Tessellation using the paper-cut method (YouTube)

2. How to make an Escher-esque Tessellation (YouTube)

3. How to create a Tessellation (YouTube)

This fantastic site, Tessellations.org, has lots more examples of tessellations and describes different methods for creating your own, including a praying mantis design submitted by an Australian student. I would love you to create a design that you are really proud of that you can also submit to the site.

# Geometry – shapes and objects

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Learning Intention:

• Students will be able to identify and describe 2D shapes and understand the terms translation, reflection, dilation and rotation.
• They will be able to identify and describe, draw, plan and construct 3D objects.

Success Criteria:

• Students will complete a poster that shows various shapes undergoing transformations and construct a tessellation from appropriate 2D shapes.
• They will identify and describe 2D and 3D shapes from photographs.
• They will draw isometric drawings with dot paper and nets and construct 3D shapes.

So far we have learnt about the properties of polygons, especially triangles and quadrilaterals,  in terms of their sides, angles, perimeter and area. Next we will be looking at TRANSFORMATIONS – how 2D shapes are translated (moved), reflected, rotated and dilated. Your task is to create a poster that shows the letters of your name undergoing each of the following transformations – translation, reflection, rotation and dilation. Draw two copies of each of four block letters of your name and then complete a transformation with one of the letters of each pair.

Polygon matching game – identifying 2D shapes.

Sort the shapes – identify and describe polygons

Polygon sorting – regular and irregular polygons.

More interactives from the Maths Zone (2D shapes)

Classifying 2D and 3D shapes – Geometric Figures Game

Drag and drop 3D shapes – Naming 3D shapes

Matching 3D shapes – identifying 3D shapes

More interactives from the Maths Zone (3D objects)

# Area of Composite Shapes

Learning Intention: “Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving. Recognise and solve problems involving simple ratios.”

Success Criteria: Students will be able to calculate the area of various 2D shapes, including triangles, squares, rectangles and composites of these shapes. They will draw a house plan to scale and calculate the floor area of the house.

Homework: Measure the length and width of your bedroom and one other room in your house in meters. Notice that your doorways are about 1.0 meter wide.

Today’s task is to draw a scale plan of a holiday house. A rough estimate of the cost to construct a home is at least \$1,000 per square meter. Your budget is \$250,000, so the house must be less than 250 square meters in area. Use a scale – 1.0m to 1.0cm is a good way to start. So, 1.0cm on the plan, represents 100cm (1.0m) on the ground. Your scale is 1:100. Your holiday house should include the following rooms:

• Lounge/Living area
• Kitchen
• Bathroom
• 2 Bedrooms
• Laundry