There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Shape. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Shape Starters:

Area Two: How many different shapes with an area of 2 square units can you make by joining dots on this grid with straight lines?

Christmas Tables: Which of the two shapes has the largest area? You will be surprised!

Goat Grazing: Find the loci of the goat's position as it eats the grass while tethered to the rope.

Hexagon: On a full page in the back of your exercise book draw a perfectly regular hexagon.

How Many Rectangles?: How many rectangles can you find in this pattern? Can you come up with a systematic method for counting them all?

How Many Squares? 1: Work out how many squares are there altogether in the given pattern then tackle the chess board.

How Many Squares? 2: How many squares can be found by joining four dots on the grid?

How Many Triangles? 1: How many Triangles can you find in the diagram?

How Many Triangles? 2: How many triangles are hidden in the pattern? What strategy might you use to count them all to ensure you don't miss any out?

How Many Triangles? 3: Find a systematic way of counting the number of triangles in the given diagram.

Mathterpiece: Memorise a picture made up of geometrical shapes

Missing Square Puzzle: The missing square puzzle is an optical illusion used to help students reason about geometrical figures.

Oblongs: Find the dimensions of a rectangle given the perimeter and area.

Overlapping Squares: If two squares overlap, what shapes can the overlapping region make?

Pentagon: On a full page in the back of your exercise book draw a perfectly regular pentagon.

Polygon Riddle 1: Solve the riddle to find the name of the polygon then sum the interior angles.

Polygon Riddle 2: A "My first is in..." type riddle leading to a polygon interior angle calculation.

Polygon Riddle 3: A 'My first is in...' riddle that describes a geometrical shape. Can you construct it?

Quad Areas: Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid.

Rows of Roses: Can you draw 4 straight lines, without taking your pencil off the paper, which pass through all 9 roses?

Square Angles: Find a trapezium, a triangle and a quadrilateral where all of the angles are square numbers.

Square Circle Kite: Write down the names of all the mathematical shapes you know.

Squared Animals: Separate three rows of three animals using three squares.

Two Squares: Using six pencils can you make two equal sized squares?

Find The Radius: Find the radius of the circle from the small amount of information provided.

Geometry Snack: Find the value of the marked angle in this diagram from the book Geometry Snacks

Quad Midpoints: What shape is created when the midpoints of the sides of a quadrilateral are joined together?

Square in Rectangle: Find the area of a square drawn under the diagonal of a rectangle

Three Right Triangles: Calculate the lengths of the unlabelled sides of these right-angled triangles.

#### Area and Perimeter of a Rectangle

Questions on the areas and perimeters of rectangles which will test your problem solving abilities.

Transum.org/go/?to=oblongs

### Curriculum for Shape:

#### Year 5

Pupils should be taught to measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres more...

Pupils should be taught to use the properties of rectangles to deduce related facts and find missing lengths and angles more...

Pupils should be taught to distinguish between regular and irregular polygons based on reasoning about equal sides and angles more...

#### Year 6

Pupils should be taught to draw 2-D shapes using given dimensions and angles more...

Pupils should be taught to compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons more...

Pupils should be taught to recognise that shapes with the same areas can have different perimeters and vice versa more...

Pupils should be taught to recognise when it is possible to use formulae for area and volume of shapes more...

#### Years 7 to 9

Pupils should be taught to derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) more...

Pupils should be taught to calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes more...

Pupils should be taught to describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric more...

Pupils should be taught to use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles more...

Pupils should be taught to derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies more...

Pupils should be taught to identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids more...

#### Years 10 and 11

Pupils should be taught to identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment more...

Pupils should be taught to {apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results} more...

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

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Could we have some on angles too please?"

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### Notes:

This topic is aimed at the learners of basic geometry, which is the study of size, shape and position. More than other areas of mathematics this topic helps pupils to learn about the definitions and properties of basic shapes.

There are many activities provided ranging from simple shape naming games to applying more advanced formulas and theorems. The most popular activities however are those involving pupils to count the number of triangles or rectangles in patterns and come up with effective strategies and justifications for their answers.

The work pupils produce for this topic can make very good display material. The use of colour can enhance the diagrams and make the learning environment more conducive to study. There are many connections between the mathematics of shape and Art. There are fascinating works of art based on symmetry, tessellations and transformations.

### Shape Teacher Resources:

Kite Maths: Can you make a kite shape from a single A4 size sheet of paper using only three folds?

Tangram Challenge: A series of tangram challenges in increasing order of difficulty. This page is designed to be projected onto a screen for a whole class to see.

Polygons: Name the polygons and show the number of lines and order of rotational symmetry.

Polygon Angles Animation: Barbara Bug walks around a regular hexagon turning through each of the exterior angles as she goes.

Pin Board: Rows and columns of dots that can be joined using straight lines to create shapes.

Optical Illusions: Don't let your brain be fooled by these geometric optical illusions in this online quiz.

The Great Dodecahedron: Pupils are not allowed to use their hands to point but must describe fully any shapes they can see in this picture.

Geometry Toolbox: Create your own dynamic geometrical diagrams using this truly amazing tool from GeoGebra.

### Shape Activities:

Area and Perimeter of a Rectangle: Questions on the areas and perimeters of rectangles which will test your problem solving abilities.

Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters.

Area of a Triangle: Calculate the areas of the given triangles in this self marking quiz.

Area and Perimeter of a Parallelogram: Many different ways to practise your skills finding the areas and perimeters of parallelograms.

Tangram Table: Use the pieces of the tangram puzzle to make the basic shapes then complete the table showing which shapes are possible.

Area and Perimeter of a Kite: A short exercise to practise using the formulae for area and perimeter of a kite.

Polygon People: Name the polygons and other geometrical shapes that make up the Polygon People.

Online Curve Stitching: Create curves with straight lines using this online alternative to needle and thread.

Area of a Trapezium: Check that you can find the area of a trapezium and use the trapezium area formula for problem solving.

Area and Perimeter: Show that you know the area and perimeter formulas of basic shapes.

Angles in a Triangle: A self marking exercise involving calculating the unknown angle in a triangle.

Area Maze: Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams.

Polygons: Name the polygons and show the number of lines and order of rotational symmetry.

Angle Parallels: Understand and use the relationship between parallel lines and alternate and corresponding angles.

How Many Squares? 2: How many different sets of four dots can be joined to form a square?

Without Lifting The Pencil: Can you draw these diagrams without lifting your pencil from the paper? This is an interactive version of the traditional puzzle.

How Many Triangles?: A self marking step by step approach to calculating the number of triangles in a design.

Quad Areas: Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid.

Online Logo: An online version of the Logo programming language with 30 mathematical challenges.

Shapes In The Stars: Join up the stars to find the hidden regular polygons.

Fractal Mosaic: Follow the precise instructions to create the ever-growing fractal mosaic pattern.

Circles: Practise using pi to calculate various circle measurements. There are six levels of difficulty.

Polygon Angles: A mixture of problems related to calculating the interior and exterior angles of polygons.

Xmas Ornaments: A hands on activity requiring students to arrange Christmas ornaments in a square box.

Optical Illusions: Don't let your brain be fooled by these geometric optical illusions in this online quiz.

Polygon Pieces: Arrange the nine pieces of the puzzle on the grid to make different polygons.

Polybragging: The Transum version of the Top Trumps game played online with the properties of polygons.

Areas of Composite Shapes: Find the areas of combined (composite) shapes made up of one or more simple polygons and circles.

Tantrum: A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid.

Sheep Herding: Arrange the sheep in the field according to the instructions. An introduction to loci.

Polygon Properties: Connect the names of the polygons with the descriptions of their properties.

Formulae Pairs: Find the matching pairs of diagrams and formulae for basic geometrical shapes.

The Great Dodecahedron: Pupils are not allowed to use their hands to point but must describe fully any shapes they can see in this picture.

Mathterpieces: Memorise eight pictures made up of geometrical shapes then sort them into order.

Congruent Triangles: Test your understanding of the criteria for congruence of triangles with this self-marking quiz.

Congruent Pairs: Match the congruent shapes, those with the same shape and size.

Faces, Edges and Vertices: Calculate the number of faces, edges and vertices on 3D Shapes.

Similar Shapes: Questions about the scale factors of lengths, areas and volumes of similar shapes.

Geometry Toolbox: Create your own dynamic geometrical diagrams using this truly amazing tool from GeoGebra.

Congruent Parts: Use the colours to dissect the outlines into congruent parts.

Similar Parts: Use the colours to dissect the outlines into similar parts.

Yes No Questions: A game to determine the mathematical item by asking questions that can only be answered yes or no.

Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world.

### Shape Investigations:

Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters.

How Many Sides?: How many different polygons can you make on a 3 by 3 pin board? What about larger pin boards?

Tridots: Find all the triangles that can be drawn by joining dots on a 3 by 3 grid of dots.

Polygon Areas: Investigate which polygons have an area of 4 square units on this interactive dotty grid.

Area shapes: Investigate polygons with an area of 4 square units. This is your starting point, you can decide how to proceed.

Tetrominoes Investigation: A tetromino is a shape made of four squares joined edge to edge. How many different tetrominoes are there?

Pin Board: Rows and columns of dots that can be joined using straight lines to create shapes.

Tessellations: Drag the shapes onto the canvas to create tessellating patterns then try the tessellations quiz.

How Many Rectangles?: Investigate the number of rectangles on a grid of squares. What strategies will be useful in coming up with the answer?

Tantrum: A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid.

Rectangle Perimeters: The perimeter of a rectangle is 28cm. What could its area be?

Rod Triangles: Using 12 rods of varying lengths how many different triangles can you make?

Hula Hoops: If a number of Hula Hoops are dropped on the floor, what is the maximum number of regions they might form?

Polygon Hunting: Find all the polygons that can be drawn by joining dots on this seven dot grid.

Featured Investigations

Diagonal Through Squares: How many squares does the diagonal of a rectangle drawn on squared paper pass through?

### Shape Videos:

Transum's Shape Video

Area And Perimeter Video: Calculate and solve problems involving perimeter and area of rectangles, triangles, parallelograms, trapezia, kites and composite shapes.

Parallelogram: Instructional video showing how the area of a parallelogram can be determined.

Different types of Triangle: Euclid and his friends explain how many different kinds of triangle there are.

Construct a congruent triangle: Construction (with compass and straight edge) of a triangle congruent to a given triangle.

Polygon Angles Video: A concise reminder about angles, both interior and exterior, in regular and irregular polygons.

Naming Polygons: An exploration of the terminology, etymology and structure of naming polygons

Folded Pentagon: Did you know that you can fold an A4 sheet of paper into a regular pentagon? This short video shows how it is done.

The 50 Cent Riddle: A 50 cent coin has 12 equal sides. If you place two coins next to each other on a table, what is the angle formed between the two coins?

### Shape Worksheets/Printables:

Curve Stitching Templates: Printable templates for curve stitching activities with mathematical instructions.

Tridots Worksheet: A printable set of three by three dotty grids to use with the Tridots challenge.

How Many Squares? 1: A printable grid containing many copies of the design used in the shape counting Starter.

Polygons Page: A printable page of polygons for pupils to name and mark on important features.

How Many Squares 2 Worksheet: A printable grid containing many copies of the design used in the second shape counting Starter.

How Many Triangles? 1: A printable grid containing many copies of the design used in the shape counting Starter.

Line Drawings: Six line drawings that may or may not be able to be traced without lifting the pencil or going over any line twice.

How Many Rectangles Worksheet: A worksheet containing many copies of the How Many Rectangles Starter diagram allowing students to record their findings.

Polybragging Cards: Printable cards for the Polybragging game. Use the properties of polygons to win.

Links to other websites containing resources for Shape are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

### Search

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### Other

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#### Yes No Questions

A game to determine the mathematical item by asking questions that can only be answered yes or no.

Transum.org/go/?to=yesno

### Teaching Notes:

Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

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Shaam, Australia

Saturday, August 20, 2011

"I think this is a fantastic website and I most certainly will use it in my class. Thank you and God bless."

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