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AO3: Use trigonometric ratios and Pythagoras' theorem in two and three dimensions.

Children

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Julie's Wheels

Apply Pythagoras’ theorem to solve a problem

Devise and use problem solving strategies to explore situations mathematically (be systematic, think).

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This unit explores the magnitudes of sides and angles of a triangle and leads to the discovery and proof of the Cosine Rule. This Rule is then used to solve triangles, some of which arise in practical situations. We note that the Cosine Rule is a generalisation of Pythagoras’ Theorem.

Note that this unit may contain more material than you need for some classes. You may want to choose from parts of this unit if you have not allotted 5 sessions on the Cosine Rule to your class.

AO2: Recognise when shapes are similar and use proportional reasoning to find an unknown length.

AO1: Deduce and apply the angle properties related to circles.

Children

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Hinea's Other Watch

Solve problems using the relationships between angles in a circle.

Devise and use problem solving strategies to explore situations mathematically (be systematic, guess and check, think, use algebra).

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Hinea's Watch's Hands

find an angle greater than 360 degrees that relates to a given position

solve a linear equation

devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, guess and check, use algebra)

AO2: Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations.

Children

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Winning Ways

This is a level 5 geometry strand activity from the Figure It Out series.

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Missing Anything!

This is a level 5 geometry strand activity from the Figure It Out series.

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Fair and Square

This is a level 5 geometry strand activity from the Figure It Out series.

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Tricky Truncations

This is a level 5 geometry strand activity from the Figure It Out series.

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Perfect Packing

This is a level 5 geometry strand activity from the Figure It Out series.

AO1: Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.

Children

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How High? and Other Problems

In this unit we use ruler and compass constructions to draw a variety of shapes and to construct angles such as 90°, 60°, 45° and 15°.

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Ruler and Compass Constructions

In this unit we discover how to use rulers and compasses to construct perpendicular lines and to bisect angles. These constructions are used to make a variety of polygons.

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Angles, Parallel Lines, and Polygons

In this unit, students will learn to investigate polygons using an instrument of their own construction. They should be able to prove the general formula for the number of degrees in any polygon (including a triangle). Finally they will investigate an interesting locus problem related to polygons.

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Flip's Flag

apply the angle properties of squares, rectangles and triangles

use fractions to express the relationships between the areas of rectangles, squares and triangles

devise and use problem solving strategies to explore situations mathematically (be systematic).

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Vince's Problem

Find the centre of a circle using common material or mathematical construction tools.

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Sol's Serviettes

Use the areas of triangles and squares to find unknown lengths

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).

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Space Tiling with Captain Planet

In this unit tessellations are used as an application of angle properties of polygons. Interior angle properties of polygons are used to justify the existence of the five platonic solids.

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Ash in the Air

This is a level 4 and 5 measurement activity from the Figure It Out theme series.

AO2: Relate three-dimensional models to two-dimensional representations, and vice versa.

Children

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Building with triangles

In this unit, students will construct three-dimensional objects with triangles with emphasis on

identifying properties of triangles
constructing triangles (both equilateral and irregular), using either ruler and protractor or ruler and compass
identifying three-dimensional objects which can be constructed using triangles
designing the net and making three-dimensional objects
naming three-dimensional objects

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The Castle

Construct 3-D shapes from 2-D drawings

Describe the symmetries of 3-D shapes

Draw 3-D shapes on isometric paper

Devise and use problem solving strategies to explore situations mathematically (guess and check, use equipment)

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Castles On The Ground

Construct 3D shapes from 2D drawings

Describe the symmetries of 3D shapes

Draw 3D shapes on isometric paper

Interpret information and results in context; make conjectures in a mathematical context;

Devise and use problem solving strategies to explore situations mathematically (guess and check, use equipment).

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Breakfast Biscuits

This unit seeks to connect learning outcomes across all five content strands, number, geometry, statistics, and measurement. However the context lends itself strongly to use of measurement and statistics. In the unit students investigate questions that involve them in experiment design, data collection and display, and drawing conclusions from data. Students investigate the measurements of breakfast biscuits, how much milk they absorb, how strong they are and the hidden truth about collecting cards.

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Volumes of Cubes

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved with subsequent recording/reporting.

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Cube Creations

This is a level 4 geometry strand activity from the Figure it Out series.

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Building Boldly

This is a level 4 geometry strand activity from the Figure It Out series.

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Blocked Plans

This is a level 4 geometry strand activity from the Figure It Out series.

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Cute Cubes

This is a level 4 geometry strand activity from the Figure It Out series.

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Fantastic Folding

This is a level 4 geometry strand activity from the Figure It Out series.

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A Different View

This is a level 4 geometry strand activity from the Figure It Out series.

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Loads of Lamingtons

This is a level 4 geometry strand activity from the Figure It Out series.

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X-ray Vision

This is a level 4 geometry strand activity from the Figure It Out series.

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Cantitowers

This is a level 4 link geometry activity from the Figure It Out series.

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Missing Links

These are level 4 geometry and level 5 number problems from the Figure It Out series.

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Fire Alarm!

This is a level 4 geometry activity from the Figure It Out theme series.

AO1: Identify classes of two- and three-dimensional shapes by their geometric properties.

Children

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Fitness

This unit examines regular tessellations, that is, tessellations that can be made using only one type of regular polygon, and semi-regular tessellations, where more than one type of regular polygon is involved. Students are required to investigate what properties tessellating shapes must have in order to cover the plane with no gaps or overlaps.

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Quadrilaterals

In this unit we conduct a couple of investigations looking at the relationship between the angle between two diagonals of a quadrilateral, the sides of the quadrilateral, and the type of quadrilateral. The main emphasis is on rectangles.

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Carrie's First Cubes

Apply the properties of 3-D shapes to solve a problem

Visualise 3-D objects

Devise and use problem solving strategies to explore situations mathematically (be systematic).

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More of Carrie's Cubes

Apply the properties of 3-D objects to solve a problem

Visualise 3-D objects

Devise and use problem solving strategies to explore situations mathematically (be systematic)

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Tiling

This is a level 3-4 geometry strand activity from the Figure it Out series.

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Compass Shapes

This is a level 4 geometry strand activity from the Figure it Out series.

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Quad Queries

This is a level 4 geometry strand activity from the Figure It Out series.

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Shaping Up

This is a level 4 geometry strand activity from the Figure It Out series.

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Pathway Patterns

This is a level 4 geometry strand activity from the Figure It Out series.

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Hexagon Hunt

This is a level 4 geometry strand activity from the Figure It Out series.

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Alien Action

This is a level 4 geometry strand activity from the Figure It Out series.

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Precision Flying

This is a level 4 geometry strand activity from the Figure It Out series.

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Tempting Tangrams

This is a level 4 geometry strand activity from the Figure It Out series.

AO2: Represent objects with drawings and models.

Children

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Logo Licenses

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 and usually involve symmetry of some kind. This is to make them aesthetically pleasing as well as functional.

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The School Fair

This unit is designed to provide students with a context in which to use number operations, as well as other strands of the mathematics curriculum. The context of a school fair could either be a hypothetical context, or could be linked to an actual school fair, with students helping to plan and run activities.

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Houses

This unit seeks to connect learning outcomes across all five content strands, number, geometry, statistics, algebra, and measurement. The context of houses is used to develop concepts such as drawing and modelling 3-dimensional objects, using co-ordinate systems to locate position, finding all the possibilities of events, and identifying paths through simple networks. The unit provides an excellent vehicle for students to use a broad range of problem solving strategies.

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Boxes of Tricks

This is a Level 3 Geometry activity from the Figure It Out Series.

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Roll Over

This is a Level 2 and Level 3 Geometry activity from the Figure It Out Series.

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Little Boxes

This is a Level 3 Geometry activity from the Figure It Out Series.

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Points of View

This is a Level 3 Geometry activity from the Figure It Out Series.

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Good Points about Triangles

This is a Level 3 Geometry activity from the Figure It Out Series.

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Crazy Cubes

This is a level 3 geometry activity from the Figure it Out series.

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Caught in the Nets

This is a level 3 geometry strand activity from the Figure it Out series.

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Out of Sight

This is a level 3 link geometry activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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Open and Shut

This is a level 3 link geometry activity from the Figure It Out series.

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Making More

These are a level 3 number, geometry, and measurement problems from the Figure It Out series.

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All Sorts

These are level 3 x problems from the Figure It Out series.

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Birthday Surprise

These are level 3 number and geometry problems from the Figure It Out series.

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Mixing Fruit

These are level 3 statistics, geometry, algebra, and number problems from the Figure It Out series.

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Money and More

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

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Working Together

These are level 3 number and geometry problems from the Figure It Out series.

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Making Boxes

This is a level 3 geometry activity from the Figure It Out theme series.

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Inventing Tenting

This is a level 3 geometry activity from the Figure It Out theme series.

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Mayan Adventure

This is a level 3 geometry and algebra activity from the Figure It Out theme series.

AO1: Classify plane shapes and prisms by their spatial features.

Children

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Shapes With Sticks

In this unit students make and investigate a variety of three dimensional shapes. By examining a wide range of shapes and looking at the relationship between the numbers of faces, edges and vertices they see whether they can “discover” Euler’s famous formula.

This unit involves a lot of exploration with three dimensional shapes and would be ideal as a lead in to the unit Building with Triangles, a level four unit which goes on to look at a group of polyhedra, the platonic solids, in more detail.

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