Transformation

In this unit, students will explore the use of trigonometry to find unknown sides and angles in right-angled triangles, taking the concepts that were developed in the previous unit Introducing Trig and looking at different ways of practising the new skills. Students will then develop and reinforce skills to solve practical problems in trigonometry using the problem solving model

reality               model                solution               check

It is important that good algebraic skills are used in setting out their work, and students can be encouraged to practice these individually and using cooperative logic problems in a group situation.

This unit introduces Pythagoras’ Theorem by getting the student to see the pattern linking the length of the hypotenuse of a right angled triangle and the lengths of the other two sides.

We also consider applications of the Theorem and see that the Theorem only cover triangles that are right angled.

This unit follows on from others that introduce students to sine, cosine and tangent. In this unit students will gain practical experience in using trigonometry in practical situations; mainly outside the classroom.

Here we explore the cosine function, eventually using it to find unknown sides in right angles triangles.

In this unit we look at various ways of measuring the height of an inaccessible object. The fundamental piece of mathematics used here is the ratio of corresponding sides of similar right angled triangles. The actual measurements needed relate to (i) an intermediately placed stick and (ii) the tangent of an angle.

In this unit we do a thorough exploration of tan, leading to the students being able to use tan to solve right angles triangles and to solve equations.

In this unit we explore the sine and related functions to find out specific values, relations between them, and applications.

This unit is an introduction to Pythagoras’ Theorem, including history, proofs, and practise in application of the theorem.

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

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

This unit provides students with the opportunity to discover the effect of a change of length by a given factor on area and volume.

In this unit a number of small boxes are produced (by folding), that fit inside one another like Russian dolls. Lengths are measured and areas and volumes are calculated in order to make scale comparisons.

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

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.

In this unit we apply our understanding of why tessellations work to form our own unique tessellating shapes. We use these shapes to create interesting pieces of art in the style of M.C. Escher.

All M. C. Escher works (C) Cordon Art, Baarn, the Netherlands. All rights reserved. Used by permission.

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

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

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

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

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

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

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

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

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

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

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

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

This is an activity based on the picture book Re-Zoom

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.

This unit examines tessellations, that is, ways of covering the plane with copies of the same shape so that there are no gaps or overlaps. Students will investigate what properties tessellating shapes must have in order to cover the plane with no gaps and with no overlapping. The tessellations investigated involve both non-regular and regular polygons.

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

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

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

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

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

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

This is a level 4 measurement activity from the Figure it Out series. It also has a Level 3 Transformation achievement objective.

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

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

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

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

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

This is a level 3 measurement and transformation activity from the Figure It Out theme series.

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

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

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

This is an activity based on the picture book A Cloak for a Dreamer

This unit explores Level 2 symmetry and transformation concepts. It involves the students making patterns that translate, reflect and rotate. The unit contains a variety of activities that explore these concepts through the context of a garden. It would be helpful to introduce the unit by reading a book to the students that had a garden setting. An aim is to make a classroom display about a garden. These activities are starting points. Be as creative as you can! A variety of art materials will be used for this unit.

In this unit students explore line symmetry and the names and attributes of two-dimensional mathematical shapes. The context of this unit is students folding and cutting out shapes to make a series of mathematical shapes.

This unit involves folding and cutting paper to see the number patterns that are produced and to see what geometric shapes can be made. This unit contains similar content to Fold and Cut.  You may want to take parts from both units when planning your own teaching

In this unit students explore tessellations using the context of bathroom tiles. Squares and dominoes are used in a variety of different colour combinations to help students develop design ideas. The unit finishes with students designing their own tile tessellation and making a model of their design.

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

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

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

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

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

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

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

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

These are level 2 number and geometry problems from the Figure It Out series.

These are level 2 number and geometry problems from the Figure It Out series.

This is a level 2 geometry activity from the Figure It Out theme series.

This is a level 2 geometry activity from the Figure It Out theme series.

In this unit students explore lines of symmetry in pictures, shapes and patterns and describe the symmetry by stating that the parts on either side of the line of symmetry are the same.

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 to show the transformations. The unit concludes with students making a picture and discussing with others how they included the different transformation elements.

This unit has a logic and reasoning focus.