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Level Five > Geometry and Measurement

AO2: Apply trigonometric ratios and Pythagoras' theorem in two dimensions.

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Children
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Tilted Squares and Right Triangles

The initial focus of this unit involves students in gathering data from their investigation of squares that can be made on different sized geoboards, (an array of dots arranged on a square grid).  Students need to be systematic in their work, and to record their results in ways that are likely to help them notice patterns and relationships.

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Poppy Meets Pythagoras

Find connections between numbers in a table

Use Pythagoras’ theorem in a general algebraic form

Measure accurately from a scale drawing.

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

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Rings and Diamonds

use Pythagoras’ theorem to find the area of a rhombus

use rulers and compasses to make a construction requiring perpendicular bisectors

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

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Bill's Badge

Construct two intersecting circles where the radius of the second circle is on the circumference of the first.

Use Pythagoras’ theorem to find the area of a rhombus

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

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Using Trigonometry

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        arrow.       model     arrow.           solution    arrow.           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.

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Gougu Rule or Pythagoras' Theorem

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.

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Trigonometric Applications Outside the Classroom

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.

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Investigating the Idea of Cos

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

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Dizzy Heights

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.

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Investigating the Idea of Tan

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.

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Investigating the Idea of Sin

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

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Pythagoras' Theorem

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

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Pythagoras Power

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

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Peanut in Trouble

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