A very good literacy focus on Mathematics Book 4: The Language of Geometry

Author: Marilyn Murray, Publisher: Mathematical Publications


  • Print book
  • CD containing PDF of the book

This series is written specifically for ESL (English as a Second Language) students, but will enhance the literacy of all English speaking students.

These books contain:

  • vocabulary and language linked to pictures
  • modelled sentences, explanations and descriptions
  • language scaffolds
  • many speaking practice activities
  • sentence structure diagrams
  • answers with many worked solutions
  • full sentence of paragraph answers.

The series is generally suitable for students from Years 5 to 11.

Each chapter starts with simpler concepts, then moves vertically along a continuum, linking both language and mathematical content. Many of the answers in the back of the books include worked solutions, complete explanations, descriptions, procedures and other modelled writing. Consequently, independent workers will work faster through each book.

The vertical movement through mathematics means that some students need to be guided along the most suitable pathway. In the books on the Language of Shape and Measurement and the Language of Geometry, students can move along different pathways determined by the pre-tests provided.

Although these books do not provide a lot of drill and practice of non-language based mathematics, there is enough so that students can move to the next literacy-based activity.

If students need further non-language based practice, most mainstream mathematics textbooks can be used for that purpose.

Book 1 in the series, Getting the Basics Right, covers the language of numbers and symbols, simple questioning, basic operations and the properties of triangles. It is suitable for students who have little English. This book is most suitable for students who are working towards level 1 on the NSW ESL scales, where level 8 is a native English speaker. To help these students further, a workbook (separate title) is also available to accompany this book.

The second and third books in the series, The Language of Fractions and Number Theory and The Language of Shape and Measurement (this title) are generally suitable for students who are working towards the ESL scale of level 2.

The remaining books listed below are suitable for students working towards the ESL scale of level 3 and beyond. Their progression will depend on their age and ability:

  • The Language of Geometry
  • The Language of Graphs and the Number Plane
  • The Language of Trigonometry
  • The Language of Consumer Arithmetic
  • The Language of Probability


  • What are the literacy demands of mathematics?
  • Literacy Focus Flowcharts
  • 1 The Language of Geometric Reasoning
    • Types of Angles
    • Complementary angles
    • Supplementary angles
    • Interior angle sum
    • Deductive Geometry
    • Naming angles
    • Two-step reasoning – Finding angle ABC
    • Further two-step reasoning
    • 3 to 5–step reasoning
    • Proofs
    • Congruent triangles
    • Similar triangles
  • 2 The Language of Circle Geometry
    • Some circle theorems
    • Chord theorems
    • Angle theorems
    • Tangent theorems
  • 3 The Language of Geometric Descriptions
    • The Passive Voice
    • Speaking and writing descriptions
    • Descriptions in circle geometry – Extension
  • 4 The Language of Construction
    • Part A – Using a compass
    • Position vocabulary
    • Bisecting intervals and angles
    • Triangles and other polygons
    • Perpendiculars
    • Constructing angles with a compass
    • Copying angles and constructing parallel lines
    • Part B – Using dynamic geometry software
    • Using GeoGebra
  • Appendix
    • How to use Wingeom
    • Constructions using Wingeom
    • Downloadable Wingeom activities
  • Answers
More Information
Year Level Year 5, Year 6, Year 7, Year 8, Year 9, Year 10, Year 11
Date of Publication 2011
ISBN 9780980763744
Subject Maths