S t P a u l ’ s C o l l e g e
MATHEMATICS AND STATISTICS UNIT PLAN
Geometry and Measurement – Level Five & Six
Term:4
Topic 6
Class:101MAT
Duration: 2 weeks
Context / Topic: Geometric Reasoning
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
They will solve problems and model situations that require them to:
GEOMETRY AND MEASUREMENT ACHIEVEMENT OBJECTIVES - Level 6
GEOMETRY AND MEASUREMENT ACHIEVEMENT OBJECTIVES – Level 6
Measurement, Shape and Transformation
Measurement and Shape
Solve problems and model situations that require them to:


Deduce the angle properties of intersecting and parallel
lines and the angle properties of polygons and apply these
properties
Apply trigonometric ratios and Pythagoras’ theorem in two
dimensions
Solve problems and model situations that require them to:

Deduce and apply the angle properties related to circles

Recognise when shapes are similar and use proportional
reasoning to find an unknown length

Use trigonometric ratios and Pythagoras Theorem in 2 or 3
dimensions
Achievement:
GLOBAL LEARNING INTENTIONS
Excellence
Merit:
 selecting and using methods in solving problems
 Demonstrating knowledge of geometrical concepts and terms
 Communicating solutions which would normally require only one or
two steps





selecting and carrying out a logical sequence of steps
connecting different concepts and representations
demonstrating understanding of concepts
forming and using a model;
relating findings to a context, or communicating thinking using
appropriate mathematical statements.



devising a strategy to investigate or solve a problem
identifying relevant concepts in context
developing a chain of logical reasoning, or proof
forming a generalisation
using correct mathematical statements, or communicating
mathematical insight.
MAINTENANCE (Looking backwards and keeping skilful):
HOMELINK ACTIVITIES:
Yes
Yes
Yes
Yes
Responsibility
Respect
Yes
Yes
Computer/Word Processing
Publisher/Excel/PowerPoint
e-mail/Fax/Phone/Scan
Internet-Research
Digital Camera/Video
Yes
KEY
COMPETENCIES
Thinking
perseverance
Passion
Courage
Brotherhood
Using Language, Symbols and Texts
Managing Self
Relating to Others
Participating and Contributing
English
Mathematics and Statistics
Science
Social Sciences
Technology
OTHER
CURRICU
LUM
LINKS
ELEARNIN
G (ICT)
VALUES &
PRINCIPLES
faith
Yes
Yes
Yes
Yes
yes
Yes
Yes
yes
Yes
Pre-test (Diagnostic)
ASSESSMENT
CAREERS:
GAPS TO
COVER
NOTES ABOUT ENTRY LEVEL OF STUDENTS (Prior Knowledge/Skills Required):

Pythagoras’ theorem

trigonometric relationships in right-angled triangles

similar triangles

angle properties of intersecting and parallel lines

angle properties of polygons

angle properties of circles.
Post-test (Summative)
Sample
Formative assessment
Self Assessment
Peer Assessment
ARB’s
Other e.g. Exemplars, asTTle, etc
Literacy Gaps:
Lots of language in this unit – use lots literacy
strategies
Numeracy Gaps:
a/std
Yes
Yes
Yes
Yes
Internet – Webquests and Web 2.0
Video Conferencing
Inspiration and Other Programmes
The Arts (Music/Dance/Drama/Visual)
Health and Physical Education
Learning Languages (Te Reo etc)
Programming
EOTC
SPECIFIC LEARNING INTENTIONS
We are learning to:
(What should the students learn?
What do I intend them to learn?)
Other Gaps:
Graphics calculator competency
ACTIVITIES, THINKING TOOLS AND OTHER RESOURCES
(What will I do to help my students achieve this?
Strategies/activities linked to Key Competencies to help students achieve)
SUCCESS CRITERIA
We know we have achieved this when we can:
(How will the students know they have achieved?
Specific ideas on which to base teaching and activities)
SPECIFIC LEARNING INTENTION/S:
Revision: giving geometric reasoning in
questions related to angles and parallel
lines properties.
SUCCESS CRITERIA: To be confident to
use angle and parallel lines rules to solve
problems and give reasoning consistently.
SPECIFIC LEARNING INTENTION/S:
Revision: how to apply geometric reasoning
related to the angle properties of
polygons.
SUCCESS CRITERIA:
To be able successfully complete worksheets
by:

Identifying and naming shapes;

Finding interior angles;

Finding exterior angles of
polygons;

Work out the sum of interior
angles of n-sided polygon.
SPECIFIC LEARNING INTENTION/S:
Revision: Use Pythagoras’ Theorem to
solve problems.
SUCCESS CRITERIA:
To be confident to use Pythagoras’ Theorem
to:

Find the hypotenuse;

Find the shorter side;

Apply your knowledge to worded
problems.
SPECIFIC LEARNING INTENTION/S:
2 Lessons
Revision: Trigonometric ratios
SUCCESS CRITERIA: To complete
worksheets by applying trigonometric ratios
and Pythagoras’ theorem to:

Find unkown angles;

Find unkown side lengths;

Solving problems using
trigonometry.
SPECIFIC LEARNING INTENTION/S:
Revision: how to apply angle properties in
different types of triangles and special
quadrilaterals to solve problems and give
reasoning.
SUCCESS CRITERIA: Be cofident to
complete worksheets by applying angle rules
as a reasoning to solve problems related to
special triangles and quadrilaterals.
SPECIFIC LEARNING INTENTION/S:
Revision: Learning to apply geometric
reasoning to solve problems with
angles related to circles.
Prior knowkedge: brainstorming ideas (concept map) about anything you know about
angle and parallel lines rules;
Summary on white board;
Geometric reasoning cards – abbreviation self – check;
Vocabulary: acute, right, obtuse, adjacent, parallel, transversal, corresponding, alternate,
co-interior.
Class=13A, 13B
Home=187-195
Mon. 20/10/14
Group work, pair-to-share.
Worksheets:

Matching exercise;

Fill in gaps, boxes and tables;

Work out values of the marked angles;

Multi choice questions and

Solving complex problems by using rules in reverse.
Modelling:

the thinking process (think aloud);

giving written geometric reasoning.
Vocabulary: regular polygon, interior and exterior angles, diagonal, vertex/vertices,
isosceles, equilateral, scalene triangles, trapezium, mediator, bisector, axes of symmetry.
Class=13c
Home=13e, 189-192
Tuesd. 21/10/14
Prior knowledge: labelling the sides of right-angled triangle.
Worksheet: Examples of two problems with diagrams providing prompts to follow and
modelling how to form right-angled triangle by including extra lines on a diagram and
drawing the axes of symmetry.
Group work, pair-to-share.
Vocabulary: hypotenuse, square root
Advanced students to do worksheet with more complex practical problems.
Class=16A / 16B
Home=226-232
Wed. 22/10/14
Prior knowledge: labelling the sides of right-angled triangle in relation to a given angle.
SOH, CAH and TOA.
Group work: completing worksheets by solving problems using trigonometric ratios.
Use calculator to work out angles - shift option.
Vocabulary: hypotenuse, opposite side, adjacent side, sine, cosine, tangent, angles of
elevation and depression.
Class=16E, 16A advanced 16G
Home=233-243
Thurs 23/10/14 double
Prior knowledge: Matching cards – quadrilaterals with special properties.
Emphasis on symmetry.
Vocabulary:
Work in pairs. Worksheets: find with reasons.
Excellence: prove with reasons.
Class=13C, 13D
Home=197-201
Tues 28/10/14
Relevance: AS 91031 geometric reasoning. Circle geometry.
Prior knowledge: group work 2 min – brainstorming 4 main circle rules, cyclic quads;
summary - on white board using different colours for pictures, abbreviation;
Vocabulary: arc, chord, radius, tangent, cyclic, semi - circle, minor and major arcs, sector,
SUCCESS CRITERIA:
Successfully solve problems on worksheets
by deducing and applying angle properties
and giving reasons.
segment, circumference, concyclic points.
Class=15A, B, C (some problems)
Home=215-226 (rest of the problems)
Wed 29/10/14
SPECIFIC LEARNING INTENTION/S:
Learning to understand geometric reasoning:

The criteria that makes two
polygons similar;

What bearing is.
SUCCESS CRITERIA:
To be able successfully

Recognise similar shapes;

Identify similar triangles;

Use proportional reasoning to find
an unknown length;

Work out bearings;

Apply your knowledge to solve
worded problems with bearings.
SPECIFIC LEARNING INTENTION/S:
To revisit and clarify some aspects of exam
papers indentified as ares of need by
students.
SUCCESS CRITERIA:
Set by students.
Revision: AS 91031 geometric reasoning. Similar shapes and objects. Bearings.
Prior knowledge: in groups discussing aspects of similarity and bearings using coloured
handouts. Summarising by highlighting the main facts.
Connection with prior knowledge: links to angle properties, parallel lines, Pythagoras’
Theorem, trigonometric ratios.
DAT: group work, pair-to-share.
Scaffolding, prompting and explaining.
Advanced students will be given individual tasks to work on.
Vocabulary: scale factor, proportional, image, corresponding angles and sides.
Class=14, exam papers-“blue book”, worksheets
Home=14A,
Thurs 30/10/14 double
Clarify AME
Group work / or pair-to-share.
Revisit vocabulary.
Class=”blue workbook”
Home= notes revision, self study
Mon 3/11/14
ASSESSMENT APPROACH
(How will I assess the Success Criteria? How can learning achievement be measured? Remember to include Formative Assessment)
BEFORE THE UNIT
Diagnostic Test to see what the students
remember (covered) about geometric
reasoning in relation to AO from Y 10 and
Term 2.
DURING THE UNIT
Complete assignments from ESA AND Learning
workbook as formative assessment at the end of
each lesson
After the unit
Apply geometric reasoning in solving problems
(AS 91031) 4 Credits External
UNIT EVALUATION
(Consider: Planning and preparation; catering to individual students’ needs; challenging all students; use of class time; overall delivery;
success of unit based on assessment and anecdotal observations; areas for future improvement – what would have worked better)
CHILDREN’S LEARNING
PERSONAL TEACHINGS
ASSESSMENT FOR FUTURE PLANNING