Mathematics KS3 - Algebra

Programme of Study

UNDERSTANDING AND USING FUNCTIONAL RELATIONSHIPS

  • Explore number patterns arising from a variety of situations, using computers where appropriate;
  • generate rules for number sequences;
  • interpret, generalise and use simple relationships;
  • express simple functions initially in words and then symbolically;
  • make and interpret tables and graphs of functions.

Learning Outcomes:

  • Create and describe simple arithmetical progressions
  • Create terms in simple sequences using rules (eg. by depending upon the previous term or position in the sequence)
  • Create sequences of shape patterns describing the general term in simple examples.
  • Recognise square numbers up to 10 multiply by 10
  • Use mapping machines with numbers and then develop to mapping symbols.

Structure of demonstration lessons:

The following suggests a skeleton framework for the work, but it will depend on the teacher’s objectives and the ability of the class. Greater detail can be found in the teacher notes. Please feel free to modify any part of the work as you wish.

Lesson
1 / Introduction (ppt) / Number Sequences (Algebra 1)
Main activity / Recognise linear sequences
Worksheet (doc) / 1
Resources
Lesson
2 / Introduction (ppt) / Function Machines (Algebra 1)
Main activity / Rules and robots-complete the number machines
Worksheet (doc) / 1-4
Resources
Lesson
3 / Introduction (ppt) / Number Patterns (Algebra 1)
Main activity / Create number patterns in shapes
Worksheet (doc) / n/a
Resources / Counters / match size wooden pieces
Lesson
4 / Introduction (ppt) / Patterns and Rules
Main activity / One or two stage Formulae
Worksheet (doc) / Worksheet 1
Resources / Tiles / Counters
Lesson
5 / Introduction (ppt) / Patterns and Rules
Main activity / Two stage Formulae
Worksheet (doc) / Worksheet 2
Resources / Tiles / Counters
Lesson
6 / Introduction (ppt) / Problem Solving
Main activity / ‘Bob the Builder’ activity - group work using formulae to resolve problems.
Worksheet (doc) / Worksheet 1
Resources (doc) / ‘Bob the Builder’ cards and rules
Lesson
7 / Introduction (ppt) / Simplifying Expressions
Main activity / Camels 1- Adding and subtracting
Worksheet (doc) / Camels – adding and subtracting worksheet
Resources / Small white boards for the short exercises
Lesson
8 / Introduction (ppt) / Simplifying Indices
Main activity / Camels 2- Multiply and divide
Worksheet (doc) / Camels – multiply and divide worksheet
Resources / Small white boards for the short and extended exercises
Lesson
9 / Introduction (ppt) / Substitution
Main activity / Camels 3 - Substitute using a simple formulae
Worksheet (doc) / Camels – substitute worksheet
Resources / Small white boards for the short and extended exercises.
Lesson
10 / Introduction (ppt) / Symbols in Algebra
Main activity / Achbar and his donkeys - substitute and use formulae to solve problems
Worksheet / Achbar’s problems
Resources (doc) / Information sheet - ‘Achbar and Hieroglyphics’

No warm up activity has been included above, so that schools can continue to follow their present schemes if they wish to do so.