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# Assessing Algebra in the Senior Phase: A Practical Guide

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This booklet was first developed in 2004, shortly after the introduction of the Revised National Curriculum Statement in South Africa. The intention of the booklet was to help teachers of senior phase (junior secondary) to integrate assessment into their teaching and learning.

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### Assessing Algebra in the Senior Phase: A Practical Guide

1. 1. Assessing Algebra in the Senior Phase:A Practical Guide
2. 2. A S S E S S M E N T I N P R A C T I C E
3. 3. Assessing Algebrain the Senior Phase: A Practical Guide This booklet demonstrates how assessment can be used in learning and teaching Mathematics in the Senior Phase.
9. 9. A S S E S S I N G A L G E B R A I N T H E S E N I O R P H A S E : A P R A C T I C A L G U I D E Table 1: Assessment standards for an introduction to algebraNote: This table gives learning outcome 2 with the relevant assessment standards from the South African National CurriculumStatement. It can, however, be adapted for other national curricula. Learning Outcome 2: The learner is able to recognise, describe and represent patterns and relationships, and solve problems using algebraic language and skills Grade 7 Grade 8 Grade 9 We know this when the learner: We know this when the learner: We know this when the learner: Investigates and extends numeric Investigates and extends numeric Investigates in different and geometric patterns looking and geometric patterns looking ways, a variety of geometric for a relationship or rules, for a relationship or rules, and numeric patterns and including patterns: including patterns: relationships by representing Represented in physical or Represented in physical or and generalising them and diagrammatic form diagrammatic form by explaining and justifying the rules that generate them Not limited to sequences Not limited to sequences (including patterns found in involving constant difference involving constant difference natural and cultural forms or ratio or ratio and patterns of the learner’s Found in natural and Found in natural and own creation) cultural contexts cultural contexts Of the learner’s own creation Of the learner’s own creation Represents and uses Represented in tables Represented in tables relationships between Represented algebraically variables in order to determine input and/or Describes, explains and justifies Describes, explains and justifies output values in a variety of observed relationships or rules observed relationships or rules ways using: in own words in own words or algebraically verbal descriptions flow diagrams Represents and uses relationships Represents and uses relationships tables between variables in order to between variables in order to formulae, equations and determine input and/or output determine input and/or output expressions values in a variety of ways using: values in a variety of ways using: verbal descriptions verbal descriptions flow diagrams flow diagrams Constructs mathematical tables tables models that represent, formulae, equations and describe and provide Constructs mathematical models expressions solutions to problem that represent, describe and situations, showing provide solutions to problem Constructs mathematical models responsibility toward the situations, showing responsibility that represent, describe and environment and the health toward the environment and the provide solutions to problem of others (including health of others (including situations, showing responsibility problems within human problems within human rights, toward the environment and the rights, social, economic, social, economic, cultural and health of others (including cultural and environmental environmental contexts). problems within human rights, contexts). social, economic, cultural and environmental contexts). 5 This work is licensed under the Creative Commons Attribution 3.0 Unported licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/
11. 11. A S S E S S I N G A L G E B R A I N T H E S E N I O R P H A S E : A P R A C T I C A L G U I D EComplete this table: Number of people 2 3 4 7 10 ? Number of cuts 1 2 3 ? ? 14 Write down a sentence to explain what the pattern or general rule is for working out how many cuts Mrs Moroko must make. If Mrs Moroko wants to share the bread between people, how many cuts must she make? If Mrs Moroko makes cuts in the bread, to how many people can she offer a piece of bread? In this problem, there are two things that change – the number of cuts and the number of people. These are called the variables. Learners should be able to discover the general rule that the number of cuts is always one less than the number of people. They should be able to write this rule using letter symbols for the variables. This would be = -1 7 This work is licensed under the Creative Commons Attribution 3.0 Unported licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/
14. 14. A S S E S S I N G A L G E B R A I N T H E S E N I O R P H A S E : A P R A C T I C A L G U I D E4. Let’s get Practical The Teaching and Lear ning Cycle 1. Plan Choose learning outcomes/topics and the more detailed assessment standards or sub-topics. What must learners know and be able to do? What are the outcomes? What learning opportunities can you provide? How can you assess what learners have achieved? 2. Facilitate Learning Teaching and learning takes place. Learners engage in learning activities. You assess learners informally while you teach, observe and mediate. 3. Assess The learners’ achievement is assessed and results recorded and interpreted. Record your assessment. Have the learners achieved the intended outcomes? Identify strengths and weaknesses. Provide constructive feedback. 4. Reflect and Decide If the group of learners has satisfactory results, you can move to the next step in your plan. Individuals or the whole group may need concepts reinforced and another opportunity to be assessed in some way.10 This work is licensed under the Creative Commons Attribution 3.0 Unported licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/
17. 17. A S S E S S I N G A L G E B R A I N T H E S E N I O R P H A S E : A P R A C T I C A L G U I D E 13 This work is licensed under the Creative Commons Attribution 3.0 Unported licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/
23. 23. A S S E S S I N G A L G E B R A I N T H E S E N I O R P H A S E : A P R A C T I C A L G U I D E 19 This work is licensed under the Creative Commons Attribution 3.0 Unported licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/
24. 24. A S S E S S I N G A L G E B R A I N T H E S E N I O R P H A S E : A P R A C T I C A L G U I D E20 This work is licensed under the Creative Commons Attribution 3.0 Unported licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/
25. 25. A S S E S S I N G A L G E B R A I N T H E S E N I O R P H A S E : A P R A C T I C A L G U I D E 21 This work is licensed under the Creative Commons Attribution 3.0 Unported licence. To view a copy of this licence visit http://creativecommons.org/licenses/by/3.0/