Year+10+Extended

=** 2014-15 Year 10 Maths (Extended) Assessments **= ==

**Assessment Schedule:**
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=**Assessment Rubric:**=

Maximum: 8 Knowing and understanding are fundamental to studying mathematics and form the base from which to explore concepts and develop skills. This criterion expects students to use their knowledge and to demonstrate their understanding of the concepts and skills of the prescribed framework in order to make deductions and solve problems in different situations, including those in real-life contexts.
 * Criterion A:** Knowing and understanding

This criterion examines to what extent the student is able to: i. **select** appropriate mathematics when solving problems in both familiar and unfamiliar situations ii. **apply** the selected mathematics successfully when solving problems iii. **solve** problems correctly in a variety of contexts.

Assessment tasks for this criterion are likely to be class tests, examinations, real-life problems and investigations that may have a variety of solutions.

i. select appropriate mathematics when solving simple problems in familiar situations ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. || i. select appropriate mathematics when solving more complex problems in familiar situations ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. || i. select appropriate mathematics when solving challenging problems in familiar situations ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. || i. select appropriate mathematics when solving challenging problems in both familiar and unfamiliar situations ii. apply the selected mathematics successfully when solving these problems iii. generally solve these problems correctly. ||
 * **Achievement level** || **Level descriptor** ||
 * 0 || The student does not reach a standard described by any of the descriptors given below. ||
 * 1–2 || The student is able to:
 * 3–4 || The student is able to:
 * 5–6 || The student is able to:
 * 7–8 || The student is able to:

1.Context: the situation and the parameters given to a problem. 2.Unfamiliar situation: challenging questions or instructions set in a new context in which students are required to apply knowledge and/or skills they have been taught. 3.Deduction: reasoning from the general to the particular/specific.
 * Notes**

Maximum: 8 Students are expected to investigate a problem by applying mathematical problem-solving techniques, to find patterns, and to describe these mathematically as relationships or general rules and justify or prove them.
 * Criterion B: Investigating patterns**

This criterion examines to what extent the student is able to: i. **select** and **apply** mathematical problem-solving techniques to discover complex patterns ii. **describe** patterns as general rules consistent with findings iii. **prove**, or **verify** and **justify**, general rules.

Assessment tasks for this criterion should be mathematical investigations of some complexity, as appropriate to the level of MYP mathematics. Tasks should allow students to choose their own mathematical techniques to investigate problems, and to reason from the specific to the general. Assessment tasks could have a variety of solutions and may be set in real-life contexts. Teachers should clearly state whether the student has to provide a justification or proof. Teachers should include a good balance between tasks done under test conditions and tasks done at home in order to ensure the development of independent mathematical thinking. i. apply, with teacher support, mathematical problem-solving techniques to discover simple patterns ii. state predictions consistent with patterns. || i. apply mathematical problem-solving techniques to discover simple patterns ii. suggest general rules consistent with findings. || i. select and apply mathematical problem-solving techniques to discover complex patterns ii. describe patterns as general rules consistent with findings iii. verify the validity of these general rules. || i. select and apply mathematical problem-solving techniques to discover complex patterns ii. describe patterns as general rules consistent with correct findings iii. prove, or verify and justify, these general rules. || 1. Pattern: the underlining order, regularity or predictability between the elements of a mathematical system. To identify pattern is to begin to understand how mathematics applies to the world in which we live. The repetitive features of patterns can be identified and described as relationships or generalized rules. 2. Justification: a clear and logical mathematical explanation of why the rule works. 3. Proof: a mathematical demonstration of the truth of a given proposition.
 * **Achievement level** || **Level descriptor** ||
 * 0 || The student does not reach a standard described by any of the descriptors given below. ||
 * 1–2 || The student is able to:
 * 3–4 || The student is able to:
 * 5–6 || The student is able to:
 * 7–8 || The student is able to:
 * Notes**

Maximum: 8 Students are expected to use mathematical language when communicating mathematical ideas, reasoning and findings—both orally and in writing.
 * Criterion C: Communicating (NEW CHANGES) **

This criterion examines to what extent the student is able to: i. **use** appropriate mathematical language (notation, symbols and terminology) in both oral and written explanations ii. **use** appropriate forms of mathematical representation to present information iii. move between different forms of mathematical representation iv. **communicate** complete, coherent and concise mathematical lines of reasoning v. **organize** information using a logical structure.

Students are encouraged to choose and use appropriate ICT tools such as graphic display calculators, screenshots, graphing, spreadsheets, databases, drawing and word-processing software, as appropriate, to enhance communication. Assessment tasks for this criterion are likely to be real-life problems, tests, examinations and investigations. Tests and examinations that are to be assessed against criterion C must be designed to allow students to show complete lines of reasoning using mathematical language.

i. use limited mathematical language ii. use limited forms of mathematical representation to present information iii. communicate through lines of reasoning that are difficult to interpret. || i. use some appropriate mathematical language ii. use appropriate forms of mathematical representation to present information adequately iii. communicate through lines of reasoning that are complete iv. adequately organize information using a logical structure. || i. usually use appropriate mathematical language ii. usually use appropriate forms of mathematical representation to present information correctly iii. usually move between different forms of mathematical representation iv. communicate through lines of reasoning that are complete and coherent v. present work that is usually organized using a logical structure. || i. consistently use appropriate mathematical language ii. use appropriate forms of mathematical representation to consistently present information correctly iii. move effectively between different forms of mathematical representation iv. communicate through lines of reasoning that are complete, coherent and concise v. present work that is consistently organized using a logical structure. || 1. Mathematical language: the use of notation, symbols, terminology and verbal explanations. 2. Forms of mathematical representation: refers to formulae, diagrams, tables, charts, graphs and models, used to represent mathematical information
 * **Achievement level** || **Level descriptor** ||
 * 0 || The student does not reach a standard described by any of the descriptors given below. ||
 * 1–2 || The student is able to:
 * 3–4 || The student is able to:
 * 5–6 || The student is able to:
 * = 7-8 || The student is able to:
 * Notes**

Maximum: 8 Reflection allows students to reflect upon their methods and findings.
 * Criterion D: Applying mathematics in real-life contexts**** (NEW CHANGES) **

This criterion examines to what extent the student is able to: i. **identify** relevant elements of authentic real-life situations ii. **select** appropriate mathematical strategies when solving authentic real-life situations iii. **apply** the selected mathematical strategies successfully to reach a solution iv. **justify** the degree of accuracy of a solution v. **justify** whether a solution makes sense in the context of the authentic real-life situation.

Assessment tasks are most likely to be investigations and real-life problems. Generally these types of tasks will provide students with opportunities to use mathematical concepts and skills to solve problems in real-life contexts.

i. identify some of the elements of the authentic real-life situation ii. apply mathematical strategies to find a solution to the authentic real-life situation, with limited success. || i. identify the relevant elements of the authentic real-life situation ii. select, with some success, adequate mathematical strategies to model the authentic real-life situation iii. apply mathematical strategies to reach a solution to the authentic real-life situation iv. discuss whether the solution makes sense in the context of the authentic real-life situation. || i. identify the relevant elements of the authentic real-life situation ii. select adequate mathematical strategies to model the authentic real-life situation iii. apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation iv. explain the degree of accuracy of the solution v. explain whether the solution makes sense in the context of the authentic real-life situation. || ii. select appropriate mathematical strategies to model the authentic real-life situation iii. apply the selected mathematical strategies to reach a correct solution to the authentic real-life situation iv. justify the degree of accuracy of the solution v. justify whether the solution makes sense in the context of the authentic real-life situation. || 1. Describe: present an account without providing reasons or explanations. 2. Explain: give a detailed account including reasons, causes or justifications. Explanations should answer the questions “why” and “how”.
 * **Achievement level** || **Level descriptor** ||
 * 0 || The student does not reach a standard described by any of the descriptors given below. ||
 * 1–2 || The student is able to:
 * 3–4 || The student is able to:
 * 5–6 || The student is able to:
 * = 7-8 || i. identify the relevant elements of the authentic real-life situation
 * Notes**