GO SOLO As91261(2.6) Algebra

Achieve

Apply algebraic methods in solving problems:

• selecting and using methods
• demonstrating knowledge of algebraic concepts and terms
• communicating using appropriate representations.

Manipulate algebraic expressions
Expand brackets up to 3 factors
Factorising expressions including quadratics
Use fractional and negative indices 
Change the subject of the formula  
Use elementary properties of logarithms 
Simplify rational expressions.

Solve equations involving. 
Multi-step linear equations or inequations,      eg 3(2x − 5) = 5x + 7
Quadratics that can be factorised      eg 2x² − 11x = 21  
Polynomials in factorised form   eg 3x²(x − 7)(2x + 6) = 0 
Simple logarithmic and exponential     eg Log₂x = 2,  2^x = 64 
Forming and solving linear/linear simultaneous equations.

Merit

Relational thinking involves one or more of:

• selecting and carrying out a logical sequence of steps
• connecting different concepts or representations
• demonstrating an understanding of concepts
• forming and using a model;

and also relating findings to a context, or communicating thinking using 

appropriate mathematical statements

Solve problems involving equations.
Assessment will be based on a selection from: 
- quadratics requiring the use of the quadratic formula 
- linear/non-linear simultaneous equations  
- exponential eg 13^4x-5 = 6.
non-linear equations may be given as appropriate to the complexity of the problem.
Students will be expected to solve problems in context.

Excellence

Extended abstract thinking involves one or more of:

• devising a strategy to investigate a situation
• identifying relevant concepts in the context
• developing a chain of logical reasoning, or proof
• forming a generalisation;

and also using correct mathematical statements, or communicating

 mathematical insight.

Choose algebraic techniques and strategies to solve problems.
Where appropriate, interpretation of a solution will be expected and

 may involve the nature of the roots of a quadratic.

Reflection As91264 (2.14) Apply systems of equations in solving equations

The students finished the internal and questionnaire. Two students gained Merit and one student gained an Excellence. They said that they found the Achieved and Merit questions quite straightforward but had a bit more trouble with the word problems.

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GO SOLO 2.14 (AS91269)

Achievement(Multi-structural)
The student has applied systems of equations in solving problems.
The student correctly selects and uses methods with systems of equations.
They have demonstrated knowledge of concepts and terms and communicated
using appropriate representations. Anyone of these three situations is required
(1) A proposed fence crosses the drain.
(2)Irrigator crosses the drain.
(3) Irrigator crosses the fence.

forming Achievement with Merit(Relational)

The student has applied systems of equations, demonstrating relational thinking

in solving problems. The student has selected and carried out a logical sequence

of steps. The student has related their findings to the context or communicated their

Thinking of using appropriate mathematical statements.

The student correctly forms the equation for the Irrigator as

and uses the equation of the drain to form a quadratic equation.

This equation is then solved to form the points. The student then indicates

that both points are important as bridges will be needed at both for the irrigator to cross the drain.

OR

Using the equation for the irrigator and the proposed fence the student correctly

forms a quadratic equation.  The student then solves this equation to indicate

that the proposed fence intersects with the irrigator at two points .

The student clearly communicates his/her findings in the context of this problem.

Sensible rounding is required

Achievement with Excellence(Extended Abstract)

The student has applied systems of equations, using extended abstract thinking, in solving problems.

The student has used correct mathematical statements or communicated mathematical insight.

For example:

Using the equation for the irrigator and the proposed fence the student

correctly forms a quadratic equation.  The student then solves this

equation to indicate that the proposed fence intersects with the irrigator at two points

sets of points. Then use discrimination set up to resolve the ranges.