**Achievement Standard 91027**

**Subject Reference** Mathematics and Statistics 1.2**Title **Apply algebraic procedures in solving problems

Level 1 | Credits 4 | Assessment External

__What’s it all about?__

This achievement standard is derived from Level 6 of The New Zealand Curriculum,

__What’s inside the Assessment?__

*Achievement Criteria*

**Achievement**

• Apply algebraic procedures in solving problems.

**Achievement with Merit**

• Apply algebraic procedures, using relational thinking, in solving problems.

**Achievement with Excellence**

• Apply algebraic procedures, using extended abstract thinking, in solving problems.

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*Apply algebraic procedures involves:*

- selecting and using procedures in solving problems
- demonstrating knowledge of algebraic concepts and terms
- ·communicating solutions using appropriate mathematical symbols.

*Relational thinking involves one or more of:*

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

and also relating findings to a context, or communicating thinking using appropriate mathematical statements.

*Extended abstract thinking involves one or more of:*

*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;*

and also using correct mathematical statements, or communicating mathematical insight.

2 . *Problems* are situations that provide opportunities to apply knowledge or understanding of mathematical concepts and procedures and methods. The situation will be set in a real-life or mathematical context.

- factorising
- expanding
- simplifying algebraic expressions involving exponents, such as or
- substituting values into formulae
- manipulating and simplifying expressions such as or
- rearranging formulae such as or
- solving linear equations or inequations such as 5x + 12 = 3 - 2x or 3(x - 2) < 7
- solving quadratic equations such as (8x + 3)(x - 6) = 0, x2 + 5x – 6 = 0, 3x2 =10x -8 (completing the square and the quadratic formula are not required)
- solving simple equations involving exponents such as x3 = 8, 5x=125
- solving pairs of simultaneous linear equations with two unknowns.

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A**lgebra without Anxiety – MCAT 1- Achievement level**

- Finding substitution solutions
- What is a formula?, Changing the subject
- Solving quadratic equations
- Simplifying fractions formed by quadratic expressions
- How to solve linear and quadratic inequations

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**Algebra without Anxiety – MCAT 1- Merit and Excellence level**

- Solving equations where the variable is an exponent
- Finding area and perimeter when dimensions are algebraic expressions
- Solve similtaneous equations using the substitution method
- Intersections of non-straight lines, Complicated or unorthodox problems
- Unearthing the equations and expressions from word problems

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Algebra without Anxiety – Brackets

- One bracket expansions
- Factorising with a common factor
- Expanding 2 brackets, FOIL
- Factorising quadratics
- Factorising advanced quadratics

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