**MATHS**

**NATIONAL 5**

**Course Description**

This Course will develop the learner’s ability to:

- Understand and use mathematical concepts and relationships
- Select and apply operational skills in algebra, geometry, trigonometry and statistics within mathematical contexts
- Select and apply skills in numeracy
- Use mathematical models
- Use mathematical reasoning skills to interpret information, to select a strategy to solve a problem, and to communicate solutions

There are three units in this course:

__Expressions and Formulae__

L.O. 1

**Numerical skills** — simplifying surds; simplifying expressions using the laws of indices

**Algebraic skills** — working with algebraic expressions involving expansion of

brackets; factorising an algebraic expression; completing the square in a quadratic

expression with unitary x2 coefficient; reducing an algebraic fraction to its simplest form;

applying one of the four operations to algebraic fractions

**Geometric skills** — determining the gradient of a straight line, given two points;

calculating the length of arc or the area of a sector of a circle; calculating the volume of

a standard solid with rounding to a given number of significant figures

L.O. 2: Evidence of reasoning skills demonstrated through responses to L.O. 1

__Relationships__

**Algebraic skills** — determining the equation of a straight line given the gradient;

working with linear equations or inequations; working with simultaneous equations;

changing the subject of a formula; recognise and determine the equation of a quadratic

function from its graph; sketching a quadratic function; identifying features of a

quadratic function; solving a quadratic equation which has been factorised; solving a

quadratic equation using the quadratic formula; using the discriminant to determine the

number of roots

**Geometric skills** — applying the converse of Pythagoras’ theorem; applying the

properties of shapes to determine an angle involving at least two steps; using similarity

to calculate a volume

**Trigonometric skills** — working with the graphs of trigonometric functions; working

with trigonometric relationships in degrees

L.O. 2 Evidence of reasoning skills demonstrated through responses to L.O. 1

__Applications__

L.O.1

**Trigonometric skills** — calculating the area of a triangle using trigonometry; using the

sine and cosine rules to find a side or angle; using bearings with trigonometry

**Geometric skills** — adding or subtracting two-dimensional vectors using directed line

segments; determining coordinates of a point from a diagram representing a 3D object;

adding or subtracting two- or three-dimensional vectors using components; calculating

the magnitude of a vector

**Numerical skills** — working with reverse percentages; working with

appreciation/depreciation; combination of operations on fractions including mixed

numbers

**Statistical skills** — comparing data sets using statistics including a measure of

spread; forming a linear model from a given set of data

L.O.2 Evidence of reasoning skills demonstrated through responses to L.O. 1

**The Work of the Course**

**In class **pupils discover, develop and practice ideas and examples from the course topics through various resources such as jotters, posters, show-me boards, group work, textbooks, IT.

**At home **there will be daily revision, practice of work covered in class and formal homework at fortnightly intervals (at least).

**Assessment **

Learning Outcomes from the units are internally assessed throughout the course and awarded on a pass/fail basis.

For each unit, learners must show competence in two areas – operation skills and reasoning skills.

A final Course Assessment consists of two externally set exam papers, non calculator and calculator.

A course award which is graded A to D requires passes at all units and the final Course Assessment.

** Possible Progression to **Higher Maths ( from grade A or B), or to National 5 Lifeskills to extend breadth of maths experience.