# Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

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1 Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation & Estimation Pupils should be able to accurately round numbers to a suitable degree of accuracy. Pupils should be able to estimate the answer to a calculation by rounding. I can round to the nearest 10, 100, 1000 etc I can round to n decimal places. I understand what is meant by the term significant figure. I can round to a given number of significant figures. I can choose a suitable degree of accuracy depending on the context of the problem I can estimate an answer by rounding. Surds & Indices recognise rational and irrational numbers. simplify expressions involving surds and indices. rationalise a surd. I can state the definition of a rational number. I can state the definition of an irrational number. I can identify rational and irrational numbers. I can simplify an expression involving surds by breaking it into a product of factors. I can identify square numbers and find their square roots. I can multiply, divide, add and subtract surds. I can evaluate a number to a given power. I can find the nth root of a number. I can multiply like terms involving indices by adding their powers.

2 express a number in scientific notation (standard form). find the reciprocal of a m. evaluate expressions involving fractional indices and nth roots. I can divide like terms involving indices by subtracting their powers. I can raise a power to a power by multiplying the indices. I know that any term raised to the power of 0 equals 1. I know that any term raised to the power of 1 equals the same term. I can state the definition of a reciprocal. I can work with negative indices. I can write a very large or very small number using scientific notation (standard form). I can change between fractional indices and roots. I can evaluate terms with a fractional index or nth root. I will know where exact values are necessary to use in real life situations. Algebraic Expressions & Algebraic Fractions simplify algebraic expressions by expanding brackets. factorise an algebraic expression. express a quadratic in the form (x ± a) 2 ± b. simplify an algebraic fraction. I can simplify an algebraic expression by collecting like terms. I can expand a multiply a single numerical or algebraic term through a bracket. I can expand an algebraic expression in the form (x ± a) (x ± b). I can factorise an algebraic expression by finding a common factor. I can factorise a quadratic expression using a difference of two squares. I can factorise a quadratic expression into the form (x ± a) (x ± b). I can factorise a quadratic expression with the x 2 coefficient > 1 into the form (ax ± b) (cx ± d). I can complete the square to express a quadratic in the form (x ± a) 2 ± b.

5 calculate the radius of a major or minor sector, given the area and the angle at the centre. apply their knowledge of finding the area of a sector to find the area of a compound shape. Volume of Solids identify a range of 3D solids. find the volume of a simple 3D solid. find the volume of a compound 3D solid. I can identify a range of 3D solids and state some of their properties. I understand what is meant by the term compound shape. I can calculate the volume of a: o Cube o Cuboid o Cylinder o Sphere o Cone o Prism I can apply my knowledge of calculating the volume of simple shapes to problems involving compound shapes.

6 Relationships Topic Learning Intention Success Criteria I understand this Straight Line Graphs sketch a straight line graph using a table of values. find the gradient and y intercept of a straight line graph and hence find the equation. find the equation of vertical and horizontal lines. re-arrange an equation into the form y = mx + c. express a straight line graph using function notation. I can find the gradient of a straight line graph using the formula. I can use a table of values to find co-ordinates that lie on a straight line. I can sketch a straight line graph using a table of values. I can recognise horizontal and vertical lines and can state their equations. I can determine the equation of a straight line graph given its gradient and y intercept. I can determine the equation of a straight line graph given its gradient and one point on the line. I can recognise the general form of a straight line equation ax + by + c = 0 and can re-arrange it into the form y = mx + c. I understand what is meant by function notation and can write straight line equations in this way. Equations & Inequalities solve a linear equation or inequality using algebraic manipulation. I can use mathematical notation to say that one quantity is equal to, less than, less than or equal to, greater than and greater than or equal to another. I can solve a simple two step equation or inequality or inequality by balancing both sides. I can solve an equation or inequality involving brackets. I can solve an equation or inequality where unknowns appear on either side.

7 Simultaneous Equations use graphs to solve simultaneous equations. use an algebraic method to solve simultaneous equations. I understand that simultaneous equations only have one unique solution. I can solve simultaneous equations by drawing the straight line graphs and finding the point of intersection. I understand that a set of simultaneous equations may have no solution and can demonstrate this by sketching the graphs. I can use the process of elimination to solve simultaneous equations with one term having a unitary coefficient. I can use the process of elimination to solve simultaneous equations with both terms having a co-efficient not equal to 1. I can use the process of substitution to solve simultaneous equations. I can use simultaneous equations to model a situation. Formulae evaluate a formula using substitution. rearrange a formula. I can distinguish between an algebraic expression and a formula. I can use formulae to model a real life situation. I can evaluate a formulae using substitution. I can change the subject of a formula by using inverse operations. I can solve problems involving rearranging a formula. Graphs of Quadratic Functions identify and sketch graphs of quadratic functions. I can sketch a quadratic graph using a table of values. I can transform a quadratic graph by stretching it and translating it both vertically and horizontally. I can identify the turning point of a quadratic graph and determine its nature.

9 Pythagoras Theorem use Pythagoras Theorem to find the length of a missing side in a right angled triangle. use the converse of Pythagoras Theorem to decide if a triangle is right angled or not. apply Pythagoras Theorem to problems in 3 dimensions. I can square and square root numbers. I can state and apply Pythagoras Theorem to find the length of the hypotenuse. I can state and apply Pythagoras Theorem to find the length of a shorter side. I can use the converse of Pythagoras Theorem to prove whether a triangle is right angled or not. I can identify right angled triangles in 3 dimensional shapes. I can apply Pythagoras Theorem to a variety of problems in 3 dimensions. Properties of Shapes identify types of triangle. use triangle properties to calculate missing angles. state the properties of a variety of quadrilaterals and use their properties to calculate missing sides and angles. Pupils will know the properties of parallel lines and associated angles. I can name and describe a range of triangles including: o Acute angled o Obtuse angled o Right angled o Scalene o Isosceles o Equilateral I can calculate an exterior angle in a triangle given its supplementary interior angle. I can calculate an interior angle in a triangle given its supplementary exterior angle. I can state the properties of a range of quadrilaterals: o Square o Rectangle o Parallelogram o Rhombus o Trapezium o Kite

10 find interior and exterior angles for regular and irregular polygons. describe all parts of a circle and use triangle properties within a circle. I can identify and calculate corresponding angles. I can identify and calculate alternate angles. I can identify and calculate allied angles. I can calculate an exterior angle in a polygon given its supplementary interior angle. I can calculate an interior angle in a polygon given its supplementary exterior angle. I can calculate the sum of the interior angles in a polygon. I can calculate the sum of the exterior angles in a polygon. I can find the number of sides in a regular polygon given its exterior angle. I can cover an area by tessellating shapes. I can name and describe a range of parts of a circle: o Circumference o Diameter o Radius o Arc o Chord o Segment o Sector o Tangent I can construct a right angled triangle inside a circle or semi-circle. I know that a tangent meets a circle at only one point and is perpendicular to the radius. I can identify the perpendicular bisector of a chord and use this to create a right angled triangle. I can apply my knowledge of circles to a variety of real life contexts.

11 Similarity use a scale factor to enlarge or reduce a length, area or volume. I can identify a linear scale factor and use it to calculate a missing length in an enlargement or reduction. I can identify an area scale factor and use it to calculate a missing length or area in an enlargement or reduction. I can identify a volume scale factor and use it to calculate a missing length or volume in an enlargement or reduction. Trigonometric Functions find the sine, cosine or tangent of any angle. sketch trigonometric graphs. apply a variety of transformations to trigonometric graphs. find the equation of a trigonometric graph. solve trigonometric equations. I can use a calculator to find the sine, cosine or tangent of any angle. I can accurately sketch the graphs of sin x, cos x and tan x. I can give the definition of the period and amplitude of a trigonometric function. I can transform a trigonometric graph by stretching it vertically and horizontally, by moving it left to right and by moving it up and down. I can solve a trigonometric equation and find all solutions. I can use trigonometric identities: o o to simplify expressions. identify and apply trigonometric identities to simplify expressions.

12 Applications Topic Learning Intention Success Criteria I understand this Trigonometry Pupils should be able to calculate the area of a non-right angled triangle. Pupils should be able to find the length of a missing length in any triangle. Pupils should be able to calculate a missing angle in any triangle. Pupils should be able to apply their knowledge of triangles and trigonometry to solve problems including bearings. I understand that trigonometry deals with the ratio of sides in triangles. I can calculate the area of a triangle given the length of two sides and an angle. I can use the sine rule to calculate the length of a missing side in a non right angled triangle. I can use the sine rule to calculate the size of an angle in a no right angled triangle. I can use the cosine rule to calculate the length of a missing side in a non right angled triangle. I can use the cosine rule to calculate the size of an angle in a no right angled triangle. I can use three figure bearings to describe direction. I can accurately measure and sketch a bearing. I can use information given to determine whether an angle is acute or obtuse. Vectors & 3D Coordinates use vectors to describe force and direction. use co-ordinates and vectors in three dimensions. I understand that a vector has both direction and size magnitude. I understand that a scalar has no direction. I can express a vector using column notation. I can express a vector using a directed line segment. I can sketch a vector given its components.

13 I understand that vectors are equal if they have the same magnitude and direction. I can multiply a vector by a scalar and understand how the vector changes. I understand that the negative of any vector changes its direction. I can calculate the magnitude of a vector. I can find a resultant vector by adding vectors. I can sketch a diagram to illustrate vector addition. I can use three dimensional co-ordinated to describe a point in space. Percentages accurately work with percentages in a variety of contexts. I can find a percentage of a quantity. I can find the original value of one quantity given its increased/decreased value. (Reverse Percentages) I can calculate simple interest. I can calculate compound interest. I know the definitions of appreciation and depreciation and know how to calculate these. Fractions apply the four basic operations to fractions. use fractions in a variety of contexts. express fractions in equivalent forms. I can identify the numerator and denominator of a fraction. I can find an equivalent fraction. I can simplify a fraction. I can write a mixed number fraction as an improper fraction. I can write an improper fraction as a mixed number fraction.

14 I can find a fraction of a quantity. I can find the reciprocal of a fraction. I can add, subtract, multiply and divide fractions Distributions use statistical analysis to compare distributions and data sets. illustrate a data set using a box plot. I can calculate the range of a data set. I can calculate the mean, median and mode of a data set. I understand that mean, median and mode are all types of averages and know which one is best to use in certain situations. I can calculate a five figure summary of a data set lowest, highest and quartiles. I can calculate the interquartile range and semiinterquartile range of a data set. I can illustrate a five figure summary on a box plot. I can compare two or more distributions using box plots and can make valid statements about all. I understand that the standard deviation of a data set gives an idea of how spread out the data set is. I can calculate the standard deviation of a data set. Scatter Graphs interpret a scatter graph. identify correlation. I can accurately plot a scatter graph. I can interpret a scatter graph to determine required information. I can identify the three types of correlation by examining a scatter graph.

15 draw a best fitting line and determine its equation. I can draw a line of best fit on a scatter graph. I understand that a line of best fit identifies the trend of the data. I can determine the equation of a line of best fit. I can estimate a value from one data set when the corresponding data is given.

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