Biggar High School S1 - S3 BGE Phase Course

S1 Block 1 Experiences & Outcomes Resources Learning Intentions Success Criteria

Whole numbers and Decimals In context wherever possible Including 4 operations, estimating and rounding MNU 1-01a MNU 1-02a MNU 1-03a MNU 2-01a MNU 2-02a MNU 2-03a MNU 3-01a MNU 3-03a & b MTH 2-03c Text Books Bronze TJ C Chapter 1, 3 & 5 TJ D Pg 11, 17 & 19 TJ D Pg 39 & 40 TJ D Pg 14, 15 & 16 & Pg 66, 67 MIA S13 Chapter 1 & 2 Silver MIA S12 Chapter 1 & 2 TJ D Chapter 1, 3 &6 TJ E Chapter 1 & 2 Gold MIA S13 Chapter 1 Pg 1-5 MIA S13 Chapter 2 MIA S13 Pg 62

Bronze Whole numbers only Maths4Life Resource 1 Adding two-digit numbers 3 Using Multiplication 5 Ordering Numbers Silver Decimals in context – money, measure Maths4Life Resource 8 Using Money 9 Exploring Properties of Number

14 Estimating Length 16 Comparing Decimals part 1 17 Comparing Decimals part 2 18 Using zero as a place holder 19 Finding a rule to compare decimals 15 Adding Decimals 21 Adding a subtracting decimals 1 26 Multiplying by powers of 10 Gold Measurements. More advanced use of decimals e.g. 0.1 x 0.04 etc Maths4Life Resource 9 Exploring Properties of Number

14 Estimating Length 18 Using zero as a place holder 19 Finding a rule to compare decimals

26 Multiplying by powers of 10 Standards Unit

Pupils can round to a sensible degree of accuracy in a variety of contexts.

Round to the nearest 10, 100, 1000. (B*/B/S/G)

Round up to the nearest whole number. (B/S/G)

Choose a sensible degree of accuracy in context. (B/S/G)

Round a given number up to 2 decimal places. (S/G)

Round a number to any decimal places. (G)

Round a number to any significant figures. (G)

Pupils can solve problems using familiar methods in a variety of contexts.

Pupils can explain their methods with reasoning.

Understand importance of zero. (B*)

Understand Place Value with whole numbers. (B*)

Know the order of place values (Th → U) and their meaning. (B/S/G)

Convert numbers between words and digits. (B*/B/S/G)

Order whole numbers according to size. (B*/B/S/G)

Explain number properties through number bonds (commutative & associative properties) (B/S/G)

Know the order of place values (Th → th) and their meaning. (S/G)

Perform calculations involving resulting in up to 3 decimal places. (S/G)

Order a variety of numbers (including decimals) according to size. (S/G)

Define associative, commutative & distributive properties of numbers. (S/G)

Know the meaning of “sum”, “product”, “quotient” and “Difference”. (G)

Order of operations using BODMAS. (S/G)

10 ticks BIDMAS Sheets Twig Animal Maths Twig Roman Numerals Twig Speed rounding Twig Decimals Twig Decimal money Twig Egyptian Multiplication

N3 Rounding Numbers

Pupils can recall number facts quickly to make accurate estimates and calculations.

Use decimals to understand money (B*)

Understand where and when decimal point is used (B*)

+, - money (B*)

+, - numbers up to 4 digits. (B*/B/S/G)

, up to 4 digit numbers by a single digit. (B*/B/S/G)

Know language such as: share, double, lots of etc (B*)

, numbers by powers of 10 (including decimals in context of money and measure) (B/S/G)

Be able to use times tables (up to 10). (B)

Be able to mentally recall times tables (up to 12). (S/G)

Know when to use decimal point in £ and p (B*)

Know what change to receive when using money (B*)

+, - numbers up to 7 digits or 3 decimal places. (S/G)

, whole numbers up to 3 digits, long multiplication and division. (S/G)

, numbers by multiples of 10. (S/G)

, decimals by decimals (G)

Multiples, Factors, Prime Numbers, Powers and Roots MTH 2-05a MTH 3-05a MTH 3-05b MTH 3-06a MTH 4-06a Text Books Bronze, Silver & Gold MIA S12 Pg 25

Bronze Time tables. Simple powers on a calculator Silver Factors and primes. Squares and cubes with and without a calculator. Gold Factors and primes. Whole number powers with and without a calculator.

Pupils can identify patterns within a number sequence and use their properties to solve problems, clearly explaining their strategies.

Pupils can identify primes in a set of numbers and explain their importance in everyday life.

Pupils can use powers and roots with the correct notation.

Find multiples of numbers from 1 to 10. (B/S/G)

Find factors of numbers less than 100. (B/S/G)

Find multiples of a number and the Lowest Common Multiple (LCM) of 2 or more numbers. (S)

Find factors of a number and the Highest Common Factor (HCF) of 2 or more numbers. (S)

Use prime decomposition to calculate HCF & LCM. (G)

Define prime and composite numbers. (S/G)

TJ E Chapter 13 MIA S13 Pg 6-10 10 Ticks Worksheets *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Primes 1 Twig Primes 2 Twig Patterns and Primes Twig Diophantine Twig Squares and Cubes

Know and solve the sequence of prime numbers. (G)

Express a composite number as a product of prime numbers (prime decomposition). (G)

Express a variety of integers using index form (i.e. 24 = 2×2×2×3 =23 x 3 ) (B/S/G)

Calculate square powers of 1 to 12, (e.g. 22, - 122 ) as well as simple multiples of 10.(e.g. 102, 202 etc) (B/S/G)

Calculate square roots of appropriate numbers, resulting in a solution being from 1 to 12 or a simple multiple of 10. (S/G)

Calculate cube powers of 1 to 12, (e.g. 23, - 123 ) as well as simple multiples of 10.(e.g. 103, 203 etc) (G)

Calculate cube roots of appropriate numbers, resulting in a solution being from 1 to 12 or a simple multiple of 10. (G)

Displaying Data & Statistics Including misleading graphs, bias etc. MNU 1-20a & b MTH 1-21 a MNU 2-20a & b MNU 3-20a & b MNU 4-20a & b MTH 2-21a MTH 3-21a MTH 4-21a Text Books Bronze, Silver & Gold MIA S11 Chapter 5 & 18 TJ C Chapter 6 MIA S12 Chapter 5 TJ D Chapter 5

Bronze Simple bar charts, line graphs Straightforward calculations of mean, median, mode & range. Silver Multiple More complex calculations and discussion on which average to use when Gold More advanced charts etc Activity 18 “Life Expectancy”

from Human Rights in the

Curriculum.

Using frequency tables to find

the mean.

Concept Cartoons:

Pupils can analyse data and draw valid conclusions, given their reasoning.

Carry out surveys (B*/B/S/G)

Interpret tables, pictograms, bar and line graphs & pie charts(B*/B/S/G)

Identify misleading information. (B/S/G)

Interpret pictograms, frequency tables, bar charts, line graphs, pie charts (with given intervals) and scatter graphs within context. (B/S/G)

Interpret data and make own conclusions, explaining reasoning. (G)

Construct frequency tables (using class intervals), pictograms, bar and line graphs. (B/S/G)

Construct pictograms, frequency tables, bar charts, line graphs, pie charts (with given intervals) and scatter graphs. (B*/B/S/G)

Identify and interpret trends and correlations. (S/G)

Construct frequency tables including cumulative and relative frequencies. (G)

MIA S13 Chapter 5, Chapter 18 Pg 295 TJ E Chapter 9 TJ F Pg 73-75 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video links Twig Most Popular pets Twig Histograms Twig Nightingale's pie chart Twig Displaying data Twig Correlations Twig Observational Bias Twig Hidden Bias Twig IQ Bias Twig Statistical Significance Twig Average Joe Twig Cumulative Frequency

1. 8.1 Pizza Pictures (pictogram)

2. 8.2 Where to start (scales in a bar chart)

3. 8.3 What Sort? (what chart to draw)

4. 8.8 Open to interpretation (interpreting a bar chart)

5. 8.9 Missing Link (table of information)

6. 8.11 Going steady (graph interpretation)

7. 8.12 Through the roof (graph interpretation)

8. 8.13 Between Places (distance tables)

9. 8.14 Popular Shoes (mode) See folder Numeracy 5 Misleading graphs and statistics

Explain why data from particular sources may/may not be reliable. (B/S/G)

Explain how the sample size affects the reliability of data. (S/G)

Calculate the mean, median, mode & range of a set of data from a variety of sources and media. (B/S/G)

Calculate mean from a frequency table. (G)

*What has not been covered due to test dates MUST be covered after test BEFORE moving

onto next topic including any project*

S1 Project 1 – Understanding Mean, Median, Mode & Range

Assessment 1: October (for Tracking + Report)

Angles MTH 1-17a MTH 2-17a MTH 2-17b MTH 3-17a MTH 4-17a Text Books Bronze TJ C Chapter 9 TJ D Pg 93-94 MIA S11 Chapter 3 Silver TJ D Chapter 8 – Pg 97 MIA S12 Chapter 3 TJ E Chapter 12 Gold MIA S13 Chapter 3 Video Links Twig Euclid angles

Bronze Measure and draw < 180, reflex, acute, obtuse Silver Use of protractor 0 – 360, 180 in a triangle, 360 in a quadrilateral Gold Parallel lines, complementary, supplementary, naming angles. Angles in a range of 2D shapes. *Textbooks are for guidance only. Some LI & SC may be covered by other resources.*

Pupils can describe angles and their properties in a familiar environment.

Pupils can name angles and calculate missing angles using properties of various lines and 2D shapes.

Understand where angles can be found I the environment (B*)

Describe angles as acute, right, obtuse, straight, reflex or a full turn/revolution. (B*/B/S/G)

Calculate missing angles in simple problems involving 90°, 180° and 360°. (B/S/G)

Use angles to give directions e.g. L 90, F 5, R90 (B*)

Measure given angles to an accuracy of ± 2°. (B*/B/S/G)

Draw an angle to an accuracy of ± 2°. (B*/B/S/G)

Name an angle. (B/S/G)

Calculate missing angle(s) round a point. (S/G)

Calculate supplementary and complementary angles. (B/S/G)

Calculate vertically opposite angles. (S/G)

Calculate corresponding and alternate angles. (S/G)

Calculate missing angles in a variety of triangles and quadrilaterals using their specific properties. (S/G)

Calculate missing angles within a circle including angles in a semi circle, diameter as a line of symmetry and tangents (G)

Calculate missing angles in a variety of regular polygons. (G)

Integers Include co-ordinate diagrams and links to grid references in geography MNU 2-04a MNU 3-04a MTH 1-18a MTH 2-18a MTH 3-18a MTH 4-18a MTH 4-18b Text Books Bronze TJ D Chapter 12 MIA S12 Pg 150 Silver TJ E Chapter 5 TJ F Pg 14 E3, Pg 17 E5 Gold TJ E Pg63-65 TJ F Chapter 2 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Why Negatives Twig -ves in context Twig Zero Twig Descartes

Bronze Temperature First quadrant Standard Units N8 (Temperature) Silver Temp and other contexts All 4 quadrants Start to formalise and go into abstract rules for adding and subtracting integers Gold All 4 quadrants Four operations on integers and include algebraic terms Standards Unit N9 & N4

Active Assessment Activities:

Rumours – Negative Rumours

Negative Thinking

Tarsia

10 ticks extra worksheets or activities: Addon-agons, Number Pyramids and Magic Squares all with negative numbers. Level 5 Pack 4 P7 – 12

Collaborative working: We can work it out (ATM)

1. Elimination game a (money)

Concept cartoons: 2.6 Temperatures, 2.12 totally mental

Pupils can show an

understanding of the relevance

of negative numbers in real-life

situations and use them to solve

problems.

Pupils can plot and describe the

position of a point on a grid.

Pupils can plot and describe the

position of a point on Cartesian

Coordinates.

Pupils can perform simple

calculations involving integers.

Order integers (-20 → 20) according to size. (B*/B/S/G)

Order integers according to size, including the use of symbols – e.g. 5 > -2. (B/S/G)

Know the meaning of “integer”. (B/S/G)

Use number lines and scales with negative numbers. (B/S/G)

Simple integer calculations using (or resulting in) negative numbers. (S/G)

Add and subtract negative numbers, including double negatives. (S/G)

Read and write coordinates. (B*/B/S)

Interpret and plot coordinates within the first quadrant. (B*)

Interpret and plot coordinates within the first quadrant, including simple decimals and fractions. (B/S/G)

Interpret and plot simple 3D coordinates on isometric paper. (G)

Interpret and plot coordinates within all four quadrants, including simple decimals and fractions. (S/G)

Reflect points and images across x and y axis (G)

Reflect points and images across any horizontal or vertical line (G)

Reflect points and images across any diagonal line (G)

Multiply and divide with negative numbers (S/G)

Algebra 1 Collecting like terms, putting words into symbols, using formulae and substitution MTH 1-15b MTH 2-15a MTH 2-03c MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a Text Books Bronze, Silver & Gold MIA S12 Chapter 4 MIA S13 Chapter 4 Pg 59-68 TJ F Chapter 11 – omit E2 &E5 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Algorithms Twig Symbols Twig Formulae

Bronze Using words or basic symbols only Silver Straightforward situations with positive numbers only Gold All of above and include single brackets and negative numbers Standards Unit A1 Interpreting Algebraic Expressions

Pupils can solve a range of problems using symbols and/or letters.

Pupils can collect like terms and simplify an algebraic expression.

Pupils can perform calculations by substituting values into a given formula.

Use number machines (B*/B/S)

Solve a range of problems using symbols, pictures and/or letters. (B*/B/S/G)

Collect like algebraic terms (including square powers). (S/G).

+, -, , simple algebraic terms. (S/G)

Substitute a given value into an algebraic formula and calculate using BODMAS. (S/G)

Four operations using algebraic terms and integers (S/G)

Breaking brackets – one bracket (S), more than one bracket (G)

*What has not been covered due to test dates MUST be covered after test BEFORE moving onto

next topic including any project*

Links between fractions Bronze Understand the terms numerator and

decimals and percentages Finding % of or fractions of MNU 2-07a MNU 2-07b MTH 2-07c MNU 3-07a MTH 3-07b & c MUN 4-07a MTH 4-07b Text Books Bronze TJ C Chapter 10 TJ D Pg 143-145 MIA S11 Chapter 15 Silver TJ D Chapter 11 & 13 MIA S12 Pg 329-350 TJ E Chapter 6 Gold MIA S13 Pg 237-243 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video links Twig finding %

Simple half, quarter and thirds Silver Fifths, 20% etc and e.g. 27% of … using a calculator Gold Full range of percentages and fractions with and without a calculator Cakes Maths4Life 6 Making Sense of Fractions 23 Comparing Fractions 24 Equivalent Fractions Standards Unit N1 Ordering Fractions and Decimals N7 Using percentages to increase quantities

Pupils can use fractions and percentages to carry out calculations within real-life situations.

Pupils can convert between a variety of equivalent fractions, decimals and percentages.

denominator (B*/B/S)

Use correct notation to write fractions (B*/B)

Identify a fraction from its picture (B*/B)

Identify equivalent fractions from pictures (B*/B)

Find simple fractions of a quantity (half, quarters, fifths, tenths, hundredths). (B*/B/S/G)

Find simple percentages of a quantity (equivalent to above). (B/S/G)

Identify fractions in their simplest form. (B*/B/S/G)

Find equivalent fractions, decimals and percentages (half, quarters, fifths, tenths, hundredths). (B*/B/S/G)

Calculate fractions and percentages of a quantity with and without a calculator. (S/G/G)

Express a quantity as a fraction and/or percentage. (S/G)

Perform partitioned percentage calculations (e.g. 17.5%, etc.). (S/G)

Calculate a percentage increase/decrease. (S/G)

Calculate (and simplify) equivalent fractions and their respective decimals and percentages. (S/G)

Order a variety of fractions, decimals and percentages according to size. (S/G)

Convert between mixed numbers and improper fractions. (G)

Add and subtract common fractions. (S/G)

Multiply and Divide fractions. (G)

Scale Drawings Enlarging and Reducing MTH 3-17c Text Books Bronze, Silver & Gold MIA S13 Pg 168 TJ F Pg 141 Worksheets recommended. *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Scale factor

Bronze Enlarge with a whole number scale factor Silver and Gold Enlarge and reduce with fractional scale factors

Pupils should know how to determine the scale factor used when given the dimensions of two similar objects

Pupils should know that the scale factor is greater than one when enlarging an object or picture

Pupils should know that the scale factor is less than one when reducing an object or picture

Calculate the scale factor when given the dimensions of two similar objects

Determine the size of an enlargement or reduction given the dimensions of an original and the required scale factor

Use appropriate technology or ICT for either measurement or representation of an enlargement or reduction Whole Numbers (B*/B/S/G) Fractions (S/G)

Assessment2 – February Bearings and Scale Drawings MTH 2-17c & d MTH 3-17b & c Text Books Bronze TJ C Pg 120-129 TJ D Pg 98-99 MIA S11 Chapter 7 Silver TJ D Pg 98-102 MIA S12 Pg 154-164 & Pg 174-179 Gold TJ D Chapter 17 MIA S13 Pg 108-116

Bronze Compass points and angles. Use this to describe routes and journeys Silver Navigation and 3 figure bearings. Scales on maps. Draw scale drawings Gold As above

Pupils can interpret maps and plans to describe the position of a certain point, relative to another.

Pupils can plan and follow directions to illustrate a journey.

Pupils can interpret maps and plans to perform calculations involving scale in familiar contexts.

Pupils can construct accurate scale drawings, using appropriate technology and methods, to represent a journey.

Use clockwise and anti-clockwise (B*)

Describe a journey using CW and ACW (B*)

Identify the 8 main compass points. (B*/B/S/G)

Follow and describe directions using compass points. (B*/B/S/G)

Interpret maps, plans and other scale drawings. (B/S/G)

Perform simple scale calculations. (S/G)

Perform simple enlargement and reduction calculations. (B/S/G)

Identify the main 8 compass points and their 3 figure bearings. (S/G)

Solve problems involving angles and bearings calculations. (S/G)

Interpret and construct scale drawings, including journeys using 3 figure bearings. (S/G)

Video links Twig Scale

Demonstrate an appropriate degree of accuracy when making a scale drawing. (S/G

Speed, Distance and Time Links to real life – Olympic times, sports, timetables, etc Include distance – time graphs. MNU 1-10a, b & c MNU 2-10a, b & c MNU 3-10a MNU 4-10a & b Text Books Bronze TJ C Chapter 4 MIA S11 Chapter 6 Silver TJ D Chapter 4 TJ F Chapter 7 MIA S12 Pg 127-146 TJ E Chapter 3 Gold TJ E Chapter 3 MIA S13 Chapter 6 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.*

Bronze Simple time intervals and straightforward s, d, t calculations Silver Time intervals over midnight s, d, and t calculations including ½ hours etc Gold Time intervals, decimal times, more advanced s, d, t calculations 1 hour 37 minutes etc

Pupils can plan events and activities using a variety of relevant sources and information.

Pupils can measure and choose an appropriate unit of time for a familiar activity.

Pupils can estimate the time taken for a journey using the link between distance, speed and time.

Pupils can convert between different units of time.

Pupils can calculate distance, speed or time when given two of the quantities, to plan a journey.

Understand time related vocabulary (B*/B/S)

Write dates (B*)

Use a year calendar (B*)

Know sequence of months and be able to group these into seasons (B*/B)

Understand 24 hours in a day – am and pm (B*/B)

Use an analogue and digital clock to tell the time (B*)

Understand different ways to write time (B*/B)

Know how many days in each month, year, leap year (B*/B/S/G)

Convert times between 12 and 24 hours. (B*/B/S/G)

Calculate time intervals. (B/S/G)

Calculate a time from a given time interval. (B/S/G)

Interpret timetables. (B/S/G)

Convert simple times between seconds, minutes, hours, days, weeks, years, decades, and centuries. (B/S/G)

Time events to an appropriate degree of accuracy (including hundredths of a second). (B/S/G)

Solve simple DST problems. (B/S/G)

DST calculations using the formula. (S/G)

Convert between hours and minutes and simple decimal hours (e.g. 2 hours 45 min = 2.75 hours). (S/G)

Convert between hours and minutes and decimal hours. (G)

Given the other two, calculate the distance travelled, time taken or average speed of a journey. (S/G)

Interpret and construct simple distance-time

graphs. (B/S/G)

S1 Project 2 – Speed, Distance & Time

Assessment 3: End of Year – March (for Tracking + Report) Algebra 2 MTH 2-15a MTH 3-15a MTH 4-14a MTH 4-15a Text Books Bronze TJ D Pg 75 - 79 MIA S11 Chapter 8 Silver TJ D Chapter 7 MIA S12 Chapter 8 TJ E Pg 96-100 Gold TJ F Pg 171-175 MIA S13 Chapter 8 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Tank equations Twig Balancing Twig Heptathlon scoring Twig Inequalities

Bronze Simple single step Use of language for < and > Silver e.g. 2x+4 = 14 Solving simple inequalities Gold Include equations with brackets and unknown on both sides More complex inequalities Standards Unit A2 Creating and Solving Equations A3 Creating and Solving Harder Equations A4 Evaluating Algebraic Expressions

Pupils should know and understand that a symbol or letter can represent a number in an equation e.g. 2a + 7 = 17/ 10 + 7 = 17/a = 5

Pupils can solve a range of problems using symbols and/or letters.

Pupils can solve a range of linear equations using appropriate methods.

Pupils can create appropriate formulae in a problem solving context to represent a variety of information.

Pupils can construct and solve a range of equations and inequalities.

use knowledge of number facts e.g. bonds and x/÷ patterns (B*/B/S/G)

work out the symbol or letter value and explain their working out to others (B*/B/S/G)

Simple 1-step linear equations and inequalities. (B*/B/S/G)

Solve simple 2-step linear equations and inequalities. (B/S/G)

Solve simple linear equations and inequalities involving fractions (1-step). (S/G)

Construct a simple formula from the information provided, within a relevant context. (B/S/G)

Read and interpret a problem in order to construct on algebraic equation (S/G)

Investigate and discover methods to solve equations (balancing, cover up, change side, change operation etc.) (S/G)

Solve more complex linear equations, including fractions and negative numbers. (S/G)

Solve linear equations with brackets including a negative multiplier. (S/G)

Solve simple equations involving powers and roots. (G)

Construct a variety of inequalities in problem solving contexts. (B/S/G)

*What has not been covered due to test dates

MUST be covered after test BEFORE moving onto next topic including any project*

Revision of S1 course to be completed before pupils change timetable in May

Biggar High School S1 - S3 BGE Phase Course

S2 BLOCK 1 2D and 3D shapes Properties and drawing Including symmetry and tiling MTH 2-16a MTH 2-16b MTH 2-16c MTH 3-16a MTH 3-19a MTH 4-19a Text Books Bronze TJ C Chapter 14 TJ D Pg 172-175, 177 Chapter 2 MIA S21 Chapter 10 Silver TJ E Chapter 18, 20 and Chapter 7 Pg 79-81 Gold TJ EFT Chapter 7, 18 and 20 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Origami Twig triangles Twig Tessellations

Bronze Name simple 2D and 3D shapes and their properties (including line symmetry)and their uses in the real world Silver As above and draw 2D shapes. Gold As above and rotational symmetry Standards Unit Classifying shapes SS1 SS6 Representing 3D shapes See folder from HC June materials

Pupils can describe the properties of a variety of 2D shapes and 3D objects.

Pupils can accurately draw 2D shapes using appropriate technology and methods.

Pupils can explain the relationship between a variety of 3D objects and their respective nets.

Pupils can construct a variety of 3D objects from their nets.

Pupils can describe the properties of various 2D shapes.

Pupils can identify and draw all lines of symmetry in a pattern or shape.

Pupils can complete a pattern or shape when given one or two lines of symmetry.

Investigate the properties of squares, rectangles & a variety of triangles. (B/S/G)

Define faces, vertices and edges of a 3D object. (B/S/G)

Investigate the properties of cubes and cuboids. (B/S/G)

Identify and explain properties of 2D shapes and 3D objects including prisms & pyramids. (S/G)

Draw a variety of 3D objects on isometric paper. (S/G)

Accurately draw a variety of squares, rectangles and triangles using rulers, protractors and compasses. (B/S/G)

Draw cube, cuboid, triangular prism, square pyramid, triangular pyramid, cylinder, cone. (B/S/G)

Construct 3D objects from a given net. (B/S/G)

Identify the nets of a cube and/or cuboid. (B/S/G)

Identify the nets of more complex 3D objects. (S/G)

Accurately draw regular polygons using rulers, protractors and compasses. (S/G)

Identify and draw line(s) of symmetry in a variety of patterns and shapes. (B/S/G)

Complete a pattern or shape using line(s) of symmetry (including diagonal lines of symmetry). (B/S/G)

Describe the order of rotational symmetry in a given 2D shape or pattern. (S/G)

Complete a 2D shape or pattern from a given

order of rotational symmetry. (S/G)

Explain the properties of various triangles and quadrilaterals given their symmetrical properties. (B/S/G)

Tile using a variety of shapes. (B/S/G)

Define and use translational symmetry (S/G)

Fractions Adding, subtracting, mixed numbers (multiplying and dividing) MNU 2-07a MTH 2-07c MTH 3-07b MTH 3-07c MTH 4-07b Text Books Bronze TJ C Chapter 10 TJ D Pg 128-131 TJ F Pg 131 Questions 1 & 2 Silver TJ F Pg 128-137 TJ E Chapter 6 Gold TJ F Pg 128-140 MIA S23 Pg 233-239 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig adding and subtracting fractions Twig Music Fractions x + -

Bronze Simple concrete examples – cake etc Silver Using mixed numbers, adding and subtracting Gold Four operations with fractions

Pupils can compare and perform simple calculations involving fractions.

Pupils can convert between different ways of writing fractions.

Pupils can perform a variety of calculations using fractions in familiar contexts.

+, - fractions with equal denominators. (B/S/G)

Express fractions in their simplest form. (B/S/G)

Find equivalent fraction (B/S/G)

Simplifying fractions (B/S/G)

Find a fraction of a quantity (B/S/G)

Percentage and Fraction Equivalency – non calculator (S/G)

Order fractions according to size using equivalent fractions. (S/G)

Identify when a fraction is proper, improper or mixed. (S/G)

Convert between mixed and improper fractions. (S/G)

Carry out calculations by +, -, (S/G) (G) fractions including mixed numbers and improper fractions.

Carry out calculations when dividing by a fraction including mixed numbers and improper fractions. (G)

Measure and Area. First introduce units and links to other subjects MNU 2-11a MNU 2-11b MNU 2-11c MTH 2-17d MNU 3-11a MTH 3-11b MTH 4-16b Text Books Bronze MIA S21 Chapter 9 & 11 TJ C Chapter 11 & 15 TJ D Chapter 14 & 17 Silver TJ E Chapter 10 Gold TJ E Chapter 10 & 19 TJ EFT Chapter 10 & 19 TJ F Chapter 23 & 29 MIA S23 Chapter 11 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Metre Twig Metric system

Bronze Practical measurement: using a ruler, measuring jug or cylinder, trundle wheel etc. Reading scales. Simple changing units of measure mm to m, ml to l etc. Area of rectangle and triangle. Silver As above but more complex and include area of triangles and compound shapes. Gold As above and include circles.

Pupils can estimate the length, area and volume of a variety of familiar objects.

Pupils can read a variety of scales.

Pupils can convert between a variety of metric units of measurement.

Pupils can find the perimeter of a variety of 2D shapes.

Pupils can calculate the areas of basic 2D shapes.

Pupils can describe the parts of a circle, using their properties and relationships to perform calculations.

Read scales showing, g, kg, l, ml, m, cm, mm. (B/S/G)

Estimate lengths, area and volumes using familiar objects. (B/S/G)

Simple conversions in length, volume and mass. (B/S/G)

Convert cubic centimetres to millilitres. (B/S/G)

Calculate the perimeter of 2D shapes. (B/S/G)

Calculate area using square cm boxes. (B/S)

Calculate the area of squares, rectangles and right-angled triangles using appropriate formulae. (B/S/G)

Calculate the area of a variety of composite 2D shapes, comprising of squares, rectangles and triangles including subtraction of areas to find a shaded area. (S/G)

Calculate the area of common quadrilaterals including kite, rhombus, parallelogram and trapezium using appropriate formulae. (G)

Calculate the area of more complex composite 2D shapes. (S/G)

Identify and name the various components of a circle. (S/G)

Calculate the circumference and area of a circle. (S/G)

Calculate the radius and diameter of a circle from its circumference and/or area. (G)

Calculate the area of a variety of regular polygons (G)

Calculate the Arcs and Sectors of a Circle (G)

*What has not been covered due to test dates MUST be covered after test BEFORE moving onto

next topic including any project*

S2 Project 1 – Measure & Area (Golden Rectangle)

Assessment 1: October/November (for Tracking + Report)

Triangle properties including Pythagoras. Include links to the world of work – bridges, joiners etc MNU 3-01a MNU 4-01a MTH 3-06a MTH 4-06a MTH 4-16a Text Books Bronze MIA S21 Chapter 13 Silver TJ F Chapter 59 Gold TJ F Chapter 59 MIA S23 Chapter 9 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Triangle properties Twig Pythagoras Proof Twig Pythag Irrational

Bronze Consolidate triangle properties and introduce Pythagoras as a famous mathematician. Square numbers. Silver Pythagoras Theorem finding a missing side Gold Converse of Pythagoras

Pupils can choose the best strategy when solving problems involving right-angled triangles, explaining their reasoning and methods.

Round to the nearest 10, 100, 1000. (B/S/G)

Round up to the nearest whole number. (B/S/G)

Choose a sensible degree of accuracy in context. (B/S/G)

Round a given number up to 2 decimal places. (S/G)

Round a number to any decimal places. (G) Round a number to any significant figures. (G)

Calculate missing angles in a variety of triangles – scale, right angles, isosceles, equilateral. (B/S/G)

Calculate square powers of 1 to 12, (e.g. 22, - 122 ) as well as simple multiples of 10.(e.g. 102, 202 etc) (B/S/G)

Calculate square roots of appropriate numbers, resulting in a solution being from 1 to 12 or a simple multiple of 10. (B/S/G)

Use Pythagoras to find the missing side of a right-angled triangle (smaller side/hypotenuse). (S/G)

Use Pythagoras to calculate the distance between two given points on Cartesian Coordinates. (S/G)

Use Pythagoras in context. (S/G)

Use Pythagoras’ Theorem twice in calculations to find any missing side. (G)

Prove a triangle is right-angled using the Converse Theorem of Pythagoras. (G)

Similar Figures including enlargement and reduction MTH 3-17c

Bronze Basic enlargement and reductions involving whole numbers and fractions where appropriate. Silver

Explain the relationship between similar figures and perform calculations in real-life situations.

Calculate the scale factor when given the dimensions of two similar objects. (B/S/G)

Determine the size of an enlargement or reduction given the dimensions of an original and the required scale factor. (B/S/G)

MTH 4-17b Video links Twig scale volume

Parallel lines and angle properties. Similar figures and being able to calculate the missing length in similar shapes. Gold Similar figures solving problems involving length, area and volume.

Use appropriate technology or ICT for either measurement or representation of an enlargement or reduction. (B/S/G)

Solve problems involving similar shapes and lengths. (S)

Calculate the linear (S)/area (G) /volume (G) scale factors from similar shapes & objects.

Solve problems involving similar areas & volumes. (G)

Volume and Surface Area including compound shapes and real life contexts MNU 2-11c MNU 3-11a MTH 3-11b MTH 4-11a, b & c MTH 4-16b N5 EF Text Books Bronze MIA S21 Chapter 11 TJ E Pg 186-187 Silver TJ E Chapter 10 & 16 TJ EFT Chapter 16 TJ F Chapter 23 Gold TJ EFT Chapter 20 TJ F Chapter 23 & 29 MIA S23 Chapter 17 Video Links Twig Counting Stars

Bronze Volume of a cube/cuboid Silver Volume of cube/cuboids. Surface Area Gold Compound area and arcs and sectors of a circle. Volume of a cuboid and cylinder. *Textbooks are for guidance only. Some LI & SC may be covered by other resources.*

Pupils can calculate the areas of basic 2D shapes and volumes of basic 3D objects.

Pupils can select appropriate strategies to solve area and volume problems, explaining their reasoning.

Calculate the volume of cubes and cuboids. (B/S/G)

Understand liquid volumes and be able to convert between litres. Millilitres and cubic centimetres. (B/S/G)

Using the correct algebraic formulae, calculate the volume of a cube and cuboid expressing your answer in cubic or liquid volume. (B/S/G)

Calculate the volume of a variety of composite 3D objects, comprising of cubes and cuboids. (S/G)

Calculate the volume of a variety of 3D objects including cylinder, sphere, cone and triangular prism. (S/G)

Calculate the surface area of cubes, cuboids and prisms. (S/G)

*What has not been covered due to test dates MUST be covered after test BEFORE

moving onto next topic including any project*

Assessment 2: January (for Tracking + Report)

S2 BLOCK 2

S2 Project 2 – Money & Finance Twig Tax % - Useful resource

S2 Project 3 – Money and Budgeting Money and Finance MNU 2-09a, b & c MNU 3-09a & b MNU 4-09a, b & c

Text Books Bronze, Silver & Gold Personal Finance Unit Internet Resources Project Group Discussion

Bronze Work out costs of items. Understand terms used e.g. Net Pay, deductions etc. Silver Understand financial products Gold Understand financial products and be able to explain their usage/benefits/drawbacks etc.

Pupils can calculate costs of

items using a variety of techniques

Pupils can select appropriate strategies to decide on a best buy, explaining their reasoning.

Explain different financial products and relate them to real-life situations.

Choose and use appropriate calculations to work out exact costs of items (+, -, x, ÷, %) (B/S/G)

Access product prices from a variety of sources (Internet, brochure, price list, advert) (B/S/G)

Check that costs include VAT (B/S/G)

Use banking terms within real life simulations (B/S/G)

Safely check bank card balance and make an ATM withdrawal through real life simulations (B/S/G)

Read and interpret bank card statements (B/S/G)

Calculate interest deposits and charges to accounts (B/S/G)

The terms profit and loss and how and where they can be used (B/S/G)

Be able to calculate profit and loss as a percentage of either the buying or selling price (B/S/G)

Investigate and explain where in life they might need to use financial products, services and contracts (mobile phones may be a good example) (B/S/G)

Calculate and compare different offers (e.g. mobile phone contracts and offers, free minutes, any networks, etc.) (B/S/G)

Choose an offer and explain their choice (B/S/G)

Understand that other choices may be

better for different people in different situations (B/S/G)

Research and investigate what basic living costs would involve (rent, council tax, bills, food, etc.) (B/S/G)

Budget given a scenario and set choices (a salary of £x and then they buy according to how much money they have and the cost, etc.) (B/S/G)

Discuss and research credit in order to develop a greater understanding of what it is (S/G)

List where credit is available (banks, loans, cards, etc.) (S/G)

Calculate gross pay (B/S/G)

Using appropriate resources, research the different items which may be deducted from gross pay (B/S/G)

Calculate these deductions (B/S/G)

Discuss why these deductions can differ from person to person (different salaries, tax codes, etc.) (B/S/G)

Calculate net pay (B/S/G)

Explain the differences between a range of financial products and develop an understanding of where, in the real world, each may be used and by whom (G)

Given a scenario choose a financial product which is most suitable for them and explain their decisions (G)

Ratio and Proportion MNU 3-08a MNU 4-08a MNU 4-20a Text Books Bronze

Bronze Simple ratio and direct proportion Silver Ratio and simple direct and inverse proportion Gold Ratio and direct and inverse

Pupils can convert between fractions and ratios, using them to solve problems in everyday situations.

Pupils can identify a link between two quantities, explain

Convert between fractions and ratios. (B/S/G)

Simplify a ratio. (B/S/G)

Use a ratio to calculate a quantity, given the other. (B/S/G)

Share a ratio in 2 or more parts. (S/G)

Define direct and inverse proportion. (S/G)

Use direct proportion to calculate a quantity, given the other. (B/S/G)

MIA S21 Chapter 14 TJ E Chapter 15 Silver TJ EFT Chapter 15 TJ F Chapter 41 Gold TJ F Chapter 41 MIA S23 Pg 206-216 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Baking Ratios Twig Ratios Twig Inverse Proportion Twig Golden Ratio Twig Mona Lisa Twig Direct&Inverse Twig Currency Ratios Twig Vitruvian man

proportion

their relationship and use this to perform calculations in everyday situations.

Use direct and inverse proportion to calculate a quantity, given the other. (S/G)

Identify and interpret graphs of direct and inverse proportion. (G)

Sequences and Algebra Include common sequences Fibonacci, triangle numbers, square numbers etc & nth term rule Equations and Inequalities Expanding brackets and Factorisation MTH 4-03b MTH 3-06a MTH 2-13a MTH 3-13a MTH 4-13a

Bronze Simple number sequences from diagrams. Extend simple pattern. Silver Extending patterns and finding nth term. Gold More complex number patterns Factorisation All investigate different sequences in as much depth as relevant.

Pupils can explain the rule of a sequence in words and thus find missing or following terms.

Pupils can explain the rule of a sequence in words.

Pupils can find missing terms in a sequence.

Pupils can identify a wide variety of patterns & sequences, establishing a formula and using it to solve related problems.

Describe in words the rule of a variety of sequences (up to 2-step). (B/S/G)

Continue the sequence and find missing terms (including linear & Fibonacci patterns, & Pascal’s Triangle). (B/S/G)

Express linear patterns algebraically using a formula. (S/G)

Use linear formulae to solve related problems. (S/G)

Identify and continue a given non-linear sequence of numbers (e.g. squares, triangular, puzzles). (S/G)

Identify and continue a given sequence of numbers (including simple quadratic, cubic and root patterns (S/G).

MTH 3-14a MTH 4-14a & b MTH 2-15a MTH 3-15a MTH 4-15a Text Books Bronze MIA S21 Chapter 12 TJ C Chapter 13 TJ D Chapter 15 Silver TJ EFT Chapter 11 TJ E Chapter 11 Gold TJ EFT Chapter 11 MIA S23 Chapter 12 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video links Twig Speed of the Earth Twig Life without numbers Twig Fibonacci Twig Gauss

Pupils can establish a formula for a linear sequence.

Use linear formulae to solve related problems. (S/G)

Establish a formula to describe patterns involving simple quadratics, cubics and roots. (G)

use knowledge of number facts e.g. bonds and x/÷ patterns (B/S/G)

work out the symbol or letter value and explain their working out to others (B/S/G)

Simple 1-step linear equations and inequalities. (B/S/G)

Solve simple 2-step linear equations and inequalities. (B/S)

Solve simple linear equations and inequalities involving fractions (1-step). (S/G)

Construct a simple formula from the information provided, within a relevant context. (B/S/G)

Read and interpret a problem in order to construct on algebraic equation (S/G)

Investigate and discover methods to solve equations (balancing, cover up, change side, change operation etc.) (S/G)

Solve more complex linear equations, including fractions. (S/G)

Solve linear equations with brackets. (G)

Solve simple equations involving powers and roots. (G)

Construct a variety of inequalities in problem solving contexts.(B/S/G)

Breaking brackets – one bracket (S), more than one bracket (G)

Factorising - common factor (S/G)

Factorising – Difference of Squares and Trinomials (G)

Probability Links to real life contexts – how risky is life resource MNU 2-22a MNU 3-22a MNU 4-22a Text Books Bronze TJ 3G Chapter 18 Silver MIA 3B Chapter 15 Gold MIA 3B Chapter 15 MIA 4A Chapter 10 Tails you win: The Science of Chance– BBC video Twig Insurance Probability Twig Fear Probability Twig Monkey Probability Twig Predicting events Twig Probability Odds Twig Card Counting Twig Monty Hall Twig Risk and Shares Twig Conditional Probability Robots Twig Birthday Paradox

Bronze Simple experiments using language of probability and make predictions Silver Finding the probability of a simple event happening and consequences when making decisions Gold Using probability determine how many times an event can happen and use this to make informed choices, risk assessment and decisions. *Textbooks are for guidance only. Some LI & SC may be covered by other resources.*

Pupils can find the probability of a simple event happening, taking its consequences into account.

Pupils can find the probability of an event happening, taking its consequences into account.

Explain the probability of an event in words and its position on the probability line (impossible = 0; certainty = 1). (B/S/G)

Calculate the probability of a simple event (e.g. toss of a coin, deck of cards, roll of a die). (B/S/G)

Using a table, show all the possible permutations (combinations) from a selection in a given context. (S/G)

Solve a variety of simple logic problems. (B/S/G)

Solve more complex logic problems. (S/G)

Interpret and draw tree diagrams representing the probability of an event happening. (G)

Calculate the probability of multiple outcomes occurring. (G)

Solve a variety of complex logic problems. (G)

Displaying Data & Statistics Including misleading graphs, bias etc. MNU 2-20a & b MNU 3-20a & b

Bronze Simple bar charts, line graphs Straightforward calculations of mean, median, mode & range. Silver Multiple More complex calculations and

Pupils can analyse data and draw valid conclusions, given their reasoning.

Interpret tables, pictograms, bar and line graphs & pie charts(B/S/G)

Identify misleading information. (B/S/G)

Interpret pictograms, frequency tables, bar charts, line graphs, pie charts (with given intervals) and scatter graphs within context. (B/S/G)

MNU 4-20a & b MTH 2-21a MTH 3-21a MTH 4-21a Text Books Bronze, Silver & Gold MIA S11 Chapter 5 & 18 TJ C Chapter 6 MIA S12 Chapter 5 TJ D Chapter 5 MIA S13 Chapter 5, Chapter 18 Pg 295 TJ E Chapter 9 TJ F Pg 73-75 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video links Twig Most Popular pets Twig Histograms Twig Nightingale's pie chart Twig Displaying data Twig Correlations Twig Observational Bias Twig Hidden Bias Twig IQ Bias Twig Statistical Significance Twig Average Joe Twig Cumulative Frequency

discussion on which average to use when Gold More advanced charts etc Activity 18 “Life Expectancy” from

Human Rights in the Curriculum.

Using frequency tables to find the

mean.

Concept Cartoons:

10. 8.1 Pizza Pictures (pictogram)

11. 8.2 Where to start (scales in a bar chart)

12. 8.3 What Sort? (what chart to draw)

13. 8.8 Open to interpretation (interpreting a bar chart)

14. 8.9 Missing Link (table of information)

15. 8.11 Going steady (graph interpretation)

16. 8.12 Through the roof (graph interpretation)

17. 8.13 Between Places (distance tables)

18. 8.14 Popular Shoes (mode)

See folder Numeracy 5 Misleading graphs and statistics

Interpret data and make own conclusions, explaining reasoning. (G)

Construct frequency tables (using class intervals), pictograms, bar and line graphs. (B/S/G)

Construct pictograms, frequency tables, bar charts, line graphs, pie charts (with given intervals) and scatter graphs. (S/G)

Identify and interpret trends and correlations. (S/G)

Construct frequency tables including cumulative and relative frequencies. (G)

Explain why data from particular sources may/may not be reliable. (B/S/G)

Explain how the sample size affects the reliability of data. (S/G)

Calculate the mean, median, mode & range of a set of data from a variety of sources and media. (B/S/G)

Calculate mean from a frequency table. (G)

*What has not been covered due to test dates MUST be covered after test BEFORE moving onto

next topic including any project*

Assessment 3: End of Year – April/May

Biggar High School S1 - S3 BGE Phase Course

S3 Block 1 Number work MNU 3-01a MNU 3-03a MNU 3-03b MNU 3-04a MNU 4-01a MNU 4-03a MNU 4-03b MTH 4-06b Text Books Bronze TJ 3G Pg 1-3, Pg 9 Ex 1 – 2, Pg 32 – 39 Silver & Gold TJ F Chapter 2, 3 and 31 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Standard Form 1 Twig Standard Form 2 Twig Infinity Twig Enigma

Bronze Consolidate four operations with whole numbers and basic fractions Silver Four operations with whole numbers and decimals. Introduce scientific notation for small and large numbers Gold Four operations with integers, decimals and fractions. Calculations involving scientific notation.

Pupils can choose a sensible degree of accuracy when performing calculations in a variety of contexts.

Pupils can solve problems using familiar methods in a variety of contexts, explaining their reasoning.

Pupils can recall number facts quickly to make accurate estimates and calculations.

Round to the nearest 10, 100, 1000. (B/S/G)

Round up to the nearest whole number. (B/S/G)

Choose a sensible degree of accuracy in context. (B/S/G)

Round a given number up to 2 decimal places. (S/G)

Round a number to any decimal places. (G)

Round a number to any significant figures. (G)

Know the order of place values (Th → U) and their meaning. (B/S/G)

Convert numbers between words and digits. (B/S/G)

Order whole numbers according to size. (B/S/G)

Explain number properties through number bonds (commutative & associative properties) (B/S/G)

Know the order of place values (Th → th) and their meaning. (S/G)

Perform calculations involving resulting in up to 3 decimal places. (S/G)

Order a variety of numbers (including decimals) according to size. (S/G)

Define associative, commutative & distributive properties of numbers. (S/G)

Know the meaning of “sum”, “product”, “quotient” and “Difference”. (G)

Order of operations using BODMAS. (S/G)

+, - numbers up to 4 digits. (B/S/G)

, up to 4 digit numbers by a single digit. (B/S/G)

, numbers by powers of 10 (including decimals in context of money and measure) (B/S/G)

Be able to use times tables (up to 10). (B)

Be able to mentally recall times tables (up to 12). (S/G)

+, - numbers up to 7 digits or 3 decimal places. (S/G)

, whole numbers up to 3 digits, long multiplication and division. (S/G)

, numbers by multiples of 10. (S/G)

Convert both large and small numbers between scientific notation and written in full. (S/G)

Perform calculations using scientific notation, with and without using a calculator. (G)

, negative numbers, including double negative. (S/G)

Research a Famous Mathematician MTH 3-12a MTH 4-12a Video Links Twig Greeks and Proof Twig Turing Twig set theory Twig Babylonians Twig Chinese maths Twig Binary Twig Computer binary Twig Alien language

Project Presentation Maths Super Hero etc

Research Present Impact in real world Work with others

S3 Project 1 – Famous Mathematician

Shape – area and volume MNU 2-11c MNU 3-11a & b MTH 4-11b & c MTH 4-16b N5 EF - TJ N5 Text Books Bronze TJ 3G Chapter 9 TJ 4G Chapters 6, 10 & 14 Silver MIA 3A Chapter 9 Gold MIA 4A Chapter 1 MIA 3B Chapter 11 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.*

Bronze Revision of basic area and volumes and area of a circle Silver 2D and 3D Compound shapes. Volume of a cylinder Gold Surface area. Volume of a prism, sphere and cone.

Pupils can describe the relationship between a 3D object and its net.

Pupils can calculate the surface area of a simple 3D object, solving problems in real-life contexts.

Pupils can calculate the volume of a variety of 3D objects.

Calculate the area of squares, rectangles and right-angled triangles using appropriate formulae. (B/S/G)

Calculate the volume of cube and cuboids. (B/S)

Calculate the circumference and area of a circle. (S/G)

Calculate the arc and sector of a circle. (G)

Identify & draw nets of a variety of 3D objects. (B/S/G)

Calculate the volume of a prism (including a cylinder). (S)

Calculate the volume of a prism area of the base and height. (S/G)

Calculate the volume of pyramids, cones & spheres (given the formulae). (G)

Calculate the volume of more complex composite 3D objects. (G)

Calculate the surface area of cubes, cuboids and prisms. (S/G)

Right angled Pythagoras and Trigonometry MTH 4-16a Text Books Bronze TJ 3G Chapter 1 & 16 Silver TJ 3G Chapter 13 & 16 MIA 4A Gold MIA S43 Chapter 11 & 12 MIA S33 *Textbooks are for guidance only. Some LI & SC may be covered by

Bronze Revision of angle properties and Pythagoras’ Theorem Silver Pythagoras’ Theorem and the use of SOH CAH TOA to find ratios in a right angled triangle Gold SOH, CAH, TOA and Pythagoras in context

Pupils can choose the best strategy when solving problems involving right-angled triangles, explaining their reasoning and methods.

Calculate square powers of 1 to 12, (e.g. 22, - 122 ) as well as simple multiples of 10.(e.g. 102, 202 etc) (B/S/G)

Calculate square roots of appropriate numbers, resulting in a solution being from 1 to 12 or a simple multiple of 10. (B/S/G)

Use Pythagoras to find the missing side of a right-angled triangle (smaller side/hypotenuse). (S/G)

Use Pythagoras to calculate the distance between two given points on Cartesian Coordinates. (S/G)

Use Pythagoras in context. (S/G)

Use Pythagoras’ Theorem twice in calculations to find any missing side. (G)

Prove a triangle is right-angled using the Converse Theorem of Pythagoras. (G)

other resources.* Video links Twig Triangles & angles Twig Trigonometry Twig SOHCAHTOA Twig SOHCAHTOA2

Correctly identify the opposite and adjacent

sides corresponding to an angle in a right

angled triangle. (S/G)

Identify whether to use the sine, cosine or

tangent function to calculate a missing side or

angle in a right angled triangle. (S/G)

Substitute into the appropriate trigonometric

function to calculate a missing side in a right

angled triangle. (S/G)

Process the appropriate trigonometric

function to calculate a missing side in a right

angled triangle. (S/G)

Substitute into the appropriate trigonometric

function to calculate a missing angle in a right

angled triangle. (S/G)

Process the appropriate trigonometric

function to calculate a missing angle in a right

angled triangle. (S/G)

Solve trigonometry problems in context.

(S/G)

Percentage Calculations and Surds and Indices Text Books Bronze TJ 3G Chapter 4 Silver TJ F Chapter 19 Gold MIA 4A Chapter 3 MIA S43 Chapter 9 TJ F Chapter 19 Video links Twig Indices *Textbooks are for

Bronze Percentage calculations Silver Percentage calculations Gold Surds and indices

Find simple fractions of a quantity (half, quarters, fifths, tenths, hundredths). (B/S/G)

Find simple percentages of a quantity (equivalent to above). (B/S/G)

Find equivalent fractions, decimals and percentages (half, quarters, fifths, tenths, hundredths). (B/S)

Calculate fractions and percentages of a quantity, with and without a calculator (B/S/G)

Express a quantity as a fraction and/or percentage. (S/G)

Perform partitioned percentage calculations (e.g. 17.5%, etc.) with and without a calculator (S/G)

Calculate a percentage increase/decrease, with and without a calculator (S/G)

guidance only. Some LI & SC may be covered by other resources.*

Calculate (and simplify) equivalent fractions and their respective decimals and percentages. (S/G)

Order a variety of fractions, decimals and percentages according to size. (S/G)

Find the original value of one quantity given its increased/decreased value. (Reverse Percentages) (S/G)

Calculate simple interest (S/G)

Calculate compound interest (S/G)

Know the definitions of “appreciation” and “depreciation” and know how to calculate these (S/G)

State the definition of a rational number.(G)

State the definition of an irrational number. (G)

Identify rational and irrational numbers. (G)

Simplify an expression involving surds by breaking it into a product of factors. (G)

Identify square numbers and find their square roots. (G)

Multiply, divide, add and subtract surds. (G)

Evaluate a number to a given power. (G)

Find the nth root of a number. (G)

Multiply like terms involving indices by adding their powers. (G)

Divide like terms involving indices by subtracting their powers. (G)

Raise a power to a power by multiplying the indices. (G)

Know that any term raised to the power of 0 equals 1. (G)

Know that any term raised to the power of 1 equals the same term. (G)

State the definition of a reciprocal. (G)

Work with negative indices. (G)

Change between fractional indices and roots. (G)

Evaluate terms with a fractional index or nth root. (G)

*What has not been covered due to test dates MUST be covered after test BEFORE moving onto

next topic including any project*

Assessment 1: November (for Tracking + Report) Further Co-ordinates Gradients and Straight Lines MTH 4-13b MTH 4-13c MTH 4-13d MTH 4-18a Text Books Bronze TJ 4G Pg 22 - 23 Silver TJ 4G Pg 63 – 72 Gold MIA S43 Chapter 7 *Textbooks are for guidance only. Some LI & SC may be covered by other resources.* Video Links Twig Gradients Twig 4th Dimension Twig Bee line

Bronze Cover all 4 quadrants Silver Simple equations and gradients, x=a, y=b, drawing graph from a table of values Gold y=mx+c, gradient formulae, identify graph from gradient and y-intercept, y-b=m(x-a) and ax+by+c=0

Pupils can plot and describe the position of a point on a grid.

Pupils can plot and describe the position of a point on Cartesian Coordinates.

Pupils can calculate the gradient of a slope and/or line, explaining their reasoning within familiar contexts.

Pupils can establish a relationship between a linear pattern and the equation of a straight line.

Pupils can identify points that lie on a given straight line using its equation.

Pupils can draw the graph of a straight line, given its equation.

Interpret and plot coordinates within all four quadrants, including simple decimals and fractions. (B/S/G)

Construct a table of values from the equation of a straight line. (S/G)

Draw the graph of a linear equation given a

table of values. (S/G)

Define the gradient of a slope and/or line. (S/G)

Recognise the gradient and y intercept of a

line from its graph. (S/G)

Write down the equation of a straight line

given the gradient and y intercept. (S/G)

Calculate the gradient of a straight line given

two points on the line. (S/G) Calculate the gradients of vertical &

horizontal lines. (S/G)

Write the equations of vertical & horizontal lines. (S/G)

Draw the graph of vertical & horizontal lines when given the equation of a straight line. (S/G)

Find the equation of a straight line given its

gradient and a point on the line. (S/G)

Plot points on Cartesian Coordinates and draw the graph when given the equation of a straight line. (S/G)

Find the solution to a pair of non-parallel

lines by plotting them on a Cartesian diagram

and identifying the point of intersection.

(S/G) Identify a positive, negative, zero and

undefined gradient. (G)

Calculate the gradient of a straight line by examining the change in the x direction and the change in the y direction. (G)

Calculate the gradient of a straight line using

the formula . (G)

Be able to find the gradient of a line parallel to the given line. (G)

Algebra 3 Algebraic expressions, algebraic fractions, factorising and change the subject of a formula MTH 3-05a MTH 3-05b MTH 4-14a MTH 4-14b Text Books Bronze TJ 3G Chapter 7 TJ 4G Pg 172 – 173 Silver TJ 4G Chapter 15 MIA 3B Pg 151 – 152 MIA S33 Pg 84 - 88 Gold MIA S33 Chapter 5 *Textbooks are for guidance only. Some LI & SC may be covered by

Bronze Factors and multiples of numbers. Further work on solving equations. Silver Finding common factor Change the subject of a formula Gold Factorising – common factor, difference of two squares and trinomials Change the subject of a formula

Pupils can identify primes in a set of numbers and explain their importance in everyday life.

Pupils can identify patterns in a variety of algebraic expressions.

Pupils can construct and solve a range of equations

Find multiples of a number and the Lowest Common Multiple (LCM) of 2 or more numbers. (B/S/G)

Find factors of a number and the Highest Common Factor (HCF) of 2 or more numbers. (B/S/G)

Define prime and composite numbers. (B/S/G)

Solve simple equations (B/S/G)

Simplify an algebraic expression by collecting like terms. (S/G)

Gather like terms including where more than

one variable is involved. (S/G)

Expand brackets in an expression with a common factor to produce a sum of terms. (S/G)

Recognise the highest common factor of two or more expressions. (S/G)

Factorise a sum of terms with a common factor. (S/G)

Evaluate expressions and formulae with one or more variables. (S/G)

Extend straightforward number or diagrammatic patterns. (S/G)

other resources.*

Determine the formula describing straightforward number or diagrammatic patterns. (S/G)

Factorise more complex algebraic expressions such as trinomials, difference of 2 squares. (G)

Change the subject of a formula by using inverse operations. (S/G)

Solve problems involving rearranging a formula. (G)

Expand and multiply a single numerical or algebraic term through a bracket. (G)

Expand an algebraic expression in the form (x ± a) (x ± b). (G)

Factorise an algebraic expression by finding a common factor. (S/G)

Factorise a quadratic expression using a difference of two squares. (G)

Factorise a quadratic expression into the form (x ± a) (x ± b). (G)

Factorise a quadratic expression with the x2

coefficient > 1 into the form (ax ± b) (cx ± d). (G)

Complete the square to express a quadratic in the form (x ± a)2 ± b. (G)

Simplify an algebraic fraction by finding the highest common factor of the numerator and the denominator. (G)

Add and subtract algebraic fraction by finding a common denominator. (G)

Multiply algebraic fractions. (G)

Divide algebraic fractions by multiplying by the reciprocal. (G)

*What has not been covered due to test dates MUST be covered after test BEFORE moving onto

next topic including any project*

Assessment 2: February (for Tracking + Report)

S3 Block 2

Probability Links to real life contexts – how risky is life resource MNU 2-22a MNU 3-22a MNU 4-22a Text Books Bronze TJ 3G Chapter 18 Silver MIA 3B Chapter 15 Gold MIA 3B Chapter 15 MIA 4A Chapter 10 Tails you win: The Science of Chance– BBC video Twig Insurance Probability Twig Fear Probability Twig Monkey Probability Twig Predicting events Twig Probability Odds Twig Card Counting Twig Monty Hall Twig Risk and Shares Twig Conditional Probability Robots Twig Birthday Paradox

Bronze Simple experiments using language of probability and make predictions Silver Finding the probability of a simple event happening and consequences when making decisions Gold Using probability determine how many times an event can happen and use this to make informed choices, risk assessment and decisions. *Textbooks are for guidance only. Some LI & SC may be covered by other resources.*

Pupils can find the probability of a simple event happening, taking its consequences into account.

Pupils can find the probability of an event happening, taking its consequences into account.

Explain the probability of an event in words and its position on the probability line (impossible = 0; certainty = 1). (B/S/G)

Calculate the probability of a simple event (e.g. toss of a coin, deck of cards, roll of a die). (B/S/G)

Using a table, show all the possible permutations (combinations) from a selection in a given context. (S/G)

Solve a variety of simple logic problems. (B/S/G)

Solve more complex logic problems. (S/G)

Interpret and draw tree diagrams representing the probability of an event happening. (G)

Calculate the probability of multiple outcomes occurring. (G)

Solve a variety of complex logic problems. (G)

S3 Project 2 – Probability

Statistics

Bronze Collecting and displaying data and

Pupils can interpret information displayed in a variety of ways,

Interpret tables, pictograms, bar and line graphs & pie charts (B)

MNU 3-20a MTH 3-20b MTH 3-21a MNU 4-20a MTH 4-20b MTH 4-21b Text Books Bronze TJ 3G Chapter 12 Silver TJ F Chapter 17 Gold MIA S33 Standard Deviation *Textbooks are for guidance only. Some LI & SC may be covered by other resources.*

forming conclusions. Mean, median and mode Silver Frequency tables. Inter quartile range and box plots. Further mean, median and mode. Gold Inter-quartile range and standard deviation.

identifying and describing any trend.

Pupils can analyse data and draw valid conclusions, given their reasoning.

Pupils can construct a variety of appropriate diagrams to represent the given information.

Interpret pictograms, frequency tables, bar charts, line graphs, pie charts (with given intervals) and scatter graphs within context. (B/S)

Construct pictograms, frequency tables, bar charts, line graphs, pie charts (with given intervals) and scatter graphs. (B/S)

Construct a frequency table with class intervals as appropriate from raw data. (S/G)

Construct a pie chart, bar graph and line graph from raw data. (S/G)

Calculate the mean, median, mode & range of a set of data from a variety of sources and media. (B/S/G)

Calculate mean from a frequency table. (S/G)

Construct frequency tables including cumulative and relative frequencies. (S/G)

Construct a scattergraph by plotting pairs of

values. (S/G)

Draw an appropriate line of best fit on a

scatter graph. (S/G)

Use a scattergraph and line of best fit to

estimate missing values. (S/G)

Use my answers to make conclusions and

explain those decisions. (S/G)

Use the context of a problem to make

reasoned decisions. (S/G) Identify and interpret trends and correlations.

(S/G)

Interpret and construct accurate pie charts, stem & leaf diagrams, dot & box plots. (B/S/G)

Calculate a five figure summary of a data set – lowest, highest and quartiles. (G)

Calculate the interquartile range and semi-interquartile range of a data set. (G)

Illustrate a five figure summary on a box plot. (G)

Compare two or more distributions using box plots and can make valid statements about all. (G)

Understand that the standard deviation of a data set gives an idea of how spread out the data set is. (G)

Calculate the standard deviation of a data set. (G)

*What has not been covered due to test dates

MUST be covered after test BEFORE moving onto next topic including any project*

Assessment 3: April/May