Scotland

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Skills available for Scotland secondary 3 maths curriculum

IXL's secondary 3 skills will be aligned to the Curriculum for Excellence Benchmarks soon! Until then, you can view a complete list of secondary 3 objectives below.

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Curriculum for Excellence Benchmarks: Fourth Level Curriculum for Excellence Benchmarks: Fourth Level
Curriculum for Excellence Benchmarks: Third Level Curriculum for Excellence Benchmarks: Third Level

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Number, money and measure

Estimation and rounding
- Rounds decimal fractions to three decimal places.
  - Round decimals (7-F.7)
  - Round whole numbers and decimals: find the missing digit (7-F.8)
- Uses rounding to routinely estimate the answers to calculations.
Number and number processes
- Recalls quickly multiplication and division facts to the 10^th multiplication table.
  - Multiplication facts to 10 (6-C.1)
  - Division facts to 10 (6-E.1)
- Uses multiplication and division facts to the 12^th multiplication table.
  - Multiplication facts to 12 (6-C.4)
  - Division facts to 12 (6-E.3)
- Solves addition and subtraction problems working with whole numbers and decimal fractions to three decimal places.
- Solves addition and subtraction problems working with integers.
- Solves multiplication and division problems working with whole numbers and decimal fractions to three decimal places.
- Solves multiplication and division problems working with integers.
Multiples, factors and primes
- Identifies common multiples, including the lowest common multiple for whole numbers and can explain method used.
  - Lowest common multiple (7-E.8)
- Identifies common factors, including the highest common factor for whole numbers and can explain method used.
  - Highest common factor (7-E.7)
- Identifies prime numbers to 100 and can explain method used.
  - Prime or composite (7-E.2)
- Solves problems using multiples and factors.
  - HCF and LCM: word problems (7-E.9)
- Writes a given number as a product of its prime factors.
  - Prime factorisation (7-E.5)
  - Prime factorisation with indices (7-E.6)
Powers and roots
- Explains the notation and uses associated vocabulary appropriately, for example, index, exponent and power.
  - Write multiplication expressions using indices (7-D.1)
- Evaluates whole number powers, for example, 2⁴ = 16.
  - Evaluate indices with whole number bases (7-D.2)
- Expresses whole numbers as powers, for example, 27 = 3³.
  - Find the missing index or base (7-D.3)
Fractions, decimal fractions and percentages
- Converts fractions, decimal fractions or percentages into equivalent fractions, decimal fractions or percentages.
  - Convert between percents, fractions and decimals (7-T.2)
  - Convert between percents, fractions and decimals: word problems (7-T.3)
- Adds and subtracts whole numbers and fractions, including when changing a denominator.
- Converts between whole or mixed numbers, improper fractions and decimal fractions.
- Uses knowledge of fractions, decimal fractions and percentages to carry out calculations with and without a calculator.
- Solves problems in which related quantities are increased or decreased proportionally.
- Expresses quantities as a ratio and where appropriate simplifies, for example, 'if there are 6 teachers and 60 children in a school find the ratio of the number of teachers to the total amount of teachers and children'.
Money
- Demonstrates understanding of best value in relation to contracts and services when comparing products.
- Chooses the best value for their personal situation and justifies choices.
- Budgets effectively, using digital technology where appropriate, showing development of financial capability.
  - Balance a budget (7-LL.1)
  - Adjust a budget (7-LL.2)
- Demonstrates knowledge of financial terms, for example, debit/credit, APR, pa, direct debit/standing order and interest rate.
  - Debit cards and credit cards (7-LL.3)
- Converts between different currencies.
Time
- Applies knowledge of the relationship between speed, distance and time to find each of the three variables.
  - Calculate speed, distance or time: word problems (7-S.)
- Calculates time durations across hours and days.
  - Elapsed time (7-X.1)
Measurement
- Chooses appropriate units for length, area and volume when solving practical problems.
  - Estimate metric measurements (7-U.1)
- Converts between standard units to three decimal places and applies this when solving calculations of length, capacity, volume and area.
- Calculates the area of a 2D shape where the units are inconsistent.
- Finds the area of compound 2D shapes constructed from squares, rectangles and triangles.
  - Area of compound figures (7-HH.11)
  - Area of compound figures with triangles (7-HH.12)
- Finds the volume of compound 3D objects constructed from cubes and cuboids.
  - Volume of compound figures (8-BB.18)
Mathematics – its impact on the world, past, present and future
- Researches and communicates using appropriate mathematical vocabulary and notation, the work of a famous mathematician or a mathematical topic and explains the relevance and impact they have on society.
Patterns and relationships
- Generates number sequences from a given rule, for example, T = 4n + 6.
  - Write variable expressions for arithmetic sequences (7-Z.7)
  - Complete a table for a two-variable relationship (7-DD.7)
- Extends a given pattern and describes the rule.
- Expresses sequence rules in algebraic notation, for example, the cost of hiring a car is £75 plus a charge of £0·05 per mile, 'm' driven, C = 0.05m + 75.
Expressions and equations
- Collects like terms, including squared terms, to simplify an algebraic expression.
  - Add and subtract like terms (7-AA.9)
- Evaluates expressions involving two variables using both positive and negative numbers.
- Solves linear equations, for example, ax ± b = c where a, b and c are integers.
- Creates a simple linear formula representing information contained in a diagram, problem or statement.
- Evaluates a simple formula, for example, C = 0.05m + 75.

Shape, position and movement

Properties of 2D shapes and 3D objects
- Demonstrates a variety of methods to accurately draw 2D shapes, including triangles and regular polygons (given the interior angle), using mathematical instruments.
  - Graph triangles and quadrilaterals (7-EE.7)
Angle, symmetry and transformation
- Names angles using mathematical notation, for example, ∠ABC.
  - Name angles (7-EE.12)
- Identifies corresponding, alternate and vertically opposite angles and uses this knowledge to calculate missing angles.
- Uses the angle properties of triangles and quadrilaterals to find missing angles.
  - Find missing angles in triangles (7-EE.8)
  - Find missing angles in quadrilaterals (7-EE.9)
- Applies knowledge and understanding of scale to enlarge and reduce objects in size showing understanding of linear scale factor.
- Uses bearings in a navigational context, including creating scale drawings.
  - Distance/direction to starting point (7-R.6)
- Identifies all lines of symmetry in 2D shapes.
  - Line symmetry (7-FF.1)
- Creates symmetrical patterns and pictures.

Information handling

Data and analysis
- Sources information or collects data making use of digital technology where appropriate.
- Interprets data sourced or given.
- Describes trends in data using appropriate language, for example, increasing trend.
  - Identify trends with scatter plots (8-HH.11)
- Determines if information is robust, vague or misleading by considering, for example, the validity of the source, scale used, sample size, method of presentation and appropriateness of how the sample was selected.
- Collects data by choosing a representative sample to avoid bias.
  - Identify representative, random and biased samples (7-JJ.3)
- Organises and displays data appropriately in a variety of forms, for example, compound bar and line graphs and pie charts, making effective use of technology as appropriate.
Ideas of chance and uncertainty
- Uses the probability scale of 0 to 1 showing probability as a fraction or decimal fraction.
- Demonstrates understanding of the relationship between the frequency of an event happening and the probability of it happening.
  - Experimental probability (7-KK.4)
- Uses a given probability to calculate an expected outcome, for example, 'the probability of rain in June is 0·25 so how many days do we expect it to rain?'.
  - Make predictions using theoretical probability (7-KK.6)
  - Make predictions using experimental probability (7-KK.7)
- Calculates the probability of a simple event happening, for example, 'what is the probability of throwing a prime number on a 12 sided die?'.
  - Probability of simple events (7-KK.1)
  - Probability of simple events and opposite events (7-KK.2)
- Identifies all of the mutually exclusive outcomes of a single event and calculates the probability of each.
  - Probability of mutually exclusive events and overlapping events (7-KK.3)
- Investigates real-life situations which involve making decisions on the likelihood of events occurring and the consequences involved.
  - Use collected data to find probabilities and make predictions (7-KK.5)

Scotland

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Actions

Number, money and measure

Estimation and rounding

Rounds decimal fractions to three decimal places.

Uses rounding to routinely estimate the answers to calculations.

Number and number processes

Recalls quickly multiplication and division facts to the 10th multiplication table.

Uses multiplication and division facts to the 12th multiplication table.

Solves addition and subtraction problems working with whole numbers and decimal fractions to three decimal places.

Solves addition and subtraction problems working with integers.

Solves multiplication and division problems working with whole numbers and decimal fractions to three decimal places.

Solves multiplication and division problems working with integers.

Multiples, factors and primes

Identifies common multiples, including the lowest common multiple for whole numbers and can explain method used.

Identifies common factors, including the highest common factor for whole numbers and can explain method used.

Identifies prime numbers to 100 and can explain method used.

Solves problems using multiples and factors.

Writes a given number as a product of its prime factors.

Powers and roots

Explains the notation and uses associated vocabulary appropriately, for example, index, exponent and power.

Evaluates whole number powers, for example, 24 = 16.

Expresses whole numbers as powers, for example, 27 = 33.

Fractions, decimal fractions and percentages

Converts fractions, decimal fractions or percentages into equivalent fractions, decimal fractions or percentages.

Adds and subtracts whole numbers and fractions, including when changing a denominator.

Converts between whole or mixed numbers, improper fractions and decimal fractions.

Uses knowledge of fractions, decimal fractions and percentages to carry out calculations with and without a calculator.

Solves problems in which related quantities are increased or decreased proportionally.

Expresses quantities as a ratio and where appropriate simplifies, for example, 'if there are 6 teachers and 60 children in a school find the ratio of the number of teachers to the total amount of teachers and children'.

Money

Demonstrates understanding of best value in relation to contracts and services when comparing products.

Chooses the best value for their personal situation and justifies choices.

Budgets effectively, using digital technology where appropriate, showing development of financial capability.

Demonstrates knowledge of financial terms, for example, debit/credit, APR, pa, direct debit/standing order and interest rate.

Converts between different currencies.

Time

Applies knowledge of the relationship between speed, distance and time to find each of the three variables.

Calculates time durations across hours and days.

Measurement

Chooses appropriate units for length, area and volume when solving practical problems.

Converts between standard units to three decimal places and applies this when solving calculations of length, capacity, volume and area.

Calculates the area of a 2D shape where the units are inconsistent.

Finds the area of compound 2D shapes constructed from squares, rectangles and triangles.

Finds the volume of compound 3D objects constructed from cubes and cuboids.

Mathematics – its impact on the world, past, present and future

Researches and communicates using appropriate mathematical vocabulary and notation, the work of a famous mathematician or a mathematical topic and explains the relevance and impact they have on society.

Patterns and relationships

Generates number sequences from a given rule, for example, T = 4n + 6.

Extends a given pattern and describes the rule.

Expresses sequence rules in algebraic notation, for example, the cost of hiring a car is £75 plus a charge of £0·05 per mile, 'm' driven, C = 0.05m + 75.

Expressions and equations

Collects like terms, including squared terms, to simplify an algebraic expression.

Evaluates expressions involving two variables using both positive and negative numbers.

Solves linear equations, for example, ax ± b = c where a, b and c are integers.

Creates a simple linear formula representing information contained in a diagram, problem or statement.

Evaluates a simple formula, for example, C = 0.05m + 75.

Shape, position and movement

Properties of 2D shapes and 3D objects

Demonstrates a variety of methods to accurately draw 2D shapes, including triangles and regular polygons (given the interior angle), using mathematical instruments.

Angle, symmetry and transformation

Names angles using mathematical notation, for example, ∠ABC.

Identifies corresponding, alternate and vertically opposite angles and uses this knowledge to calculate missing angles.

Uses the angle properties of triangles and quadrilaterals to find missing angles.

Applies knowledge and understanding of scale to enlarge and reduce objects in size showing understanding of linear scale factor.

Uses bearings in a navigational context, including creating scale drawings.

Identifies all lines of symmetry in 2D shapes.

Creates symmetrical patterns and pictures.

Information handling

Data and analysis

Sources information or collects data making use of digital technology where appropriate.

Interprets data sourced or given.

Describes trends in data using appropriate language, for example, increasing trend.

Determines if information is robust, vague or misleading by considering, for example, the validity of the source, scale used, sample size, method of presentation and appropriateness of how the sample was selected.

Collects data by choosing a representative sample to avoid bias.

Organises and displays data appropriately in a variety of forms, for example, compound bar and line graphs and pie charts, making effective use of technology as appropriate.

Ideas of chance and uncertainty

Uses the probability scale of 0 to 1 showing probability as a fraction or decimal fraction.

Demonstrates understanding of the relationship between the frequency of an event happening and the probability of it happening.

Recalls quickly multiplication and division facts to the 10^th multiplication table.

Uses multiplication and division facts to the 12^th multiplication table.

Evaluates whole number powers, for example, 2⁴ = 16.

Expresses whole numbers as powers, for example, 27 = 3³.