3.2.1

Estimating & Measuring

Test yourself on Estimating & Measuring

Test your knowledge with free interactive questions on Seneca — used by over 10 million students.

Estimating & Measuring

Learn how to choose suitable metric units and estimate length, mass and capacity.

Choosing units

Choosing units

We use different units for different types of measurement
- Length measures how long, wide or tall something is
- Mass measures how heavy something is
- Capacity measures how much liquid a container can hold
Choose a unit that fits what you are measuring

Estimating length

Estimating length

Length can be measured in millimetres, centimetres, metres or kilometres
Use smaller units for smaller lengths and bigger units for bigger lengths

Estimating mass

Estimating mass

Mass can be measured in grams or kilograms
Use grams for lighter objects and kilograms for heavier objects

Estimating capacity

Estimating capacity

Capacity can be measured in millilitres or litres
Use millilitres for small amounts of liquid
- A cup could hold about $250$ millilitres
Use litres for larger amounts of liquid
- A bottle could hold about $1$ litre

1

Number

1.1

Place Value & Ordering

1.1.1Ordering Integers 1.1.2Ordering Decimals 1.1.3Equal Symbols 1.1.4Place Value

1.2

Numerical Operations

1.2.1Adding Integers 1.2.2Subtracting Integers 1.2.3Multiplying Integers 1.2.4Dividing Integers 1.2.5Dividing with a Remainder 1.2.6Adding & Subtracting Decimals 1.2.7Multiplying Decimals 1.2.8Dividing Decimals 1.2.9Adding & Subtracting Negative Numbers 1.2.10Multiplying & Dividing Negative Numbers 1.2.11Multiplying by Powers of Ten 1.2.12Dividing by Powers of Ten

1.3

Fractions

1.3.1Writing Fractions 1.3.2Simplifying Fractions 1.3.3Equivalent Fractions 1.3.4Constructing Fractions 1.3.5Ordering Fractions 1.3.6Recurring Decimal Notation 1.3.7Mixed Numbers & Improper Fractions

1.4

Numerical Operations (Fractions)

1.4.1Adding & Subtracting Fractions 1.4.2Add & Subtract Mixed Numbers & Improper Fractions 1.4.3Multiplying Fractions 1.4.4Multiplying Mixed Numbers 1.4.5Reciprocals 1.4.6Dividing Fractions 1.4.7Dividing Mixed Numbers

1.5

Roots & Powers

1.5.1Roots 1.5.2Integer Powers 1.5.3Estimating Powers & Roots 1.5.4Laws of Indicies (Multiplication)

1.6

Structure of Calculations

1.6.1Order of Operations (BIDMAS)

1.7

Numerical Skills

1.7.1Using a Calculator - Powers, Roots & Fractions

1.8

Factors & Multiples

1.8.1Divisibility Rules 1.8.2Finding Multiples 1.8.3Finding Factors 1.8.4Finding Prime Numbers

1.9

Systematic Listing

1.9.1Systematic Listing

1.10

Standard Form

1.10.1Reading Standard Form 1.10.2Converting to Standard Form (Positive Powers)1.10.3Converting to Standard Form (Negative Powers)1.10.4Converting Form Standard Form (Positive Powers)1.10.5Converting From Standard Form (Negative Powers)1.10.6Adding & Subtracting Standard Form 1.10.7Standard Form on a Calculator

1.11

Fractions, Decimals & Percentages

1.11.1Converting Fractions, Decimals & Percentages 1.11.2Numbers as Percentages 1.11.3Fractions of Amounts

1.12

Percentage Change

1.12.1Percentages of Amounts (Calculator)1.12.2Percentages of Amounts (No Calculator)1.12.3Percentage Change

1.13

Rounding & Estimation

1.13.1Rounding Integers 1.13.2Estimating Calculations 1.13.3Rounding Decimals 1.13.4Rounding With Significant Figures

1.14

Bounds & Accuracy

1.14.1Finding Error Intervals

2

Algebra

2.1

Algebraic Notation

2.1.1Function Machines 2.1.2Using Algebraic Notation

2.2

Substitution & Simplification

2.2.1Substituting into Expressions with Operations 2.2.2Substituting into Algebraic Expressions 2.2.3Substituting into Real-Life Expressions 2.2.4Simplifying Expressions by Collecting Like Terms

2.3

Brackets

2.3.1Expanding Single Brackets 2.3.2Expanding & Simplifying with Single Brackets 2.3.3Expanding Double Brackets 2.3.4Factorising Into One Bracket

2.4

Algebraic Fractions

2.4.1Operations with Algebraic Fractions

2.5

Rearranging

2.5.1Changing the Subject

2.6

Functions

2.6.1Finding the Input of a Function

2.7

Solving Linear Equations

2.7.1Solving Linear Equations (One Step)2.7.2Solving Linear Equations (Multi-Step)2.7.3Solving Linear Equations (Unknown Both Sides)2.7.4Solving Equations (Unknown in Denominator)2.7.5Forming & Solving Linear Equations

2.8

Inequalities

2.8.1Representing Inequalities on a Number Line 2.8.2Solving Linear Inequalities 2.8.3Linear Inequalities with Unknowns on Both Sides

2.9

Simultaneous Equations

2.9.1Solving Simultaneous Equations Graphically 2.9.2Solving Simultaneous Equations by Elimination

2.10

Sequences

2.10.1Term-to-Term Rules (Patterns)2.10.2Term-to-Term Rules (Numerical)2.10.3Substituting into a Given Rule 2.10.4Position-to-Term Rules 2.10.5Finding the Nth Term (Linear Sequences)2.10.6Simple Geometric Progressions

2.11

Coordinates

2.11.1Midpoints of Line Segments

2.12

Linear Graphs

2.12.1Equations of Straight Lines 2.12.2Finding Line Equation from Point & Gradient 2.12.3Finding Line Equations from Two Points 2.12.4Parallel Line Equations

2.13

Quadratic Graphs

2.13.1Interpreting Quadratics

3

Ratio, Proportion & Rates of Change

4

Geometry & Measures

4.1

Area & Perimeter

4.1.1Perimeter of Simple Shapes 4.1.2Perimeter of Compound Shapes 4.1.3Area of Triangles 4.1.4Area of Rectangles & Parallelograms 4.1.5Area of Trapezia 4.1.6Area of Compound Shapes 4.1.7Area of Compound Shapes with Triangles

4.2

Properties of Shapes

4.2.1Naming & Classifying Triangles 4.2.2Naming & Classifying Quadrilaterals 4.2.3Properties of Lines 4.2.4Shortest Distance from a Point to a Line 4.2.5Properties of 3D Shapes

4.3

Angles

4.3.1Classification of Angles 4.3.2Angles on a Line & Around a Point 4.3.3Combining Angle Facts in Triangles 4.3.4Angles on Parallel Lines 4.3.5Interior & Exterior Angles in Polygons

4.4

Trigonometry

4.4.1Pythagoras' Theorem 4.4.2Sides in Right-Angles Triangles 4.4.3Angles in Right-Angled Triangles

4.5

Similarity & Congruence

4.5.1Congruent Shapes 4.5.2Length Scale Factors in Similar Shapes

4.6

Circle Geometry

4.6.1Identifying Parts of a Circle 4.6.2Calculating Circumference 4.6.3Calculating Area of a Circle 4.6.4Calculating Arc Lengths 4.6.5Calculating Area of Sectors

4.7

3D Representations

4.7.1Nets of 3D Shapes

4.8

Surface Area

4.8.1Surface Area of Cubes & Cuboids 4.8.2Surface Area of Prisms 4.8.3Surface Area of Cylinders

4.9

Volume

4.9.1Volume of Prisms 4.9.2Volume of Cylinders

4.10

Transformations

4.10.1Translation using Vectors 4.10.2Rotations 4.10.3Enlargements & Positive Scale Factors

4.11

Scale Drawings

4.11.1Scale Drawings

4.12

Bearings

5

Probability

5.1

Single Events

5.1.1Writing Probabilities as Fractions 5.1.2Mutually Exclusive Events 5.1.3Expected Results

5.2

Combined Events

5.2.1Reading Venn Diagrams 5.2.2Venn Diagrams (Set Notation)5.2.3Independent & Mutually Exclusive Events

5.3

Experimental Probability

5.3.1Relative Frequency & Convergence

6

Statistics

6.1

Averages & Range

6.1.1Range 6.1.2Median 6.1.3Mode 6.1.4Mean 6.1.5Interpreting Two-Way Tables

6.2

Scatter Graphs

6.2.1Lines of Best Fit

6.3

Collecting & Presenting Data

6.3.1Types of Data

Jump to other topics

1

Number

1.1

Place Value & Ordering

1.1.1Ordering Integers 1.1.2Ordering Decimals 1.1.3Equal Symbols 1.1.4Place Value

1.2

Numerical Operations

1.2.1Adding Integers 1.2.2Subtracting Integers 1.2.3Multiplying Integers 1.2.4Dividing Integers 1.2.5Dividing with a Remainder 1.2.6Adding & Subtracting Decimals 1.2.7Multiplying Decimals 1.2.8Dividing Decimals 1.2.9Adding & Subtracting Negative Numbers 1.2.10Multiplying & Dividing Negative Numbers 1.2.11Multiplying by Powers of Ten 1.2.12Dividing by Powers of Ten

1.3

Fractions

1.3.1Writing Fractions 1.3.2Simplifying Fractions 1.3.3Equivalent Fractions 1.3.4Constructing Fractions 1.3.5Ordering Fractions 1.3.6Recurring Decimal Notation 1.3.7Mixed Numbers & Improper Fractions

1.4

Numerical Operations (Fractions)

1.4.1Adding & Subtracting Fractions 1.4.2Add & Subtract Mixed Numbers & Improper Fractions 1.4.3Multiplying Fractions 1.4.4Multiplying Mixed Numbers 1.4.5Reciprocals 1.4.6Dividing Fractions 1.4.7Dividing Mixed Numbers

1.5

Roots & Powers

1.5.1Roots 1.5.2Integer Powers 1.5.3Estimating Powers & Roots 1.5.4Laws of Indicies (Multiplication)

1.6

Structure of Calculations

1.6.1Order of Operations (BIDMAS)

1.7

Numerical Skills

1.7.1Using a Calculator - Powers, Roots & Fractions

1.8

Factors & Multiples

1.8.1Divisibility Rules 1.8.2Finding Multiples 1.8.3Finding Factors 1.8.4Finding Prime Numbers

1.9

Systematic Listing

1.9.1Systematic Listing

1.10

Standard Form

1.10.1Reading Standard Form 1.10.2Converting to Standard Form (Positive Powers)1.10.3Converting to Standard Form (Negative Powers)1.10.4Converting Form Standard Form (Positive Powers)1.10.5Converting From Standard Form (Negative Powers)1.10.6Adding & Subtracting Standard Form 1.10.7Standard Form on a Calculator

1.11

Fractions, Decimals & Percentages

1.11.1Converting Fractions, Decimals & Percentages 1.11.2Numbers as Percentages 1.11.3Fractions of Amounts

1.12

Percentage Change

1.12.1Percentages of Amounts (Calculator)1.12.2Percentages of Amounts (No Calculator)1.12.3Percentage Change

1.13

Rounding & Estimation

1.13.1Rounding Integers 1.13.2Estimating Calculations 1.13.3Rounding Decimals 1.13.4Rounding With Significant Figures

1.14

Bounds & Accuracy

1.14.1Finding Error Intervals

2

Algebra

2.1

Algebraic Notation

2.1.1Function Machines 2.1.2Using Algebraic Notation

2.2

Substitution & Simplification

2.2.1Substituting into Expressions with Operations 2.2.2Substituting into Algebraic Expressions 2.2.3Substituting into Real-Life Expressions 2.2.4Simplifying Expressions by Collecting Like Terms

2.3

Brackets

2.3.1Expanding Single Brackets 2.3.2Expanding & Simplifying with Single Brackets 2.3.3Expanding Double Brackets 2.3.4Factorising Into One Bracket

2.4

Algebraic Fractions

2.4.1Operations with Algebraic Fractions

2.5

Rearranging

2.5.1Changing the Subject

2.6

Functions

2.6.1Finding the Input of a Function

2.7

Solving Linear Equations

2.7.1Solving Linear Equations (One Step)2.7.2Solving Linear Equations (Multi-Step)2.7.3Solving Linear Equations (Unknown Both Sides)2.7.4Solving Equations (Unknown in Denominator)2.7.5Forming & Solving Linear Equations

2.8

Inequalities

2.8.1Representing Inequalities on a Number Line 2.8.2Solving Linear Inequalities 2.8.3Linear Inequalities with Unknowns on Both Sides

2.9

Simultaneous Equations

2.9.1Solving Simultaneous Equations Graphically 2.9.2Solving Simultaneous Equations by Elimination

2.10

Sequences

2.10.1Term-to-Term Rules (Patterns)2.10.2Term-to-Term Rules (Numerical)2.10.3Substituting into a Given Rule 2.10.4Position-to-Term Rules 2.10.5Finding the Nth Term (Linear Sequences)2.10.6Simple Geometric Progressions

2.11

Coordinates

2.11.1Midpoints of Line Segments

2.12

Linear Graphs

2.12.1Equations of Straight Lines 2.12.2Finding Line Equation from Point & Gradient 2.12.3Finding Line Equations from Two Points 2.12.4Parallel Line Equations

2.13

Quadratic Graphs

2.13.1Interpreting Quadratics

3

Ratio, Proportion & Rates of Change

4

Geometry & Measures

4.1

Area & Perimeter

4.1.1Perimeter of Simple Shapes 4.1.2Perimeter of Compound Shapes 4.1.3Area of Triangles 4.1.4Area of Rectangles & Parallelograms 4.1.5Area of Trapezia 4.1.6Area of Compound Shapes 4.1.7Area of Compound Shapes with Triangles

4.2

Properties of Shapes

4.2.1Naming & Classifying Triangles 4.2.2Naming & Classifying Quadrilaterals 4.2.3Properties of Lines 4.2.4Shortest Distance from a Point to a Line 4.2.5Properties of 3D Shapes

4.3

Angles

4.3.1Classification of Angles 4.3.2Angles on a Line & Around a Point 4.3.3Combining Angle Facts in Triangles 4.3.4Angles on Parallel Lines 4.3.5Interior & Exterior Angles in Polygons

4.4

Trigonometry

4.4.1Pythagoras' Theorem 4.4.2Sides in Right-Angles Triangles 4.4.3Angles in Right-Angled Triangles

4.5

Similarity & Congruence

4.5.1Congruent Shapes 4.5.2Length Scale Factors in Similar Shapes

4.6

Circle Geometry

4.6.1Identifying Parts of a Circle 4.6.2Calculating Circumference 4.6.3Calculating Area of a Circle 4.6.4Calculating Arc Lengths 4.6.5Calculating Area of Sectors

4.7

3D Representations

4.7.1Nets of 3D Shapes

4.8

Surface Area

4.8.1Surface Area of Cubes & Cuboids 4.8.2Surface Area of Prisms 4.8.3Surface Area of Cylinders

4.9

Volume

4.9.1Volume of Prisms 4.9.2Volume of Cylinders

4.10

Transformations

4.10.1Translation using Vectors 4.10.2Rotations 4.10.3Enlargements & Positive Scale Factors

4.11

Scale Drawings

4.11.1Scale Drawings

4.12

Bearings

5

Probability

5.1

Single Events

5.1.1Writing Probabilities as Fractions 5.1.2Mutually Exclusive Events 5.1.3Expected Results

5.2

Combined Events

5.2.1Reading Venn Diagrams 5.2.2Venn Diagrams (Set Notation)5.2.3Independent & Mutually Exclusive Events

5.3

Experimental Probability

5.3.1Relative Frequency & Convergence

6

Statistics

6.1

Averages & Range

6.1.1Range 6.1.2Median 6.1.3Mode 6.1.4Mean 6.1.5Interpreting Two-Way Tables

6.2

Scatter Graphs

6.2.1Lines of Best Fit

6.3

Collecting & Presenting Data

6.3.1Types of Data

Unlock your full potential with Seneca Premium

Unlimited access to 10,000+ open-ended exam questions
Mini-mock exams based on your study history
Unlock 800+ premium courses & e-books

Get started with Seneca Premium

Converting Units of Area & Volume

Calculating Speed