Maths · Key Stage 3 Year 9
Year 9 Maths: Number
Compare standard form, write error intervals, handle compound percentage change, and judge whether an answer is reasonable.
About this topic
This course consolidates number work and turns it towards problems that do not announce their own method. It opens by comparing numbers in standard form and converting between fractions and decimals in both directions, because a mixed set of values cannot be ordered until everything is written the same way. Error intervals follow, bringing with them the idea the whole course rests on: a rounded value stands for a range rather than a single point. Percentages are applied to money, first as a single multiplier and then as compound change repeated over several years, on savings that rise and on a car that loses value. Rational and irrational numbers give a way of describing every value that can sit on a number line, alongside multi-step problems where a percentage may apply to only part of a total. Approximation comes next, together with what a calculator display can and cannot tell you, and how an estimate differs from an error interval. The last two lessons hand over unfamiliar situations, ask the learner to choose and justify a method, and then to check the answer and carry a range through it. Each lesson names the errors that cost marks and ends with a quiz. The course finishes with a final test and one project.
What you will learn
- Compare and order numbers written in standard form.
- Convert between fractions and decimals in both directions.
- Explain why a recurring decimal is not the same as its rounded version.
- Find the lower and upper bounds of a rounded value.
- Write an error interval using the correct inequality sign at each end.
- Apply a percentage increase or decrease to a money amount.
- Calculate compound percentage change on a rising and on a falling value.
- Explain why repeated percentage changes never add together.
- Order fractions, decimals, negatives and roots on one number line.
- Identify rational and irrational numbers and explain the difference.
- Solve multi-step problems and decide which part a percentage applies to.
- Estimate an answer by rounding to one significant figure.
- Interpret a calculator display and say what it cannot show.
- Choose an efficient method for an unfamiliar problem and justify the choice.
- Compare items of different sizes using a unit price.
- Check whether an answer is reasonable and carry an error interval through a calculation.
Vocabulary
Words to know
You will meet these words in this topic. Press the speaker to hear one. Inside a lesson you can tap any word to hear it and see what it means.
Words this topic teaches
- multiply
Find the result when a number is added to itself a certain number of times.
- decimal
A number that uses a decimal point to show values smaller than one.
- column
A vertical position indicating a digit's value in a number.
- recurring
A part repeats forever without ending.
- recurs
It repeats in a pattern that does not stop.
- negative
A number smaller than zero, written with a minus sign.
- interval
The distance between two numbers, measured by counting steps.
- bound
The smallest or largest value possible.
- depreciation
The drop in value of something over time.
- route
A method or path for doing something.
- percent
A way to show a number as parts out of 100.
- cube
A three-dimensional shape with six equal squares as sides.
- fraction
A number written as one value above another, showing a part of a whole or a division. The number underneath gives how many equal parts one whole has been split into, and the number above counts how many of those parts are being described.
- quarter
A share that is one of four equal parts of a whole.
- root
A value that, when multiplied by itself a certain number of times, equals another number.
- ratio
How one amount compares to another, shown by two numbers.
- calculation
Working something out with numbers.
- significant
It means important in a number.
- operation
A calculation such as addition, subtraction, multiplication or division.
- groups
A set where all items belong together.
- practical
Makes sense for real tasks or situations.
- contract
A formal agreement to pay for something, like a phone, for a set time.
- rank
To put in order by how good or big.
- unit
A single part or amount, often meaning one in maths.
- compound
Something made by joining two or more things.
Other words in these lessons
- order
Arrange numbers according to size or value in sequence.
- routine
A usual set of actions taken in the same order each time.
- match
Make sure two things are the same.
- mix
To combine things so you change their order.
- detail
A part of something that gives extra or more exact information.
- direction
The way something moves or changes.
- calculator
An electronic device used to do mathematical calculations.
- include
To add something as a part of a group or set.
- transaction
An event or process in which money is exchanged, such as buying or selling something.
- mark
Draw a sign or spot to show something.
- separate
Each one is apart, not together.
- repeat
To do the same thing again.
- shrunk
Got smaller in size or value.
- exact
Completely correct or without any mistake.
- pattern
A set of things that repeat in an order.
- predict
Say what is likely to happen next.
- charge
An added amount of money you must pay for a service.
- total
The whole amount after adding everything up.
- difference
The way in which things are not the same.
- discount
A cut in price by taking some money off.
- fix
Make something correct.
- apart
Separated or not touching each other.
- likely
There is a good chance it will happen.
- occur
It happens or takes place.
- behave
To act in a certain way.
- carry
Continue or move forward with something.
- save
Prevent a loss or mistake by acting early.
- settle
To bring something to an end by making a decision.
- obvious
Easily noticed, understood or recognised. Not hidden.
- noticeable
Clear enough to be seen or recognised.
- amount
A quantity or total of something.
- value
The amount represented by a digit depending on its position.
- label
A word or sign that shows what something means
- exceed
Be greater than a given value or limit.
- share
To have a part in common with someone or something.
- undo
To reverse an action and go back to before.
- clause
A part of a sentence that contains a subject and predicate
- record
To write or keep a note of information.
- circle
A round shape or a line that goes round.
Lessons
- 1How Do We Compare Standard Form and Work Interchangeably with Fractions and Decimals?Free to try
- 2How Do We Use Inequality Notation for Rounding Errors and Apply Percentages to Money? Locked
- 3How Do We Solve Compound Percentage Change and Order Real Numbers on a Number Line? Locked
- 4How Do We Recognise Rational and Irrational Numbers and Solve Multi-Step Problems? Locked
- 5How Do We Use Approximation and Interpret Calculator Displays? Locked
- 6How Do We Apply Number Skills to Unfamiliar Contexts and Justify the Best Method? Locked
- 7How Do We Check Reasonableness and Explain a Non-Routine Solution? Locked