# Year 9 Maths: Laying Down The Foundations For The GCSE Years

**By Year 9 maths, our children are well and truly teenagers! Many struggle to motivate themselves to get out of bed in the morning let alone concentrate on their 9am maths lesson. With hormones running through their bodies, there always seems to be one** **drama or another for them to worry about.**

Whilst Year 9 can be difficult for students, parents and teachers to navigate, it is a pleasure to see that our children are growing up. They are able to engage in more meaningful conversations and when they are concentrating on their work, we can challenge them to think more deeply and critically.

The spread of abilities is vast by Year 9 with the higher achievers able to tackle some quite complex topics. Keeping the level of challenge appropriate to the students, and the work relevant, will help attract their attention and keep them focussed.

- What will students learn in Year 9 maths?
- Applied and problem solving questions
- Year 9 maths example questions for mathematical thinking
- What students are likely to struggle with in Year 9 maths
- What students can do to help themselves with Year 9 maths
- How adults can support students with Year 9 maths
- Preparing for GCSE maths

### What will students learn in Year 9 maths?

The study of maths can be broken down into a number of sub-categories. Within the National Curriculum, these are:

Number, Algebra, Ratio, proportion and rates of change, Geometry and measures, Probability and Statistics

In year 9 students will build on the topics that they have covered in Years 7 and 8. These include:

- Number: fractions, decimals, percentages, place value, negative numbers, factors and multiples, rounding, order of operations
- Algebra: manipulating algebraic expressions, expanding and factorising, solving linear equations, using formulae, sequences, straight line graphs, inequalities
- Ratio, proportion and rates of change: ratio, direct proportion, conversion rates
- Geometry and measures: area and perimeter, surface area and volume of 3D shapes, angles, parallel lines, properties of polygons, transformations, speed/distance/time, construction and loci, bearings, congruence
- Probability: theoretical probability, experimental probability, sample space diagrams, venn diagrams
- Statistics: data collection, pie charts, scatter diagrams, averages

**See also:** Year 7 Maths & Year 8 Maths

15 Algebra Questions and Practice Problems (KS3 & KS4) Worksheet

Download a free, printable algebra worksheet for KS3 & KS4 containing practice questions and word problems.

Year 9 maths students will also be introduced to a number of new topics. Let’s have a look at some of the topics that may be introduced for the first time in Year 9:

**Number**:- Indices
- Standard form
- Significant figures

Example questions:

1.Write down the value of 9^{1/2}

2.Write the number 74000 in standard form

3.Round the number 3402 to 2 significant figures

**Ratio, proportion and rates of change:**- Direct and inverse proportion

Example questions:

1.a is directly proportional to b. When a=16, b=4. Find the value of a when

b=9

**Algebra:**- Expanding quadratics
- Plotting quadratic graphs
- y=mx+c

Example questions:

1.Expand and simplify (x+3)(x-6)

2.Plot the graph y=x^{2}+5x-14

3.Write down the equation of a line parallel to y=3x-4

**Geometry and measures:**- Volume and surface area of cylinders
- Congruence
- Interior/exterior angle
- Pythagoras’ Theorem
- Trigonometry

Example questions:

1.Find the volume of this cylinder

2.Calculate the size of one exterior angle of a regular pentagon

3. Calculate the length of the hypotenuse

**Probability:**- Probability of combined events

Example question:

1.What is the probability of rolling 2 sixes when rolling 2 dice?

**Statistics:**- Averages from a frequency table
- Correlation

Example questions:

1.Estimate the mean of this data:

Foot size Frequency

4 3

5 8

6 4

### Applied and problem solving questions

As students progress through Key Stage 3, one aim is that they develop their skills in ‘working mathematically’. This means that they will:

- Develop fluency in the number system, the language of algebra and mathematical terminology.
- Practise their mathematical reasoning; making links between numerical, algebraic and graphical representations, deducing mathematical relationships and constructing mathematical proofs or counter examples.
- Develop their problem solving skills and begin to model problems mathematically.

These skills are particularly important, both as students progress through their mathematical studies as well as throughout their lives. Problem solving questions and word problems feature widely in GCSE papers as a way of testing students’ understanding of maths topics and their ability to work mathematically.

Reasoning and deduction, along with the ability to form arguments and solve problems are skills that will benefit our children for the whole of their lifetime. Students should be given the opportunity to develop these skills throughout different areas of the Year 9 maths curriculum. One way of doing this is to get them regularly thinking about applied questions and solving problems.

### Year 9 maths example questions for mathematical thinking

- Ben earns £1800 per month. He spends 30% of his money on rent. He spends ¼ of his total money on bills. The rest of his money he spends and saves in the ratio 4:5. How much money does Ben save each month?

- The area of this shape is 40cm
^{2}. Calculate the value of x.

- A drinks company wants to produce a new can size. The volume of the can needs to be at least 400cm
^{3}. The drinks company wants to minimise the amount of packaging they use. Which shape should the company produce, A or B? You must show how you decide. - Can you design a shape that uses less packing but still has a volume of at least 400cm
^{3}?

- I have five cards, all showing different numbers. The mean of the numbers is 5, the median is 6 and the range is 8. What could the numbers on my cards be?

**Read more:** Maths problems for KS3

### What students are likely to struggle with in Year 9 maths

#### Motivation

By Year 9, the novelty of secondary school has well and truly worn off. Students haven’t started their GCSEs yet and many are a little lacking in motivation!

We can help to keep them motivated by providing them with interesting and relevant tasks, recognising their effort and achievements and supporting them to feel confident and secure within the subject. It is much easier to feel motivated when you are enjoying a subject and feel confident with it.

#### Definitions and technical vocabulary

The amount of technical vocabulary that students are expected to know and use increases throughout KS3. Some of the terms they are expected to know by Year 9 maths are: prime, factor, multiple, integer, mixed number, quadrilateral, denominator, numerator, significant figure, factorise, congruent, similar, Pythagoras theorem, hypotenuse, SOHCAHTOA, correlation, mean, median, mode and range.

#### Problem solving and reasoning

As we have discussed, problem solving is an important skill for students to develop, though some may find it tricky.

#### Making links

Maths is often seen as a number of separate topics. However, this is not the case. Students often struggle to use the maths they know when they see it in an unfamiliar context, for example algebra within shape or probability work.

### What students can do to help themselves with Year 9 maths

#### Complete homework

When learning maths, nothing is more important than practice. Students will be given the opportunity to practise maths at school but, particularly as they get older and the concepts that they are learning become more difficult, there is a benefit to sitting down independently and focussing on maths at home.

Away from the distraction of classmates and the help of the teacher, students have the opportunity to really focus on a topic and secure their understanding. Extra practice will also help them recall facts more easily at a later stage, as well as identifying any areas where they might require extra support.

#### Use recommended books or websites for help

There is a wealth of information and help available to our children, particularly online. There are some brilliant websites which provide students with detailed explanations and examples as well as practice materials to help them with Year 9 maths. Check out the GCSE maths resources section on the Third Space Learning site for step by step lessons and maths worksheets designed to develop students’ skill and understanding.

For those in need of additional support Third Space Learning also offers online 1-to-1 tuition with a professional tutor, tailored to the needs of the individual student.

Being able to work independently is an important skill for students to develop. It will prove useful when they are preparing for exams and are starting their maths revision.

#### Ask for help if necessary

Students, especially those in Year 9, often struggle to ask for help. However, talking things through with a teacher or an adult is one of the most effective ways of overcoming a problem or area of difficulty.

### How adults can support students with Year 9 maths

#### Be positive about learning and about maths

Our children are always watching us and taking in everything that we say and do. By having a positive attitude towards learning and maths, we are helping to pass that on to our children. If they feel positively about it, they are more likely to feel motivated and confident.

In the maths classroom, making maths tasks interesting and relevant can go a long way to keeping a positive attitude among students.

#### Talk about maths

Children don’t see maths as something that is used in real life when in fact it is used everywhere! Point out when you are using maths – if you are cooking, budgeting or measuring something. You could have discussions with your child about what skills might be involved in designing a building or planning a trip to space!

In the maths classroom, allowing students to see real life applications of the maths they are using can encourage good discussions. Functional skills tasks, which focus on real life scenarios, can also be engaging for students whilst allowing them to apply a variety of skills.

#### Familiarise yourself with the resources available for your children

If your child’s school recommends certain resources or websites, make yourself familiar with them. That way you can point your child in the right direction if they are struggling with a topic. You could even work through it together.

#### Encourage good study habits

When students are in Year 9, the work that they are doing is forming a basis for their GCSE years. Now is a good time to make sure that their study habits are appropriate for learning. Good habits to get into can include:

- Having a set time and space for homework
- Removing distractions such as technology
- Having the right equipment available
- Having a suitable routine at home to promote wellbeing and readiness for learning

By setting regular homework, based directly on work that has been completed in class, teachers can help encourage students to regularly study independently at home. It can also help to have a set routine in the classroom so that students know what to expect during Year 9 maths lessons.

### Preparing for GCSE maths

As they enter Year 10, students usually begin their GCSE course. To help ensure students are ready for this you could:

- Provide a KS3 revision book to make sure they are confident with the key topics. One that includes questions to practise would be the most effective. An alternative to this would be a list of topics to revise from an online site containing explanations and practice questions.
- Ensure they have the correct equipment such as a protractor, compass and scientific calculator

**Is Year 9 maths hard?**

Maths is taught in such a way that topics are built on year by year so if you were happy with maths in Years 7 and 8 then there is no reason that you would find Year 9 maths any more difficult.

If there are particular areas that you enjoyed in Years 7 and 8, you could challenge yourself to excel at these in Year 9 maths.

If there are topics that you found more difficult in Year 7 or 8, you might want to spend some time working on these before you cover them in Year 9. Have a look through our library of GCSE lessons (many of which are also appropriate to Year 9 students) to see if there is a lesson that can help you.

**How can I be good at maths KS3?**

Everyone has different strengths. Some students are naturally very good at maths and find it easy. Others have to work a bit harder. The great thing is that there are plenty of resources available to help you. Find out what resources your school has available – they might have books or subscriptions to sites that can help you.

Ask teachers for a list of topics to look over. Once you have these, it is up to you to put in the required work until you feel confident. The best way to improve at maths is to practise, practise, practise!

**Do you have students who need extra support in maths?**

Every week Third Space Learning’s maths specialist tutors support thousands of students across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress.

Since 2013 we’ve helped over 130,000 primary and secondary students become more confident, able mathematicians. Find out more about our GCSE Maths tuition or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Our online tuition for maths programme provides every child with their own professional one to one maths tutor