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Year 9 Maths Worksheets

Maths Worksheets / Year 9 Maths Worksheets

A superb range of maths worksheets for secondary school children in year 9 (aged 13-14). Cazoom Maths is a trusted provider of maths worksheets for secondary school children. Our mathematics resources are perfect for use in the classroom or for additional home learning. Our maths worksheets are used by over 50,000 teachers, parents and schools around the world and we are a Times Educational Supplement recommended resource for helping key stage 3 and key stage 4 students learn mathematics.

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Outstanding Year 9 Maths Worksheets

• Separate answers are included to make marking easy and quick.
• Over 350 pages of the highest quality year 9 maths worksheets. Each worksheet is differentiated, including a progressive level of difficulty as the worksheet continues.
• Single user licence for parents or teachers. Separate school licences are also available.
• Single digital pdf download, with worksheets organised into high level chapters of Algebra, Statistics, Number and Geometry, and further by subtopics. See below for the extensive range of sheets included.

List of Topics

See below the list of topics covered. All our maths worksheets can be accessed here .

• Expanding Brackets
• Factorising
• Inequalities
• Linear Functions
• Real Life Graphs
• Rearranging Equations
• Simplification
• Solving Equations
• Substitution
• Calculator Methods
• Fractions Decimals Percentages
• Mental Methods
• Negative Numbers
• Percentages
• Place Value
• Types of Number
• Written Methods
• Area and Perimeter
• Bearings Scale and Loci
• Compound Measures
• Constructions
• Coordinates
• Lines and Angles
• Similarity and Congruence
• Transformations
• Volume and Surface Area
• Histograms and Frequency Polygons
• Mean Median Mode
• Pie Charts and Bar Charts
• Probability
• Scatter Graphs
• Stem-and-Leaf Diagrams
• Two-Way Tables and Pictograms

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• Year 9 Maths Worksheets

Year 9 maths worksheets – 72 free, editable printables

Editable Word docs

Give out these Year 9 maths worksheets every week for homework or integrate them into your classroom sessions to reinforce essential maths concepts.

The collection comprises six booklets, with two options for each academic term.

The first term consists of 14 worksheets, followed by ten in the second term, and 12 in the third term. Each worksheet comprises 20 questions, providing a comprehensive set of materials for 36 weeks of homework.

In total, there are over 1,000 questions available for students to have a go at!

Other year groups

Check out similar worksheet packs for Years  7 , 8 and GCSE maths . You can also download 100+ problem-solving questions in our  KS3 maths worksheets pack  from White Rose Maths.

Year 9 maths worksheets

Each worksheet covers the following 20 topics:

Term 1 – scheme 1

• Equivalent fractions
• Add & subtract fractions
• Multiply & divide fractions
• Parts of a circle
• Circumference/perimeter & circles
• Area & circles
• Writing expressions
• Simplifying
• Substituting
• Order of operations
• Factorising
• Linear equations
• Times tables

Term 2 – scheme 1

• Ratio & proportion
• Expressions and formulae
• Expanding and factorising
• Solving equations
• Averages from raw data
• Frequency tables
• Translations
• Reflections & rotations
• Enlargements
• Percentage calculations
• Percentage change
• Fractions, decimals, percentages, changes
• Coordinates
• Straight line graphs
• Inequalities

Term 3 – scheme 1

• Fractions, ratio & proportion
• Expressions & equations
• Transformations
• Percentages
• Graphs & inequalities
• Probability
• Relative frequency
• Pythagoras’ theorem
• Data representations
• Scatter graphs & stem & leaf
• Calculations
• Rounding & estimation
• Area & perimeter
• Surface area & volume

Term 1 – scheme 2

• nth term linear
• nth term quadratic
• Parts of circles
• Constructions & loci
• Expanding single brackets
• Expanding double brackets
• Factorising single brackets
• Factorising double brackets
• Rearranging formulae – variable once
• Rearranging formulae – variable more than once
• Trial and improvement

Term 2 – scheme 2

• Ratio and proportion
• Expanding brackets
• Rearranging formulae
• Cumulative frequency & boxplots
• Translation
• Reflection & rotation
• Enlargement
• Congruence & similarity
• Reversing percentage change
• Simultaneous equations

Term 3 – scheme 2

• Expressions & formulae
• Accuracy & estimation
• Standard form
• Scatter graphs & frequency polygons
• Volume & surface area
• Dimension & units

Peter Mattock is an assistant head and author of  Visible Maths .   Contact Peter   to request answers for these worksheets.

Similar resources

• Maths games GCSE – Million Pound Drop & other games
• Factorising quadratics worksheet – 13 exam-style questions
• Factorising quadratic expressions – Unpick what’s going on
• Factorising quadratics – Construct your own quadratic equations
• Arithmetic sequence worksheet – Free KS3/4 maths resource

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Part 1: Year 9 Algebraic Techniques and Equations | Free Worksheet

Guide Chapters

• 1 Algebraic techniques
• 2. Inequalities
• 5. Surface area
• 7. Trigonometry
• 8. Simultaneous equations

Year 9 Algebraic Techniques and Equations

Mastering Algebraic Techniques in Year 9 is crucial to successfully navigate through senior mathematics and secure your fundamentals. Here are some tips that you must know before moving on to Year 10.

NSW Syllabus Outcome

This article deals with the following NESA Syllabus Outcomes:

In this article we’ll discuss:

• Optimising BODMAS Equations (with fractions!)

Expanding Binomial Products

• Factorising Quadratics to Binomial Products
• Tackling Word Equations

Assumed knowledge

Students should understand basic equation solving and algebra. This guide aims to enrich these skills with techniques and advice from our knowledgeable Matrix Mathematics Teachers and Tutors.

Solving Algebraic Equations (BODMAS)

The key to solving algebraic equations is a matter of following a few simple rules. These rules are not necessarily set in stone, but they can streamline the process of answering questions.

As you already know, BODMAS is the acronym for the order used to solve equations – Bracket, Of, Division, Multiplication, Addition and Subtraction.

1. Isolate the variable

This should be the end goal of any given question, but keeping it in mind can help you get there. To isolate a variable, make one variable the subject while moving all other variables to the other side of the equation .

For example, if the equation was:

\(10x + 2=22\)

We identify that the pronumeral \(x\) is on the left-hand side (LHS) of the equation, so we must move everything else to the other side. This starts by subtracting the 2 to the right-hand side (RHS).

So we have:

Now the \(x\) term is isolated on the LHS, and the final step is to divide both sides by 10.

2. Remove any fractions

If there are fractions in the equation, they should be “undone”. This can be achieved by multiplying the entire equation by the lowest common multiple (LCM) of all the denominators.

For example:

\(\frac{k}{4} -\frac{k}{3}= 7\)

The denominators 4 and 3 would form the LCM of 12! So now we must multiply EVERY term in the equation by 12.

\begin{align*} 12 \Big{(} \frac{k}{4} \Big{)}-12 \Big{(} \frac{k}{3} \Big{)}=12(7) \\ 3k-4k=84 \\ -k=84 \\ k=-84 \end{align*}

3. Expand any brackets

This will be explained in proper detail in the “Expanding Binomial Products” section of this guide. However, there are some cases where a faster method can be used: Rule 1!

\(6(3x+1)= 12\)

If we were to expand the brackets we would have to solve the following:

\(18x+6=12\)

But instead of expanding the brackets, we can use Rule 1 and try to isolate \(x\) by dividing 6 on both sides.

Now this is a much simpler equation to solve.

4. Collect all the variables

Questions with multiple instances of the same variable require you to collect the variables onto one side of the equation . Again, we need to keep Rule 1 in mind, as we must isolate the variable once we have collected it.

\(3d – 8 = 5d + 4\)

Notice there are instances of variable \(d\) on both sides of the equation. We want collect them all onto the LHS. So, we have to subtract \(5d\) to both sides:

\(-2d – 8 = 4\)

Again, we should apply Rule 1 and isolate the variable:

\(-2d = 12\) \(d = -6\)

Once you get comfortable with these type of questions, you can solve them faster by “moving terms around” through inverse operations.

Binomials are simply two terms which add or subtract from each other, like:

\(x-2\) or \(a+b\)

When these binomials are multiplied by each other, we have a binomial product. This is not as easy as using the multiplication table!

Luckily we have an important arithmetic law known as the distributive law which shows us how to expand expressions with brackets.

Consider the example below:

In this example, “ a ” is being distributed to each term within the second bracket. “ b ” is similarly distributed afterwards.

Consider this example

Common Mistakes

• Forgetting to multiply across the negative
• Forgetting to simplify the expression after expansion
• Not changing the sign when two negatives are multiplied

Factorising Quadratics

Similarly, we can go backwards from an expanded quadratic like \(x^2-4x+3\) to a binomial product by factorising. Being able to do this confidently will be important before moving onto Year 10.

Here is an example:

\(x^{2}+5x+6=(x+3)(x+2)\)

You can verify that this is true by expanding the RHS.

The factorisation process can be explained by examining the constant terms on the RHS: 3 and 2. Now,

• When these constants are multiplied, the result is 6
• When they are added, the result is 5

This matches with what we see on the LHS.

Here is another example:

\(x^{2}+x-12=(x+4)(x-3)\)

The constant terms from the brackets are 4 and -3. Now,

• \(4×(-3)=-12 \) and \(-12\) is the constant term on the LHS
• \(4+(-3)= 1 \) and 1 is the coefficient of x on the LHS

Thus, to factorise any quadratic in the form \(x^{2}+bx+c\):

Find two numbers whose product equals \(c\), and whose sum equals \(b\).

This can be tracked by using what is known as the cross method , which is demonstrated below.

Cross method

Factorise \(x^{2}+5x+4\)

\(x^{2}+5x+4\)

Explanation

Find the two factors of \(2x\) and write them as shown.

Next, find two numbers that multiply to give \(4\).

Next, multiply across the diagonals to get the terms \(2x\) and \(2x\).

Then add these two terms:

\(2x + 2x = 4x\)

Since this does not match with \(5x\) the the two numbers are not correct.

Try two different numbers.

Therefore \( x^{2}+5x+4 = (x+4) (x+1)\)

Using the cross method again,

Therefore, these two numbers are the ones you want, and now you’re ready to factorise.

To factorise, read the cross horizontally:

\( \color{Orange}{x \rightarrow 4 }\) \( \color{DarkGreen}{x \rightarrow 1} \)

Reading off the cross,

• Not applying simple factorisations first e.g. \(3x^2-3x-36=3(x^2-x-12)\) \(=3(x-4)(x+3)\)
• Forgetting to factorise out the negative from an equation (when applicable).

Solving Problems Using Algebra

In the real world, equations can be applied to solve practical problems. These problems won’t be given simply as “find \(x\)”, but instead we have to be able to interpret and solve worded problems.

Common types of word problems can include number, measurement, money, or age problems.

To solve these problems, we must convert the problem into equations that can be solved algebraically:

• Read the problem carefully and underline the key information.
• Let x be the unknown quantity. Usually we choose the value that we are finding.
• Translate the word problem into an algebraic equation.
• Solve the equation.
• Answer the question in words.

Example: Number Problem

The sum of two numbers is 24. When the larger number is subtracted from 4 times the smaller number, the result is 16. Find the two numbers.

First, we must define our unknown. Since we are trying to find the two numbers, let us make \( \color{DarkGreen}{x}\) the smaller number.

From the question, we also know that the sum of the two numbers is 24.

Hence, the larger number must be \(\color{orange}{24-x}\).

Translating “When the larger number is subtracted from 4 times the smaller number, the result is 16” into mathematical form, we get:

\(4×\color{DarkGreen}{smaller \ number}-\color{Orange}{larger \ number}=16\)

Now we can substitute the unknown values that we just defined to form an algebraic equation:

\(4×\color{DarkGreen}{x}-\color{orange}{(24-x)}=16\)

At this point, we can simply solve for x.

\(4x-24+x=16\) \(5x=40\) \(x=8\)

Using our definition of \(x\), we know that the smaller number is 8. Therefore, the larger number must be \(24-8=16\).

Answering the original question in words:

The two numbers are 8 and 16 .

Example: Measurement Problem

The length of a rectangular house block is 15 metres greater than twice its street width. A fence around the perimeter of the block, except for the side facing the street is 80 metres long. Find the dimensions of the block.

Let us make the width \(\color{DarkGreen}{w}\) metres. Since the length of the block is 15 metres greater than twice the width, the length can be written as \(\color{Orange}{2w+15}\) metres.

Now that we have defined our unknowns, we can draw a diagram to illustrate the question:

From the question, we know that the combined length of three fenced sides is 80 metres. This can be translated mathematically as:

\(2×\color{Orange}{length}+\color{DarkGreen}{width}=80\)

Substituting in the values we have defined, we get an algebraic equation:

\(2×\color{Orange}{(2w+15)}+\color{DarkGreen}{w}=80\)

At this point, we can solve for w.

\(4w+30+w=80\) \(5w=50\) \(w=10\)

Hence the width of the block is 10 metres. Therefore, the length must be \(2×10+15=35\) metres.

Finally, we must answer the original question:

The block is 10 metres wide and 35 metres long .

Example: Age Problem

3 years ago, John was twice Ryan’s age. Now, the sum of their ages is 36.

How old are they now?

In age problems, the best thing to do is to draw up a table, with columns and rows representing each person and time period give in the question.

We will let one of the cells be x, in this case it will be John’s age 3 years ago.

We can now fill out the rest of the table, in terms of \(x\). For example, Ryan’s age 3 years ago will be \(2x\), as given by the question. Afterwards, we can fill in the “Now” row, just by adding 3 to each expression (since it is 3 years later). So our table looks like this.

Finally, we can use the final part of the question to create an equation to solve. We know the sum of their ages now is 36, so we have:

\begin{align*} x + 3 + 2x + 3 = & \ 36 \\ 3x = & \ 30 \\ x =  & \ 10 \end{align*}

Now we have the value for x, so we can find the value for each of their ages. John’s present age is \(x+3\), so his age is now 13. Similarly, Ryan’s age is \(2x+3\), so his age now is 23.

Final answer:

John is 13 and Ryan is 23

Common mistakes

Common mistakes students make in problem-solving questions are:

• Forgetting to use brackets when substituting in the unknown values
• Forgetting to answer the original question in words.

Checkpoint Questions

1. Expand and simplify the following

\(3(2x+1)-1\)

2. Factorise the expression below

\(x^{2}-5x+6\)

3. Expand and simplify the following

\((2x-1)(x+3)\)

4. The area of a rectangle is \(10cm^{2}\). What are the dimensions of the rectangle if the length is 3cm longer than the width? (Note: Let \(w\) be the width of the rectangle)

5.Factorise the following

\(6x^{2}-12x+6\)

6. Expand and simplify the following

\(3((x-2)^{2}-1)÷(x-1)\)

7. Sam’s brother is 3 years older than twice his sister’s age.  If the product of Sam’s brother’s and sister’s ages is 65. What is Sam’s brother’s age?

8. Expand the following then factorise.

\((x+x^{-1} )(x+3)-\frac{3}{x}+1\)

9. 4 years ago, Andy’s age was 5 less than twice Jessica’s. In 2 years from now, the sum of their ages will be 25. How old are they currently?

10. Given that \(c=\frac{a}{b}\), prove that:

\(\frac{a}{(a+b)}+\frac{a}{(b-a)}=\frac{2c}{(1-c^2 )}\)

\(6x+3-1=6x+2\)

2. We need to find to numbers that multiply to be 6 and sum to -5. From cross method, we see the numbers are -2 and -3. Hence the factorised form is

\((x-2)(x-3)\)

\((2x-1)(x+3)=2x^{2}+(2x)(3)-x-3\) \(=2x^{2}+5x-3\)

4. Note the length will be \(w+3\). The area is hence \(w(w+3)\). From the question:

\(w(w+3)=10\) \(w^{2}+3w-10=0\) \((w-2)(w+5)=0\) \(w=2\) or \(w=-5\) Since \(w>0\), \(w=2\) only. So the dimensions of the rectangle is \(w=2\) and \(l=5\)

5. Using the cross method,

\(6x^{2}-12x+6=6(x^{2}-2x+1)\)

Hence the solution is \(6(x-1)^{2}\)

6. Converting the division symbol into a fraction and expanding the perfect square we get

\(\frac{3((x^{2}-4x+4)-1)}{(x-1)}\) \(=\frac{3(x^2-4x+3)}{(x-1)}\) \(=\frac{3(x-3)(x-1)}{(x-1)}\) \(=3(x-3)\)

By cancelling \(x-1\).

7. Let Sam’s sister’s age be \(s\), so then Sam’s brother’s age is \(2s+3\). Since the product of their ages is 65, this must mean:

\(s(2s+3)=65 \) \(2s^{2}+3s-65=0 \) \((2s+13)(s-5)=0 \) \(s=-\frac{13}{2} \  \text{or} \ s=5\)

Since \(s\geq0\) (ages are positive), \(s=5\).

8. Remember from index laws, \(x^{-1}=\frac{1}{x}\)

\begin{align*} (x+x^{-1} )(x+3)-\frac{3}{x}+1 \\ =x^{2}+3x+\frac{x}{x}+\frac{3}{x}-\frac{3}{x}+1 \\ =x^{2}+3x+1+1 \\ =x^{2}+3x+2 \\ =(x+2)(x+1) \\ \end{align*}

9. By letting Jessica’s age 4 years ago be \(x\), we can work out that Andy’s age was \(2x-5\) then. We proceed to add 4 and 6 to get their ages now and 2 years later respectively.

We are told that the sum of their ages 2 years later is 25. So,

\(2x+1+x+6=25\) \(3x+7=25\) \(x=6\)

Therefore their current ages (now) is obtained by substituting \(x=6\).

Andy is 11 and Jessica is 10

\begin{align*} LHS=\frac{a}{a+b}+\frac{a}{b-a} \\ =\frac{(a(b-a)+a(a+b))}{b^{2}-a^{2}} \\ =\frac{ab-a^{2}+a^{2}+ab}{b^{2}-a^{2}} \\ =\frac{2ab}{b^{2}-a^{2}}                             (*) \\ \end{align*}

Recall \(c=\frac{a}{b}\), so \(a=bc\)

\begin{align*} =\frac{2(bc)b}{b^{2}-(bc)^{2}} \\ =\frac{2b^{2} c}{b^{2}-b^{2} c^{2}} \\ =\frac{2c}{1-c^{2}} \\ \end{align*} (Note you can also divide top and bottom of (*) by \(b^{2}\) to get the answer immediately however this is slightly unnatural)

Additional Challenging Examples (From the Year 9 Maths MAX Series)

Need more practice questions?

Be more prepared for your next ‘Algebraic Techniques’ exam with Year 9 Max Series Exam Preparation Book.

Part 2: Inequalities

© Matrix Education and www.matrix.edu.au, 2023. Unauthorised use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Matrix Education and www.matrix.edu.au with appropriate and specific direction to the original content.

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Grade 9 Algebra Word Problems

Related Pages Grade 8 Algebra Word Problems Algebra Word Problems Solving Equations More Algebra Lessons

These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions. It includes various examples and solutions for algebra word problems that you will commonly encounter in 9th grade.

Age Word Problems

Age Problems with two unknowns or variables

Example: Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?

Solution: Let x represent Spenser’s age Therefore, Taylor’s age is 5x x + 5x = 18 6x = 18 x = 3 Therefore, Spenser is 3 years old and Taylor is 15 years old.

Grade 9 Algebra Word Problems - Age

Example 1: A mother is three times as old as her daughter. Six years ago, the mother’s age was six tines that of her daughter. How old are they now?

Solution: Let x represent the daughter’s age. Therefore, 3x is the mother’s age. 6(x - 6) = 3x - 6 6x - 6 = 3x - 6 3x = 30 x = 10 Therefore, the daughter’s is 10 years old and the mother is 30 years old.

Example 2: A father is now three times as old as his son. Eight years ago, the father was five times as old as his son. How old are they now?

Rate, Distance, Time Word Problems

Grade 9 Algebra Word Problems - Rate, Distance, Time

Example: A bus leaves the terminal and averages 40 km/hr. One hour late, a second bus leaves the same terminal and averages 50 km/hr. In how many hours will the second bus overtake the first?

Grade 9 Rate, Distance, Time Word Problems

Example 1: One motorist travels 5 km.hr faster than another. They leave from the same place and travel in opposite directions. What is the rate of each if they are 195 km apart after 3 hours?

Example 2: A pilot flew from airport A to airport B at a rate of 100 km/hr and flew back from airport B to airport A at 120 km/hr. The total time it took was 11 hours. How far is it from airport A to airport B?

Coin Word Problems

Grade 9 Algebra Word Problems - Coins

Example: A coin collection amounting to $25 consists of nickels and dimes. There are 3 times as many nickels and dimes. There are 3 times as many nickels as dimes. How many coins of each kind are there?

Solution: Let x = number of dimes 3x = number of nickels 10x + 5(3x) = 2500 25x = 2500 x = 100 Therefore, there are 100 dimes and 300 nickels.

Grade 9 Coin Algebra Word Problems

Example: Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of each kind does he have?

Coin Algebra Word Problems - Grade 9

Example: Bob has in his pocket a number of pennies, 5 times as many nickels as pennies and 5 more quarters than pennies. The coins amount to $2.27. Find the number of each kind of coin.

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Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

• Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
• Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
• Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
• Calculate : Use your strategy to solve the problem.
• Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

Most Popular Math Word Problems this Week

Arithmetic Word Problems

• Addition Word Problems One-Step Addition Word Problems Using Single-Digit Numbers One-Step Addition Word Problems Using Two-Digit Numbers
• Subtraction Word Problems Subtraction Facts Word Problems With Differences from 5 to 12
• Multiplication Word Problems One-Step Multiplication Word Problems up to 10 × 10
• Division Word Problems Division Facts Word Problems with Quotients from 5 to 12
• Multi-Step Word Problems Easy Multi-Step Word Problems

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Year 9 Problem Solving Maths

Showing top 8 worksheets in the category - Year 9 Problem Solving Maths .

Some of the worksheets displayed are Money and financial mathematics year 9, Year 9 mathematics, Patterns and algebra year 9, Year 9 foundation maths checklist, L6 solving linear equations c, Word problem practice workbook, Puzzles and problems for year 1 and year 2, Edshop upper primary maths work up 09 16.

Once you find your worksheet, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. Money and financial mathematics: Year 9

2. year 9 mathematics, 3. patterns and algebra: year 9, 4. year 9 foundation maths checklist, 5. l6 solving linear equations (c), 6. word problem practice workbook, 7. puzzles and problems for year 1 and year 2, 8. edshop upper-primary maths worksheet up 09 16.

The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.

This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.

The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.

These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons.  When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here , then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.

Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.

@TessMaths has written some great stuff for BBC Bitesize.

There are some intersting though-provoking problems at Open Middle.

I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.

MathsBot  by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.

I may be a little biased because I love Edexcel, but these question packs are really useful.

The UKMT has a mentoring scheme that provides fantastic problem solving resources , all complete with answers.

I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!

Year 7 Tutoring Programme

"Without a doubt our Year 7 students are enjoying it. The feedback from the whole of SLT has been fantastic."

FREE KS3 maths resources

Here you can find all of our free KS3 resources; explore the collections or navigate to each section to filter resources by topic

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

Beki Christian

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?

Ratio, proportion and rates of change:, geometry and measure, probability, read more: mean in maths and mean median mode, applied and problem solving questions, year 9 maths example questions for mathematical thinking, additional ks3 & ks4 maths questions suitable for year 9, 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, you may also be interested in:.

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

Year 9 Maths Test

Download this free, printable Year 9 end of year maths test. Includes student-friendly mark scheme and grade boundaries.

New year 9 maths topics

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:

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

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

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

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

Example question:

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

1.Estimate the mean of this data:

Foot size      Frequency

4                       3

5                       8

6                       4

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.

• 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

• 15 Algebra questions
• 15 Trigonometry questions
• 15 Ratio questions
• 15 Probability questions
• 15 Venn diagram questions
• 15 Simultaneous equations questions
• 15 Pythagoras theorem questions
• Long division questions

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. 

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.

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.

Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test Other valuable maths practice and ideas particularly around reasoning and problem solving at secondary can be found in our KS3 and KS4 maths blog articles. Try these fun maths problems for KS2 and KS3, SSDD problems , KS3 maths games and 30 problem solving maths questions . For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.

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.
• As a free alternative to this take a look at the Third Space Learning secondary resource library which has hundreds of resources for GCSE maths revision including practice papers, revision mats, GCSE maths worksheets and lots of GCSE maths questions.
• Ensure they have the correct equipment such as a protractor, compass and scientific calculator
• Divisibility rules
• Ration table
• Year 8 Maths
• Maths curriculum

Maths is taught in such a way that topics are built on year by year so if you were happy with Year 7 Maths and Year 8 Maths 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. 

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 MORE SUPPORT IN MATHS?

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

Since 2013 these personalised one to one lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn about the Year 7 programme or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Related articles

Free Year 9 Maths Test with Answers And Mark Scheme

Free Year 8 Maths Test With Answers and Mark Scheme

What Is A Ratio Table And How Can A Ratio Table Help In Problem Solving

The 12 Divisibility Rules You Should Know By Secondary School (Plus One That’s Totally New)

FREE KS3 Maths Tests Pack (Year 7, 8 and 9)

These tests are designed to be used within a one-hour lesson at the end of year 7, 8 and 9 to assess your students' understanding.

Each test includes a student friendly mark scheme and suggested grade boundaries.

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Maths Problem Solving Booklets

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

23 August 2022

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Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability.

Designed to be printed as A5 booklets.

Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have forgotten. I am a maths problem magpie and collect maths problems wherever I find them. All I have done is bundled these ones up to make it convienent.

If you find a problem that is yours and you don’t want it used please comment and I’ll remove it - cheers.

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Very impresses. Ta.

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Excellent resource

Great resource to use at KS3

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Just what I have been looking for. Thanks so much!

Good resources. Thanks you!

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