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Teaching Algebra KS2: A Guide For Primary School Teachers From Year 3 To Year 6

Neil almond.

At Key Stage 2, pupils are introduced to algebra as a curriculum objective for the first time. Here is a great way to introduce algebra KS2 to your pupils by use of pictorial representation, particularly Cuisenaire rod models.

This being said, when you look through the objectives for this section there is a high chance that some objectives would have been touched on in previous years in KS2 maths ; teaching the formula for finding the area of different shapes, for example.

This is no excuse to not teach these objectives in the context of it being algebra. It is, however, possible that pupils have been using algebraic thinking even before KS2. 

Where could pupils have encountered algebraic thinking before?

Cuisenaire rods: algebraic thinking in eyfs, algebra ks2: what year 6 pupils should be taught, algebra lesson ideas for year 6 pupils, theory behind teaching algebra ks2 , algebra questions and word problems in year 6, you may also be interested in: what is mean in maths.

Algebra can be interpreted as the generalisation of relationships between symbols. Whereas purely numerical equations show particular equivalences and transformations, by using letters to represent unknown values, algebraic equations seek to generalise.

Simple function machines may have been used in KS1 when looking at the four operations – this is where you put a number into the machine (the input), the machine provides instructions about what happens to that number, and delivers it as an output. 

It is possible still that pupils’ experience of algebra goes back further than this, all the way back to the Early Years Foundation Stage (EYFS) in fact, when working with Cuisenaire rods (and if your reception teacher does not have a set, invest in them). 

Before examining the algebra curriculum in Y6, it is worth examining the algebraic thinking that can happen in an Early Years classroom.

FREE Algebra Independent Recap Worksheets

Help your Year 6 students revise algebra with our free independent recap worksheets

Cuisenaire Rods are a set of 10 rods that are of different lengths and different colours as can be seen by the picture below (note that the actual physical rods do not have the letters printed on).

There is not enough time to explain the usefulness of these resources in the entirety of these blogs but one thing to note about their use is that they do not come predefined with a value. 

While adults may look at the rods and quite quickly assign the values of w =1, r = 2 g = 3 etc, pupils in the Early Years will not.  The unknown or unstated values given to different colour Cuisenaire rods can be thought of as children’s first exposure to algebraic generalisation. 

They will, however, be able to put them into order. Ordinality comes before cardinality. It is from this that the teacher can leverage some algebraic thinking from the pupils across the whole year. 

Take, for example, the following:

Children of reception age are quite happy in understanding that a green rod and a red rod are the equivalent length of a yellow rod or, to write it symbolically,  y = g + r. 

Or when they construct a set of trains like below:

Pupils can see the length of p and b is equal to the length of g, d and r and understand when this is presented as p + b = g + d + r. 

Finally, with this example:

Using the rods as a manipulative, the pupils are happy that five red rods are equivalent to one orange rod. This can be written as r + r + r + r + r = O. Or, an even quicker way would be  5r = 0.

Here we are dealing exclusively in unknown values. As pupils progress through the year and they learn their numbers and become secure in them, these unknowns can begin to  manifest themselves into cardinality.

y = g + r quickly becomes 5 = 3 + 2, p + b = g + d + r can become 4 + 7 = 3 + 6 + 2  and 5r can become 2 + 2 + 2 + 2 + 2 = 10 or even 5 x 2 = 10. 

The fact that mathematical symbols are used in conjunction with letters that represent the rods, the value of which are unknown, does not provide such a cognitive challenge as it does when children are introduced to algebra in Year 6 when x is first introduced as an unknown variable.

It cannot be overstated that this type of thinking will NOT happen within a lesson or by the end of one sequence of lessons. Pupils in the Early Years Foundation Stage will need plenty of time to play, experiment and explore with the rods as well as developing their sense of cardinality in other ways before the level of understanding demonstrated above will be realised. Many may not reach this understanding until KS1 and that is okay.

If you believe your pupils have not been introduced to Cuisenaire Rods or that it may have been some time since they have used them, then beginning the algebra unit in this way would be a successful way to begin pupils’ thinking.

In the national curriculum for maths in England, for each area of maths outlined, there is both a statutory requirement and a non-statutory requirement. The statutory requirement is as follows:

  • Use simple formulae
  • Generate and describe linear number sequences
  • Express missing number problems algebraically
  • Find pairs of numbers that satisfy an equation with 2 unknowns
  • Enumerate possibilities of combinations of 2 variables

The non-statutory notes and guidance suggests: 

  • Missing numbers, lengths, coordinates and angles
  • Formulae in mathematics and science
  • Equivalent expressions (for example, a + b = b + a)
  • Generalisations of number patterns
  • Number puzzles (for example, what 2 numbers can add up to)

A fun way to introduce algebra into Year 6 is to look at the etymology (history) of the word itself. ‘Algebra’ comes from the Arabic ‘al-jabr’ which roughly translates as ‘the reunion of broken parts.’ This is a nice visual representation to give pupils as it promotes the idea that algebra is like a puzzle to be solved by reuniting an unknown number to an equation.

The objective I will focus on here will be:

‘Find pairs of numbers that satisfy an equation with two unknowns.’

It is worth remembering that this objective from the National Curriculum is the end result. In order to reach this, it may be appropriate to break this down into smaller steps, and fulfil the other objectives first. 

For this example, I will look at satisfying equations with one unknown. As this is Y6, this should be done using all four operations. Using a bar model or Cuisenaire Rods can be invaluable here.

I would first begin to get pupils to link the abstract to a concrete or pictorial representation, as demonstrated below.

If your pupils are familiar with bar models then this will look very familiar. It is important, however, to ensure that you approach these models from an algebraic perspective and ensure that your pupils are too. 

Relating the abstract to the pictorial is key to this so that pupils can see 4x means 4 lots of the same unknown, for example.

Once pupils are comfortable, move on to models that have an unknown and a numerical value which equate to another numerical value.

Notice this time that all the bars are of the same colour and length, yet the numerical values are different. This is done purposefully so that pupils can see that we are merely representing the problem, not using them to actually perform the arithmetic.

When they have successfully matched the representations to the algebraic expressions, the pupils can then find the value of x.

I am a great believer that the more experiences pupils have had with manipulatives and bar modelling, the easier they will find algebra. Where pupils’ misconceptions and difficulties arise is when they do not have these mental models to draw upon. 

Coupled with the general fear the word strikes into young mathematicians who may have heard it spoken at home from older siblings with much disdain, algebra seems to be a topic within mathematics where pupils have developed negative preconceptions.

 Our role, as educators and proponents of mathematics, is to make children realise they have been performing algebra, hopefully, since they were in reception, before they even began to play with number cardinality. 

A typical example of a word problem that pupils may be expected to solve by themselves would look like this:

Jason is 9 years old

Jack is 12 years old

Gran is x + 12 years old.

The sum of their ages is 100.

Demonstrate this algebraically and find x.

The pupils are expected to use the information in the question to show the representation. This would look like this:

Pupils could then calculate the numerical values of the ages that are known – 9 + 12 + 12 = 33. Then subtract this from the total sum to get 67. Pupils now know that x = 67, they can then calculate that 67 + 12 = 79. Gran’s age is 79.

Addition and subtraction: reasoning and problem solving in algebra KS2

There is, of course, more to the learning of maths than just learning these objectives, and reasoning and problem solving should not just be limited to word problems. We want pupils to be able to conjecture, experiment (and dare I say have some fun) with algebraic thinking.

A question like this does just that:

Because the value of the triangle and rectangle are consistent throughout, the content is similar to the previous questions but in a slightly different context. With the sum of the equations all being within the tens or hundreds, it allows pupils to focus on the algebra and not get confused due to their lack of understanding of larger numbers. 

The teacher could model the use of converting the shapes to bar models if they think pupils need some more scaffolding to access this task. For example:

The above can become the following bar model:

From here pupils can see that x =1 as 17 + 7 = 24 and 1 is needed to make 25.

The questions gradually get harder but are scaffolded in such a way that the subsequent questions only get slightly harder making this a very accessible problem for pupils to solve.

a) Red shape = 1 b) Red shape = 10 c) Red shape = 44 d) Red shape = 16 e) Red shape = 32.5

Looking for some more ideas of how to do this? You can find plenty of free resources and algebra KS2 worksheets on the Third Space Learning maths hub . For guidance on other KS2 subjects, check out the rest of the series:

  • Teaching Decimals KS2
  • Teaching Place Value KS2
  • Teaching Fractions KS2
  • Teaching Percentages KS2
  • Teaching Statistics KS2
  • Teaching Ratio and Proportion KS2
  • Teaching Multiplication KS2
  • Teaching Division KS2
  • Teaching Addition and Subtraction KS2

Looking to get ahead on other KS2 maths topics? We have the lowdown from expert primary teachers on all the trickiest KS2 maths concepts to teach, including teaching times tables , telling the time , as well as the long division method and the long multiplication method .

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to address learning gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Primary school tuition targeted to the needs of each child and closely following the National Curriculum.

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Balancing Math Equations Worksheets & Help

Welcome to the Math Salamanders Balancing Math Equations Worksheets. Here you will find a wide range of free printable Worksheets, which will help your child learn how to balance an equation, with the amount on either side of the equal sign being the same value.

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What is a balanced equation?

  • How to Balance a Math Equation

Balancing Math Equations Worksheets

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Balancing Math Equations Online Quiz

Balancing math equations.

A balanced equation is an equation where both sides are equal to the same amount.

The answer to the expression on the left side of the equals sign (=) should be equal to the value on the right side of the equals sign.

In an unbalanced equation, either the left hand side of the equation has a greater value than the right hand side, like the example below.

Or the right hand side of the equation has a greater value than the left side, like the example below.

How to balance math equations

When you balance an equation, you make sure that both sides of your equation are equal to the same value.

Balancing equations is a great way to start your algebra journey without having to worry about algebraic expressions or letters.

Much of what you learn when you are balancing equations, you will need to draw on when you are doing algebra and solving equations.

How to balance a mathematical statement

Step 1) Find the value of the side of the equation without any missing numbers.

Step 2) Make sure the value on the other side of the equation is equal to this value.

Example 1) 7 x ___ = 20 + 8

Step 1) Work out the value on the right hand side: 20 + 8 = 28

Step 2) The value on the left hand side must equal this number: 7 x 4 = 28 so the missing value must be 4.

Answer: the missing value is 4.

Example 2) 5 x 7 = 50 - ___

Step 1) Work out the value on the left hand side: 5 x 7 = 35

Step 2) The value on the right hand side must equal this number: 50 - 15 = 35 so the missing value must be 15.

Answer: the missing value is 15.

Balancing Math Equations Worksheets 3rd Grade

The first worksheet is the most basic, with only a single value on the right hand side.

The 2nd worksheet involves addition and subtraction only.

The 3rd and 4th worksheets are more challenging and include multiplication and larger numbers.

  • Balancing Equations Sheet 3a
  • PDF version
  • Balancing Equations Sheet 3b
  • Balancing Equations Sheet 3c
  • Balancing Equations Sheet 3d

Balancing Math Equations Worksheets 4th Grade

These worksheets get progressively trickier: the first sheet involves +, - and x only.

The second sheet includes division, and the 3rd sheet involves harder values.

The 4th sheet involves balancing fraction expressions.

  • Balancing Equations Sheet 4a
  • Balancing Equations Sheet 4b
  • Balancing Equations Sheet 4c
  • Balancing Equations Sheet 4d

Balancing Math Equations Worksheets 5th Grade

All the worksheets in the 5th grade section involve balancing decimal equations.

The 1st sheet only involves addition and subtraction.

The 2nd sheet involves multiplication as well as addition and subtraction.

The 3rd sheet involves using all 4 operations.

  • Balancing Equations Sheet 5a
  • Balancing Equations Sheet 5b
  • Balancing Equations Sheet 5c

Balanacing Equations Sheet 4A Walkthrough Video

This short video walkthrough shows the problems from our Balancing Equations Sheet 4A being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Inequalities, Multiples and Factors

If you are looking for some more pre-algebra worksheets based around inequalities, multiples or factors, then take a look at this page.

The questions on this page are aimed at a 4th grade level.

  • Factors and Multiples Worksheet
  • PEMDAS Problems Worksheets

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

  • know and understand how parentheses works;
  • understand how exponents work in simple calculations.
  • understand and use PEMDAS to solve a range of problems.
  • Basic Algebra Worksheets

If you are looking for some basic algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of worksheets covering the following concepts:

  • Generate the algebra - and write your own algebraic expressions;
  • Calculate the algebra - work out the value of different expressions;
  • Solve the algebra - find the value of the term in the equation.
  • Algebra Math Games

If you are looking for a fun printable algebra game to play then try out our algebra game page.

You will find a range of algebra games that make learning algebra fun and non-threatening.

The only equipment you need is a scientific calculator, some dice, and a few counters!

Interactive Balancing Activity

Take a look at this Balancing Act app produced by PhET.

This a great activity to use for developing an understanding of where objects need to be put along a plank to make it balance.

The closer the object is to the center of the plank, the less the downward force on the plank will be.

The further the object is from the center of the plank, the greater the downward force on the plank will be.

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  • Balancing Act app produced by PhET

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This quick quiz tests your skill at balancing a range of equations. It is aimed at 4th and 5th graders.

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Algebra - Notation and Solving Unknown Values - KS2 Numeracy Y6

Algebra - Notation and Solving Unknown Values - KS2 Numeracy Y6

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Mr Hastey's Shop

Last updated

18 March 2023

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solving algebraic equations ks2

These lessons are designed for Upper Key Stage 2 Maths lessons (year 6 pupils) - Algebra. Main lesson activities are differentiated to allow for higher, middle and lower ability tasks. Mathematics involving algebraic equations.

Lesson 1 - Multiple part lesson building through early algebra skills - focuses on children being able to understand common algebra notation. Recognising how mathematicians will emit the multiplication symbol and others. Connection task uses shapes representing numerical values. Before the activation and main activyt start to use alphabetical letters for the use in algebraic equations. BODMAS can be reinforced throughout the lesson.

L.O. - To recognise and apply the common notation associated with algebra. Achieve - I can identify the notation used for algebraic equations. Challenge - I ensure I follow the BODMAS order of operations while using algebraic equations. Aspire - I can explore the available solutions for unknown values in algebraic equations.

Lesson 2 - Builds on the previous lesson, to start solving algebraic equations where the representative letter is worth an unknown value. Children can be taught how an equation is balanced and the final values for any unknowns should keep the algebraic equation balanced.

L.O. - To be able to identify unknown values in algebraic equations. Achieve - I can identify a value for a single unknown in an algebraic equation. Challenge - I explore the values of multiple unknowns in an algebraic equation. Aspire - I can explain a selection of efficient processes for identifying the values of unknowns.

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solving algebraic equations ks2

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Algebra has a reputation for being difficult, but Math Games makes struggling with it a thing of the past. Kids can use our free, exciting games to play and compete with their friends as they progress in this subject!

Algebra concepts that pupils can work on here include:

  • Solving and writing variable equations to find answers to real-world problems
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Algebra Worksheets

Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets for middle school students on topics such as algebraic expressions, equations and graphing functions.

This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra. The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems.

Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics. And there is nothing like a set of co-ordinate axes to solve systems of linear equations.

Most Popular Algebra Worksheets this Week

Solving Quadratic Equations with Positive 'a' Coefficients of 1

Algebraic Properties, Rules and Laws Worksheets

solving algebraic equations ks2

The commutative law or commutative property states that you can change the order of the numbers in an arithmetic problem and still get the same results. In the context of arithmetic, it only works with addition or multiplication operations , but not mixed addition and multiplication. For example, 3 + 5 = 5 + 3 and 9 × 5 = 5 × 9. A fun activity that you can use in the classroom is to brainstorm non-numerical things from everyday life that are commutative and non-commutative. Putting on socks, for example, is commutative because you can put on the right sock then the left sock or you can put on the left sock then the right sock and you will end up with the same result. Putting on underwear and pants, however, is non-commutative.

  • The Commutative Law Worksheets The Commutative Law of Addition (Numbers Only) The Commutative Law of Addition (Some Variables) The Commutative Law of Multiplication (Numbers Only) The Commutative Law of Multiplication (Some Variables)

The associative law or associative property allows you to change the grouping of the operations in an arithmetic problem with two or more steps without changing the result. The order of the numbers stays the same in the associative law. As with the commutative law, it applies to addition-only or multiplication-only problems. It is best thought of in the context of order of operations as it requires that parentheses must be dealt with first. An example of the associative law is: (9 + 5) + 6 = 9 + (5 + 6). In this case, it doesn't matter if you add 9 + 5 first or 5 + 6 first, you will end up with the same result. Students might think of some examples from their experience such as putting items on a tray at lunch. They could put the milk and vegetables on their tray first then the sandwich or they could start with the vegetables and sandwich then put on the milk. If their tray looks the same both times, they will have modeled the associative law. Reading a book could be argued as either associative or nonassociative as one could potentially read the final chapters first and still understand the book as well as someone who read the book the normal way.

  • The Associative Law Worksheets The Associative Law of Addition (Whole Numbers Only) The Associative Law of Multiplication (Whole Numbers Only)

Inverse relationships worksheets cover a pre-algebra skill meant to help students understand the relationship between multiplication and division and the relationship between addition and subtraction.

  • Inverse Mathematical Relationships with One Blank Addition and Subtraction Easy Addition and Subtraction Harder All Multiplication and Division Facts 1 to 18 in color (no blanks) Multiplication and Division Range 1 to 9 Multiplication and Division Range 5 to 12 Multiplication and Division All Inverse Relationships Range 2 to 9 Multiplication and Division All Inverse Relationships Range 5 to 12 Multiplication and Division All Inverse Relationships Range 10 to 25
  • Inverse Mathematical Relationships with Two Blanks Addition and Subtraction (Sums 1-18) Addition and Subtraction Inverse Relationships with 1 Addition and Subtraction Inverse Relationships with 2 Addition and Subtraction Inverse Relationships with 3 Addition and Subtraction Inverse Relationships with 4 Addition and Subtraction Inverse Relationships with 5 Addition and Subtraction Inverse Relationships with 6 Addition and Subtraction Inverse Relationships with 7 Addition and Subtraction Inverse Relationships with 8 Addition and Subtraction Inverse Relationships with 9 Addition and Subtraction Inverse Relationships with 10 Addition and Subtraction Inverse Relationships with 11 Addition and Subtraction Inverse Relationships with 12 Addition and Subtraction Inverse Relationships with 13 Addition and Subtraction Inverse Relationships with 14 Addition and Subtraction Inverse Relationships with 15 Addition and Subtraction Inverse Relationships with 16 Addition and Subtraction Inverse Relationships with 17 Addition and Subtraction Inverse Relationships with 18

The distributive property is an important skill to have in algebra. In simple terms, it means that you can split one of the factors in multiplication into addends, multiply each addend separately, add the results, and you will end up with the same answer. It is also useful in mental math, an example of which should help illustrate the definition. Consider the question, 35 × 12. Splitting the 12 into 10 + 2 gives us an opportunity to complete the question mentally using the distributive property. First multiply 35 × 10 to get 350. Second, multiply 35 × 2 to get 70. Lastly, add 350 + 70 to get 420. In algebra, the distributive property becomes useful in cases where one cannot easily add the other factor before multiplying. For example, in the expression, 3(x + 5), x + 5 cannot be added without knowing the value of x. Instead, the distributive property can be used to multiply 3 × x and 3 × 5 to get 3x + 15.

  • Distributive Property Worksheets Distributive Property (Answers do not include exponents) Distributive Property (Some answers include exponents) Distributive Property (All answers include exponents)

Students should be able to substitute known values in for an unknown(s) in an expression and evaluate the expression's value.

  • Evaluating Expressions with Known Values Evaluating Expressions with One Variable, One Step and No Exponents Evaluating Expressions with One Variable and One Step Evaluating Expressions with One Variable and Two Steps Evaluating Expressions with Up to Two Variables and Two Steps Evaluating Expressions with Up to Two Variables and Three Steps Evaluating Expressions with Up to Three Variables and Four Steps Evaluating Expressions with Up to Three Variables and Five Steps

As the title says, these worksheets include only basic exponent rules questions. Each question only has two exponents to deal with; complicated mixed up terms and things that a more advanced student might work out are left alone. For example, 4 2 is (2 2 ) 2 = 2 4 , but these worksheets just leave it as 4 2 , so students can focus on learning how to multiply and divide exponents more or less in isolation.

  • Exponent Rules for Multiplying, Dividing and Powers Mixed Exponent Rules (All Positive) Mixed Exponent Rules (With Negatives) Multiplying Exponents (All Positive) Multiplying Exponents (With Negatives) Multiplying the Same Exponent with Different Bases (All Positive) Multiplying the Same Exponent with Different Bases (With Negatives) Dividing Exponents with a Greater Exponent in Dividend (All Positive) Dividing Exponents with a Greater Exponent in Dividend (With Negatives) Dividing Exponents with a Greater Exponent in Divisor (All Positive) Dividing Exponents with a Greater Exponent in Divisor (With Negatives) Powers of Exponents (All Positive) Powers of Exponents (With Negatives)

Knowing the language of algebra can help to extract meaning from word problems and to situations outside of school. In these worksheets, students are challenged to convert phrases into algebraic expressions.

  • Translating Algebraic Phrases into Expressions Translating Algebraic Phrases into Expressions (Simple Version) Translating Algebraic Phrases into Expressions (Complex Version)

Combining like terms is something that happens a lot in algebra. Students can be introduced to the topic and practice a bit with these worksheets. The bar is raised with the adding and subtracting versions that introduce parentheses into the expressions. For students who have a good grasp of fractions, simplifying simple algebraic fractions worksheets present a bit of a challenge over the other worksheets in this section.

  • Simplifying Expressions by Combining Like Terms Simplifying Linear Expressions with 3 terms Simplifying Linear Expressions with 4 terms Simplifying Linear Expressions with 5 terms Simplifying Linear Expressions with 6 to 10 terms
  • Simplifying Expressions by Combining Like Terms with Some Arithmetic Adding and simplifying linear expressions Adding and simplifying linear expressions with multipliers Adding and simplifying linear expressions with some multipliers . Subtracting and simplifying linear expressions Subtracting and simplifying linear expressions with multipliers Subtracting and simplifying linear expressions with some multipliers Mixed adding and subtracting and simplifying linear expressions Mixed adding and subtracting and simplifying linear expressions with multipliers Mixed adding and subtracting and simplifying linear expressions with some multipliers Simplify simple algebraic fractions (easier) Simplify simple algebraic fractions (harder)
  • Rewriting Linear Equations Rewrite Linear Equations in Standard Form Convert Linear Equations from Standard to Slope-Intercept Form Convert Linear Equations from Slope-Intercept to Standard Form Convert Linear Equations Between Standard and Slope-Intercept Form
  • Rewriting Formulas Rewriting Formulas (addition and subtraction; about one step) Rewriting Formulas (addition and subtraction; about two steps) Rewriting Formulas ( multiplication and division ; about one step)

Linear Expressions and Equations

solving algebraic equations ks2

In these worksheets, the unknown is limited to the question side of the equation which could be on the left or the right of equal sign.

  • Missing Numbers in Equations with Blanks as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Blanks in Any Position )
  • Missing Numbers in Equations with Symbols as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Symbols in Any Position )
  • Solving Equations with Addition and Symbols as Unknowns Equalities with Addition (0 to 9) Symbol Unknowns Equalities with Addition (1 to 12) Symbol Unknowns Equalities with Addition (1 to 15) Symbol Unknowns Equalities with Addition (1 to 25) Symbol Unknowns Equalities with Addition (1 to 99) Symbol Unknowns
  • Missing Numbers in Equations with Variables as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Variables Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Variables in Any Position )
  • Solving Simple Linear Equations Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Left Side) Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Left Side) Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Right or Left Side) Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Right or Left Side)
  • Determining Linear Equations from Slopes, y-intercepts and Points Determine a Linear Equation from the Slope and y-intercept Determine a Linear Equation from the Slope and a Point Determine a Linear Equation from Two Points Determine a Linear Equation from Two Points by Graphing

Graphing linear equations and reading existing graphs give students a visual representation that is very useful in understanding the concepts of slope and y-intercept.

  • Graphing Linear Equations Graph Slope-Intercept Equations
  • Determinging Linear Equations from Graphs Determine the Equation from a Graph Determine the Slope from a Graph Determine the y-intercept from a Graph Determine the x-intercept from a Graph Determine the slope and y-intercept from a Graph Determine the slope and intercepts from a Graph Determine the slope, intercepts and equation from a Graph

Solving linear equations with jelly beans is a fun activity to try with students first learning algebraic concepts. Ideally, you will want some opaque bags with no mass, but since that isn't quite possible (the no mass part), there is a bit of a condition here that will actually help students understand equations better. Any bags that you use have to be balanced on the other side of the equation with empty ones.

Probably the best way to illustrate this is through an example. Let's use 3 x + 2 = 14. You may recognize the x as the unknown which is actually the number of jelly beans we put in each opaque bag. The 3 in the 3 x means that we need three bags. It's best to fill the bags with the required number of jelly beans out of view of the students, so they actually have to solve the equation.

On one side of the two-pan balance, place the three bags with x jelly beans in each one and two loose jelly beans to represent the + 2 part of the equation. On the other side of the balance, place 14 jelly beans and three empty bags which you will note are required to "balance" the equation properly. Now comes the fun part... if students remove the two loose jelly beans from one side of the equation, things become unbalanced, so they need to remove two jelly beans from the other side of the balance to keep things even. Eating the jelly beans is optional. The goal is to isolate the bags on one side of the balance without any loose jelly beans while still balancing the equation.

The last step is to divide the loose jelly beans on one side of the equation into the same number of groups as there are bags. This will probably give you a good indication of how many jelly beans there are in each bag. If not, eat some and try again. Now, we realize this won't work for every linear equation as it is hard to have negative jelly beans, but it is another teaching strategy that you can use for algebra.

Despite all appearances, equations of the type a/ x are not linear. Instead, they belong to a different kind of equations. They are good for combining them with linear equations, since they introduce the concept of valid and invalid answers for an equation (what will be later called the domain of a function). In this case, the invalid answers for equations in the form a/ x , are those that make the denominator become 0.

  • Solving Linear Equations Combining Like Terms and Solving Simple Linear Equations Solving a x = c Linear Equations Solving a x = c Linear Equations including negatives Solving x /a = c Linear Equations Solving x /a = c Linear Equations including negatives Solving a/ x = c Linear Equations Solving a/ x = c Linear Equations including negatives Solving a x + b = c Linear Equations Solving a x + b = c Linear Equations including negatives Solving a x - b = c Linear Equations Solving a x - b = c Linear Equations including negatives Solving a x ± b = c Linear Equations Solving a x ± b = c Linear Equations including negatives Solving x /a ± b = c Linear Equations Solving x /a ± b = c Linear Equations including negatives Solving a/ x ± b = c Linear Equations Solving a/ x ± b = c Linear Equations including negatives Solving various a/ x ± b = c and x /a ± b = c Linear Equations Solving various a/ x ± b = c and x /a ± b = c Linear Equations including negatives Solving linear equations of all types Solving linear equations of all types including negatives

Linear Systems

solving algebraic equations ks2

  • Solving Systems of Linear Equations Easy Linear Systems with Two Variables Easy Linear Systems with Two Variables including negative values Linear Systems with Two Variables Linear Systems with Two Variables including negative values Easy Linear Systems with Three Variables; Easy Easy Linear Systems with Three Variables including negative values Linear Systems with Three Variables Linear Systems with Three Variables including negative values
  • Solving Systems of Linear Equations by Graphing Solve Linear Systems by Graphing (Solutions in first quadrant only) Solve Standard Linear Systems by Graphing Solve Slope-Intercept Linear Systems by Graphing Solve Various Linear Systems by Graphing Identify the Dependent Linear System by Graphing Identify the Inconsistent Linear System by Graphing

Quadratic Expressions and Equations

solving algebraic equations ks2

  • Simplifying (Combining Like Terms) Quadratic Expressions Simplifying quadratic expressions with 5 terms Simplifying quadratic expressions with 6 terms Simplifying quadratic expressions with 7 terms Simplifying quadratic expressions with 8 terms Simplifying quadratic expressions with 9 terms Simplifying quadratic expressions with 10 terms Simplifying quadratic expressions with 5 to 10 terms
  • Adding/Subtracting and Simplifying Quadratic Expressions Adding and simplifying quadratic expressions. Adding and simplifying quadratic expressions with multipliers. Adding and simplifying quadratic expressions with some multipliers. Subtracting and simplifying quadratic expressions. Subtracting and simplifying quadratic expressions with multipliers. Subtracting and simplifying quadratic expressions with some multipliers. Mixed adding and subtracting and simplifying quadratic expressions. Mixed adding and subtracting and simplifying quadratic expressions with multipliers. Mixed adding and subtracting and simplifying quadratic expressions with some multipliers.
  • Multiplying Factors to Get Quadratic Expressions Multiplying Factors of Quadratics with Coefficients of 1 Multiplying Factors of Quadratics with Coefficients of 1 or -1 Multiplying Factors of Quadratics with Coefficients of 1, or 2 Multiplying Factors of Quadratics with Coefficients of 1, -1, 2 or -2 Multiplying Factors of Quadratics with Coefficients up to 9 Multiplying Factors of Quadratics with Coefficients between -9 and 9

The factoring quadratic expressions worksheets in this section provide many practice questions for students to hone their factoring strategies. If you would rather worksheets with quadratic equations, please see the next section. These worksheets come in a variety of levels with the easier ones are at the beginning. The 'a' coefficients referred to below are the coefficients of the x 2 term as in the general quadratic expression: ax 2 + bx + c. There are also worksheets in this section for calculating sum and product and for determining the operands for sum and product pairs.

  • Factoring Quadratic Expressions Factoring Quadratic Expressions with Positive 'a' coefficients of 1 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients of 1 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients of 1 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 4 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 4 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 4 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 5 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 5 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 5 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 9 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 9 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 9 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 81 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 81 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 81 with a Common Factor Step Calculating Sum and Product (Operand Range 0 to 9 ) ✎ Calculating Sum and Product (Operand Range 1 to 9 ) ✎ Calculating Sum and Product (Operand Range 0 to 9 Including Negatives ) ✎ Calculating Sum and Product (Operand Range 1 to 9 Including Negatives ) ✎ Calculating Sum and Product (Operand Range -20 to 20 ) ✎ Calculating Sum and Product (Operand Range -99 to 99 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 9 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 9 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 12 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 12 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 9 Including Negatives ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 9 Including Negatives ) ✎ Determining Operands from Sum and Product Pairs (Operand Range -20 to 20 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range -99 to 99 ) ✎

Whether you use trial and error, completing the square or the general quadratic formula, these worksheets include a plethora of practice questions with answers. In the first section, the worksheets include questions where the quadratic expressions equal 0. This makes the process similar to factoring quadratic expressions, with the additional step of finding the values for x when the expression is equal to 0. In the second section, the expressions are generally equal to something other than x, so there is an additional step at the beginning to make the quadratic expression equal zero.

  • Solving Quadratic Equations that Equal Zero Solving Quadratic Equations with Positive 'a' coefficients of 1 Solving Quadratic Equations with Positive or Negative 'a' coefficients of 1 Solving Quadratic Equations with Positive or Negative 'a' coefficients of 1 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 4 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 4 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 4 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 5 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 5 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 5 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 9 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 9 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 9 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 81 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 81 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 81 with a Common Factor Step
  • Solving Quadratic Equations that Equal an Integer Solving Quadratic Equations for x ("a" coefficients of 1) Solving Quadratic Equations for x ("a" coefficients of 1 or -1) Solving Quadratic Equations for x ("a" coefficients up to 4) Solving Quadratic Equations for x ("a" coefficients between -4 and 4) Solving Quadratic Equations for x ("a" coefficients up to 81) Solving Quadratic Equations for x ("a" coefficients between -81 and 81)

Other Polynomial and Monomial Expressions & Equations

solving algebraic equations ks2

  • Simplifying Polynomials That Involve Addition And Subtraction Addition and Subtraction; 1 variable; 3 terms Addition and Subtraction; 1 variable; 4 terms Addition and Subtraction; 2 variables; 4 terms Addition and Subtraction; 2 variables; 5 terms Addition and Subtraction; 2 variables; 6 terms
  • Simplifying Polynomials That Involve Multiplication And Division Multiplication and Division; 1 variable; 3 terms Multiplication and Division; 1 variable; 4 terms Multiplication and Division; 2 variables; 4 terms Multiplication and Division; 2 variables; 5 terms
  • Simplifying Polynomials That Involve Addition, Subtraction, Multiplication And Division All Operations; 1 variable; 3 terms All Operations; 1 variable; 4 terms All Operations; 2 variables; 4 terms All Operations; 2 variables; 5 terms All Operations (Challenge)
  • Factoring Expressions That Do Not Include A Squared Variable Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Negative and Positive Multipliers
  • Factoring Expressions That Always Include A Squared Variable Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Negative and Positive Multipliers
  • Factoring Expressions That Sometimes Include Squared Variables Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Negative and Positive Multipliers
  • Multiplying Polynomials With Two Factors Multiplying a monomial by a binomial Multiplying two binomials Multiplying a monomial by a trinomial Multiplying a binomial by a trinomial Multiplying two trinomials Multiplying two random mon/polynomials
  • Multiplying Polynomials With Three Factors Multiplying a monomial by two binomials Multiplying three binomials Multiplying two binomials by a trinomial Multiplying a binomial by two trinomials Multiplying three trinomials Multiplying three random mon/polynomials

Inequalities

solving algebraic equations ks2

  • Writing The Inequality That Matches The Graph Writing Inequalities for Graphs
  • Graphing Inequalities On Number Lines Graphing Inequalities (Basic)
  • Solving Linear Inequalities Solving Inequalities Including a Third Term Solving Inequalities Including a Third Term and Multiplication Solving Inequalities Including a Third Term, Multiplication and Division

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solving algebraic equations ks2

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  •    Algebraic Equations: 10 Solved Questions for GSCE Exams Preparations

solving algebraic equations ks2

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Algebraic equations: 10 solved questions for gsce exams preparations.

  • Chloe Daniel
  • Published On: April 21 ,2022

Algebraic Equations 10 Solved Questions for GSCE Exams Preparations

Algebra is one of the most complex and most interesting parts of Mathematics. Yes, hard when you don’t understand it and super interesting when you realize how easy it is. Algebra questions involve numbers, letters, and symbols to find hidden values. Algebra can help determine values that can change.

Since the GSCE exams are just around the corner, we felt the need to prepare the students for Algebra. Therefore, we will compile a list of 10 solved Algebra problems and explanations below to help you practice.

But before that, let’s go through a few more details related to algebra and its techniques briefly!

Algebra in KS2, KS3, and KS4

There are three main techniques for solving Algebra problems: KS2, KS3, and KS4. In KS2, we simplify and write the expressions and solve and substitute the equations.

In KS3 questions, we learn and practice writing the basic linear equations and algebraic expressions.

In KS4, we deal with more complex Algebraic expressions, including the system of linear equations and quadratic equations. In short, KS4 is the most complicated and advanced technique for solving Algebraic problems.

Below, you will find solved examples involving all these three techniques. But first, let us see the basic methods of solving Algebraic problems.

How to Solve Algebraic Questions?

The first to solve an Algebraic question is to determine and identify what you need to find. For that, you need to go through the question carefully and thoroughly. Here are a few examples of what algebraic problems can ask you to find:

  • Solve the Equation:  In this question, you need to find the value of the unknown variable.
  • Expand the Brackets:  You need to multiply all the brackets in this type.
  • Substitute:  In substitution, you need to put the given values inside the algebraic equation.
  • Factorise:  You need to find the factors of the algebraic expressions in this type.
  • Simplify:  In this type, you solve all the factors and brackets to simplify an algebraic expression.
  • Make x the Subject:  In this type of question, you need to rewrite the expression in the form of x.

Another thing you need to keep in mind while solving algebraic expressions is that you always need to apply the BODMAS or BIDMAS rule. The full form of these terms is Brackets, Indice, Division, Multiplication, Addition, and Subtraction.

According to this rule, you need to solve the equation in the same sequence and order as mentioned above, i.e., First, solve the brackets/indices, then perform division, etc.

KS2 Algebra Questions

We simplify, substitute, and solve equations in the KS2 type questions as we briefly mentioned above. Like we promised, here are a few solved examples with explanations:

We have two products; a chocolate bar and a drink. The chocolate costs c dollars, and the drink costs d dollars. What will be the algebraic equation if we want to find the cost of 2 chocolates and 2 drinks?

Answer:  2c + 2d

Explanation:  Since we need to find the cost of 2 drinks and 2 chocolates, their lots will be 2c and 2d respectively.

KS2 Algebra Questions example 1

4m + 5 + 2m – 1: Simplify this equation.

Answer: 6m + 4

Explanation: First, you need to organize the equation in order, i.e., 4m + 2m + 5 -1. Now, 4m + 2m will be 6m, and 5 – 1 will be 4. Hence, 6m + 4.

KS2 Algebra Questions Example 2

KS3 Algebra Questions

In the KS3 Algebraic equations, we use the following techniques and steps:

  • Simplifying equations.
  • Writing algebraic equations with the help of word problems.
  • Expanding the brackets and factorizing.
  • Solving inequalities and equations.
  • Changing subjects of the equations.
  • Substituting.
  • Solving problems with straight-line and real-life graphs.

Now, here are a few solved examples of the KS3 Algebra questions, along with their explanations.

Here is a pyramid with 3 values given in boxes, and you need to find the box’s value above. You will need to add two more adjacent blocks to find the answer. What expression should be in the box above?

solving algebraic equations ks2

Answer:  12a – b

Explanation:

solving algebraic equations ks2

Josh is a window cleaner, and he calculates the charging amount of his customers using this formula:

Charge = £20 + 4n

In this formula, n is the number of windows in a house. So, how much will Josh charge if a house has 7 windows?

Answer: £48

Explanation: Since n is the number of windows, we put n = 7. So, 20 + 4 x 7 = 48. Hence, Charge = £48.

KS3 Algebra Questions Example 2

We have a rectangle with an area of 4x – 6. What will be the length and width of this rectangle?

Answer: 2 and 2x -3

Explanation: We solved this problem through factorization.

= 4x – 6 = 2(2x -3)

This means the length and width are 2 and 2x – 3, respectively.

KS3 Algebra Questions Example 3

For changing Celsius to degrees Fahrenheit, the formula is:

F = 9C/5 + 32

How can you make c the subject of this formula?

Answer: C = 5 (F – 32) / 9

F = 9C/5 + 32 Now, subtract 32. F – 32 = 9C / 5 Now, multiply by 5. 5 (F – 32) = 9c Now, divide by 9. 5 (F – 32) / 9 = C

KS3 Algebra Questions Example 4

In this triangle, what is the size of the smallest angle?

solving algebraic equations ks2

Answer:  34 degrees

Explanation:  A triangle has angles with a sum of 180 degrees, right? Hence, we can write:

4x + 2x – 10 + 3x – 8 = 180

Now, we will solve this equation:

9x – 18 = 180 Now, we add 18 9x = 198 Now, we divide it by 9 x = 22 degrees

Now, the angles are:

4 x 22 = 88 degrees 2 x 22 – 10 = 34 degrees 3 x 22 – 8 = 58 degrees

Hence, the smallest angle is 34 degrees.

KS3 Algebra Questions Example 5

Kate’s dad is 4 times older than her. After 14 years, Kate’s dad will be twice her age. What is the sum of kate and her dad’s age right now?

Answer:  35

Explanation:  To solve this word problem, we will need to write an equation with the given variables and values.

Suppose Kate’s age is x, and her dad’s age is 4x. After 14 years, Kate’s age will be x + 14, and her dad’s age will be 4x + 14.

Now, we know that Kate’s dad is 2 times her age, our equation will be:

4x + 14 = 2(x + 14)

Now, we will solve this equation.

4x + 14 = 2(x + 14) Now, we will expand the brackets. 4x + 14 = 2x + 28 Now, we will subtract 2x. 2x + 14 = 28 Now, we will subtract 14. 2x = 14 X = 7

Hence, kate is currently 7 years old, and her dad is 28 years old. The sum of their age will be 35.

KS3 Algebra Questions Example 6

KS4 Algebra Questions

KS4 is the most advanced and complicated type of algebraic problem. Here is the list of topics and techniques included in it:

  • Expand and factorize the polynomials.
  • Inequalities.
  • Algebraic Fractions.
  • Solving quadratic and simultaneous equations.

Here are a few solved examples of KS4 algebraic questions:

Find the volume of this cuboid with an x expression:

solving algebraic equations ks2

Answer:  30×3 – 49×2 + 4x + 3

Explanation: Since the volume of a cuboid is Length x Width x Height

Volume = (5x + 1)(2x – 3)(3x – 1) Volume = (10x 2  + 2x – 15x – 3)(3x – 1) Volume = (10x 2  – 13x – 3)(3x – 1) Volume = 30x 3  – 39x 2  – 9x – 10x 2  +13x + 3 Volume = 30x 3  – 49x 2  + 4x + 3

KS4 Algebra Questions Example 1

The area of this given triangle is 24 cm2, what will be its perimeter?

solving algebraic equations ks2

Answer:  24 cm

Explanation:  The formula to find the area of a triangle is:

Area = ½ x b x h.

Now, we will fill it in.

24 = ½ x 6 x (3x – 1) Simplify 24 = 3(3x -1) Multiply the brackets 24 = 9x – 3 Add 3 27 = 9x Divide by 9 X = 3

Now that x = 3, the side lengths of the triangle will be 6 cm, 8 cm, and 10 cm.

Perimeter = 6 + 8 + 10 = 24 cm.

KS4 Algebra Questions Example 2

X + 2 – 15/x = 0 Solve this equation?

Answer:  x = -5 04 x = 3

x + 2 – 15/x = 0 Multiply b x x2 + 2x – 15 = 0 Factorize (x + 5)(x – 3) = 0 Solve x = 15 or x = 3

KS4 Algebra Questions Example 3

What will be the minimum value of the function f(x) = x 2  + 4x + 5?

Explanation:  To find the minimum value of this function, first you will have to complete the square.

f(x) = x 2  + 4x + 5 f(x) = (x + 2) 2  – 4 + 5 f(x) = (x + 2) 2  + 1

Hence, the minimum value is 1.

KS4 Algebra Questions Example 4

Final Words

I hope our list of 10 solved algebraic questions helps you prepare for your GSCE exams. We tried to cover almost all types of algebraic expressions and equations. Now it’s your turn to practice these questions, understand the methods and concepts, and ace your exam!

If you still have questions or confusion, you can always contact us and ask for a professional Mathematics tutor to clear your concepts. Your tutor is only a click away!

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5 letter words starting with r

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5 letter words starting with t

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5 letter words starting with c

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5 letter words starting with s

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5 letter words starting with i

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5 letter words starting with vi

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  1. Algebra- Equations

    solving algebraic equations ks2

  2. 3 Ways to Solve Two Step Algebraic Equations

    solving algebraic equations ks2

  3. Formulae and Equations KS2

    solving algebraic equations ks2

  4. 2 Step Equations Worksheet

    solving algebraic equations ks2

  5. Solving Equations KS2

    solving algebraic equations ks2

  6. Algebra 2 Worksheets With Answers Pdf

    solving algebraic equations ks2

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  1. Math Olympiad Question

  2. Solving Algebraic equation (easy problem) #youtubeshorts #mathtrick #satmath #mathsuccess #algebra

  3. A Nice Algebra Equation • X=?

  4. Solving algebraic equations 2

  5. RS 113 Q3

  6. Solving Algebraic Equations with Galois theory Part 3

COMMENTS

  1. Algebra

    Teachit KS2 Maths Algebra learning resources for adults, children, parents and teachers.

  2. Basic Algebra Worksheets

    Solve the algebra - find the value of the term in the equation. By splitting the algebra up into sections, you only need to concentrate on one aspect at a time! Each question sheet comes with its own separate answer sheet. Want to test yourself to see how well you have understood this skill?. Try our NEW quick quiz at the bottom of this page.

  3. Equations

    Solving an equation When solving an equation it is important to find the value of one letter. Let's solve the equation 3 x + 4 = 10 To remove the + 4 we complete the inverse (opposite)...

  4. Algebra Worksheets PDFs

    Additional Algebra Resources. Our algebra worksheets PDFs and activities will help you teach your KS2 students in an engaging manner. Typically introduced in Year 6, algebra can be a tricky topic, involving new vocabulary and new mathematical concepts. Our fantastic collection of algebra PDF worksheets contains everything your Year 6 class need ...

  5. How to solve simple algebraic equations

    STEP 1 - Write the maths problem on the board. STEP 2 - Draw a bar model to represent the first part of the problem. Loaves are represented by x. STEP 3 - Remove the 4 from the end (the price of...

  6. Solving Equations Worksheets

    Solving Equations Worksheets. Tes classic free licence. Reviews. 4.5. Something went wrong, please try again later. aahmed070807. a year ago. report. 5. very helpful Empty reply does not make any sense for the end user. Submit reply Cancel. jamescollett. 2 years ago. report. 4. Very useful. Thank you! Empty reply does not make any sense for the ...

  7. All About Algebra

    Learn important maths skills by using this KS2 All About Algebra -Solve One-Step Equations Concept Video. It features: Short, pacey explanation of how children can answer algebra questions about how to solve one-step equation questions. Opportunities for independent practice to build confidence in answering algebra questions. Pause, rewind and ...

  8. Year 6 KS2 Solving Equations Maths PowerPoint

    Here are our top 5 picks of teaching resources that you can use to teach KS2 equations: Expressing Missing Numbers Activity Pack. Simplifying Algebraic Expressions Worksheet. Alphabet Algebra Worksheet. Balancing Equations Worksheet Pack. Balance Equations Using Missing Numbers Worksheet.

  9. KS2 Alphabet Algebra Equations Worksheet

    This handy alphabet algebra equations worksheet is ideal for introducing children to solving math equations in algebra, and is great for independent working. Show more algebra algebra for beginners algebra year 6 algebra year 5 algebra worksheets mrswelch - Verified member since 2015 Reviewed on 25 August 2021 I would welcome more versions of this.

  10. Teaching Algebra At KS2: A Guide For Primary School Teachers

    While adults may look at the rods and quite quickly assign the values of w =1, r = 2 g = 3 etc, pupils in the Early Years will not. The unknown or unstated values given to different colour Cuisenaire rods can be thought of as children's first exposure to algebraic generalisation. They will, however, be able to put them into order.

  11. Algebra Resources

    Using solving equations games for the classroom is a great way to recap this area of maths while adding a competitive edge. From dominoes-style games to challenge cards and a revision quiz, you'll find a great selection of activities to keep KS2 students entertained and inspire enthusiasm for maths. Why play maths games?

  12. Balancing Math Equations

    Step 1) Work out the value on the right hand side: 20 + 8 = 28 Step 2) The value on the left hand side must equal this number: 7 x 4 = 28 so the missing value must be 4. Answer: the missing value is 4. Example 2) 5 x 7 = 50 - ___ Step 1) Work out the value on the left hand side: 5 x 7 = 35

  13. Unit Overview: Forming and solving equations

    In this lesson, we will look at more difficult linear equations and solve them using algebraic methods. Copy Lesson Link. View Lesson in classroom. Lesson overview. 1 Quiz; 11; m VideoPresentation(PPT) Worksheet; Solving geometric problems using linear equations Key Learning.

  14. Solving Equations

    File previews. ppt, 1.84 MB. Full sequence of lessons back-to-back for 'Solving Equations'. Including. -One step equations (addition, subtraction, multiplication, division and mixed problems) -Two step equations. -Unknowns on both sides.

  15. Algebra

    Lesson 2 - Builds on the previous lesson, to start solving algebraic equations where the representative letter is worth an unknown value. Children can be taught how an equation is balanced and the final values for any unknowns should keep the algebraic equation balanced. L.O. - To be able to identify unknown values in algebraic equations.

  16. How to solve algebraic equations using guess and check

    Include 3 'h' squares (representing the hats), a 5 (representing the scarf) and a 17 (the overall value). STEP 3 - Guess that h = 5; this is wrong because the total will equal 20. It is too ...

  17. Algebra

    Kids can use our free, exciting games to play and compete with their friends as they progress in this subject! Algebra concepts that pupils can work on here include: Solving and writing variable equations to find answers to real-world problems. Writing, simplifying and evaluating variable expressions to figure out patterns and rules.

  18. Solving Equations Practice Questions

    equation, solve. Practice Questions. Previous: Ray Method Practice Questions. Next: Equations involving Fractions Practice Questions. The Corbettmaths Practice Questions on Solving Equations.

  19. Primary Resources: Maths: Solving Problems: Simple Algebra

    Algebraic Equations (Bayswater School) PDF. Algebra Challenges (Carole Buscombe) DOC. Sweet Bag Algebra 1 (Phil Rhodes) Sweet Bag Algebra 2 (Phil Rhodes) Sweet Bag Equations (Phil Rhodes) Finding a Formula for a Pattern (Cherie Rothery) DOC. Algebra and Glossary Patterns Glossary Task (Cherie Rothery) DOC. Missing Numbers & Algebra (Jennifer ...

  20. Algebra Worksheets

    Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets for middle school students on topics such as algebraic expressions, equations and graphing functions. This page starts off with some missing numbers worksheets for younger students.

  21. Algebra

    Number and algebra. The Number System and Place Value; Calculations and Numerical Methods; Fractions, Decimals, Percentages, Ratio and Proportion; Properties of Numbers; Patterns, Sequences and Structure; Algebraic expressions, equations and formulae; Coordinates, Functions and Graphs

  22. Maths4Everyone

    Popular with both teachers and students, the questions in these free maths resources are carefully crafted and include the answers. They are designed to help students to take the first steps in each topic, then strengthen and extend their knowledge and skills. The resources include revision questions for KS2 SATs and GCSE.

  23. Algebraic Equations: 10 Solved Questions for GSCE Exams ...

    Algebra in KS2, KS3, and KS4. There are three main techniques for solving Algebra problems: KS2, KS3, and KS4. In KS2, we simplify and write the expressions and solve and substitute the equations. In KS3 questions, we learn and practice writing the basic linear equations and algebraic expressions.