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Оқушылар теңдеулерді шешу жолдарын түсінеді және қолдану арқылы есептер шығара алады. Олар әртүрлі теңдеулер түрлерін ажыратып, дұрыс шешу жолдарын табуды үйренеді.

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Негізгі сұрақ

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Негізгі сұрақ

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Теңдеулерді шешу дегеніміз не және неге оларды дұрыс шешу маңызды?

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Жаңа материалды түсіндіру

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Жаңа материалды түсіндіру

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Теңдеулердің негізгі түрлері (сызықтық, квадраттық) және оларды шешу әдістері туралы түсіндіру.

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Топтық жұмыс: Теңдеулерді талдау

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Топтық жұмыс: Теңдеулерді талдау

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Оқушыларды топтарға бөліп, әр топқа түрлі теңдеу түрлерін беріңіз. Олар теңдеуді шешу жолдарын талқылайды.

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My history with teaching multi-step equations hasn't been a pretty one, but spoiler alert, there's a happy ending. A few years ago I was co-teaching with a relatively new teacher and I felt a lot of pressure to show him the ropes. I was new to the 8th grade math standards. Everything was going well for the first month of school until we got to solving multi-step equations. We worked for two full weeks and taught students just how multi-step equations had been taught to us. The kids bombed the unit test. It was devastating. Then, we had a chance to reteach the majority of the kids and we tried something else. It also failed. It was a humbling experience to say the least.

I stepped back and looked at the concept. I spent a lot of time trying to figure out where the kids were getting baffled. For so many kids there were just to many things to remember. So I came up with a way to solve these equations called the boxes method. A few weeks later, we taught the students how to solve multi-step equations again, this time using the boxes, but we only had two days to do it. Even with just two days, it was clearly the most successful thing we had done.

I knew that the next year when it came time to teach multi-step equations, we'd teach it with the boxes method from the very beginning. And I felt confident that we'd have success. Amazingly, this turned out to be even more right than I'd hoped. The second year we started the teaching with this method and the vast majority of kids got it the first time around. We used this method throughout the year and our students were so much better than ever before. To see a step by step guide to teaching with this boxes method, check out the post "How to Teach Multi-Step Equations Like a Boss".

Regardless of how you teach students about multi-step equations, once they've learned how to solve multi-step equations, there are so many different ways to practice. And however you choose to practice, students need lots of opportunities to practice this skill. Here's a collection of some of the activities that I like to use in my classroom.
Solving Multi-Step Equations Mazes (Printable & Digital) Gallery Walk Variables on Both Sides Target Game with Task Cards Interactive Balance Model Multi-Step Equations Skill Jeopardy Illustrative Mathematics Challenge Activity Algebra Meltdown Online Game
The Activities for Solving Multi-Step Equations

The activities below can be used for different parts of the lesson. Some work well as anticipatory sets while others are great for practicing. They all are engaging and many of them encourage collaboration. Some of the activities are completed on the computer while others use paper.

Here's a description of each of the activities and some tips for how to use them:

We do a lot of mazes in my classroom. It's a great way to start off the day. They can be used for bellwork after an introduction lesson or as cyclical review. These particular mazes have variables on both sides. Also, they increase in difficulty from maze to maze. There are integers and some fractions in the equations they're solving. Students love doing them and they don't even realize that they are completing work.

These mazes now have a digital version too! This version is built in Google Slides and can be easily assigned in Google Classroom (or other LMS). They're easy to use and interactive for students, with drag-and-drop arrows to mark their path.

By the way, this is a great chance to sign up for the FREE Maze of the Month Club if you haven't already. I send MotM Club members a free, exclusive maze on various middle school math concepts right to their inboxes each month (with both a digital & printable version!) Join today and try out some math mazes in your classroom:

This gallery walk activity is a free resource (follow link here). When you get to the website you have to scroll down and then download the Gallery Walk. There are a variety of other activities that are shown on this website. The great thing about this activity is that it's all ready to go. The 30 problems included in this gallery walk increase in complexity and many of them could be used as challenge problems. Some of the problems would challenge fast finishers or might be good to use in an advanced class. Finally, gallery walks really get kids engaged and moving around the classroom.

Task cards can be used in a lot of different ways. One way is to use them with the whole class and to play a game with it. You can do this with a Target Game on the board or a Trashketball using a trashcan. Both games require students to complete a problem and then you model the answer for the class. Then, someone gets a turn at throwing a sticky ball at a target on the board or shooting a crumpled paper into a trashcan. They love the challenge of the target part and the whole class usually really gets into it. So simple, yet so fun.

I use some of the task cards from this multi-step equations task card set as the problems for this game (it comes in both a printable & digital version). It's easy, and then I have all the problems that I need for the game. I give points to all the kids who got the question right. The amount of points depends on how the person who threw the ball or took the shot does. Even though I don't put a huge emphasis on the points, the kids still get excited.

4- Whiteboarding with Worksheets

I love having students work on whiteboards. In my class I have a set of 6 large whiteboards and the students love working on them. They can be on the wall or students can take them down to work on them. Follow this to a series of worksheets. You'll find 15 worksheets that go from easy to difficult and work with decimals and fractions

We rarely just do a worksheet in my class, but I love that these problems are ready for use. For example, when whiteboarding I have a group of 2 or 3 work on the same problem together. I model the math talk that I want to happen and try to be very aware of how I group students. Then, students get to work solving together on the white board, showing their mathematical reasoning on the board and talking about their problem solving strategy with their classmates. This activity works well as practice activity, anticipatory set, or a sponge activity.

Sometimes you want students to work with equations in a concrete way. This balance model from Math Playground helps your kids to see what they're doing when they are solving equations. They'll need a little background in equations before you assign this model. One of the cool parts is that it has the equations set for them and then students work through them on the balance. This is a go-to anticipatory set for me on the 3rd or 4th day of the unit for solving multi-step equations.

Jeopardy has been around for a long time as a way to review concepts. We played Jeopardy back when I was in Junior High (and that was during the 80s- yikes!). You can play Jeopardy as a whole class where everyone has to answer the question. Students keep track of their individual points.

This particular Jeopardy game from Jeopardy Labs is based on prerequisite skills for multi-step equations, including distributive property and combining like terms. It's a fairly quick game for my 8th graders. I like to use games like this as an anticipatory set. We don't finish the whole game, but we play it for about 5 to 7 minutes. It's a perfect way to activate prior knowledge and get kids into the lesson.

Bingo is one of my favorite ways to review any topic. Usually, we do this activity the day of a test or the day before the test. It depends on how long the test will take. You can have students put the bingo cards in a SmartPal sleeve or you can have them mark their paper with different symbols. It takes a long time to get through the 30 problems and we don't usually do all of them. Usually, I pick and choose the equations that I think will give student confidence and will practice key stumbling blocks. This Bingo game includes equations with fractions and equations with variables on both sides.

Bingo is a great cyclical review game. There rarely is someone who doesn't want to play Bingo. I do give prizes for the winners. Often the prize is a Jolly Rancher or some little pencil or eraser. It's amazing how hard kids will work for this little incentives.

Using cootie catchers, or what some people call fortune tellers, is a fun way to engage students. I find that these activities work well with kids that are apprehensive of the topic of multi-step equations. This topic can be a little difficult for many students and when they solve the equations with a partner while playing a little game they seem to let their guard down.

Each partner has a cootie catcher with different problems. Then, each partner works on a different problem. Students can play head to head and see who gets the most correct answers completed in a certain amount of time.

The problems in this particular cootie catcher activity include fractions and distributive property. I've learned that students need to different situations when it comes to equations. Otherwise they just memorize some steps and then, after the unit test, they quickly forget what they're doing.

(2020 addition- we recently had a teacher share that she had her students use this activity to practice, making sure they were socially distanced so they didn't "actually catch cooties". So fun!)

This silly video from Shmoop gives an example of why you have to perform any operation to both sides when you solve an equation. The video uses the story of Rudolph the Red-Nosed Reindeer. This video is an excellent choice for an anticipatory set a couple of days into the unit. Also, it could be used a closure activity new the end of the unit to see what students understand.

I love it when students get the chance to do more than just practice problems, when they really get to apply what they are learning. Well, this activity from Illustrative Mathematics is perfect for that. It gives students a simple example of how we model math. Then, it challenges students to solve an equation mathematically and symbolically. This really challenges students' thinking, especially if math comes easy to them. Something like this can really get them out of their comfort zone.

This activity is an extended response and will take students 15-45 minutes to complete. There are multiple parts and if you have less time they could use do part of it. Fast finishers can work on this as the unit progresses when they finish class work. Below is the beginning of the task. Clicking on the picture will take you to the entire task.

Algebra Meltdown is an online game that makes learning algebra concepts fun and concrete. Students have to navigate through a series of equations and inside a scientist's lab. The tasks get harder and harder as they go and works up to multi-step equations. This might be challenging to some students at first. Because this is a game, it's a great way to remind students that, just like when they play video games, it's okay to fail and to try again. That's how we learn new things.

Students love to play games like this and have a leader board in the classroom. You can keep track of the leaders over the course of the day or week. You can also give the top 5 winners some type of small prize- it's amazing how far a Jolly Rancher or cute eraser can go!

Try One Thing...

This collection of ideas might seem like a lot of activities if you try and implement them all at once. Just try one activity and see how it goes in your classroom. After that you can try a different one. The more engagement strategies you try you'll probably it's easy to become hooked on finding even more ways to add pizzazz to math practice activities.

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Activities to Make Practicing Multi-Step Equations Awesome - Idea Galaxy

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My history with teaching multi-step equations hasn't been a pretty one, but spoiler alert, there's a happy ending. A few years ago I was co-teaching with a relatively new teacher and I felt a lot of pressure to show him the ropes. I was new to the 8th grade math standards.

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Жеке жұмыс: Теңдеулерді шешу

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Жеке жұмыс: Теңдеулерді шешу

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Оқушыларға бірнеше теңдеу шешуге арналған тапсырмалар беріңіз.

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One-step equation worksheets
This set of worksheets requires students to solve one-step equations involving integers, fractions and decimals by performing addition, subtraction, multiplication or division operations. It also contains math riddles, finding the cost of the objects, translating the phrases into one-step equation and more.
Two-step equation worksheets
Click on the link to access exclusive worksheets on solving two-step equations that include integers, fractions and decimals. A number of MCQ's, equations in geometry, translating two-step equations and many more exercises are available for practice.
Multi-step equation worksheets
These worksheets require students to perform multiple steps to solve the equations. Use the knowledge gained in solving one-step and two-step equations to solve these multi-step equations. A number of application oriented problems based on geometrical shapes are also included here.
Equation word problems worksheets
Download and print this enormous collection of one-step, two-step and multi-step equation word problems that include integers, fractions, and decimals. MCQ worksheets form a perfect tool to examine a learner's perception on the topic.
Rearranging Equations worksheets
Literal equation worksheets help to hone the skills like rearranging the literal equations, rearrange and evaluate, word problems containing real-life applications and a lot more are included.
Equation of a line worksheets
Click here for worksheets on equation of a line. Write the equation of a line in standard form, two-point form, slope-intercept form and point-slope form. Download the complete set of worksheets on equation of a line that comprise worksheets on parallel and perpendicular lines as well.
Graphing linear equation worksheets
You are just a click away from a huge collection of worksheets on graphing linear equations. Plot the points and graph the line. Use the x values to complete the function tables and graph the line. The MCQ worksheets form a perfect tool to test student's knowledge on this topic.
Quadratic equation worksheets
Click on the link for an extensive set of worksheets on quadratic equations. Solve the quadratic equations by factoring, completing the square, quadratic formula or square root methods. Find the sum and product of the roots. Analyze the nature of the roots.
Absolute value equation worksheets
Use these worksheets to teach your students about the absolute value of integers. This module includes exercises like evaluating the absolute value expression at a particular value, input and output tables, graph the absolute value function and solve the various types of absolute value equation.
Systems of equations worksheets
Solve these systems of equations by elimination or substitution methods. The equations contain two or three variables. Equation with two variables represents straight lines, whereas equations with three variables represent a plane.

Sample Worksheets

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Equation worksheets contain solving one-step, two-step and multi-step equation; linear, quadratic and absolute value equation; graphing and more.

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Дифференциалды тапсырмалар

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Дифференциалды тапсырмалар

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Күрделі тапсырмаларды жоғары деңгейдегі оқушылар үшін дайындаңыз. Қосымша көмек қажет оқушыларға үлгі бойынша есептер беріңіз.

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Differentiated WORKSHEET on Solving Equations (with Answers)

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This has always been an effective worksheet, clearly showing the different leveled steps of solving equations. This is one of the worksheets that accompanies the thr

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Формативті бағалау

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Формативті бағалау

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Оқушылардың жұмысын бақылау арқылы олардың түсінгенін тексеріңіз. Сұрақтар қойып, талқылауға шақырыңыз.

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Суммативті бағалау

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Суммативті бағалау

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Оқушыларға теңдеулер бойынша шағын тест беріңіз.

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Білімді қорытындылау

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Білімді қорытындылау

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Оқушыларды топта талқылауға шақырыңыз: "Сіз бүгін не үйрендіңіз?" деген сұрақ қойыңыз.

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Әр оқушыдан теңдеулер туралы бір сұраққа жауап беруін сұраңыз.

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Үй тапсырмасы: Теңдеулерді шешу

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Үй тапсырмасы: Теңдеулерді шешу

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Оқушыларға қосымша теңдеулерді шешуге арналған жаттығулар беріңіз.

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One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

Learn more

Here we break down everything you need to know about solving equations. You'll learn what linear and quadratic algebraic equations are, and how to solve all the different types of them.

At the end you'll find solving equations worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you're still stuck.

What is an equation?

An equation is a mathematical expression that contains an equals sign.

E.g.

\[\begin{aligned} y+6&=0\\ 3(x-3)&=12\\ \frac{2x+2}{4}&=\frac{x-3}{3}\\ 2x^{2}+3x-2&=0 \end{aligned}\]

There are two sides to an equation, with the left side being equal to the right side.

Equations will often involve algebra and contain unknowns (variables) which we often represent with letters such as x or y.

We can solve simple equations and more complicated equations to work out the value of these unknowns; they could involve fractions, decimals or integers.

Solving equations worksheets

Get your free solving equations worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Solving equations worksheets

Get your free solving equations worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

How to solve equations

In order to solve equations, we need to work out the value of the unknown variable by adding, subtracting, multiplying or dividing both sides of the equation by the same value.

In GCSE Maths there are two main types of equations that we need to solve, both of which are covered below.

Explain how to solve equations

Solving equations methods

Within solving equations, you will find lessons on linear equations and quadratic equations.

Each method of solving equations is summarised below. For detailed examples, practice questions and worksheets on each one follow the links to the step by step guides.

1. Linear equations

There are 5 main types of linear equations we can solve.

Example of solving an equation with:

One unknown

2Unknown on both sides

3With brackets

4With fractions

5Powers (exponents) and roots

We can check that our solution is correct by substituting it into the original equation.

Step-by-step guide: Linear equations
Step-by-step guide: Equations with fractions

2. Quadratic equations

There are 4 main ways to solve quadratic equations.

Example of solving a quadratic equation by:

Factorising

Step-by-step guide: Solving quadratic equations by factorising
2Quadratic Formula
Step-by-step guide: Quadratic formula

\[\begin{aligned} x^{2}+4x-5&=0\\ \\ x&=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ a&=1, \quad b=4, \quad c=-5\\ x&=\frac{-4\pm\sqrt{4^2-4(1)(-5)}}{2(1)}\\ \\ x&=1, \qquad x=-5\\ \end{aligned}\]

Step-by-step guide: Completing the square
3Complete the square

\[\begin{aligned} x^{2}+4x-5&=0\\ \\ (x+2)^{2}-9&=0\\ (x+2)^{2}&=9\\ x+2&=\pm\sqrt{9}\\ \\ x&=3-2\\ &=1\\ \\ x&=-3-2\\ &=-5 \end{aligned}\]

4Graphically
Step-by-step guide: Solving quadratic equations graphically

The solutions/roots are found when the graph equals 0 (crosses the x-axis).

We can check that our solution is correct by substituting it into the original equation.

See also: Quadratic equations

Practice solving equations questions

Solving equations GCSE questions

2. Solve: x ² − 5x − 24 = 0

(3 marks)

Learning checklist

Use algebraic methods to solve linear equations

Solve quadratic equations algebraically by factorising

Solve quadratic equations algebraically by completing the square (H)

Solve quadratic equations algebraically by using the quadratic formula (H)

Solve quadratic equations by finding approximate solutions using a graph

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths revision programme.

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FREE GCSE maths practice papers (Edexcel, AQA & OCR)

8 sets of free exam practice papers written by maths teachers and examiners for Edexcel, AQA and OCR.

Each set of exam papers contains the three papers that your students will expect to find in their GCSE mathematics exam.

Download free

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One to one maths interventions built for KS4 success Weekly online one to one GCSE maths revision lessons now available Learn more Here we break down everything you need to know about solving equations. You'll learn what linear and quadratic algebraic equations are, and how to solve all the different types of them.

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Қосымша оқу материалы

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Қосымша оқу материалы

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Теңдеулерді шешу туралы бейнематериалдарды көру.

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Learn How To Solve Equations – Understand In 7 Minutes