steps in problem solving in math grade 6

• 6th Grade Math
• Solving word problems

Grade 6 Math Word Problems: Tips, Tricks, and Answers

Do you want to stimulate your 6 th grader’s creative thinking skills? Then, enjoy this brilliant math article. In this comprehensive guide, we will provide you with a treasure trove of fun solving strategies, tips, tricks, and answers to tackle those tricky grade 6 math word problems that have been confusing your students for some time now.

In this page, you will discover why math word problems are important for 6th-graders and simple methods of breaking down complex word problems into manageable steps.

Nevertheless, we will introduce you to Mathskills4kids.com , an outstanding website with thousands of common types of grade 6 math word problems and a step-by-step approach to solving them. Interestingly, we will illustrate how to use diagrams and models to solve math word problems efficiently.

Learn to love Grade 6 Math word problems with these worksheets and answers

Hello and welcome to Grade 6 Math word problems worksheets and answers , where your 6 th Grade students will learn to love and solve math problems and activities at all times.

We understand that word problems can often frustrate students, as they require a solid understanding of mathematical concepts and the ability to interpret and apply them to real-life situations. That's why we have compiled a collection of proven strategies and techniques to empower your students to approach word problems confidently and accurately.

From understanding problem-solving strategies to breaking down complex questions into manageable steps, this guide will equip you with the knowledge and resources to make math word problems a breeze. So, let's dive in and unlock the secrets to conquering grade 6 math word problems together!

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Why are math word problems important for 6th-graders.

Math word problems are about more than just doing calculations. They are also about applying your math knowledge to real-world situations. Math word problems are important for 6 th graders because they help them to:

• Learn how to use different math concepts and skills in various contexts
• Develop their logical thinking and reasoning abilities
• Enhance their communication and literacy skills
• Prepare them for standardized tests and future math courses

Math word problems also make math more exciting and relevant. They show us how math can solve everyday problems and challenges. They also expose us to different topics and scenarios we may not encounter in our regular math lessons.

Strategies for solving Grade 6 math word problems

Solving Grade 6 math word problems can be intimidating, especially involving multiple steps or operations. But don't worry. Some general strategies will help your students confidently approach any word problem. Here are some of them:

• Please encourage them to read the problem carefully and identify the given information, the unknowns, and the question.
• They should rewrite the problem in their own words or summarize it in a sentence.
• Let them choose a suitable method or strategy to solve the problem. Some standard methods are guessing and checking, making a table or chart, drawing a picture or diagram, using a formula or equation, working backward, or using logical reasoning.
• They must show their work and explain each step clearly. Use appropriate units, labels, symbols, and terms.
• Lastly, tell them to check their answer by plugging it back into the problem or using a different method. Ensure their answer makes sense and answers the question.

Breaking down complex word problems into manageable steps

Some word problems may seem too complex or confusing at first glance. They may have too much information, too many steps, or too many operations. In such cases, breaking down the problem into smaller and simpler parts is helpful. Here are some tips on how to do that:

Words like "difference," "subtract," "take away," or "minus" indicate s ubtraction .

Words like "product," "multiply," "times," or "of" indicate multiplication .

Words like "quotient," "divide," "per," or "out of" indicate division .

Words like "ratio," "fraction," "percent," or "part" indicate fractions or decimals .

Words like "equal," "same as," or "is" indicate equations .

Words like "more than,” “less than," "greater than," or "smaller than" indicate inequalities .

Words like "average," "mean," or "median" indicate statistics .

Words like "area," "perimeter," "volume," or "surface area" indicate geometry , etc.

• Use parentheses, brackets, or other symbols to group the parts of the problem that belong together . For example, if the problem says:

You can rewrite it as:

• (John has 12 apples) + (Mary has 8 apples) = (total number of apples) / (4 people) = (number of apples per person)

This way, you can see the structure of the problem more clearly and focus on one part at a time.

• Solve each part of the problem separately and write down the intermediate results . For example, using the previous problem:
• (John has 12 apples) + (Mary has 8 apples) = (total number of apples)
• 12 + 8 = 20
• (total number of apples) / (4 people) = (number of apples per person)

This way, you can keep track of your work and avoid making mistakes.

• Combine the intermediate results to get the final answer. For example, using the previous problem :

This way, you can answer the question and check your answer.

Common types of grade 6 math word problems

There are many types of word problems that you may encounter in grade 6 math . Some of the most common ones found on Mathskills4kids.com are:

• Ratio and proportion problems : These problems involve finding the relationship between two quantities with the same unit or measure. For example, if 12 pencils cost $3, how much do 20 pencils cost?
• Percent problems : These problems involve finding the part, whole, or percent of a quantity. For example, if 30% of a class is boys, and there are 24 students, how many boys are there?
• Fraction problems : These problems involve adding, subtracting, multiplying, or dividing fractions. For example, how much pizza do you have left if you have 2/3 of a pizza and eat 1/4?
• Decimal problems : These problems involve adding, subtracting, multiplying, or dividing decimals. For example, if you buy a shirt for $12.50 and a pair of jeans for $24.75, how much change do you get from $50?
• Measurement problems : These problems involve converting between different units of measurement or finding the perimeter, area, or volume of shapes. For example, if a rectangle has a length of 15 cm and a width of 10 cm, what is its area in square meters?
• Algebra problems : These problems involve finding the value of an unknown variable or expression. For example, if x + 5 = 13, what is the value of x?

A step-by-step approach to solving different types of word problems

No matter what type of word problem your 6 th graders are faced with, they can use the following steps to solve it:

• They should read the problem carefully and identify the given information and the question.
• They must choose a variable to represent the unknown quantity and write an equation or expression that relates the given information and the question.
• They can now solve the equation or expression and find the variable's value.
• They can check their answer by plugging it back into the equation or expression to see if it makes sense.
• They can now write their answer in complete sentences and include the appropriate units.

Using diagrams and models to solve math word problems

Sometimes, it can be helpful to use diagrams and models to visualize the problem and make it easier to solve. Some examples of diagrams and models for solving math word problems are:

• Tape diagrams : These are horizontal or vertical bars showing the relationship between two quantities. For example, you can use a tape diagram to show how much money each person gets when $60 is shared equally among 4 people.
• Number lines : These horizontal lines show numbers and their relative positions. For example, you can use a number line to show how to add or subtract fractions with different denominators.
• Tables : These are grids that show data in rows and columns. For example, you can use a table to show how to find equivalent ratios or fractions.
• Charts : These are graphical representations of data using bars, circles, lines, or other shapes. For example, you can use a chart to show how to find the percent of a quantity or compare different quantities.
• Drawings : These are sketches or illustrations that show shapes or objects. For example, you can use a drawing to show how to find a shape's perimeter, area, or volume.

Providing answers and explanations to sample Mathskills4kids’ Grade 6 math word problems

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com :

Answer : 6 cups of flour

Explanation : This is a ratio problem. We can use a tape diagram to show the relationship between flour and sugar.

Flour →|<---2 cups--->|<---2 cups--->|<---2 cups---> = 6

Sugar→|<---3 cups--->|<---3 cups--->|<---3 cups---> = 9

We can see that for every 3 cups of sugar, we need 2 cups of flour. So, for 9 cups of sugar, we need 6 cups of flour.

Answer : $15

Explanation : This is a percent problem. We can use a formula to find the sale price of the shirt.

Sale price = Original price - Discount

Discount = Percent off x Original price

We know the percent off is 40%, and the original price is $25. So, we can plug these values into the formula and solve for the sale price.

Discount = 40% x $25

Discount = 0.4 x $25

Discount = $10

Sale price = $25 - $10

Sale price = $15

Tips for improving problem-solving skills in Grade 6 math

Here are some tips that can help students improve their problem-solving skills in grade 6 math :

• Please encourage them to practice regularly and try different types of word problems.
• They should review the concepts and skills they have learned and apply them to new situations.
• They can use different strategies and methods to solve word problems and compare their results.
• Let them ask for help from the teacher, parents, or peers if they get stuck or confused.
• They should learn from their mistakes and try to avoid them in the future.

Bonus: additional resources to reinforce Grade 6 math problem skills

If you want to enhance your student's Grade 6 math word problem skills , or if you need some extra help, here are some additional and useful web links that you can check out:

• Math Playground : This website has a lot of fun and interactive games that let 6 th graders practice different types of math word problems, such as fractions, decimals, ratios, proportions, and more. They can also watch videos explaining how to solve some problems. https://www.mathplayground.com/wordproblems.html .
• Khan Academy : This website has many videos and exercises covering various topics in Grade 6 math, including word problems. Students can learn at their own pace and track their progress. https://www.khanacademy.org/math/cc-sixth-grade-math .
• IXL : This website has many practice questions aligned with the Common Core standards for Grade 6 math. Students can choose from different categories of word problems, such as expressions and equations, geometry, statistics, and more. They can also get instant feedback and explanations for their answers. https://www.ixl.com/math/grade-6 .
• Math Goodies : This website has a lot of worksheets and lessons that teach 6 th graders how to solve different types of word problems, such as percent, ratio, proportion, and more. They can also find tips and tricks for solving word problems faster and easier. https://www.mathgoodies.com/math-mammoth/worksheets/pdf/grade_6_word_problems.pdf .

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Math word problems can be challenging for many 6th-graders, but they are also important for developing their mathematical thinking and reasoning skills.

Using the strategies and steps we discussed in this article, your student's ability to solve different types of word problems in Grade 6 math can be improved.

You can also use the diagrams and models we have shown you to help your students visualize the problem and find the solution. Encourage them to practice as much as possible, and they must not be afraid to ask for help if needed.

You can also use the web links that we have provided to reinforce your student’s learning and have fun with math. We hope this article has helped your 6th-grade students feel more confident and prepared for tackling Grade 6 math word problems.

Happy problem-solving!

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Problem solving - flowchart (6th grade math)

This is a multi-step math word problem. I make a flowchart for it, to show the solution steps. And then of course we solve the problem, with the help of a bar model. :)

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Virginia Standards Of Learning (sol) Curriculum

Students are entering a new section of math that consists of algebra, geometry, decimals, and more complicated division problems. When there is not a parent or teacher around, students have access to on-demand videos for their sixth-grade mathematical lessons. Our video tutorials are taught by math teachers who go through the problem solving process.

• The key to learning math is repetition, and our math teachers go through multiple examples. 
• Math teachers show students step-by-step directions on how to solve these more complex problems.
• Students learn money, ratios, decimals, graphing, and other concepts from the 6th grade curriculum.

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Problem-Solving Strategies

October 16, 2019

There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.

Problem-solving strategies

1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.

Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.

Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?

2. Guess and check

Teach students the same strategy research mathematicians use.

With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.  By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.

Find two numbers that have sum 11 and product 24.

Try/guess  5 and 6  the product is 30 too high

  adjust  to 4 and 7 with product 28 still high

  adjust  again 3 and 8 product 24

3. Make a table or a list

Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.

To make sure you are listing all the information correctly read the problem carefully.

Find the common factors of 24, 30 and 18

Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.

Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?

A table or list is useful in solving logic problems.

Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.

Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.

Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.

5. Find a pattern.

Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.

 The “rule” can then be used to find the answer to the question and complete the table/list.

Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?

6. Working backward

Problems that can be solved with this strategy are the ones that  list a series of events or a sequence of steps .

In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.

Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.

For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.

The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.

8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took

8+31+5+4= 48   Answer: The box came with 48 pieces of candy.

Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.

Print and digital activities

I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.

sample below

How to use the activity cards

Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.

Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.

For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.

Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.

Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions

There are 2 versions of the resource

70 google slides with explanations + 70 printable task cards

70 google slides with explanations + 11 worksheets

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6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution. 

1. Link problem-solving to reading

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it. 

3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process. 

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks. 

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.” 

6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process. 

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

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Expressions and Equations 6th Grade

Welcome to our Expressions and Equations 6th Grade Worksheets.

Here you will find a range of algebra worksheets to help you learn about basic algebra, including generating and calculating algebraic expressions and solving simple equations.

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Generate the expression worksheets, calculate the expression worksheets.

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Want to gain a basic understanding of algebra?

Looking for some simple algebra worksheets?

Do you need a bank of useful algebra resources?

Look no further! The pages you need are below!

Here is our selection of basic algebra sheets to try.

We have split the worksheets up into 3 different sections:

• 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.
• Mixed questions involving all 3 of the above.

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.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

• 2a + 5 is an expression involving the variable a
• 5(y 2 - 6) is another expression

What is an algebraic equation?

An equation is where an algebraic expression is equal to something, which might be a number, or another algebraic expression.

• 2a + 5 = 7 is an equation
• 5(y 2 - 6) = 3y + 8 is another equation

How to Generate an Expression

When we are generating an expression, we are taking a rule and turning it into algebra.

• Subtract 6 from n could be written as n - 6.
• Multiply d by 4 could be written as d x 4 or 4d.
• Add 5 to p and then double the result is written as (p + 5) x 2 or 2(p + 5)

How to Calculate an Expression

When we are calculating the value of an expression, we work out the value of the expression when we give a value to the variable.

• p + 5 has a value of 11 when p = 6 because 6 + 5 = 11
• 4 - q has a value of 1 ½ when q = 2 ½ because 4 - 2 ½ = 1 ½
• 4(n - 2) has a value of 32 when n = 10 because 4 x (10 - 2) = 4 x 8 = 32
• 4(n - 2) has a value of -8 when n = 0 because 4 x (0 - 2) = 4 x (-2) = -8

How to Solve a Simple Equation

When we are solving an equation, we are finding out the value(s) of the variable in the equation.

• then p = 4 because 4 + 5 = 9
• Answer: p = 4
• then n = 56 ÷ 7 = 8
• Answer: n = 8
• means that f = 4 because 12 - 4 = 8
• Answer: f = 4
• then t = 5 because 0.6 x 5 = 3
• Answer: t = 5
• then r = 32 because ½ x 32 = 16
• Answer: r = 32

Expressions and Equations 6th Grade Worksheets

• Generate the Expressions Sheet 6:1
• PDF version
• Generate the Expressions Sheet 6:2
• Calculate the Expression Sheet 6:1
• Calculate the Expression Sheet 6:2

Calculate the Expressions Walkthrough Video

This short video walkthrough shows several problems from our Calculate the Expression Worksheet 6:1 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, please check out the video below!

Simplifying Expressions Worksheets

• Simplifying Expressions Sheet 6:1
• Simplifying Expressions Sheet 6:2

Simplifying Expressions Walkthrough Video

This short video walkthrough shows several problems from our Simplifying Expressions Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

Solve the Equation Worksheets

• Solving Equations Sheet 6:1
• Solving Equations Sheet 6:2

Expressions and Equations 6th Grade Mixed Worksheets

These questions involve solving equations, working out the value of expressions and also generating expressions.

They are a combination of questions from all the above categories.

• Expressions and Equations Mixed Questions Sheet 6:1
• Expressions and Equations Mixed Questions Sheet 6:2

Expressions and Equations Walkthrough Video

This short video walkthrough shows several problems from our Expressions and Equations Mixed Questions Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

More Recommended Math Worksheets

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

Inequalities Worksheets

• Inequalities on a Number Line
• Writing Inequalities from Word Problems
• 6th Grade Distributive Property Worksheets

The sheets on this page have been designed to factorize and expand a range of simple expressions using the distributive property..

• Basic Algebra Worksheets

We have a selection of basic algebra worksheets which are aimed at 6th and 7th graders and involve similar skills to the sheets here.

Input and Output Function Tables

Have a go at these input and output tables.

Test your skills at finding inputs, outputs and rules.

Our easier sheets have rules instead of algebraic functions.

Our harder sheets use algebraic functions.

• Input and Output Tables Worksheets (easier)
• Input and Output Function Tables with Algebraic Functions

Free Algebra Problem Solver

The Mathway Calculator is a great way to solve algebra problems that you can type into a calculator.

Try using this online calculator tool to solve one of your problems and watch it work!

There are a range of calculators to choose from to meet your needs.

The Mathway problem solver will answer your problem instantly and also give you a link to view each of the steps needed.

If you choose to 'View the steps' you will be directed to the Mathway website where you will be able to see in more detail each of the steps needed to solve the problem. Please note that Mathway may charge you a small fee for this!

Factorising Quadratic Equations

Are you stuck on a quadratic equation and don't know what to do?

Are you looking for some worksheets on factorising quadratic equations to print out?

Take a look at our support pages on quadratic equations where you will hopefully find what you are looking for.

• Factorising Quadratic Equations Support page
• Factoring Quadratic Equations worksheets
• 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!

PEMDAS 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.
• PEMDAS Problems Worksheets 5th Grade
• 6th Grade Order of Operations

Interactive Equality Explorer

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

• Interactive Equality Explorer by PhET

Expressions and Equations 6th Grade Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick expressions and equations 6th grade quiz tests your knowledge and skill at generating and calculating expressions, as well as solving equations.

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Math word Problems With Answers for Grade 6

Grade 6 maths word problems with answers are presented. Some of these problems are challenging and need more time to solve. Also detailed solutions and full explanations are included.

• Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
• If the area of a circle is 81pi square feet, find its circumference.
• Find the greatest common factor of 24, 40 and 60.
• In a given school, there are 240 boys and 260 girls. a) What is the ratio of the number of girls to the number of boys? b) What is the ratio of the number of boys to the total number of pupils in the school?
• If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
• Find k if 64 ÷ k = 4.
• Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
• What is x if x + 2y = 10 and y = 3?
• A telephone company charges initially $0.50 and then $0.11 for every minute. Write an expression that gives the cost of a call that lasts N minutes.
• A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
• A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
• A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?
• A small square of side 2x is cut from the corner of a rectangle with a width of 10 centimeters and length of 20 centimeters. Write an expression in terms of x for the area of the remaining shape.
• A rectangle A with length 10 centimeters and width 5 centimeters is similar to another rectangle B whose length is 30 centimeters. Find the area of rectangle B.
• A school has 10 classes with the same number of students in each class. One day, the weather was bad and many students were absent. 5 classes were half full, 3 classes were 3/4 full and 2 classes were 1/8 empty. A total of 70 students were absent. How many students are in this school when no students are absent?
• The perimeter of square A is 3 times the perimeter of square B. What is the ratio of the area of square A to the area of square B.
• John gave half of his stamps to Jim. Jim gave gave half of his stamps to Carla. Carla gave 1/4 of the stamps given to her to Thomas and kept the remaining 12. How many stamps did John start with?
• Two balls A and B rotate along a circular track. Ball A makes 4 full rotations in 120 seconds. Ball B makes 3 full rotation in 60 seconds. If they start rotating now from the same point, when will they be at the same starting point again?
• A segment is 3 units long. It is divided into 9 parts. What fraction of a unit are 2 parts of the segment?
• A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
• Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's & Jim's age. Find the present age of each one of them.
• Linda spent 3/4 of her savings on furniture. She then spent 1/2 of her remaining savings on a fridge. If the fridge cost her $150, what were her original savings?
• The distance bewteen Harry and Kate is 2500 meters. Kate and Harry start walking toward one another and Kate' dog start running back and forth between Harry and Kate at a speed of 120 meters per minute. Harry walks at the speed of 40 meters per minute while Kate walks at the speed of 60 meters per minute. What distance will the dog have travelled when Harry and Kate meet each other?

Answers to the Above Questions

• a) 13:12 b)12:25
• 0.50 + N * 0.11
• 4.5 gallons
• 450 centimeters squared
• 108 cubic centimeters
• 1250 meters/minute
• Carla:5 years, Jim: 6 years, Peter: 19 years.
• 3000 meters

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• 6th Grade Mathematics

Education Standards

Wyoming standards for mathematics.

Learning Domain: Ratios and Proportional Relationships

Standard: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

Standard: Use ratio and rate reasoning to solve real-world and mathematical problems.

Standard: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Standard: Solve unit rate problems including those involving unit pricing and constant speed.

Maryland College and Career Ready Math Standards

Standard: Understand the concept of a unit rate a/b associated with a ratio a:b with b ‰äĘ 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to non-complex fractions.)

Standard: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Standard: Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Common Core State Standards Math

Cluster: Understand ratio concepts and use ratio reasoning to solve problems

Standard: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to non-complex fractions.)

Distance, Time, and Speed

Dollars and pesos, hours, speed, and miles, prepare a presentation, price per gallon, stack of books, using rates to solve problems.

Students use their knowledge of rates to solve problems.

Key Concepts

Given any two values in a rate situation, you can find the third value.

These three equations are equivalent, and they all describe rate relationships:

y = rx ,   r = yx ,   x = yr

At the beginning of this lesson (or for homework), students will revise their work on the pre-assessment Self Check. Their revised work will provide data that you and your students can use to reassess students' understanding of rate. You can use this information to clear up any remaining misconceptions and to help students integrate their learning from the past several days into a deeper and more coherent whole.

The work students do in this lesson and in revising their pre-assessments will help you and your students decide how to help them during the Gallery. In this lesson, students will reveal the depth and clarity of their understanding of rate.

• Students whose understanding of rate is still delicate should get extra help during the Gallery.
• Students who feel that they have a robust understanding of rate may choose from any of the problem-solving or deeper mathematics problems in the Gallery.

Goals and Learning Objectives

• Uncover any partial understandings and misconceptions about rate.
• Develop a more robust understanding of rate.
• Identify which Gallery problems to work on.

Revise and Extend Your Work

Lesson guide.

Have students work in pairs to revise their work from the Self Check. Encourage students to incorporate ideas from their partner in their revisions. Then students will work together on a similar task.

Students have worked with rate in a variety of contexts. At this point, their understanding is still very delicate, containing a mix of good conceptualization, partial conceptions, and some misconceptions.

While students work with their partners, note different approaches to the task:

• How do they organize their work?
• Do they notice if they have chosen a strategy that does not seem to be productive? If so, what do they do?
• He can multiply the rate $3.00 per pound by 5.75 pounds to find the price in dollars.
• She can divide 12 miles by 1.5 hours to find her speed in miles per hour.
• He can divide 325 square feet of wall by 85 square feet per quart to find the number of quarts.
• She can divide 13.1 miles by 2.6 hours to find her speed in miles per hour.

Work with your partner to revise your work on the Self Check.

• Explain what calculation the person can perform to find what he or she wants to know.
• Explain what the unit of the answer is.
• At the store, Jason sees that the price of cherries is $3.00 per pound. What calculation can he perform to find the price of 5.75 pounds of cherries?
• Rosa knows that she can skate to the park in 1.5 hours. The park is 12 miles away. What calculation can she perform to find her speed?
• Denzel knows that 1 quart of paint will cover about 85 square feet of wall. He needs enough paint to cover 325 square feet of wall. What calculation can Denzel perform to find how many quarts of paint he will need?
• Mina ran a half marathon (13.1 miles) this weekend. She completed the run in 2.6 hours. What calculation can Mina perform to find her speed during this run?

Math Mission

Discuss the Math Mission. Students will work through several rate problems using what they have learned about rates.

Use what you know about rates to work through problems.

Pay attention to how students are finding values for their tables. Do they start with the first row? With some other row? How are students navigating between the rows?

The different approaches you notice will allow you to engage students in a rich conversation during Ways of Thinking.

SWD: Consider the prerequisite skills for this Putting it Together lesson. Students with disabilities may need direct instruction and/or guided practice with the skills needed to complete the tasks in this lesson. It may be helpful to pull individual students and/or a small group for direct instruction or guided practice with the skills they have learned thus far in this unit.

Mathematical Practices

Mathematical Practice 1: Make sense of problems and persevere in solving them.

• In these problems, students can enter any numbers into the tables as long as the relationship between the numbers is correct. As students work, identify a variety of work with an eye to making connections among different methods. For example, look for the following different approaches:
• Choosing a speed and a time, and then calculating distance; choosing a distance and a time, and then calculating speed; and choosing a speed and a distance, and then calculating time.

Mathematical Practice 8: Look for and express regularity in repeated reasoning.

• Look for students who understand that they can choose any two numbers to find the third number; these students are using a general method to solve all rate problems.

Interventions

Student has difficulty connecting the problem to familiar situations.

• What do you think a typical bike riding speed might be?
• How long might you ride your bike? If you ride for that length of time at that speed, how far would you ride?
• What is the relationship among speed, distance, and time?
• What is a common rate for the speed of a car?
• If a car travels for two hours, how far would it go at that constant speed?

Student has difficulty getting started.

• Describe the Task in your own words to your partner.
• Can you use your definition of rate to help you get started?

Student has an incorrect solution.

• Have you checked your work?
• Do your answers make sense?
• Explain the relationship among your numbers in this problem.
• Where do you see the rate in this problem? Describe it.

Student has a solution.

• Why did you approach this problem in the way that you did?
• Could you have used another method to solve this problem? Explain.
• What still confuses you about rate?
• Answers will vary, but the relationships should show that speed is equal to distance divided by the time.

In this problem, you will work with three quantities: distance, time, and speed.

Create a set of three numbers that shows the relationship among the quantities. For instance, if you chose a time of 3 hours and a speed of 25 miles per hour, the distance would be 75 miles.

• The first set contains any numbers.
• The second set contains numbers greater than 10.
• The third set contains decimal numbers.

INTERACTIVE: Distance, Time, and Speed

Students will fill in a table showing the relationship between gallons, total price, and price per gallon.

• Students can enter any numbers into the tables as long as the relationship between the numbers is correct. As students work, identify a variety of work with an eye to making connections among different methods. For example, look for the following different approaches:
• Choosing a number of gallons and a total price, and then calculating unit price; choosing a total price and a unit price, and then calculating a number of gallons; and choosing a number of gallons and a unit price, and then calculating total price.
• Answers will vary, but the relationships should show that price per gallon is equal to price divided by gallons.

In this problem, you will work with three quantities: gallons, total price, and price per gallon.

Create a set of three numbers that shows the relationship among the quantities.

INTERACTIVE: Price per Gallon

Have the students look up the current exchange rate of pesos per dollar or dollars per peso. Students fill in a table reflecting one of those rates.

• Choosing a number of dollars and a rate, and then calculating a number of pesos
• Choosing a number of pesos and a rate, and then calculating a number of dollars.
• Answers will vary, but the relationships should show that dollars per peso is equal to dollars divided by pesos.

In this problem, you will work with three quantities: dollars, pesos, and dollars per peso.

Create a set of three numbers that show the relationship among the quantities.

INTERACTIVE: Dollars and Pesos

Student will fill in a table showing the relationship of hours, speed, and miles.

• Answers will vary, but the relationships should show that speed is equal to the miles divided by the hours.

In this problem, you will work with three quantities: hours, speed, and miles.

Lesson guide

Students will fill in a table showing the relationship of the number of books in a stack, the height of the stack, and the thickness of each book (inches per book).

• Answers will vary, but the relationships should show that the thickness of a book is equal to the height of the stack divided by the number of books.

In this problem, you will work with three quantities: the number of books in a stack, the height of the stack, and the thickness of each book (inches per book).

INTERACTIVE: Stack of Books

Students fill in a table on a runner to find out if a runner runs at a constant speed. Then they prepare a presentation on their method.

Preparing for Ways of Thinking

Look for students who understand that they can choose any two numbers to find the third number. These students are using a general method to solve all rate problems.

• Did you remember to convert minutes to hours?

10 kilometers per hour

Prepare a presentation of your work.

• Does the table support this statement?
• Complete the table.
• Express the speed of the runner in kilometers per hour.

INTERACTIVE: Prepare a Presentation

Make Connections

By the end of the discussion, students should understand each other's methods and make connections between methods. All students should also understand that given any two values in a rate situation, they can find the third value. Encourage students to critique each method.

Mathematics

Discuss the different approaches students use. Ask questions such as the following to help students critique each other's work and to help them see relationships among the different methods:

• How did the student make sense of the problem?
• What was similar about their approaches?
• What was different?
• Did anyone try a method that did not work? What did you do? Why didn't your method work?

Performance Task

Ways of thinking: make connections.

As you listen to other students present their work, find ways to understand how to think about rate.

As your classmates present, ask questions such as:

• Where is the rate in your numbers?
• Where do you see the other two quantities?
• How would you describe the relationship among the three numbers?

Reflect On Your Work

Have each student write a brief reflection before the end of class. Review students' reflections.

If any reflections look interesting enough to pursue later, share them with the class at an appropriate time.

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

Something I still wonder about rates is …

Free Printable Multi-Step Word Problems Worksheets for 6th Grade

Multi-Step Word Problems: Discover a collection of free printable math worksheets for Grade 6 students, designed to help them master solving complex problems through a series of smaller, manageable steps. Empower your teaching with Quizizz!

Explore Multi-Step Word Problems Worksheets by Grades

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Explore printable Multi-Step Word Problems worksheets for 6th Grade

Multi-Step Word Problems worksheets for Grade 6 are an essential resource for teachers looking to enhance their students' math skills and problem-solving abilities. These worksheets provide a variety of challenging and engaging math word problems that require students to use multiple steps and operations to find the solution. By incorporating these worksheets into their lesson plans, teachers can help their Grade 6 students develop a deeper understanding of mathematical concepts, improve their critical thinking skills, and build confidence in their ability to tackle complex problems. With a wide range of topics covered, from fractions and decimals to geometry and algebra, these Multi-Step Word Problems worksheets for Grade 6 are a valuable tool for any math teacher looking to challenge and inspire their students.

In addition to Multi-Step Word Problems worksheets for Grade 6, teachers can also utilize Quizizz, an interactive platform that offers a variety of engaging and customizable quizzes, games, and activities to supplement their math curriculum. Quizizz allows teachers to create their own quizzes or choose from a vast library of pre-made quizzes, covering a wide range of topics and difficulty levels. This platform not only provides a fun and interactive way for students to practice their math skills but also offers valuable insights and analytics for teachers to track their students' progress and identify areas for improvement. By incorporating Quizizz into their lesson plans, teachers can provide a well-rounded and engaging learning experience for their Grade 6 students, helping them excel in math and build a strong foundation for future success.

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What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
• The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
• The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
• The calculus section will carry out differentiation as well as definite and indefinite integration.
• The matrices section contains commands for the arithmetic manipulation of matrices.
• The graphs section contains commands for plotting equations and inequalities.
• The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

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