Realistic Math Problems Help 6th-graders Solve Real-Life Questions

Solving math problems can intimidate sixth-graders: It shouldn t. Using a few simple formulas and a bit of logic can help students quickly calculate answers to seemingly intractable problems. Explain to students that you can find the rate (or speed) that someone is traveling if you know the distance and time that she traveled. Conversely, if you know the speed (rate) that a person is traveling as well as the distance, you can calculate the time he traveled. You simply use the basic formula: rate times the time equals distance, or r * t d (where * is the symbol for times.)

The free, printable worksheets below involve problems such as these, as well as other important problems, such as determining the largest common factor, calculating percentages, and more. The answers for each worksheet are provided through a link in the second slide right after each worksheet. Have students work the problems, fill in their answers in the provided blank spaces, then explain how they would arrive at the solutions for questions where they are having difficulty. The worksheets provide a great and simple way to do quick formative assessments for an entire math class.

Worksheet No 1

On this PDF, your students will solve problems such as: Your brother traveled 117 miles in 2.25 hours to come home for school break. What’s the average speed that he was traveling? and You have 15 yards of ribbon for your gift boxes. Each box gets the same amount of ribbon. How much ribbon will each of your 20 gift boxes get?

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Worksheet No. 1 Solutions

To solve the first equation on the worksheet, use the basic formula: rate times the time distance, or r * t d. In this case, r the unknown variable, t 2.25 hours, and d 117 miles. Isolate the variable by dividing r from each side of the equation to yield the revised formula, r t ÷ d. Plug in the numbers to get: r 117 ÷ 2.25, yielding r 52 mph.

For the second problem, you don t even need to use a formula—just basic math and some common sense. The problem involves simple division: 15 yards of ribbon divided by 20 boxes, can be shortened as 15 ÷ 20 0.75. So each box gets 0.75 yards of ribbon.

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Worksheet No. 2

On worksheet No. 2, students solve problems that involve a little bit of logic and a knowledge of factors, such as: I’m thinking of two numbers, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What’s the other number I’m thinking of?

Other problems require only a basic knowledge of percentages, as well as how to convert percentages to decimals, such as: Jasmine has 50 marbles in a bag. 20% of the marbles are blue. How many marbles are blue?

Worksheet No. 2 Solution

For the first problem on this worksheet, you need to know that the factors of 12 are 1, 2, 3, 4, 6, and 12; and the multiples of 12 are 12, 24, 36. (You stop at 36 because the problem says that this number is the largest common multiple.) Let s pick 6 as a possible greatest common multiple because it s the largest factor of 12 other than 12. The multiples of 6 are 6, 12, 18, 24, 30, and 36. Six can go into 36 six times (6 x 6), 12 can go into 36 three times (12 x 3), and 18 can go into 36 twice (18 x 2), but 24 cannot. Therefore the answer is 18, as 18 is the largest common multiple that can go into 36.

For the second answer, the solution is simpler: First, convert 20% to a decimal to get 0.20. Then, multiply the number of marbles (50) by 0.20. You would set up the problem as follows: 0.20 x 50 marbles 10 blue marbles.

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A Grade 7 Math syllabus is descriptive and informative for students. All basic topics and their sub-topics including algebra, geometry, mensuration and their sub-topics are added in this syllabus. Grade 7 Math is a foundation for higher-level studies. Tutorvista offers online learning assistance to cover syllabus in an organized manner. We also provide useful learning sessions for each Math topic, these sessions are well-organized, cost-effective and meets student’s learning requirements successfully. Students can work with proficient subject experts and they can share as well as solve all learning problems to improve their knowledge and prepare well before exams.

7th Grade Math Topics

Number and Operations

Understanding of rational numbers with respect to square roots of perfect square, proportional reasoning, percents involving discounts, tax and rates.

Identify, compare and order decimals, fractions and integers.

Scientific notation, radicals, absolute value, irrational or real numbers.

Geometry and Measurement

Properties of angles (adjacent angle, vertical, straight or angle formed by intersection of two non – parallel lines).

Hypothesis, sketch, identify, sort, classify, construct, measure, and apply a variety of geometric shapes and figures and problems.

Analyze and identify shapes that have been rotated, reflected, translated and describe those that are congruent.

Understanding of the area of circles or the area or perimeter of figures (quadrilaterals, triangles, or parts of circles), and the surface area of rectangular prisms, or volume of rectangular prisms, triangular prisms, or cylinders.

Functions and Algebra

Extend, analyze and justify the explanations for patterns and their rules and a more complex level using words and symbols.

Solving problems involving the relationship between slope and rate of change or describes how change in the value of one variable relates to change in the value of a second variable.

Be able to write algebraic expressions and write statements to understand simple formulas and simplify algebraic equations with the four operations.

Data, Statistics, and Probability

Analyze the data to formulate or justify conclusions, to make predictions (circle graphs, linear relationship).

Simple or composite experiments, independent events, dependent events.

Representations of data.

Mean, median, mode, and range.

Predicts and determines event in which the sample space may or may not contain equally likely outcomes.

Math websites allow your child to review concepts, practice problems similar to those covered by schoolwork and play fun online games. Math help for 6th graders is available online for free.

6th Grade Math Games from MathPlay.com

Your kids will think they’re playing recreational video games as they learn math. Flashy graphics adorn these interactive math games, which are geared specifically toward 6th graders. Fractions, decimals and geometric figures are some of the math topics which are reviewed in these action-packed themed games. Some of the math games use sports, like soccer and baseball, to engage children, while others use a Jeopardy-like game show format.

Free Practice Problems at IXL.com

Math practice problems can be instantly generated online for supplemental at-home practice. Problems get harder with the more correct answers your child enters. Topics cover the spectrum of 6th grade math, including integers, decimals, charts and graphs, square roots and lowest term fractions.

Each main category is divided into subsections to help isolate skills. For example, multiplication is a main heading, and underneath it are several types of operations, including multiplying integers and multiplying whole numbers. If your son grasps some of the concepts related to a main unit, this site can help him focus at-home practice on the subjects that he finds more challenging.

Math Help for 6th Graders from AAAMath.com

Explanations of 6th grade math topics are offered online, including sample problems and details on how to solve them. Like the IXL website, AAA Math lists topics commonly covered in 6th grade math class. Topics are organized by mathematical operations, such as comparing and ordering integers, subtracting 7-digit numbers and estimating the sum of decimals.

Your daughter may refer to this page in between working on practice problems or games, whenever she needs a refresher. If your own math skills are rusty, you may also find AAA Math helpful when your daughter asks you to go over a certain unit with her.

Math websites allow your child to review concepts, practice problems similar to those covered by schoolwork and play fun online games. Math help for 6th graders is available online for free.

6th Grade Math Games from MathPlay.com

Your kids will think they’re playing recreational video games as they learn math. Flashy graphics adorn these interactive math games, which are geared specifically toward 6th graders. Fractions, decimals and geometric figures are some of the math topics which are reviewed in these action-packed themed games. Some of the math games use sports, like soccer and baseball, to engage children, while others use a Jeopardy-like game show format.

Free Practice Problems at IXL.com

Math practice problems can be instantly generated online for supplemental at-home practice. Problems get harder with the more correct answers your child enters. Topics cover the spectrum of 6th grade math, including integers, decimals, charts and graphs, square roots and lowest term fractions.

Each main category is divided into subsections to help isolate skills. For example, multiplication is a main heading, and underneath it are several types of operations, including multiplying integers and multiplying whole numbers. If your son grasps some of the concepts related to a main unit, this site can help him focus at-home practice on the subjects that he finds more challenging.

Math Help for 6th Graders from AAAMath.com

Explanations of 6th grade math topics are offered online, including sample problems and details on how to solve them. Like the IXL website, AAA Math lists topics commonly covered in 6th grade math class. Topics are organized by mathematical operations, such as comparing and ordering integers, subtracting 7-digit numbers and estimating the sum of decimals.

Your daughter may refer to this page in between working on practice problems or games, whenever she needs a refresher. If your own math skills are rusty, you may also find AAA Math helpful when your daughter asks you to go over a certain unit with her.

Mark and Fred had some money in the ratio 6:1. Mark gave half of his money to Fred. Find the ratio of the amount of money Mark had left to the amount of money Fred had in the end.

The ratio of the amount of money Mark had left to the amount of money Fred had in the end is 3:4.

Carol puts some green and red unit cubes in a box. The ratio of the number of green cubes to the number of red cubes is 2:1. She adds 12 more red cubes in the box and the ratio becomes 4:5.

a) How many green cubes are there in the box?

b) How many red cubes does Carol have in the end?

From the model, we see that:

a) 3 units = 12 cubes

1 unit = 12 3 = 4 cubes

4 units = 4 4 = 16 cubes

There are 16 green cubes in the box.

b) 5 units = 5 4 = 20 cubes

Carol has 20 red cubes in the end.

1. A board was cut into two pieces whose lengths are in the ratio 2:5. The longest piece was 85 inches. How long was the shortest piece?

1. The ratio of pigs to cows to sheep on the farm is 2:4:7. There are 65 more sheep than pigs. How many cows are there on the farm?

a) Draw a bar model representing the situation

b) Elmer is 5 years older than Sam. How old is Sam?

1. At Al’s Catering Service, they often make a large batch of fruit salad. The ratio of cups of apples to cups of oranges in the recipe is 8 : 5.

a) If they use 15 cups of oranges, how many cups of apples should they use?

b) If they only use 2 cups of apples, how many cups of oranges should they use?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Welcome to tlsbooks.com, where you’ll find a variety of free printable sixth grade worksheets for you to print and share with your child or students.

Our sixth grade worksheets are a convenient way to supplement the work your child is already doing in school. Depending on your child’s abilities, you may wish to refer to our fifth grade worksheets and multi-grade worksheets for additional practice materials.

You may print these educational materials for your own personal includes printing materials for your classroom , non-commercial use only. Please be familiar with these Terms of Use before using any worksheets from this site.

In order to view and print worksheets from this site you will need Adobe Reader version 6 or later. You may download the latest version of the free Adobe Reader here.

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Sixth Grade Math and Language Arts Worksheets

Sixth Grade Math Worksheets

Sharpen Your Skills Worksheet 10 – This fraction review worksheet for 5th and 6th grade instructs students to reduce fractions to lowest terms, change mixed numbers to improper fractions , and change improper fractions to mixed numbers .

Math Symbol Matching – Draw a line to match each math symbol with its name or meaning.

Fraction Review Worksheet 1 – This fraction review worksheet provides students the opportunity to reduce fractions to lowest terms, convert mixed numbers to improper fractions, and convert improper fractions to mixed numbers.

Evaluating Expressions Riddle 1 – What athlete always gives refunds Your students will substitute numbers for variables then use the answers to solve this riddle.

Dividing Decimals Worksheet 1 – This worksheet provides practice dividing decimals .

Alien Algebra Worksheet 2 – Students will solve the equations and color the spaces in which the answer contains a number 6 to help the alien get to the spaceship.

Sharpen Your Skills Worksheet 6 – Students gain valuable practice multiplying and dividing fractions .

Sharpen Your Skills Worksheet 7 – Students will multiply decimals by 10, 100, and 1000.

Finding Percentages Worksheet 6a – This sixth grade math worksheet requires students to find the percentage and show their work.

Multiplying by a Fraction – Students will practice multiplying fractions and mixed numbers by a fraction.

Addition Equations Worksheet 4 – Students will learn to solve addition equations .

Addition Equations Worksheet 3 – This worksheets provides examples of the process of adding equations.

Addition Equations Worksheet 2 – Practice solving single-digit addition equations.

Addition Equations 1 – Students will solve to find the value of X with sums to 10.

Multiplication Worksheets A-C – Students will practice multiplying 3 and 4-digit numbers by a 3-digit number.

Reduce Improper Fractions – Students will reduce each improper fraction to its lowest terms .

Sharpen Your Skills Worksheet 2 – This worksheet provides your students with practice multiplying and adding, whole numbers, fractions, and decimals.

Bicycle Math – Students will use multiplication and division to solve these life skills word problems . Calculator math worksheet.

Bicycle Metric Math – Students will use a calculator to solve these metric word problems .

Estimating Products of Mixed Numbers – Students will round each factor to the nearest whole number and multiply the whole numbers.

Find the Product Worksheet H-1 – Can your students solve these horizontal multiplication problems

Sixth Grade Language Arts Worksheets

Analogies – Write the word that completes each analogy .

Synonym Sleuth – Identify synonyms for given word and use in a sentence.

Blues and Folk Music Workshop – Students will utilize reading , math, and thinking skills when they read the promotional flyer and answer the questions. This three page worksheet is appropriate for sixth grade and as a life skills activity for special needs students of all ages.

Mark and Fred had some money in the ratio 6:1. Mark gave half of his money to Fred. Find the ratio of the amount of money Mark had left to the amount of money Fred had in the end.

The ratio of the amount of money Mark had left to the amount of money Fred had in the end is 3:4.

Carol puts some green and red unit cubes in a box. The ratio of the number of green cubes to the number of red cubes is 2:1. She adds 12 more red cubes in the box and the ratio becomes 4:5.

a) How many green cubes are there in the box?

b) How many red cubes does Carol have in the end?

From the model, we see that:

a) 3 units = 12 cubes

1 unit = 12 3 = 4 cubes

4 units = 4 4 = 16 cubes

There are 16 green cubes in the box.

b) 5 units = 5 4 = 20 cubes

Carol has 20 red cubes in the end.

1. A board was cut into two pieces whose lengths are in the ratio 2:5. The longest piece was 85 inches. How long was the shortest piece?

1. The ratio of pigs to cows to sheep on the farm is 2:4:7. There are 65 more sheep than pigs. How many cows are there on the farm?

a) Draw a bar model representing the situation

b) Elmer is 5 years older than Sam. How old is Sam?

1. At Al’s Catering Service, they often make a large batch of fruit salad. The ratio of cups of apples to cups of oranges in the recipe is 8 : 5.

a) If they use 15 cups of oranges, how many cups of apples should they use?

b) If they only use 2 cups of apples, how many cups of oranges should they use?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

The following are some examples of 6th Grade Math Word Problems that deals with percentages.

In this lesson, we will learn how to solve percent word problems

using block diagrams or bar models or tape diagrams

using the grid method

Using Bar Models

15% of the number of people who attended a concert arrived late. If 30 people arrived late, find the number of people who attended the concert.

From the above model, we see that

100% 100 2 = 200 people

200 people attended the concert.

Kathy earned $75 an hour. Andy earned 20% more money than Kathy. How much money did Andy earn in an hour?

Andy s earnings was 120% of Kathy s earnings.

Andy earned $90 an hour.

1) Marilyn saves 30% of the money she earns each month. She earns $350 each month. How much does she save?

2) At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many visitors altogether are at the museum?

3) Bill bought cards to celebrate Pi day. He sends 60% of his cards to friends. He sent 42 cards to friends. How many cards did he buy altogether?

4) Bruce cookies 80% of the pancakes at the pancake breakfast last weekend. They made 1120 pancakes. How many pancakes did Bruce cook?

1) Alejandro bought a television set for $900 and paid a sales tax of 8%. How much did he pay for the television set?

2) Alice saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was $270. How much did she pay for the bike?

Show Step-by-step Solutions

Using Grid Method

Describes how to set up a percent problem using the grid method. Uses examples with the total given and looking for the parts.

There are 250 chairs in a room

a) If 150 chairs are full, what % are full?

Examples of how to solve percent word problems with the grid method.

Example 1: A stereo listed for $350 is on sale for 20% off the list price. The sales tax is 6%. What price does a customer pay for the stereo if she buys it on sale?

Example 2: Stacey just received her annual cost-of-living raise. She previously earned $1450 a month. Her new salary is $1508. What is the rate of increase?

Example 3: At a playoff game, paid attendance was 39,900. The total attendance was 42,000. What percent of those attending had free tickets?

Show Step-by-step Solutions

Using Proportions

Shows how to solve “percent of” word problems using proportions

1. What is 15% of 40?

2. 12 is 20% of what number?

3. 22 is what percent of 5?

Solving percent word problems that involve finding a sale price given original price and discount, finding an original price given sale price and discount, and finding sale price given profit.

Example 1: A laptop that normally costs $600 is offered at a discount of 35%. What is the new sale price?

Example 2: A pair of shoes is marked down 20% during a sale and costs $60. What was the original price?

Show Step-by-step Solutions

Solving percent word problems that involve finding the percentage profit.

Example 1: Te total cost of producing a tablet is $150. If the manufacturer wants to make a 20% profit, at what price must they sell the tablet?

Example 2: Kevin bought a concert ticket for $50 and sold it for $54. What was the percentage profit?

Show Step-by-step Solutions

Solving percent word problems that involve percent increase and decrease

Example 1: 15 fans attended a band’s first concert. 18 fans attended their second concert. What was the percent increase in the number of fans from the first concert to second?

Example 2: Last year, a football team won 15 games. This year, the team won 20% fewer games. How many games did the team win this year?

Show Step-by-step Solutions

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

158=___ + 106.What number will come in the blank to make the number sentence true?

shown below is a part of a triangle with one of its angles missing. The measure of the missing angle is

Faizal has 918 marbles. he wants to make packets of marbles, with 9 marbles in each packet. how many packets will he be able to make?

What value of “x” makes the equation below true?-15 + (-5x) = 0

Two angles of a triangle measure 35 degrees and 65 degrees. What is the measure of the third angle of the triangle?

If 6x+3 = 15, what is the value of 6x-3?

What is the order of the following set of numbers from greatest to least? 1 1/3, 2/3, -1/3, 9/5

The weekly milk order for the Tranquility Inn includes 40 gallons of low-fat milk and 15 gallons of chocolate milk. What is the ratio of the number of low-fat gallons to chocolate gallons in the Tranquility Inn s weekly milk order?