Realistic Math Problems Help 6th-graders Solve Real-Life Questions
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Solving math problems can intimidate sixth-graders but 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 multiplication.)
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 in the next 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
Print PDF : 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?"
Worksheet No. 1 Solutions
Print Solutions PDF : 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.
Worksheet No. 2
Print PDF : 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
Print PDF Solutions : 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 least 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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Proportions word problems
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Build Confidence with Math Problem Solving
Daily Problem Solving will help your 6th grade students master the skills they need to be successful with challenging word problems...and have fun doing it .
What you'll get with this download:
Your download includes a full week of Daily Problem Solving for Grade 6 to try out in your own classroom. Developed with the brain in mind, these multi-step word problems will challenge your learners without overwhelming them. Best of all, you'll be able to watch their skills and confidence grow as they begin to internalize strategies for conquering this difficult math skill.
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Themed-problems and a weekly fun fact make it easy to keep learners engaged
Formatted for quick & easy implementation that won't add stress to your planning
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Help Students Master Math Word Problems
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These have given me such an insight into my students' abilities, and I've watched them improve their skills and successfully solve multi-step word problems.
You'll receive a full week of printable Daily Problem Solving practice for your students. This format includes:
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Daily digital slides offer your remote or online learners the opportunity to build problem-solving skills in a structured format designed for success.
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Teachers: Resources for Middle Grades (6-8)
The North Carolina Collaborative for Mathematics Learning (NC 2 ML) aims to support NC math educators in implementing the revised mathematics content standards in ways that align with what we know from research on students’ mathematical thinking, mathematics teaching, and teacher learning. To do so, we bring together mathematics educators to co-design research-based resources and professional learning opportunities.
6-8 Resources Home
First Week Problem Solving Tasks
The Instructional Frameworks at each grade level recommend spending the first week of school doing general, high cognitive demand tasks with students in order to establish strong communication practices (SMP 3). Students can be enculturated into the discourse, listening and writing practices essential for strong mathematical reasoning while working these problems.
Additional Supporting Articles
Herbel-Eisenmenn, B. & Breyfogle, M. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484-489.
Stephan, M. (2014). Establishing standards for mathematical practice. Mathematics Teaching in the Middle School, 19(9), 532-538.
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Free Printable Math Word Problems Worksheets for 6th Grade
Math Word Problems: Discover a vast collection of free printable worksheets for Grade 6 students, created by educators to enhance their mathematical skills and problem-solving abilities. Dive into the world of numbers with Quizizz!
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Explore printable Math Word Problems worksheets for 6th Grade
Math Word Problems worksheets for Grade 6 are an essential resource for teachers who want to help their students develop strong problem-solving skills and a deep understanding of mathematical concepts. These worksheets provide a variety of engaging and challenging problems that require students to apply their knowledge of math in real-world situations. With a wide range of topics covered, including fractions, decimals, percentages, and geometry, Grade 6 Math Word Problems worksheets are designed to align with the Common Core State Standards and support teachers in their efforts to create a well-rounded math curriculum. By incorporating these worksheets into their lesson plans, teachers can ensure that their students are receiving the practice and reinforcement they need to excel in math.
Quizizz is an excellent platform for teachers to access a vast library of Math Word Problems worksheets for Grade 6, along with other valuable resources to enhance their students' learning experience. This interactive platform offers a variety of features, such as customizable quizzes, real-time feedback, and gamification elements, to keep students engaged and motivated. In addition to Grade 6 Math worksheets, Quizizz also provides resources for other subjects and grade levels, making it a one-stop-shop for teachers looking to diversify their instructional materials. By utilizing Quizizz in conjunction with Math Word Problems worksheets for Grade 6, teachers can create a dynamic and effective learning environment that fosters a love for math and sets their students up for success.
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Grade 6 Maths word Problems With Answers
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 distsnce 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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