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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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6th Grade Math Worksheets

6th Grade Math Worksheets dig deeper into the math topics introduced in earlier grades like decimals, measurement, frac tions, and geometry. They also introduce a number of crucial new topics like percentages, exponents, integers, and proportions. Grade 6 Math Worksheets equip students with the skills and knowledge needed to excel not just in math, but in other subjects such as physics, as well. Proper comprehension of new topics like integers and algebra is extremely crucial for more advanced math classes and competitive exams. Grade 6 Online Math Worksheets are more interactive and engaging than typical textbooks, and can prove to be helpful in developing math intuition and problem-solving skills among students.  ...Read More Read Less

Benefits of Grade 6 Worksheets

Printable 6th Grade Math Worksheets   are designed to aid students in strengthening their understanding of core math concepts. They make math education engaging and fun for students, and help children develop a true thirst for knowledge. In contrast to typical textbooks,  Grade 6 Math Worksheets feature activities and puzzles that allow students to understand difficult concepts in a manner that is truly engaging. This facilitates superior knowledge retention as well.  

Some benefits of Grade 6 Math Worksheets:

Expansive coverage

Grade 6 Math Worksheets  cover a number of relevant topics that students will learn during their school year. With the help of these worksheets, students can practice a variety of crucial concepts and develop superior knowledge that allows them to ace their math exams. 

Time management

Many students encounter problems solving math sums within a deadline in 6th grade, especially while dealing with more advanced concepts and newly learned equations. This ultimately harms their grades, as they are unable to complete their math exams in time. Practicing using   6th Grade Math Worksheets online  can be quite helpful in preventing such an eventuality. With consistent practice, students will become proficient in solving even the most complex math problems relatively fast. 

Preparation for the future

Grade 6 Math Worksheets  help students gain a high degree of understanding in addition, subtraction, multiplication, and division. Subsequently, they are able to move on to topics such as fractions, percentages, and simple geometry. After gaining confidence in these basic topics, sixth graders will be ready for pre-algebra and more advanced concepts taught in their school year. 

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Choose math worksheets by topic, grade 6 math worksheets explained.

Printable Grade 6 Math Worksheets can   help students earn high grades on their exams while also allowing them to develop a strong foundation in mathematics that prepares them for middle school. These worksheets cover almost all the core math topics taught in the previous grades, as well as introducing many new concepts. 

Major topics covered by  6th Grade Math Worksheets  include fraction conversions, measurements, mean and median, number patterns, exponents, ratio, percent, prime factorization, GCF, LCM, integers, and geometry. Many of the topics are presented through engaging word problems, which helps make the learning experience exciting for students. 

Here are some of the types of  Grade 6 Math Worksheets   for students  that will help them get ready for middle school math:

• Pre-algebra addition, subtraction, multiplication, and division word problems. These problems deal with the relationship between numbers in simple equations, and can be a great way for easing into more complex algebra equations. 
• Basic investing concepts are introduced to the students, including dividends, price-to-earnings ratio, and market capitalization. 
• Combining negative numbers with other integers using basic math operations, long division with negative numbers, and multiplication of multi-digit negative numbers. 
• Determining mean, median, and mode for sets of numbers. Problems presented in this worksheets tend to include sets of negative and positive integers, as well as mixed sign sets.
• Factoring progressively larger integers into their prime factors. The first step of doing so would be to determine the greatest common divisor of two numbers or to determine the least common multiple of two numbers. Prime factorization also introduces the concepts of prime numbers and composite numbers.
• Students are introduced to squares, cubes, and exponents mixed with other basic operations through these worksheets, and are vital for developing a good understanding of common exponential terms.

Printable Grade 6 Math Worksheets  can cover multiple topics, and feature problems with diverse difficulty levels. These worksheets can be downloaded as a PDF or printed out instantly for exam preparation or revision work.  

How are the 6th grade math worksheets interactive in nature?

The 6th grade online math worksheets are designed in a unique way, keeping in mind the  need for child to use various math or visual mother, use various strategies to solve along with usage of real life contexts wherever possible. Each and every question has a fun element for the child to be engaged while solving the 6th grade online math worksheets within the time limit.

What are the math topics covered in the grade 6 math worksheets?

The math topics included in the 6th grade math worksheets are powers and exponents, prime factorization, G.C.F and L.C.M, multiplication and division of fractions and decimals, ratios and rates, percent, fractions and decimals, algebraic expressions and their properties, area, surface area and volume of 2D and 3D shapes, comparison and ordering of integers, sums on coordinate plane, statistical measurements and understanding data display.

What are the different levels of difficulty in sixth grade math worksheets?

The sixth grade math worksheets are segregated into three levels – easy, medium and hard. Every student has the option of choosing any level based on their understanding of the math concepts and how confident they are. We do encourage students to try all three levels for getting a robust understanding of the math concepts which can result in a definite growth in their math learning.

Are the grade 6 math worksheets timed?

Yes, the sixth grade interactive math worksheets are timed. This will encourage the students more to participate in such time-bound activities and get a better grasp on how prepared they are with the math concepts.

In what all formats are the 6th grade math worksheets available?

The interactive math worksheets are available for the children in two different formats. The pdf based printable worksheets can be solved offline once downloaded while the others are tech based online math  worksheets which are interactive in nature are solved in online mode.

Who prepares the questions for the sixth grade math worksheets?

The questions for sixth grade interactive math worksheets are prepared by highly qualified subject matter experts who are experienced with the subject. Each and every question is prepared after  deep thought to ensure that the questions are original and engaging enough for every level.

Can the grade 6 math worksheets be worked on more than once?

Yes, the student can practice different math concepts using the BYJU’s free online math worksheets for sixth grade by attempting them more than once. In fact, for every new submission, the student may come across a fresh set of questions to practice and enhance their knowledge.

• 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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Start practice on Sixth Grade here

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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6th Grade Math Worksheets

Count on our printable 6th grade math worksheets with answer keys for a thorough practice. With strands drawn from vital math topics like ratio, multiplication, division, fractions, common factors and multiples, rational numbers, algebraic expressions, integers, one-step equations, ordered pairs in the four quadrants, and geometry skills like determining area, surface area, and volume, organizing numerical data as dot plots, histograms and box plots, finding mean, median, and quartiles of datasets, these pdfs become your often go-to place. Grab your ticket to a great start with our free math worksheets for grade 6 students!

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Explore 4,600+ Sixth Grade Math Worksheets

Division | 4-Digit by 2-Digit and 3-Digit

Divide a 4-digit number by a 2-digit or 3-digit number, starting from the largest place value and dividing your way down to the last digit to find the quotient and remainder (if any).

Drawing Shapes to Represent the Ratio

Jazz up your ratio skills with our 6th grade math worksheet pdfs. Direct students to visually represent the terms of each ratio by sketching the specified number of shapes.

Multiplying Two Fractions by Cross Cancelling

Breaking down the numerator and denominator into prime factors, cross-cancelling the common factors, and multiplying the uncancelled parts of the fraction are all grade 6 learners are expected to do!

Expressing Decimals in Words | Up to Millionths

Let your understanding of decimal place value soar to new heights as you dive into these printable 6th grade math worksheets and express decimals up to millionths in words and vice versa.

Finding the GCF of Two Numbers

Follow the step-by-step process of finding the GCF by listing out all the factors of each pair of 2-digit numbers, then compare the factors, figure out the common ones and the greatest among them is your answer.

Representation of Integers

Laying a strong foundation in integers becomes easy with a touch of real-world offered in these grade 6 math pdf worksheets, where each scenario should be represented with a positive or negative integer.

One-Step Equation: Addition and Subtraction | Integers

Rearrange the equation, making the variable the subject, and take the integer constant to the other side and change its sign, add or subtract to find the value of the unknown variable.

Identifying Ordered Pairs in All Quadrants

Get acquainted with the coordinate plane, the four quadrants, and the ordered pairs. Identify the point representing each ordered pair in Part A; and locate and write the x-y coordinates of each point in part B.

Determining the Area of a Square

Equip grade 6 children with these printable math worksheets, if practice in determining the area of a square is on your mind. Get students to square the fractional side lengths and compute the area.

Identifying Nets of 3D Shapes

Get 6th grade learners to imagine folding the 2D nets presented in this printable math worksheet along the edges and visualize the 3D shapes that can be constructed from them.

Surface Area using Nets | Counting Squares

Whether it is refining or testing skills in counting the unit squares to determine the surface area of rectangular prisms, cubes or triangular prisms from their nets, these pdfs serve the purpose.

Five-Number Summary

Descriptively analyze each dataset, by rearranging the values in ascending order and figuring out the maximum and minimum values, and the lower or 1st, median or 2nd, and upper or 3rd quartiles.

Division of 5-Digit Numbers by 1-Digit and 2-Digit Divisors

Push boundaries and brush up your division skills with adequate practice provided by these exercises in dividing 5-digit numbers with single and double-digit divisors.

Ratio Word Problems | Part-to-Part

Put your analytical skills to test with our 6th grade math worksheet pdfs. Study the data given in the pictogram and answer the set of questions detecting the part-to-part ratio in each scenario.

Multiplying Mixed Numbers and Fractions

Effortlessly multiply mixed numbers and fractions by converting the mixed numbers to improper fractions, cross cancelling the common factors and then multiplying what's left over.

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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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Grade 6 Maths word Problems With Solutions and Explanations

Detailed solutions and full explanations to grade 6 maths word problems are presented.

• Two numbers N and 16 have LCM = 48 and GCF = 8. Find N. Solution The product of two integers is equal to the product of their LCM and GCF. Hence. 16 × N = 48 × 8 N = 48 × 8 / 16 = 24
• If the area of a circle is 81π square feet, find its circumference. Solution The area is given by π × r × r. Hence π × r × r = 81π r × r = 81 ; hence r = 81 feet The circumference is given by 2 × π × r = 2 × pi × 9 = 18 π feet
• Find the greatest common factor (GFC) of 24, 40 and 60. Solution We first write the prime factorization of each given number 24 = 2 × 2 × 2 × 3 = 2 3 × 3 40 = 2 × 2 × 2 × 5 = 2 3 × 5 60 = 2 × 2 × 3 × 5 = 2 2 × 3 × 5 GFC = 2 2 = 4
• In a given school, there 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? Solution a) ratio of girls to boys 260:240 or 13:12 b) ratio of boys to the total number of pupils 240:(240+260) or 240:500 or 12:25
• If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend? Solution The tip is 20% of what he paid for lunch. Hence tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60
• Find k if 64 ÷ k = 4. Solution Since 64 ÷ k = 4 and 64 ÷ 16 = 4, then k = 16
• 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? Solution John spent and gave to his two friends a total of 1.25 + 1.20 + 1.20 = $3.65 Money left 8.50 - 3.65 = $4.85
• What is x if x + 2y = 10 and y = 3? Solution Substitute y by 3 in x + 2y = 10 x + 2(3) = 10 x + 6 = 10 If we substitute x by 4 in x + 6 = 10, we have 4 + 6 = 10. Hence x = 4
• 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. Solution Cost C for a call of 1 minute C = 0.50 + 0.11 Cost C for a call of 2 minutes C = 0.50 + 0.11 + 0.11 = 0.50 + 2 × 0.11 Cost C for a call of 3 minutes C = 0.50 + 0.11 + 0.11 + 0.11 = 0.50 + 3 × 0.11 We note that the cost C is equal to C = 0.50 + (number of minutes) × 0.11 If N is the number of minutes, the cost C is given by C = 0.50 + N × 0.11
• A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers? Solution Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers? 180 ÷ 40 = 4.5 × 1 gallon = 4.5 gallons
• A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles? Solution 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles? 675 ÷ 150 = 4.5 = 4 and 1/2 For each of these groups 8 minutes are needed. For 4 groups and 1/2 8 × 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time) We can also find the final answer as follows 4.5 x 8 = 32 minutes
• A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours? Solution During each hour, the car travels 65 miles. For 5 hours it will travel 65 + 65 + 65 + 65 + 65 = 5 × 65 = 325 miles
• 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. Solution Let us first find the total area A of the rectangle before cutting the small is cut A = length × width = 20 × 10 = 200 A square of side 2x has an area B given by B = (2x) × (2x) = 4 × x × x = 4 x 2 The small square of area B is cut from the large rectangle of area A. Hence the area of the remaining shape is given by A - B = 200 - 4 x 2
• 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. Solution Two rectangles A and B are similar if their lengths and widths are proportinal. Let L1 = 10 cm and W1 = 5 cm be the length and width of rectangle A. Let L2 = 30 cm and W2 be the length and width of rectangle B. Proportionality of the dimensions of the two rectangles is written as: L2 / L1 = W2 / W1 Substitute by the known quantities and find W2 30 / 10 = W2 / 5 For the above ratios to be equal, W2 must be equal to 15. Hence the area of rectamgle B is given by L2 × W2 = 30 cm × 15 cm = 450 cm 2
• 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 1/8 of the students in the last two classes were absent. A total of 70 students were absent. How many students are registered in this school? Solution The given information is related to different classes and since we have 10 classes with the same number of students we need to find the number of registered students in each class. Let x be the number of registered students in each class. Hence the number of students absent in the 5 classes that were half full is given by: (1/2 of the students were absent in each class) 5 × ( 1/2 × x) = 5 x / 2 The number of students absent in the 3 classes that were 3/4 full is given by: ( a class that 3/4 full has 1/4 of the students absent) 3 × ( 1/4 × x) = 3 x / 4 The number of students absent in the 2 classes that were 1/8 full is given by: 1/8 × (2 × x) = 2 x / 8 The total number of students who were absent is equal to 70 (given). Hence 5 x / 2 + 3 x / 4 + 2 x / 8 = 70 rewrite fractions with same denominator (4 / 4) × 5 x / 2 + (2/ 2) × 3 x / 4 + 2 x / 8 = 70 Simplify 20 x / 8 + 6 x / 8 + 2 x / 8 = 70 add fractions 28 x / 8 = 70 Multiply both sides of the above equation by 8 / 28 (8 / 28) × 28 x / 8 = (8 / 28) × 70 Simplify to solve for x. x = 20 students per class total number of students for all 10 classes in the school: 10 × 20 = 200 students
• 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. Solution Let x be the size of the side of square A and y be the size of the side of square B. The perimeters of the two squares are given by: Perimeter of A: 4 x and Perimeter of B: 4 y The expression "The perimeter of square A is 3 times the perimeter of square B" is written mathematically as: 4 x = 3(4 y) = 12 y Divide both sides of the above equation by 4 x = 3 y Square both sides of the above equation. (x) 2 = (3 y) 2 Simplify to obtain. x 2 = 9 y 2 The area of the two squares are given by Area of square A := x 2 and Area of square B = y 2 The ratio of the area of square A to the area of square B is given by x 2 / y 2 Divide both sides of the equation x 2 = 9 y 2 obtained above by y 2 x 2 / y 2 = 9 y 2 / y 2 Simplify to obtain the ratio of the two areas x 2 / y 2 = 9
• 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? Solution Let x be the number of stamps that John started with. John gave half of his stamps to Jim: Jim got (1/2) x Jim gave gave half of his stamps to Carla: Carla got (1/2) ((1/2) x) Carle gave 1/4 and therefore kept 3/4 of the stamps given to her. Carla kept 3/4 of (1/2) ((1/2) x ) = (3/4) ((1/2) ((1/2) ) x) Simplify the expression (3/4) ((1/2) ((1/2) ) ) x . (3/4) ((1/2) ((1/2) ) x) = (3 × 1 × 1) / (4 × 2 × 2) x = 3 x / 16 The number of stamps kept by Carla is equal to 12. Hence the equation to solve 3 x / 16 = 12 Mutliply both side of the above equation by 16 / 3 (16/3) × (3 x / 16) = (16 / 3) ×12 Simplify and solve for x x = (16 / 3) ×12 = 64
• 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, how long will take them to be at the same starting point again? Solution It will take 120 / 4 = 30 seconds for ball A to make one full rotation It will take 60 / 3 = 20 seconds for ball B to make one full rotation Let us calculate the time for whole rotations of ball A and B Ball A : 1 rot: 30 sec , 2 rot: 60 sec , 3 rot 90 sec, 4 rot 120 sec, .... Ball B: 1 rot: 20 sec , 2 rot: 40 sec , 3 rot 60 sec, 4 rot 80 sec, .... The first time that they have made a whole number of rotations and therefore be at the same starting point is after 60 seconds which is the lowest common (LCM) multiple of 30 and 20.
• A segment is 3 units long. It is divided into 9 parts. What fraction of a unit are 2 parts of the segment? Solution To divide a 3 unit segment to make 9 parts, you need to divide each unit by 3. Hence 1 part = 1/3 of a unit and therefore 2 parts = 2/3 of a unit

• A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute? Solution Rewrite the rate 75 kilometers per hour converting kilometers in meters and hours in minutes 1 kilometer = 1000 meters 1 hour = 60 minutes Hence 75 kilometers per hour = 75 × 1000 meters per 60 minutes = 75 000 / 60 meters/minute = 1250 meters/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 and Jim's age. Find the present age of each one of them. Solution Let x be Peter's age now. Hence the present age of Carla, Jim and Peter are given by Carla : 5 Peter : x Jim : x - 13 One year ago their ages were Carla : 5 - 1 = 4 Peter : x - 1 Jim : x - 13 - 1 = x - 14 One year ago, Peter's age was twice the sum of Carla's and Jim's age which is written mathematically as x - 1 = 2 (4 + x - 14) Simplify and expand the right side of the above equation x - 1 = 2 (x - 10) x - 1 = 2x - 20 Add + 20 to both sides and simplify x - 1 + 20 = 2x - 20 + 20 x + 19 = 2x Subtract x to both sides and simplify x + 19 - x = 2x - x 19 = x , Peter's age now Jim's age: x - 13 = 19 - 13 = 6 Carla's age: 5
• 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? Solution Let x be Linda's savings. If she spent 3/4 of her savings on furniture then 1/4 of her savings are remaining and are written as (1/4) x She spent 1/2 of her remaining saving on a fridge that costs 150. Hence (1/2) × ((1/4) x ) = 150 Simplify the above and rewrite as x / 8= 150 Multiply both sides of the above equation by 8 and solve for x 8 × (x / 8) = 8 × 150 x = $1200
• The distance between 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? Solution The dog runs during all the period of time while Kate and Harry are walking. This period of time may be calculated as follows: 2500 meters / (40 + 60) meters / minutes = 25 minutes The dog runs during 25 minutes at the rate of 120 meters per minutes. Hence the total distance covered by the dog is given by 120 meters/minute × 25 minutes = 3000 meters

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Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

Free Printable Fraction Word Problems Worksheets for 6th Grade

Fraction Word Problems: Discover a collection of free printable Math worksheets for Grade 6 students, focusing on solving real-life scenarios involving fractions. Enhance learning and problem-solving skills with Quizizz's resources.

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Fraction Word Problems worksheets for Grade 6 are an essential resource for teachers looking to help their students master the challenging world of fractions in math. These worksheets provide a variety of math word problems that incorporate fractions, allowing students to practice their skills in a fun and engaging way. Teachers can use these worksheets to supplement their lesson plans, provide extra practice for struggling students, or even as a form of assessment to gauge their students' understanding of the material. With a wide range of topics covered, from addition and subtraction of fractions to more complex problems involving ratios and proportions, these Grade 6 worksheets are a valuable tool for any math teacher looking to enhance their students' learning experience.

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enVision Mathematics - Middle School Math Curriculum

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• Problem-Based Learning Real-world math problems foster collaboration skills. By evaluating options and presenting their own solutions, students stay engaged throughout the lesson.
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• Concept Visualization Embedded interactivities throughout lessons help students visualize concepts
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Frequently Asked Questions

enVision® Mathematics © 2024 for grades K-5 is the only middle grades math program that combines problem-based learning and visual learning to deepen students’ conceptual understanding. enVision is used by classrooms across the country and around the world. The latest enVision is even better with new digital Let’s Investigate! lessons which provide students with opportunities to take ownership of deeper exploration into problem-based learning. Ensure successful implementation with the comprehensive teacher support based on the 5 Practices.

enVision packs a unique one-two punch. Lessons start with Problem-Based Learning (PBL), where students must think critically about a real-world math problem, evaluate options, collaborate, and present solutions. This is followed by Visual Learning to solidify the underlying math concepts. It’s the best way to help kids better understand math ideas.

The program is made up of the following program components:

• Teacher’s Edition - Available in digital or print, the Teacher’s Edition includes wrap-around pages that provide direct instruction and teaching suggestions to engage students. The Interactive Teacher’s Edition online features annotation models and downloadable lesson resources.
• Student Edition - Interactive Student Edition—available in digital or print write-in format.
• enVision Digital - enVision digital courseware on Savvas Realize® includes robust digital tools that give teachers flexibility to use a digital, print, or blended format in their classrooms. Teachers can customize the program to rearrange content, upload their own content, add links to online media, and edit resources and assessments. All program resources, including personalized practice, remediation, and assessments are available in one location for easy lesson planning and presentation Students will use technology to interact with text and activities, and they can write directly in their digital Student Edition to make interaction with text more meaningful. Students will engage in activities that will inspire conceptual understanding, classroom discourse, and build their mathematical thinking skills, while learning to formulate and defend their own opinions.

The learning model in the enVision program—problem-based learning, visual learning, and data-driven differentiated instruction—has been researched and verified as effective. Core instruction used for every lesson has been shown to be effective for developing conceptual understanding.

enVision Mathematics features comprehensive differentiated instruction and intervention support to allow access for all students. The program’s balanced instructional model provides appropriate scaffolding, differentiation, intervention, and support for a broad range of learners, and is designed to facilitate conceptual understanding of mathematics for students at a range of learning levels.

Comprehensive, built-in differentiation resources support all levels of learners, including those with learning disabilities and ELLs, through personalized, adaptive learning. The program meets a variety of student needs and provides Response to Intervention (RtI) during each lesson, at the end of each lesson, at the end of each Topic, and any time as indicated in the Teacher’s Edition. A description of RtI tiered instructional resources for the program is included in the Teacher’s Program Overview for each grade. The following are examples of tiered instructional support found online for each lesson.

Tier 1 ongoing Intervention includes the following resources that can be used during the lesson:

• Prevent Misconceptions. During the Visual Learning Example, a remediation strategy is included to address a common misconception about the lesson concept.
• Error Intervention (If... Then...). During Practice & Problem Solving, error intervention identifies a common error and provides remediation strategy
• Reteaching Set. This set is provided before independent practice to develop understanding prior to practice.
• MathXL for School: Practice & Problem Solving, during the lesson, includes personalized practice for the Practice & Problem Solving portion of the lesson, along with Additional Practice or Enrichment; auto‐scored with on‐screen help, including Help Me Solve This and View an Example tools, tutorial videos, Math Tools, and one‐click animated glossary access.

Tier 2 strategic intervention includes the following resources that can be used at the end of the Lesson:

• Intervention Activity. This supports teachers working with small groups of struggling students.
• Reteach to Build Understanding. This provides guided reteaching as a follow‐up to the intervention activity.

Tier 3 intensive intervention instruction is delivered daily outside of the core math instruction, often in a one‐to‐one situation. The Math Diagnosis and Intervention System can be used for this purpose, for example.

• Variety of Instructional Strategies
• Multisensory instruction is provided in online Solve & Discuss It!/Explore It!/Explain It! activities that include audio, Visual Learning
• Animation Plus, Virtual Nerd videos, interactive MathXL for School: Practice & Problem Solving, Additional Practice, and Enrichment, online digital math tools, and online math games.

The authorship team is made up of respected educational experts and researchers whose experiences working with students and study of instructional best practices have positively influenced education. Contributing to enVision with a mind to the evolving role of the teacher and with insights on how students learn in a digital age, these authors bring new ideas, innovations, and strategies that transform teaching and learning in today’s competitive and interconnected world.

• Dr. Robert Q. Berry, III is an Associate Professor at the University of Virginia in the Curry School of Education with an appointment in Curriculum Instruction and Special Education. A former mathematics teacher, he teaches elementary and special education mathematics methods courses in the teacher education program at the University of Virginia. Additionally, he teaches a graduate level mathematics education course and courses for in-service teachers seeking a mathematics specialist endorsement.
• Zachary Champagne taught elementary school students in Jacksonville, Florida for 13 years. Currently he is working as an Assistant in Research at the Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCRSTEM) at Florida State University.
• Dr. Randall Charles is Professor Emeritus in the Department of Mathematics at San Jose State University, San Jose, California. His research interests have focused on problem solving with several NCTM publications including Teaching and Assessing Problem Solving, How to Evaluate Progress in Problem Solving, and Teaching Mathematics Through Problem Solving. In recent years Dr. Charles has written and talked extensively on Big Ideas and Essential Understandings related to curriculum, teaching, and assessment.
• Francis (Skip) Fennell, PhD, is emeritus as the L. Stanley Bowlsbey professor of education and Graduate and Professional Studies at McDaniel College in Maryland, where he continues to direct the Brookhill Institute of Mathematics supported Elementary Mathematics Specialists and Teacher Leaders Project. A mathematics educator who has experience as a classroom teacher, principal, and supervisor of instruction, he is a past president of the Association of Mathematics Teacher Educators (AMTE), the Research Council for Mathematics Learning (RCML), and the National Council of Teachers of Mathematics (NCTM).
• Eric Milou is a Professor in the Department of Mathematics at Rowan University in Glassboro, NJ. He is an author of Teaching Mathematics to Middle School Students. Recently, his focus has been on approaches to mathematical content and the use of technology in middle grades classrooms.
• Dr. Jane Schielack is Professor Emerita in the Department of Mathematics and a former Associate Dean of Assessment and PreK-12 Education in the College of Science at Texas A&M University. A former elementary teacher, Dr. Schielack has pursued her interests in working with teachers and students to enhance mathematics learning in the elementary and middle grades. She has focused her activities for improving mathematics education in two main areas: teacher education and professional development and curriculum development.
• Jonathan Wray has involvement and leadership in a number of organizations and projects. His interests include the leadership roles of mathematics coaches/specialists, access and equity in mathematics classrooms, the use of engaging and effective instructional models to deepen student understanding, and the strategic use of technology in mathematics to improve teaching and learning.
• How do I sign up for an enVision digital demo? enVision digital courseware on Savvas Realize® includes robust digital tools that give teachers flexibility to use a digital, print, or blended format in their classrooms. Teachers can customize the program to rearrange content, upload their own content, add links to online media, and edit resources and assessments. Program resources, personalized practice, remediation, and assessments are available in one location for easy lesson planning and presentation.

enVision Mathematics is designed to achieve a coherent progression of mathematical content within each course and across the program, building lesson to lesson. Every lesson includes online practice instructional examples as the progression of topics builds, allowing students additional practice with these skills and to develop a deeper conceptual understanding.

At the beginning of every topic, teachers are provided with support for the focus of the topic, how the topic fits into an overall coherence of the grade and across grades, the balance of rigor in the topic, and how the practices enrich the mathematics in the topic. Carefully designed learning progressions achieve coherence across grades:

Coherence is supported by common elements across grades, such as Thinking Habits questions for math practices and diagrams for representing quantities in a problem. Coherence across topics, clusters, and domains within a grade is the result of developing mathematics as a body of interconnected concepts and skills. Across lessons and standards, coherence is achieved when new content is taught as an extension of prior learning—developmentally and mathematically. (For example, Solve & Share at the start of lessons engages students in a problem-based learning experience that connects prior knowledge to new ideas.)

Look Back! and Look Ahead! connections are highlighted in the Coherence part of Topic Overview pages in the Teacher’s Edition.

The Topic Background: Rigor page shows teachers how the areas of rigor will be addressed in the topic, and details how conceptual understanding, procedural skill and fluency, and application builds within each topic to provide the rigor required.

On the first page of every lesson, the Lesson Overview includes sections titled Focus, Coherence, and Rigor. The Rigor section highlights the element or elements of rigor emphasized in the lesson, which may be one, two, or all three. Features in every lesson support each element, but the emphasis will vary depending on the standard being developed in the lesson. The core instructional model features support for conceptual understanding, procedural fluency, and application during both instruction and practice, as described below.

• Problem-Based Learning Step 1 Problem-Based Learning supports coherence by helping students connect what they already know to a problem in which new math ideas are embedded. When students make these connections, conceptual understanding emerges. Students are given time to struggle to make connections to the mathematical ideas and conceptual understandings. They can choose to represent their thinking and learning in a variety of ways. Physical and online manipulatives are available.
• Visual Learning Step 2 Visual Learning further develops understanding of the lesson ideas through classroom conversations. The Visual Learning Example features visual models to help give meaning to math language. Instruction is stepped out to help students visually organize important ideas. Students perform better on procedural skills when the procedures make sense to them. Procedural skills are developed through careful learning progressions in the Visual Learning Example.
• Assess and Differentiate Step 3 Assess and Differentiate features a Lesson Quiz and a comprehensive array of intervention, on-level, and advanced resources for all learners, with the goal that all students have the opportunity for extensive work in the state standards. Leveled practice with scaffolding is included at times. Varied problems are provided and math practices are identified as appropriate. Higher Order Thinking problems offer more challenge. Students have ample opportunity to focus on conceptual understanding and procedural skills and to apply the mathematics they just learned to solve a range of problems.
• How does the program identify performance gaps? At the start of the school year, schools have the opportunity to implement norm-referenced and validated assessments to identify students’ strengths and areas for growth. The new award-winning Math Screener and Diagnostic Assessments and Growth work directly with the enVision Mathematics course on Savvas Realize to inform instruction and provide robust student data. As a result of the Diagnostic assessment, teachers are armed with flexible instructional recommendations personalized to every student.

enVision Mathematics portrays diverse individuals and groups in a variety of settings and backgrounds. The program has been reviewed and approved for unbiased and fair representation. The selections in enVision Mathematics include a wide variety of contemporary, classic, and multicultural authors.

Our educational materials feature a fair and balanced representation of members of various cultural groups, including racial, ethnic, and religious groups; males and females; older people; and people with disabilities. The program integrates social diversity throughout all of its lessons, and includes a balanced representation of cultures and groups in multiple settings, occupations, careers, and lifestyles. We strive to accurately portray diverse groups within our society as well as diversity within groups. Our programs use language that is appropriate to and respectful of our cultural diversity. We involve members of diverse ethnic and cultural groups in the concept development of our products as well as in the writing, editing, illustration, and design.

• What is Pick a Project? Pick a Project is one of the motivating activities in enVision Mathematics , giving students a choice by letting them pick from a selection of math projects. Pick a Project launches each enVision topic and engages students in a real-world math project that accommodates different learning styles and interests. Students work independently, with a partner, or in small groups. The math problem activates prior knowledge and is a great way to deepen understanding during the entire topic.
• How does the relationship between enVision Mathematics and Desmos benefit students? Exclusive integration of Desmos into Savvas Realize® offers a groundbreaking interactive experience designed to foster conceptual understanding through highly visual interactives that bring mathematical concepts to life. Embedded interactives powered by Desmos and animated examples engage students and deepen conceptual understanding. Allowing students to manipulate data and see an immediate effect on graphs, number lines, etc. clarifies concepts as students are learning new content. Unique to enVision , the Desmos best-in-class graphing calculator and brand new geometry tools are available to middle and high school enVision students anytime, anywhere, both online and offline through Savvas Realize.

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Grade 10 Mathematics (MATH) November Paper 2 and Memo - 2023 (2)

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Description

Grade 10 Mathematics November Paper 2 and Memo: Total:  100 Marks.

Contents: The question paper covers the following topics:

• Statistics and data handling | Analytical geometry | Trigonometry (identities, graphs and problem solving) | Euclidean geometry.

This is a practice paper with memorandum meant to test the student's knowledge, and will not be the same paper written for the exam.

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• Decimals - add & subtract

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Grade 6 Decimals - Addition & Subtraction

Math worksheets: add and subtract decimals.

These grade 6 decimals worksheets provide practice in adding and subtracting decimals of varying lengths , a skill for which pencil and paper practice is critical to attain mastery.

Sample Grade 6 Decimal Subtraction Worksheet

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Find all of our decimals worksheets , from converting fractions to decimals to long division of multi-digit decimal numbers.

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