6th Grade Math Worksheets (Grade 6 - For Ages 11 to 12)

6th grade worksheets focus on relevant skills for ten and eleven year olds. These skills include exponent operations, factoring, fraction operations, measurement, ratios, and proportions. Students at this point should be comfortable with decimals, fractions, and percentages. They are working towards mastery of fractions.

Make sure to check out our Grade 6 Do Now math section for quick starter problems that are aligned to the core curriculum.Our curriculum will make teaching and learning 6th grade math a breeze. The answers to everything is found as page 2 of the files.

1. Completing Equivalent Proportions - Find the variable in each proportion. A simple cross multiply should get it done for you.
2. Converting Exponents - You are givien an integer in exponential format. Please convert it to standard form.
3. Converting Measurement Units - Convert between different U.S. Standards of measurement units. All units of measure are for length.
4. Division of Whole Numbers by Fractions - Divide each of the whole numbers by a fractional entry. The fractions should not be that hard to work with.
5. Extended Fraction and Percentage Word Problems - Students will most likely need to draw these scenarios or at the very least, outline the problems.
6. Factoring to Prime Factors - Determine the prime factors of the integers . You can write it as a factor tree, if that works for you.
7. Find the Area Right Triangles, Quadrilaterals, and Polygons - A nice mix of shapes for you to work with. Two right triangles followed by a quadrilateral and a polygon.
8. Finding Equal Measures of Volume - Time to get your beaker on. More appropriately this should be called equal measure of volume and mass. There are some mass problems in there.
9. Fraction Addition with Mixed Numbers - Find the sum of mixed numbers. Students should be advanced enough at this level to handle differing denominators. Some of these denominators will be a challenge.
10. Fraction Division (Differing Denominators) - Divide one fraction into another. The denominators may be a bit mixed, but they are relatively easy to work with.
11. Greatest Common Factors and Least Common Multiple - Find the GCF and LCM for each pair of integers. A nice and quick activity for you.
12. Multiplication between Fractions and Mixed Numbers - Multiply Mixed Numbers and Fractions with different denominators. This is a true test of fraction skills.
13. Mixed Number Subtraction - The denominators differ between each mixed number. This adds an extra level of difficulty.
14. Unit Rate Percentage Problems - These types of worksheets can give students a bit of trouble when it comes to the vocabulary involved.
15. Units of Length Conversions - Convert the measurements between metric units. All measures are for length.
16. Using Graphs to Understand the Central Tendency of Data - A simple and nice introduction to central tendencies and statistics.
17. Rate Word Problems - You know the type of problem, "A train leaving from New York travelling at 85 miles per hour..." These carry over to science very well.
18. Ratio Word Problems - All of the problems involve ratios and proportions in order to solve them. This is an interesting skill for students to learn.
19. Rational Numbers Systems - Tell the differences between negative and positive temperatures. A good extension beyond number lines.
20. Recognizing Relationships as an Equation - This is a big critical thinking set of problems. Hope you enjoy the challenge!
21. Writing and Evaluating Expressions - This is just a really good indication of whether or not your students have grasped the concepts of what expressions are.
22. Writing Equivalent Expressions - We work on simplifying expressions and find their equal values.

What Do Students Learn in the 6th Grade Math?

Sixth graders have a lot of solid math concepts under their belt, which is why the 6th grade math curriculum covers many exciting topics. The point of teaching them varied math topics is to help them build a good math base for more complicated equations later on. They don't just need to know their fractions. They must also see the connection between fractions, decimals, and percentages. Here are some of the concepts that 6th grade math for students covers.

Geometry

Students have been introduced to 2D and 3D shapes several times. They'll now explore basic shapes in more depth, particularly parallel and perpendicular lines in polygons. 6th grade math for students will also include an introduction to symmetry and transformation of shapes. They're also taught how to find the area and volume of different shapes. 6th grade math activities might include blocks to build and break shapes so that they better understand how to find the area and volume of real world objects.

More Fractions

Students are comfortable with fractions and decimals at this stage, so they're prepared to use these concepts for word problems. They'll also learn how to work with percentages below 100. They know learn how to place these numbers on a number line. This means they won't just be working with positive numbers but also negative ones.

Factors, Multiples and Prime Numbers

They'll learn about cumulative and distributive properties so that they can apply these concepts to multiplication and addition problems. Students will also learn how to use the associative property to equations.

Measurement

In younger grades, students learned how to do some basic measurements. They'll now know how to use standard and non-standard units of measurement. With their geometric knowledge of shapes, they'll calculate the area and volume of different shapes and express them with these units. They'll learn how to apply their understanding of area and perimeter to real-life objects.

Data Sets

Students will now learn how to express different data sets in a table and on a graph. They'll use data samples for various word problems like when calculating probability. They'll also learn how to draw a connection between two data samples. Students learn how to gather and arrange data. The data is then used to tackle problems. Answers are provided as physical and social models. They utilize the data to create graphs, tables and other visual representations of how they addressed an issue.

Absolute Value

Students will be introduced to absolute values and learn how to compare absolute values of rational numbers. Students describe their mathematical results and problem-solving approaches using logical reasoning and proof. This notion is frequently utilized by students to justify the results they obtain. This notion is used to develop mental math abilities and make connections with other areas of math.

Algebraic Expressions

In order to learn how to solve complex algebraic equations, students need to be comfortable with expressing problems in algebraic language. They'll now use the distributive property to form algebraic expressions, as well as learn how to write them in single and multiple operations. It also includes terms like variables, constants, and coefficients.

Graphs

The 6th grade math curriculum will introduce students to various graphs. They'll learn how to present their data through each of these graphs and then how to show it visually. Some of the graphs they'll cover include:

- Bar Graphs
- Venn Diagrams
- Simple Line Graphs
- Pictograms
- Mean, Median and Mode
- Survey Results on a Graph
- Frequency Tables

Ratios

When it comes to ratios and proportions, students will learn how to solve ratio problems with decimals and percentages involved. They'll be taught how to calculate rates and interest from the available information. This is important because it's frequently applicable to the everyday use of math. They'll also use diagrams to find unit rates. Apart from fractions, they'll also learn how to express a fraction form. They'll apply this knowledge of percentages to real-world retail discount situations. Ratios are important to teach students simplified ways of understanding the relationship between objects. For example, they're particularly important when assessing cooking measurements so many math problems might include hypothetical ingredients.

Integers

Students learn how to express integers as real life numbers and tell the difference between integers and real numbers. These concepts are established before developing into solving equations and word problems that involve integers.

Probability

They're taught to identify and solve function relationships on a graph and calculate the distance between coordinate points. 6th grade math for students introduces them to expressing probabilities through ratios; in this way, they learn how to calculate the probability of an event occurring.

Equations

6th grade students are old enough to solve complex sums. They'll solve equations with real-world problems so they know how to apply their mathematical knowledge to the world around them. 6th grade math involves tricky algebra concepts like solving equations with two variables to find an unknown. They'll learn how to accurately express these equations and how to show them on a graph.

Now that you know what the 6th grade math curriculum includes, you can prepare your child in advance by teaching them some concepts of 6th grade math at home. The number of topics might be overwhelming, but they build upon the math base already established in lower middle school. 6th grade math activities ultimately prepare students for complex upper middle school equations. Maintain your child's growing math abilities by considering ratios, rates, and other number relationships in everyday life, such as how many times you ask her to take out the trash before she does it, or splitting that final half-cup of ice cream into smaller portions.