Mathematics

for 6th Grade Students

6th grade students will spend most of their time learning the following topics. They should understand them well by the end of the year.

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6th

6th

Expectations for Students

In 6th grade, students learn about ratios & proportions. They also learn to simplify expressions , & solve equations. Students should work together in class, talk about how they solve problems, & learn from each other. 6th graders should make mathematical arguments & try different ways to solve problems. They should solve both number & word problems, including real world problems. Lastly, they should estimate solutions before solving & know if their estimate is reasonable.

See all 6th grade state standards for math.

By the end of the year 6th grade students should know:

Learning 6th Grade Mathematics

Add, subtract, multiply & divide with big numbers & decimals quickly.

Find common factors & multiples of whole numbers quickly.

Understand ratios & rates, & solve problems involving proportional relationships.

If it took 7 hours to mow 4 lawns, how many lawns could be mowed in 35 hours?

Solve problems involving percentages. Find the part when given the whole & the percentage.

Would you prefer 33% of a $100 prize or 75% of a $50 prize?

Multiply & divide fractions. Calculate equivalent fractions, decimals, & percents.

Understand absolute values . Be able to put the absolute value of positive & negative numbers in order.

Read, write, & rearrange expressions using order of operations & basic properties of algebra.

24x + 18y can be rewritten as 6(4x + 3y)
y + y + y can be rewritten as 3y

Use variables to stand for quantities. Write equations & inequalities to solve word problems & describe relationships between variables.

A farmer uses a tractor to plant corn quickly in the springtime. The farmer plants 216 acres every 12 hours. Write an equation for the number of acres the farmer plants in “n” hours.

Solve simple equations with one unknown quantity or variable.

7x = 22 then x = ?

Find area, surface area, & volume of 2D & 3D shapes. Explain the formulas used.

Develop understanding of statistics. Determine & interpret measures of center (including mean, median, & mode) & measures of variability (including range). Select the right measures to use to solve a question.

6th Grade Math Examples

These are examples of math problems at a sixth grade level. 1,2

1Released items from Minnesota Comprehensive Assessment. Copyright MDE https://education.mn.gov/
MDE/dse/test/items/

2 Math problems obtained with permission from Student Partners. “Mathematics Assessments.” Achieve the Core, https://achievethecore.org/category/1020/mathematics-assessments

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There are 24 adults and 30 children at a science museum. What is the ratio of children to total people at the science museum?

5 : 9

Brennan is b years old. Shin is 1 year less than 2 times Brennan’s age. Marcos is 1 year less than 3 times Brennan’s age. The sum of the ages for all 3 boys is 22. Which equation shows this situation?

6b – 2 = 22

A study showed that the ratio of the number of people who get their news from social media to the number of people who get their news from other sources is 3:7.

270

It takes Mildred about 3 minutes to walk 2 blocks. A point has been plotted in the coordinate plane to show this situation.

a.) Plot a second point that represents an equivalent ratio.

b.) Explain what the coordinates of the point you plotted represent.

Answers may vary, points (1.5, 1), (6,4), and (9,6) are all equivalent

Answers may vary, points (6, 4) represents Mildred walking 4 blocks in 6 minutes

A store has two different sizes of ice cream. The smaller
container costs $3.87 for 48 ounces. The larger container costs $6.42 for 128 ounces. Which ice cream costs less per ounce? Explain your answer using numbers, words, and/or pictures.

The larger container costs less per ounce

462.8 + 1/5 = ?

463

Jenna’s family is going on a trip to visit relatives.

  • After driving 72 miles, they used 3.2 gallons of gas.
  • Her family has 850 miles remaining on their road trip.
  • The gas tank in their car can hold 15 gallons.

They filled the gas tank at the start of the road trip. They plan to only stop to fill up when their gas tank nears empty. There are plenty of gas stations along their route.

How many additional stops for gas will Jenna’s family need to make to get to their destination? Explain your answer using numbers, words, and/or pictures.

Number of additional stops ~1.516, since we can’t have a fraction of a stop, we must round up. Jenna’s family will need to make 2 additional stops for gas to reach their destination.

A water tank shaped like a rectangular prism is 78 inches tall, 66 inches wide, and 2 feet long. A cubic foot of water weighs approximately 62.43 pounds. What is the weight of the water the tank can hold when it is full?

4463.745 pounds

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Everyday Activities to Support Learning

Check in with Your Child

Talk to your 6th grader about the math they can do. What new things are they learning? Are they having any trouble? Can you help them?

Get Ideas from Teachers

Help your 6th grader find things that will help them learn. Ask your student to talk to their teachers about things that can help, such as practice activities, extensions, or more resources.

Invite Your Child Along on Shopping Trips

Ask your child to compare prices to
find the best deal. Ask them to estimate the tax

Experiment with Statistics

Ask your 6th grader to do statistical research in categories that interest them. For example, have them find the top 30 songs they’ve listened to this month. Find range, mean, & mode song duration.

Allow Your Child to Solve Problems Independently

When your 6th grader needs help with homework, ask them questions that help them learn how to solve the problem. Don’t solve the problem for them.

Real-World Skill Applications

Show your 6th grader how they can use what they learn at school later in life:

  • Ask your 6th grader about math problems they want to solve. Can they use this math when they are older at their jobs?
  • Have your child talk about the things they are learning & where they see these things in the world around them. For example, where do they see negative numbers outside of math class?
  • Show them where you use math in your everyday life
6th Grade Language Arts

English Language Arts for 6th Graders

What students should know and be able to do

Tips for Talking to Teachers

A strong relationship between families and teachers is key to ensuring students have what they need to succeed. Parent involvement not only leads to higher grades and test scores, but also helps students develop self-confidence, motivation, and social skills. Knowing what questions to ask at school visits and parent-teacher conferences can help you feel confident when it comes to addressing your child’s’ academic needs.

The numeric value of a digit in a number. The value of the digit is based on its position in the number. See the chart below for the number 4,367.082.

A group of words that means something different than its literal meaning. For example: “raining cats & dogs” means “to rain heavily” & “piece of cake,” means “something that is easy to do.”

The skills needed to read, write, & speak.

How sentences are put together, & how the order of words can change what it means. It’s like building with blocks – knowing a lot of words is like having a lot of different blocks, but understanding sentence structure is like knowing how to put the blocks together to build something bigger and more meaningful.

When we already know something about a topic before we read about it. When we know more about the topic, we can understand the text better.

When we know a word without having to sound it out. Good readers do this with words that are very common or with words that do not follow the “rules” of phonics.

The ability to read & write. Students get better at literacy with clear & specific instruction & with practice.

Synonyms are words that mean the same thing. “Big” & “enormous” are synonyms.

Words that mean the opposite of each other. “Big” and “small” are antonyms.

Addition is when we find the total amount by combining two or more values. Adding 2 & 3 gives us a total of 5. Adding 4, 1, & 3 gives us a total of 8. When we add, the total becomes more.

Counting numbers in order (1,2,3,4,5…)

Knowing that words are made up of many individual sounds (or phonemes). Students should be able to identify, produce & play with these individual sounds. You can find a video with all 44 English phonemes at https://www.youtube.com/watch?v=wBuA589kfMg.

Books with sound & spelling patterns that teachers have already taught in class. Students can decode or sound out most words in the text.

When students can read with speed, accuracy, & proper expressions that shows they understand what they read.

A number consisting of both a whole number & a fraction, such as 1 3/8.

A fraction in which the top is bigger than the bottom, such as 7/5.

After ordering the data set from lowest to highest, the median is the value in the middle of the data set.

The mean is sometimes also referred to as the average. The mean is found by adding together all of the values in a data set & then dividing by the total number of values.

The relationship between two sets of numbers that are not equal. Inequalities typically include an unknown number. For example, 7x < 28.

Factors are numbers we can multiply together to get another number. For example, 2 & 3 are factors of 6 because 2 times 3 equals 6.

The author’s point of view describes from what perspective the story is being told. For example, it may be a character in the story that is narrating, or the author may be an outside observer.

The amount of 3-dimensional (3D) space that an object takes up. Volume tells us the amount we need to fill the object. For example, the amount of water needed to fill a bottle. We measure the volume of an object in cubic units such as cubic centimeters, cubic inches, cubic feet, etc.

The chance of something happening. Probability is expressed as a decimal or fraction from 0-1 or as a percent from 0-100%. For example, the probability of flipping a coin & it being “tails” is .5, 1/2, or 50%.

Properties of algebra describe the different ways that numbers can be combined. In 6th grade students use the associative, commutative & distributive properties of algebra.

The order of operations is the rule that tells us the order we should use to solve an expression with many steps. The order we follow can be remembered with the acronym PEMDAS:
1) Parentheses
2) Exponents
3) Multiplication & Division from left to right
4) Addition & Subtraction from left to right

Equivalent expressions are expressions that work the same even though they look different. If two expressions are equivalent, then the two expressions have the same value when we put in the same value for the variable. For example, 2x + x + x is equivalent to 4x.

A coordinate plane is a flat plane formed by the intersection of a vertical number line called y-axis & a horizontal number line called x-axis. These are perpendicular lines that intersect each other at zero, & this point is called the origin.

Circumference is the distance around a shape. It is found by adding the length of all of the sides. For a circle, the circumference is proportional to the diameter by a factor of pi

The distance a number is from zero. The symbol “|” is placed on both sides of a number to mean absolute value, so we the absolute value of x is written as |x|. |4|=4 |-5|=5

A variable is an unknown numerical value in an equation or a math expression. Variables are shown with a symbol (usually a letter).

A thesis statement is one or two sentences that summarize the essay’s main idea.

Scientific notation is a way of showing numbers that are too
large or too small to be easily written. For example the number 0.0000000000073 can be written more easily as 7.3 x 10-12

The square root is a factor of a number that, when multiplied by itself, gives the original number. For example, both 5 and -5 are square roots of 25

The slope of the line describes the direction & steepness of the line. It is found by dividing the change in y over the change in x between any two points on the graph.

A rational number is any number that can be shown as a fraction of two integers. An irrational number cannot be shown as a fraction. A decimal is irrational if it never ends & it has no repeating pattern.

After ordering the data set from lowest to highest, the median is the value in the middle of the data set.

Claiming someone else’s work or ideas as your own.

Rewording a sentence or paragraph in your own words.

An equation between two variables that makes a straight line when plotted on a graph

An expression that defines a relationship between one variable (the independent variable) & another variable (the dependent variable). If the function is linear, then when it is graphed on a coordinate plane, it will create a straight line with a constant slope.

Numbers, symbols, & operations (such as + and ÷) grouped together that show the value of something. For example, y + 4 is an expression, & 3 − x/2 is also an expression.

An exponent refers to the number of times the base number is multiplied by itself.
73 = 7 x 7 x 7

A statement in which two things are equal. Equations often have unknown numbers (called variables) that are shown as a letter. For example: 3b + 5 = 14

The information about a person that exists on the internet as a result of their online activity. This includes posts on social media, photos, online purchases & reviews, passwords, subscriptions, & many other types.

The y-intercept is the point at which the graph of a line passes the y axis.

Recognizing the sounds of language. For example. rhyme, syllables, & the sounds in words.

Words are made up of individual sounds called phonemes. Children should practice identifying, producing, & rhyming with these individual sounds.

When students learn to write, they write the sounds they
hear. They may not spell the words correctly. Teachers
call this “inventive spelling”. Students use the letter &
sound connections taught in school to sound out words.

Any words that a child can read quickly & naturally. For example, “to”, “the,” “at.”

Subtraction is when we take away from the total
amount. If we start with 7 & we subtract 4, we have
3 left. When we subtract the total becomes less.

The answer we get by adding two or more numbers.

Figurative language uses figures of speech to be more
interesting, effective, & impactful. (“My dog’s coat is as
black as coal.” “He fought with the strength of a lion.”)

The numerator is the top number in a fraction. It shows how many parts we have. The denominator is the bottom number in a fraction. It shows how many parts there are in the whole item.

Teachers often measure a student’s reading level, usually
marked by a letter or number. This helps teachers know what
students need to learn. But sometimes, children are only
allowed to read texts at that level (typically a lexile number).
Be wary of this practice. Children should not be limited to
reading only texts that are at or below their grade level goal.

Text complexity is a measure of how difficult a text is. Text complexity is based on many factors, including the structure of the text, how difficult the language is, how much knowledge students need to understand what is read, & how difficult it is to understand what the text means. Students should be exposed to high-quality & complex texts. Complex texts provide opportunities for students to think deeply & to gain knowledge of the world, which will help them succeed in college, career, & life.

A suffix is a group of letters added to the end of a word. Suffixes
can change the meaning of a word. Adding “less” to the end
of the word “end” changes its meaning to “without end.” A
suffix can also change how the word is used. The noun “child”
becomes an adjective “childish” when you add the suffix “ish.”

A prefix is a group of letters added to the beginning of a
word that changes its meaning. Adding “un” in front of the
word “clean” makes the word mean “not clean.” Other
common prefixes are “re,” “dis,” “over,” “mis,” & “out.”

Using letter-sound relationships to correctly sound out & pronounce words. For example, children who have learned the English sounds /a/, /c/, & /t/ can decode “cat.”

A popular leveling system used by students, teachers, & parents to show two things:

  1. A student’s individual reading level
  2. The difficulty of the text

You can often find the Lexile number on the back of the book or by searching the title on lexile.com.

Grade-appropriate Lexile levels:

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