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Mathematics

for 5th Grade Students

See what skills your child will learn in Mathematics, examples of student work and how you can help at home.

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5th

5th

Expectations for Students

In 5th grade, students learn more about place value & work on doing the four operations (+ – x ÷) with big numbers & decimals. They add & subtract fractions with unlike denominators , & find volume. Students should work together in class, talk about how they solve problems, & learn from each other. 5th 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 5th grade state standards for math

By the end of the year, 5th graders should know:

Learning 5th Grade Mathematics

Multiply & divide numbers with multiple digits easily.

(6,951 ÷ 63 = 110 1/3 )

Add & subtract decimals & fractions with denominators that are not the same.

(2 1/4 – 1 1/3 )

Recognize, put in order, & write decimals, fractions, mixed numbers , & improper fractions .

Write simple equations & expressions to represent a situation & find the answer when the variable is known.

Determine whether the inequality 1.5 + x < 10 is true for x = 2.8

Graph points in the coordinate plane .

Understand the concept of perimeter, area, & volume . Develop & use formulas to find each.

Read & write tenths & hundredths as both decimals & fractions (rewriting 0.62 as 62⁄100).

Understand that the volume of a three-dimensional figure can be found by counting the total number of same-sized cubes that fill the shape shapes by multiplying length & width.

This diagram represents swimming pool with dimensions in feet.

How many cubic feet of water are needed to fill the pool all the way to the top?

5th Grade Math Examples

Here are examples of math problems at the 5th grade level.

Math problems obtained with permission from Student Partners. “Mathematics Assessments.”
Achieve the Core

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A store owner ordered 24 packages of candy. Each package contains 72 candies. He plans to make bags of candy with 18 candies in each bag to sell. How many bags of candy can he make?

96 bags of candy

Callan has 1/3 of his birthday cake left. He wants to share it equally between himself & 3 other boys. How much of the original birthday cake will each of the 4 boys get?

1/12

The data table below shows the length of a meerkat measured at different times during its first 20 months of life.

a. Graph the set of points to represent the data in the table
b. What are the coordinates of the point that represents the month when the meerkat was first measured at its adult length (greatest length)?

(14,12)

Jasmine is walking to her friend’s house, which is 2 3⁄4 miles away. She is half of the way there. How much farther, in miles, does Jasmine have to walk?

1 3/8 mile

What is the product of 9 & 740?

6,660

Write 11 ÷ 5 as a fraction & show on the number line below:

11/5

Write >, =, or < to make each comparison true

7a: <
7b: <
7c: >

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Everyday Activities to Support Learning

Practice Multiplication and Division with Big Numbers

Practice multiplication & division with big numbers (4,378 × 615; 2,560 ÷ 24). Ask your child to guess the
answer before calculating it. This will help the child strengthen their sense of numbers & recognize when
they may have made errors in their calculation.

Find Volumes

Find the volume of different rectangular objects around the home (cereal or shoe box).

Practice Adding and Subtracting Fractions

Practice adding & subtracting fractions with the different denominator. For example, 1 1/3 + 2 3/5

Play Games

Play board & card games together that incorporate math in strategy or scoring.

5th Grade Language Arts

English Language Arts for 5th 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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