ratio homework 6th grade

6th Grade Ratio Worksheets

6th Grade ratio worksheets are used to give students a good understanding of how to deal with ratio and proportion problems. The questions in these worksheets range from simple interpretation sums to word problems that require analysis.

Benefits of 6th Grade Math Ratios Worksheets

Ratios are used very frequently in daily life. It is good for young minds to have a clear foundation of this concept. By solving the problems in 6th grade ratio worksheets, children can increase their speed and accuracy. Questions are structured in a way to improve a student's logical and analytical abilities. These 6th grade math worksheets are provided with answer keys with step-by-step solutions to help students in case they get stuck while solving a question.

Printable PDFs for Grade 6 Ratio Worksheets

6th Grade math ratio worksheets are easy to use and available in PDF format that is free to download, enabling students to access quality education offline.

• Math 6th Grade Ratio Worksheet
• 6th Grade Ratio Math Worksheet
• Sixth Grade Ratio Worksheet
• Grade 6 Math Ratio Worksheet

Explore more topics at Cuemath's Math Worksheets .

• Number Charts
• Multiplication
• Long division
• Basic operations
• Telling time
• Place value
• Roman numerals
• Fractions & related
• Add, subtract, multiply,   and divide fractions
• Mixed numbers vs. fractions
• Equivalent fractions
• Prime factorization & factors
• Fraction Calculator
• Decimals & Percent
• Add, subtract, multiply,   and divide decimals
• Fractions to decimals
• Percents to decimals
• Percentage of a number
• Percent word problems
• Classify triangles
• Classify quadrilaterals
• Circle worksheets
• Area & perimeter of rectangles
• Area of triangles & polygons
• Coordinate grid, including   moves & reflections
• Volume & surface area
• Pre-algebra
• Square Roots
• Order of operations
• Scientific notation
• Proportions
• Ratio word problems
• Write expressions
• Evaluate expressions
• Simplify expressions
• Linear equations
• Linear inequalities
• Graphing & slope
• Equation calculator
• Equation editor
• Elementary Math Games
• Addition and subtraction
• Math facts practice
• The four operations
• Factoring and number theory
• Geometry topics
• Middle/High School
• Statistics & Graphs
• Probability
• Trigonometry
• Logic and proof
• For all levels
• Favorite math puzzles
• Favorite challenging puzzles
• Math in real world
• Problem solving & projects
• For gifted children
• Math history
• Math games and fun websites
• Interactive math tutorials
• Math help & online tutoring
• Assessment, review & test prep
• Online math curricula

Use the generator to make customized ratio worksheets. Experiment with the options to see what their effect is.

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.

Child Login

• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
• More Number Sense Worksheets
• Size Comparison
• Measuring Length
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature
• More Measurement Worksheets
• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
• Box-and-whisker Plot
• Permutation and Combination
• Probability
• Venn Diagram
• More Statistics Worksheets
• Shapes - 2D
• Shapes - 3D
• Lines, Rays and Line Segments
• Points, Lines and Planes
• Transformation
• Quadrilateral
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
• Surface Area
• Pythagorean Theorem
• More Geometry Worksheets
• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Squaring Numbers
• Square Roots
• Scientific Notations
• Speed, Distance, and Time
• Absolute Value
• More Pre-Algebra Worksheets
• Translating Algebraic Phrases
• Evaluating Algebraic Expressions
• Simplifying Algebraic Expressions
• Algebraic Identities
• Quadratic Equations
• Systems of Equations
• Polynomials
• Inequalities
• Sequence and Series
• Complex Numbers
• More Algebra Worksheets
• Trigonometry
• Math Workbooks
• English Language Arts
• Summer Review Packets
• Social Studies
• Holidays and Events
• Worksheets >
• Pre-Algebra >

Ratio Worksheets

Immerse yourself in practice with our printable ratio worksheets. Whether it is part-to-part ratios, part-to-whole ratios, identifying parts from the whole, or finding the whole from the parts, dividing quantities, generating equivalent ratios, or expressing the ratio in three different ways, that you are looking for, these pdfs have them all covered for your grade 5 through grade 8 learners. Instantly evaluate your ratio problems with the answer keys provided. Our free ratio worksheets are a must-have to get the ball rolling!

Part-to-Part Ratio | Level-1

Perk up with these part-to-part ratio worksheets and get children in grade 5 and grade 6 to count how many of one thing there is as compared to another and express it as a ratio.

• Download the set

Part-to-Part Ratio | Level-2

Fuel learning with these ratio pdfs where the two sets of objects are mixed up. Count the number of each kind and frame a ratio comparing the size of one number to the size of the other.

Part-to-Whole Ratio | Level-1

Comparing the number of butter cookies to the assorted cookies in a jar is an example of part-to-whole ratios. Measure the quantity of one item against the total and write the ratio.

Part-to-Whole Ratio | Level-2

Upscale with these printable part-to-whole ratio worksheets. Direct children to count the number of specified objects, add the three terms to find the whole and express them as a ratio.

Expressing Ratio in Three Ways | Pictures

Get acquainted with the different representations of a ratio. Count the two different sets of pictures and express the ratio by using "to", the colon symbol ":", and the fraction notation.

Representing Ratio in Three Ways | Standard

Doing away with pictures and presenting ratio in word format, these ratio worksheets are a sure-fire way to help learners transit easily as they read phrases and express the ratio in three ways.

Drawing Shapes to Represent the Ratio

Break away from the humdrum of regular printable ratio worksheets and get children to stay in the groove as they follow the instructions and sketch shapes to represent the ratio.

Coloring Objects to Represent the Ratio

Add a splash of color with these pdf worksheets where 5th grade, and 6th grade children are expected to color the specified number of objects as instructed and figure out the ratio.

Reducing Ratios to the Lowest Terms | Easy

Reducing is nothing but converting the ratio to its simplest form. Divide the antecedent and the consequent terms of the ratio, which are numbers within 50, by the GCF to reduce the ratio.

Reducing Ratios to the Lowest Terms | Moderate

Raise the bar for grade 6 and grade 7 learners with these reducing the ratios to the lowest terms worksheets where the number range gradually increases to 100.

Simplifying Ratios Involving Unit Conversion | Easy

Take your simplifying ratio skills to new heights with these pdfs. Using appropriate conversion formulas, make the units uniform and reduce the ratio to the simplest terms.

Simplifying Ratios Involving Unit Conversion | Moderate

Bring uniformity in the units before reducing the ratio to lowest terms as you make headway with these printable simplifying ratio worksheets involving numbers within 100.

Finding the Parts from the Whole

Add up the terms of the ratio. Divide the whole quantity by the sum of the parts to find the unit rate. Multiply each term with the unit rate to find the two parts. Not as complicated as it sounds!

Finding the Whole from Parts

The ratio of two numbers and the quantity of one part is provided. Scale up the other term by multiplying it and figure out the other quantity, add the two quantities to find the whole.

Dividing Quantities into 3-Part Ratios

Add the three terms to find the total number of parts the quantity should be divided into. Multiply each term in the ratio with the unit rate and share the quantity in the given ratio.

Writing the Equivalent Ratios

Scale up each ratio by multiplying the antecedent and the consequent terms by the same number and write an equivalent ratio and complete the table with the missing equivalent ratios.

Finding Unknown Quantities from Equivalent Ratios

Instruct 7th grade and 8th grade learners to simplify ratios and check for equivalence, work out the unknown quantity in an equivalent equation, and solve word problems too.

Ratio Word Problems

Go beyond books and practice the real-time application of ratio concepts as you solve word problems involving part-to-part ratios, part-to-whole ratios, and much more.

(27 Worksheets)

Proportion Worksheets

Comprehend the distinction between ratio and proportion with this batch of proportion worksheets offering exercises like finding proportions, identifying them from graphs, and more!

(120 Worksheets)

Related Worksheets

» Equivalent Fractions

» Decimals

» Percent

» Fractions

Become a Member

Membership Information

Privacy Policy

What's New?

Printing Help

Testimonial

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

Addition (Basic)

Addition (Multi-Digit)

Algebra & Pre-Algebra

Comparing Numbers

Daily Math Review

Division (Basic)

Division (Long Division)

Hundreds Charts

Measurement

Multiplication (Basic)

Multiplication (Multi-Digit)

Order of Operations

Place Value

Probability

Skip Counting

Subtraction

Telling Time

Word Problems (Daily)

More Math Worksheets

Reading Comprehension

Reading Comprehension Gr. 1

Reading Comprehension Gr. 2

Reading Comprehension Gr. 3

Reading Comprehension Gr. 4

Reading Comprehension Gr. 5

Reading Comprehension Gr. 6

Reading & Writing

Reading Worksheets

Cause & Effect

Fact & Opinion

Fix the Sentences

Graphic Organizers

Synonyms & Antonyms

Writing Prompts

Writing Story Pictures

Writing Worksheets

More ELA Worksheets

Consonant Sounds

Vowel Sounds

Consonant Blends

Consonant Digraphs

Word Families

More Phonics Worksheets

Early Literacy

Build Sentences

Sight Word Units

Sight Words (Individual)

More Early Literacy

Punctuation

Subjects and Predicates

More Grammar Worksheets

Spelling Lists

Spelling Grade 1

Spelling Grade 2

Spelling Grade 3

Spelling Grade 4

Spelling Grade 5

Spelling Grade 6

More Spelling Worksheets

Chapter Books

Charlotte's Web

Magic Tree House #1

Boxcar Children

More Literacy Units

Animal (Vertebrate) Groups

Butterfly Life Cycle

Electricity

Matter (Solid, Liquid, Gas)

Simple Machines

Space - Solar System

More Science Worksheets

Social Studies

Maps (Geography)

Maps (Map Skills)

More Social Studies

Mother's Day

Father's Day

More Holiday Worksheets

Puzzles & Brain Teasers

Brain Teasers

Logic:  Addition Squares

Mystery Graph Pictures

Number Detective

Lost in the USA

More Thinking Puzzles

Teacher Helpers

Teaching Tools

Award Certificates

More Teacher Helpers

Pre-K and Kindergarten

Alphabet (ABCs)

Numbers and Counting

Shapes (Basic)

More Kindergarten

Worksheet Generator

Word Search Generator

Multiple Choice Generator

Fill-in-the-Blanks Generator

More Generator Tools

Full Website Index

Ratio Worksheets

Compare two quantities with ratios. These worksheets feature basic and intermediate-level ratio activities.

Logged in members can use the Super Teacher Worksheets filing cabinet to save their favorite worksheets.

Quickly access your most used files AND your custom generated worksheets!

Please login to your account or become a member and join our community today to utilize this helpful feature.

Learn to calculate the probability of certain events with these printable worksheets.

This page contains the full index of math worksheets on our website.

Images of Worksheets

PDF with answer key:

PDF no answer key:

• 6th Grade Math
• Ratios and rates problems

Solving ratios and rates problems in 6th Grade: Tips, Examples, and Worksheets

Are you a 6th-grader who wants to learn how to solve ratios and rates problems ? Or are you a parent or teacher who wants to help your child or student master this vital math skill? If so, you've come to the right place! In this article, we will provide fun tips, examples, and worksheets that your students can practice daily and are free to download.

Simplify learning ratios and rates: Download Free 6th Grade Worksheets PDF with step-by-step solutions.

Like fractions, this article will help 6 th graders learn how to simplify ratios and rates to their lowest forms using a simple step-by-step solution . You can download these free 6th Grade Worksheets PDF from Mathskills4kids.com and start practicing now.

In this article, we'll explain what ratios and rates are, why they are important for 6th-graders, and how to write, represent, compare, and solve them in different ways.

We'll also provide tips, examples, and worksheets to practice and improve your ratios and rates skills. And as a bonus, we'll share some web links with more resources that you can use to learn more about ratios and rates.

So, let's get started!

BROWSE THE WEBSITE

Download free worksheets, grade 6 math topics.

• Whole numbers

Multiplication

• Exponents and square roots
• Number theory
• Add & subtract decimals
• Multiply & divide decimals
• Fractions & mixed numbers
• Add & subtract fractions
• Multiply fractions
• Divide fractions
• Operations with integers
• Mixed operations
• Rational numbers
• Problems solving
• Ratio & proportions
• Percentages
• Measuring units
• Consumer math
• Telling time
• Coordinate graph
• Algebraic expressions
• One step equations
• Solve & graph inequalities
• Two-step equations
• 2D Geometry
• Symmetry & transformation
• Geometry measurement
• Data and Graphs
• Probability

Start practice on Sixth Grade here

What are ratios and rates.

A ratio compares two quantities of the same kind by division. For example, if 12 boys and 18 girls are in a class, the ratio of boys to girls will be 12:18 or 12/18. A rate is a special ratio that compares two quantities of different kinds by division. For example, if you can run 3 miles in 30 minutes, the rate of your speed is 3 miles per 30 minutes or 3/30.

Why are ratios and rates important for 6th-graders?

Ratios and rates are important for 6th-graders because they help them understand the relationships between different quantities and measure how fast or slow something changes.

Ratios and rates also help them solve real-world problems involving proportions, fractions, decimals, percentages, unit conversions, and more.

In addition, ratios and rates are the foundation for learning more advanced math topics such as ratios and proportional relationships, unit rate, unit analysis, scaling, slope, and linear equations.

How to write ratios and rates in different ways

There are three main ways to write ratios and rates : using words, colons (:), or fractions (/). For example, the ratio of boys to girls in a class can be written as:

• "12 boys to 18 girls" using words
• "12:18" using colons
• "12/18" using fractions

The rate of your speed can be written as:

• "3 miles per 30 minutes" using words
• "3:30" using colons
• "3/30" using fractions

We can also simplify ratios and rates by dividing both quantities by a common factor. For example, the ratio of boys to girls in a class can be simplified by dividing both numbers by 6:

• "12 boys to 18 girls" simplifies to "2 boys to 3 girls"
• "12:18" simplifies to "2:3"
• "12/18" simplifies to "2/3"

The rate of your speed can be simplified by dividing both numbers by 3:

• "3 miles per 30 minutes" simplifies to "1 mile per 10 minutes."
• "3:30" simplifies to "1:10"
• "3/30" simplifies to "1/10"

How to find equivalent ratios and simplify rates

Equivalent ratios are ratios that have the same value when simplified. For example, the ratios 2:3, 4:6, and 6:9 are equivalent because they all simplify to 2/3. We can multiply or divide both quantities by the same factor to find equivalent ratios . For example, to find an equivalent ratio to 2:3, we multiply both numbers by 2 to get 4:6 or divide both numbers by 2 to get 1:1.5.

Simplifying rates is similar to simplifying ratios, except that we have to make sure that the units of the quantities are consistent. For example, to simplify the rate of 3 miles per 30 minutes, we will convert the units of distance and time to the same unit, such as miles per hour or minutes per mile. To do this, we can use unit conversions or unit fractions.

For example, to convert 3 miles per 30 minutes to miles per hour, we can multiply by the unit fraction 60 minutes/1 hour, which is equal to 1:

3 miles / 30 minutes x 60 minutes / 1 hour = 180 miles / 1800 minutes = 1 mile / 10 minutes = 6 miles / 60 minutes = 6 miles per hour

How to compare ratios and rates using cross-multiplication

Cross-multiplication is a method that helps you compare ratios and rates by finding a common denominator. To use cross-multiplication, we will set up a proportion, an equation that states that two ratios or rates are equal. For example, if we want to compare the ratio of boys to girls in two classes, we can write a proportion like this:

12/18 = x/24,

Where x is the number of boys in the second class. Then, we can cross-multiply by multiplying the numerator of one ratio by the denominator of the other ratio and setting them equal. For example:

12 x 24 = 18 x (x)

Then, we can solve for x by dividing both sides by 18:

x = (12 x 24) / 18

x = 288 / 18

So, the ratio of boys to girls in the second class is 16:24, equivalent to 2:3.

We can also use cross-multiplication to compare rates by ensuring consistent units. For example, if we want to compare the speed of two runners who run different distances at different times, we can write a proportion like this:

3 miles / 30 minutes = x miles / 45 minutes

Where x is the distance run by the second runner. Then, we can cross-multiply and solve for x:

3 x 45 = 30 x x

x = (3 x 45) / 30

x = 135 / 30

So, the second runner runs 4.5 miles in 45 minutes.

How to solve word problems involving ratios and rates

One of the most common applications in 6th Grade math is solving ratios and rates problems . Word problems are mathematical questions that use words and numbers to describe a real-life situation. To solve word problems involving ratios and rates , we can follow these steps:

• Read the problem carefully and identify the given information and the unknown quantity.
• Write a ratio or a rate to represent the relationship between the given information and the unknown quantity.
• Use equivalent ratios, cross-multiplication, or unit rates to find the value of the unknown quantity.
• Check your answer by plugging it back into the ratio or rate and see if it makes sense in the problem context.
• Write a complete sentence to answer the question.

Let's look at examples of applying these steps to different word problems involving ratios and rates.

10 ratios and rates word problems with solutions for 6th-Grade

Here are 10-word problems selected from Mathskills4kids.com that your students can practice with to improve their ratios and rates skills in Grade 6. Please encourage them to solve these problems independently, then check the solutions below.

• In a class of 24 students, 18 students like chocolate ice cream, and the rest like vanilla ice cream. What is the ratio of students who like chocolate ice cream to vanilla ice cream? Write your answer in the simplest form.
• A recipe for lemonade calls for 6 cups of water and 1 cup of lemon juice. How many cups of lemon juice are needed to make 18 cups of lemonade?
• A car travels 120 miles in 3 hours. What is the average speed of the car in miles per hour?
• A bag of candy contains 12 red candies, 8 blue candies, and 10 green candies. What is the probability of picking a red candy from the bag?
• A map has a scale of 1 inch: 50 miles. How many inches on the map represent a distance of 300 miles?
• A printer can print 15 pages in 2 minutes. How long will it take to print 60 pages?
• A bag of oranges weighs 12 pounds. If each orange weighs 0.25 pounds, how many oranges are in the bag?
• A bicycle costs $180 and is on sale for 25% off. What is the sale price of the bicycle?
• A cookie recipe makes 24 cookies and uses 2 cups of flour. How many cups of flour are needed to make 36 cookies?
• A painter can paint a wall in 4 hours. How much of the wall can he paint in 1 hour?
• The ratio of students who like chocolate ice cream to vanilla ice cream is 18:6, which can be simplified by dividing both terms by 6, giving 3:1.

Therefore, we need 3 cups of lemon juice to make 18 cups of lemonade.

120 miles / 3 hours = 40 miles/hour

The average speed of the car is 40 miles per hour.

12 / 30 = 0.4

The probability of picking a red candy from the bag is 0.4 or 40%.

x inches on the map represent 300 miles in reality.

Then, we can solve for x by cross-multiplying:

1 x 300 = (x) x 50

x = (1 x 300) /50

Therefore, 6 inches on the map represents a distance of 300 miles.

15 pages / 2 minutes = 1 page / (2/15) minutes

The printer can print one page in (2/15) minutes, equivalent to 0.133 minutes or 8 seconds. To print 60 pages, we can multiply both terms by 60:

1 page / (2/15) minutes = 60 pages / (120/15) minutes

The printer can print 60 pages in (120/15) minutes, equivalent to 8 minutes.

12 pounds / x oranges

To find x, we can use the fact that each orange weighs 0.25 pounds, which means that x oranges weigh x x 0.25 pounds. We can then set up an equation and solve for x:

12 pounds = x x 0.25 pounds

x = 12 / 0.25

There are 48 oranges in the bag.

25% = 25 / 100 = 0.25

To find the amount of discount, we can multiply the percentage by the original price:

0.25 x $180 = $45

The amount of discount is $45. To find the sale price, we can subtract the amount of discount from the original price:

$180 - $45 = $135

The sale price of the bicycle is $135.

2 cups of flour / 24 cookies = x cups of flour / 36 cookies

To find x, we can cross-multiply and solve for x:

2 x 36 = (x) x 24

x = (2 x 36) /24

We need 3 cups of flour to make 36 cookies.

1 wall / 4 hours = x wall / 1 hour

1 x 1 = (x) x4

x = (1 x 1) /4

He can paint 0.25 or one-fourth of the wall in one hour.

Bonus: More resources for solving ratios and rates problems in 6th Grade

If you want more practice for your 6 th graders on solving ratios and rates problems , then check out these web links:

This video from Khan Academy introduces the concept of ratios and how to write them in different ways.

This webpage from Math is Fun explains what ratios are and how to use them in various situations.

This webpage from Math Playground has interactive games and activities that help 6 th graders practice ratios and proportions.

This webpage from IXL has online exercises with unit-rate word problems for Grade 6.

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Conclusion: the benefits of mastering ratios and rates in everyday situations

Your 6th-grade students have learned much about ratios and rates in this article. They have seen how to write them in different ways, how to use tables, graphs, and diagrams to represent them, how to find equivalent ratios and simplify rates, how to compare them using cross-multiplication, and how to solve word problems involving them. They have also practiced their skills with 10 ratios and rates word problems with solutions for 6th grade.

But why are ratios and rates important to us? How can they help us in our daily life? Here are some examples of how we can use ratios and rates in everyday situations:

• Cooking : We can use ratios and rates to measure ingredients, adjust recipes, compare prices, and calculate nutritional values. For example, if we want to make a cake that serves 12 people, but the recipe is for 8 people, we can use a ratio to determine how much each ingredient is needed.
• Sports : We can use ratios and rates to analyze performance, compare players, and predict outcomes. For example, if we want to compare two basketball players, we can use ratios to compare their points, rebounds, assists, and other statistics.
• Art : We can use ratios and rates to create designs, patterns, and proportions. For example, if we want to draw a face, we can use ratios to divide the head into sections and place the features accordingly.
• Science : We can use ratios and rates to explore nature, conduct experiments, and interpret data. For example, if we want to know how many birds are in a park, we can use a ratio to compare the number of birds we see in a sample area to the total park area.

As we can see, ratios and rates are useful for many aspects of our lives. They help us make sense of the world around us and solve problems creatively.

By mastering ratios and rates in 6th grade, your students will be ready for more advanced math topics in the future. They will also develop critical thinking skills that benefit them in school and beyond.

WHAT’S THIS ALL ABOUT?

This is mathskills4kids.com a premium math quality website with original Math activities and other contents for math practice. We provide 100% free Math ressources for kids from Preschool to Grade 6 to improve children skills.

Subtraction

Measurement

Telling Time

Problem Solving

Data & Graphs

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

SUBSCRIBE TO OUR NEWSLETTER

Privacy policy.

Our team Don't Pass on to third parties any identifiable information about mathskills4kids.com users. Your email address and other information will NEVER be given or sold to a third party.

USE OF CONTENTS

Many contents are released for free but you're not allowed to share content directly (we advise sharing website links), don't use these contents on another website or for a commercial issue. You're supposed to protect downloaded content and take it for personal or classroom use. Special rule : Teachers can use our content to teach in class.

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Course: 6th grade   >   Unit 1

• Intro to ratios
• Basic ratios
• Part:whole ratios

Ratio review

• There are 4 ‍   monkeys for every 5 ‍   bananas.
• The ratio of monkeys to bananas is 4 ‍   to 5 ‍   .
• The ratio of monkeys to bananas is 4 : 5 ‍   .
• There are 5 ‍   bananas for every 4 ‍   monkeys .
• The ratio of bananas to monkeys is 5 ‍   to 4 ‍   .
• The ratio of bananas to monkeys is 5 : 4 ‍   .

Let's practice!

• (Choice A)   14 : 6 ‍   A 14 : 6 ‍  
• (Choice B)   3 : 24 ‍   B 3 : 24 ‍  
• (Choice C)   14 : 3 ‍   C 14 : 3 ‍  
• (Choice D)   24 : 3 ‍   D 24 : 3 ‍  

Want to join the conversation?

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

Ratio Worksheets

• Kindergarten

Math  /  6th Grade  /  Unit 1: Understanding and Representing Ratios

Understanding and Representing Ratios

Students are introduced to the concept of ratios, learning ratio language to describe the association between two or more quantities and different strategies to solve ratio problems.

Unit Summary

In Unit 1, 6th grade students have the opportunity to study a concept that is brand new to them: ratios. They learn how to use ratio language to describe the association between two or more quantities, expanding their abilities to analyze relationships and see multiplicative patterns. Students learn many ways to represent ratios, starting with discrete drawings and working their way to abstract tables. These representations become important tools in their ratios toolkit, enabling students to be strategic about which tools to use for different problems (MP.5). When students work with tables and double number lines, they discover how structure can shine light on a relationship, especially when comparing multiple ratio situations (MP.7).

Throughout the unit, students see similar problems posed to them in different lessons. This is to support students learning new strategies to solve ratio problems and to compare and contrast different approaches. By the end of the unit, students should be able to select a strategy they think is best for a problem and to explain their choice. 

In 4th grade and 5th grade , students learned the difference between multiplicative and additive comparisons and they interpreted multiplication as a way to scale. Students will access these prior concepts in this unit as they investigate patterns and structures in ratio tables and use multiplication to create equivalent ratios. 

The work students do in this unit connects directly to Unit 2  and re-appears in Unit 6  when students analyze and graph relationships between independent and dependent variables. Beyond 6th grade, students extend their understanding of ratios and rates to investigate proportional relationships in 7th grade . This sets the groundwork for the study of functions, linear equations, and systems of equations, which students will study in 8th grade and high school . 

Pacing: 21 instructional days (18 lessons, 2 flex days, 1 assessment day).

Fishtank Plus for Math

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

The following assessments accompany Unit 1.

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

Pre-Unit Student Self-Assessment

Have students complete the Mid-Unit Assessment.

Use the resources below to assess student understanding of the unit content and action plan for future units.

Post-Unit Assessment

Post-Unit Assessment Answer Key

Post-Unit Student Self-Assessment

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Intellectual Prep

Suggestions for how to prepare to teach this unit

Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.

Internalization of Standards via the Post-Unit Assessment

• Standards that each question aligns to
• Strategies and representations used in daily lessons
• Relationship to Essential Understandings of unit 
• Lesson(s) that Assessment points to

Internalization of Trajectory of Unit

• Read and annotate the Unit Summary.
• Notice the progression of concepts through the unit using the Lesson Map.

Essential Understandings

• Connection to Post-Unit Assessment questions
• Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

• The Progressions for the Common Core State Standards in Mathematics 6-7, Ratios and Proportional Relationships  is valuable to read before the unit.
• UnboundEd also has a great 6th grade content guide on ratios:  Ratios: Unbound, A Guide to Grade 6 Mathematics Standards .
• Read the following table that includes models used throughout the unit.

The central mathematical concepts that students will come to understand in this unit

• A ratio is a set of numbers that associates two or more quantities. The order of the values in a ratio relates directly to the order of the quantities described. 
• Equivalent ratios are useful in understanding a situation more deeply or in comparing multiple situations. Two ratios are equivalent if there is a nonzero number that can be multiplied by both quantities in one ratio to equal the corresponding quantities in the second ratio. 
• Ratio problems can be represented and solved using a variety of strategies, tools, and representations, including a discrete diagram, a double number line, a ratio table, and tape diagrams. Each tool has its advantages and disadvantages and can be selected strategically.

Terms and notation that students learn or use in the unit

double number line

equivalent ratio

multiplicative relationship

part to part ratio

part to whole ratio

ratio table

tape diagram

To see all the vocabulary for Unit 1, view our 6th Grade Vocabulary Glossary .

The materials, representations, and tools teachers and students will need for this unit

• Calculators (1 per student) — This lesson involves calculations with decimals. Students have worked with decimals in 5th grade, however, in order to keep the emphasis on the ratio reasoning, it is recommended to give students calculators to support their computations throughout this lesson (MP.5).
• Ratio Shapes Handout (1 per student)

To see all the materials needed for this course, view our 6th Grade Course Material Overview .

Topic A: Understanding & Describing Ratios

Define ratio and use ratio language to describe associations between two or more quantities.

Represent ratios using discrete drawings. Understand that the order of numbers in a ratio matters.

Create a free account to access thousands of lesson plans.

Already have an account? Sign In

Topic B: Equivalent Ratios

Define and find equivalent ratios.

Reason with equivalent ratios and determine if two ratios are equivalent.

Represent ratios using double number lines and identify equivalent ratios. 

Solve ratio problems using strategies including double number lines.

Find equivalent ratios using ratios with “per 1” unit.

6.RP.A.3 6.RP.A.3.B

Compare situations using equivalent ratios and double number lines.

Use ratio reasoning to solve a three-act task.

Topic C: Representing Ratios in Tables

Represent ratios in tables.

6.RP.A.3 6.RP.A.3.A

Understand the structure of tables of equivalent ratios. Solve ratio problems using tables.

Solve ratio problems using tables, including those involving total amounts.

Compare ratios using tables.

Solve ratio problems using different strategies.

6.RP.A.1 6.RP.A.3 6.RP.A.3.A

Topic D: Solving Part:Part:Whole Ratio Problems

Solve part:part ratio problems using tape diagrams.

6.RP.A.1 6.RP.A.3

Solve part:whole ratio problems using tape diagrams.

Solve more complex ratio problems using tape diagrams.

Solve ratio problems using a variety of strategies, including reasoning about diagrams, double number lines, tables, and tape diagrams. Summarize strategies for solving ratio problems.

Common Core Standards

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

Ratios and Proportional Relationships

6.RP.A.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.RP.A.3.A — Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.A.3.B — Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Foundational Standards

Standards covered in previous units or grades that are important background for the current unit

Measurement and Data

4.MD.A.1 — Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

Number and Operations—Fractions

5.NF.B.3 — Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.B.5 — Interpret multiplication as scaling (resizing), by:

5.NF.B.5.A — Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

5.NF.B.5.B — Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

Operations and Algebraic Thinking

4.OA.A.2 — Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

5.OA.B.3 — Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Future Standards

Standards in future grades or units that connect to the content in this unit

Expressions and Equations

6.EE.C.9 — Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

6.RP.A.2 — Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Expectations for unit rates in this grade are limited to non-complex fractions. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."

6.RP.A.3.C — Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.RP.A.3.D — Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ^1/2/_1/4 miles per hour, equivalently 2 miles per hour.

7.RP.A.2 — Recognize and represent proportional relationships between quantities.

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 — Attend to precision.

CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Unit Rates and Percent

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School information, what courses are you interested in, are you interested in onboarding professional learning for your teachers and instructional leaders, any other information you would like to provide about your school.

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice

Measurement

• Factoring & prime factors

Proportions

• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

Download & Print From only $2.60

Sixth Grade Math Worksheets

Free grade 6 worksheets from k5 learning.

Our printable grade 6 math worksheets delve deeper into earlier grade math topics (4 operations, fractions, decimals, measurement, geometry) as well as introduce exponents, proportions, percents and integers .

Choose your grade 6 topic:

4 operations.

Place Value & Scientific Notation

Add & Subtract

Multiply & Divide

Decimals & Percents

Fractions to / from Decimals

Decimals - Add and Subtract

Decimals  - Multiply

Decimals - Divide

Add & Subtract Fractions

Multiply & Divide Fractions

Converting Fractions

Sample Grade 6 Math Worksheet

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

Join K5 to save time, skip ads and access more content. Learn More

• Forgot Password?

ratio reasoning 6th grade

All Formats

Resource types, all resource types.

• Rating Count
• Price (Ascending)
• Price (Descending)
• Most Recent

Ratio reasoning 6th grade

Ratios and Proportional Reasoning Review Booklet for 6th Grade Math

6th Grade Ratios and Proportional Reasoning Escape Room Activity

6th Grade Math Ratios Proportional Reasoning Interactive Notebook Unit Printable

Proportional Reasoning with Ratios and Rates - Unit 5- 6th Grade + Distance Learn

6th Grade Ratios & Proportional Reasoning (6.RP) Common Core Test

Proportional Reasoning w/ Ratios and Rates Unit 5- 6th Grade -Worksheets+Distance

• Google Drive™ folder

Ratios and Proportional Reasoning Vocabulary Math Crossword Puzzle 6th Grade

Ratio Reasoning 6th Grade Common Core

Proportional Reasoning w/ Ratios and Rates Unit 5 - 6th Grade - Notes + Distance

Proportional Reasoning w/ Ratios and Rates Unit 5 - 6th Grade -Activites+Distance

( 6th Grade ) Rate, Ratio and Proportional Reasoning QUIZ

• Easel Assessment

6.RP.3A Ratios Proportional Relationship( 6th Grade Math)Concept Reasoning Table

6th Grade Ratio , Rate, & Proportional Reasoning Study Guide

6TH GRADE RATIOS AND PROPORTIONAL REASONING (6.RP) TEST PREP

Sixth Grade Ratio and Proportional Reasoning Practice

6.RP.2 Ratio Proportional Relationships( 6th Grade Math) Concepts Reasoning

6.RP.1 Ratio Proportional Relationships ( 6th Grade Math) Reasoning Solving Order

Unit 5- Proportional Reasoning with Ratios & Rates (Part 1)- 6th Grade Hyperdoc

• Word Document File
• Internet Activities

Unit 5- Proportional Reasoning with Ratios & Rates (Part 2)- 6th Grade Hyperdoc

Ratios Unit | Ratios with Tables, Graphs, and Proportions | 6th Grade Worksheets

• Google Apps™

⭐ 6th Grade SPIRAL MATH REVIEW Common Core | Print & Digital

6th Grade Math STAAR Practice Bundle - Progress Monitoring by Domain

6th Grade Math Digital Pixel Art Bundle Math Review Math Centers Test Prep

6th Grade Math Word Problems Spiral Review

• We're hiring
• Help & FAQ
• Privacy policy
• Student privacy
• Terms of service
• Tell us what you think

• Skip to main content

Maneuvering the Middle

Student-Centered Math Lessons

• All Products

Ratios and Rates Unit 6th Grade TEKS

A 10 day Ratios and Rates TEKS-Aligned complete unit including: ratios as comparisons, ratio application, ratio tables and graphs, rates as comparisons, rate application, and measurement conversions.

Description

Additional information.

• Reviews (0)

This Ratios and Rates Unit 6th Grade TEKS includes: ratios as comparisons, ratio application, ratio tables and graphs, rates as comparisons, rate application, and measurement conversions.

Students will practice with both skill-based problems, real-world application questions, and error analysis to support higher level thinking skills.  You can reach your students and teach the standards without all of the prep and stress of creating materials!

Standards:   TEKS: 6.4B, 6.4C, 6.4D, 6.4H, 6.5A;  Looking for CCSS-Aligned Resources?  Grab the CCSS-Aligned Ratios and Proportions Unit.  Please don’t purchase both as there is overlapping content.

Learning Focus:

• represent ratios and rates with examples of comparisons
• convert units within a measurement system
• apply ratios and rates to real-world situations using scale factors, tables, graphs, and proportions

What is included in the 6th grade teks Ratios and Rates Unit?

1. Unit Overviews

• Streamline planning with unit overviews that include essential questions, big ideas, vertical alignment, vocabulary, and common misconceptions.
• A pacing guide and tips for teaching each topic are included to help you be more efficient in your planning.

2. Student Handouts

• Student-friendly guided notes are scaffolded to support student learning.
• Available as a PDF and the student handouts/homework/study guides have been converted to Google Slides™ for your convenience.

3. Independent Practice

• Daily homework is aligned directly to the student handouts and is versatile for both in class or at home practice.

4. Assessments

• 1-2 quizzes, a unit study guide, and a unit test allow you to easily assess and meet the needs of your students.
• The Unit Test is available as an editable PPT, so that you can modify and adjust questions as needed.

5. Answer Keys

• All answer keys are included.

***Please download a preview to see sample pages and more information.***

How to use this resource:

• Use as a whole group, guided notes setting
• Use in a small group, math workshop setting
• Chunk each student handout to incorporate whole group instruction, small group practice, and independent practice.
• Incorporate our  Ratio Activity Bundle  for hands-on activities as additional and engaging practice opportunities.

Time to Complete:

• Each student handout is designed for a single class period. However, feel free to review the problems and select specific ones to meet your student needs. There are multiple problems to practice the same concepts, so you can adjust as needed.

Is this resource editable?

• The unit test is editable with Microsoft PPT. The remainder of the file is a PDF and not editable.

Looking for more 6th Grade Math Material? Join our All Access Membership Community! You can reach your students without the “I still have to prep for tomorrow” stress, the constant overwhelm of teaching multiple preps, and the hamster wheel demands of creating your own teaching materials.

• Grade Level Curriculum
• Supplemental Digital Components
• Complete and Comprehensive Student Video Library 

Click here to learn more about All Access by Maneuvering the Middle®!

Licensing: This file is a license for ONE teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

Customer Service: If you have any questions, please feel free to reach out for assistance .  We aim to provide quality resources to help teachers and students alike, so please reach out if you have any questions or concerns. 

Maneuvering the Middle ® Terms of Use: Products by Maneuvering the Middle®, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online in an LMS such as Google Classroom, Canvas, or Schoology. Students should be the only ones able to access the resources.  It is a copyright violation to upload the files to school/district servers or shared Google Drives. See more information on our terms of use here . 

If you are interested in a personalized quote for campus and district licenses, please click here . 

©Maneuvering the Middle® LLC, 2012-present

This file is a license for one teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

Customer Service

We strive to provide quality products to help teachers and students alike, so contact us with any questions.

Maneuvering the Middle® Terms of Use

Products by Maneuvering the Middle, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online if they are behind a password-protected site.

Campus and district licensing is available please contact us for pricing.

©Maneuvering the Middle LLC, 2012-present

There are no reviews yet.

Only logged in customers who have purchased this product may leave a review.

This resource is included in the following products:

MTM All Access

This resource is often paired with:.

Ratios Unit 6th Grade CCSS

Ratios Activity Bundle 6th Grade

6th Grade Digital Math Activity Bundle