Ratios & Proportional Relationships

What are Ratios?

  • Focused Standards Board

    Topic: Ratios

    Standard: MAFS.6.RP.1.1 - Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.  

    Essential Question: What is a ratio and how do I use ratios to describe the relationship between two quantities?

    Objective: I can describe the relationship between two quantities. 

    Check for Understanding: 5 Question Quiz

     

    Achievement Level Descriptors

    The rubric below shows the extent to which you can be assessed in the Limits column and summarizes the levels of ability you can demonstrate for the standard under each Achievement Level. Note: Our goal is to work towards achieving at least a Level 3 for all standards. 

    ratio language descriptors  


    Refresher

    In elementary school, we learned how to _____________________


    If you need a quick refresher on this concept, click here. {Insert link}

    Now we're going to move on to _________________________


    Lesson

    Preview: 
    (Note, the 2-page of your notebook should already be set up for this lesson. If it isn't, please go back to Focused Notes and then return to the lesson). 

    In the preview section of the first 2-page spread, answer the following two prompts:

    1. Question 1

    Notes:
    1. Take Notes

    You can write down the words, phrases, numbers, symbols, expressions, and equations that help you answer the Essential Question, as well as the answers and definitions to the guiding questions and vocabulary below. 

    Guiding Questions & Vocabulary:

    • Word 1

     

     

    2. Process Notes

    Take a moment the read through your notes and ensure that they make sense and answer the EQ. They should also include responses to the guiding questions and vocabulary. 

    3. Connecting Thinking

    Answer the following two prompts in the far right margin of your 2-page spread.

    1. How does this relate to what you've already learned? 
    2. What, if anything, about this concept that is confusing? (If something is confusing, ask during an appropriate time, email me, or find the answer to your question by communicating with peers or searching online. 

    4. Summarize & Reflect on Learning

    Think about how your understanding of this topic relates to your ability to answer the essential question for this lesson.  

    5. Apply Learning 

    Answer the following questions on looseleaf paper. (This does not go in your notes!) I encourage you to work with a partner. 

    1. Ex 1

    Process:

    Answer the essential question in the process section of your notebook. 


    Practice:

    Please complete as many as you feel you need to in order to master the standard. 

    1. Practice 1
    2. Practice 2
    3. Practice 3

     


    Check for Understanding:

    Remember, only submit 1 and wait for feedback before moving on to the next one. If you complete the first one with a rubric score of at least three, you will not be required to complete the other two. 

    1. Assessment 1 
    2. Assessment 2
    3. Assessment 3

Unit Rates

  • Focused Standards Board

    Topic: Unit Rates

    Standard: MAFS.6.RP.1.2 - Use 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. 

    Essential Question: How do I describe unit rates?

    Objective: I can use the concept of and explain unit rates.

    Check for Understanding: 5 Question Quiz

     

    Achievement Level Descriptors

    The rubric below shows the extent to which you can be assessed in the Limits column and summarizes the levels of ability you can demonstrate for the standard under each Achievement Level. Note: Our goal is to work towards achieving at least a Level 3 for all standards. 

     unit rate descriptors


    Refresher

    In elementary school, we learned how to _____________________


    If you need a quick refresher on this concept, click here. {Insert link}

    Now we're going to move on to _________________________


    Lesson

    Preview: 
    (Note, the 2-page of your notebook should already be set up for this lesson. If it isn't, please go back to Focused Notes and then return to the lesson). 

    In the preview section of the first 2-page spread, answer the following two prompts:

    1. Question 1

    Notes:
    1. Take Notes

    You can write down the words, phrases, numbers, symbols, expressions, and equations that help you answer the Essential Question, as well as the answers and definitions to the guiding questions and vocabulary below. 

    Guiding Questions & Vocabulary:

    • Word 1

     

     

    2. Process Notes

    Take a moment the read through your notes and ensure that they make sense and answer the EQ. They should also include responses to the guiding questions and vocabulary. 

    3. Connecting Thinking

    Answer the following two prompts in the far right margin of your 2-page spread.

    1. How does this relate to what you've already learned? 
    2. What, if anything, about this concept that is confusing? (If something is confusing, ask during an appropriate time, email me, or find the answer to your question by communicating with peers or searching online. 

    4. Summarize & Reflect on Learning

    Think about how your understanding of this topic relates to your ability to answer the essential question for this lesson.  

    5. Apply Learning 

    Answer the following questions on looseleaf paper. (This does not go in your notes!) I encourage you to work with a partner. 

    1. Ex 1

    Process:

    Answer the essential question in the process section of your notebook. 


    Practice:

    Please complete as many as you feel you need to in order to master the standard. 

    1. Practice 1
    2. Practice 2
    3. Practice 3

     


    Check for Understanding:

    Remember, only submit 1 and wait for feedback before moving on to the next one. If you complete the first one with a rubric score of at least three, you will not be required to complete the other two. 

    1. Assessment 1 
    2. Assessment 2
    3. Assessment 3

Ratios IRL - Tables

  • Focused Standards Board

    Topic: Equivalent Ratio Tables

    Standard: MAFS.6.RP.1.3 - 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. 

    1. 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.

    2. 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?

    3. 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.

    4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

    5. Understand the concept of Pi as the ratio of the circumference of a circle to its diameter.

    Essential Question: What strategies can I use to solve problems involving ratios. 

    Objective: I can use equivalent ratio tables to solve problems on plot them on a coordinate grid.

    Check for Understanding: 5 Question Quiz

     

    Achievement Level Descriptors

    The rubric below shows the extent to which you can be assessed in the Limits column and summarizes the levels of ability you can demonstrate for the standard under each Achievement Level. Note: Our goal is to work towards achieving at least a Level 3 for all standards. 

     table descriptors


    Refresher

    In elementary school, we learned how to _____________________


    If you need a quick refresher on this concept, click here. {Insert link}

    Now we're going to move on to _________________________


    Lesson

    Preview: 
    (Note, the 2-page of your notebook should already be set up for this lesson. If it isn't, please go back to Focused Notes and then return to the lesson). 

    In the preview section of the first 2-page spread, answer the following two prompts:

    1. Question 1

    Notes:
    1. Take Notes

    You can write down the words, phrases, numbers, symbols, expressions, and equations that help you answer the Essential Question, as well as the answers and definitions to the guiding questions and vocabulary below. 

    Guiding Questions & Vocabulary:

    • Word 1

     

     

    2. Process Notes

    Take a moment the read through your notes and ensure that they make sense and answer the EQ. They should also include responses to the guiding questions and vocabulary. 

    3. Connecting Thinking

    Answer the following two prompts in the far right margin of your 2-page spread.

    1. How does this relate to what you've already learned? 
    2. What, if anything, about this concept that is confusing? (If something is confusing, ask during an appropriate time, email me, or find the answer to your question by communicating with peers or searching online. 

    4. Summarize & Reflect on Learning

    Think about how your understanding of this topic relates to your ability to answer the essential question for this lesson.  

    5. Apply Learning 

    Answer the following questions on looseleaf paper. (This does not go in your notes!) I encourage you to work with a partner. 

    1. Ex 1

    Process:

    Answer the essential question in the process section of your notebook. 


    Practice:

    Please complete as many as you feel you need to in order to master the standard. 

    1. Practice 1
    2. Practice 2
    3. Practice 3

     


    Check for Understanding:

    Remember, only submit 1 and wait for feedback before moving on to the next one. If you complete the first one with a rubric score of at least three, you will not be required to complete the other two. 

    1. Assessment 1 
    2. Assessment 2
    3. Assessment 3

Ratios IRL - Percentages

  • Focused Standards Board

    Topic: Equivalent Percentages

    Standard: MAFS.6.RP.1.3 - 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. 

    1. 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.

    2. 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?

    3. 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.

    4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

    5. Understand the concept of Pi as the ratio of the circumference of a circle to its diameter.

    Essential Question: What strategies can I use to solve problems involving ratios. 

    Objective: I can use solve problems that require me to find the whole, given the part and the percent. 

    Check for Understanding: 5 Question Quiz

     

    Achievement Level Descriptors

    The rubric below shows the extent to which you can be assessed in the Limits column and summarizes the levels of ability you can demonstrate for the standard under each Achievement Level. Note: Our goal is to work towards achieving at least a Level 3 for all standards. 

     percent descriptor


    Refresher

    In elementary school, we learned how to _____________________


    If you need a quick refresher on this concept, click here. {Insert link}

    Now we're going to move on to _________________________


    Lesson

    Preview: 
    (Note, the 2-page of your notebook should already be set up for this lesson. If it isn't, please go back to Focused Notes and then return to the lesson). 

    In the preview section of the first 2-page spread, answer the following two prompts:

    1. Question 1

    Notes:
    1. Take Notes

    You can write down the words, phrases, numbers, symbols, expressions, and equations that help you answer the Essential Question, as well as the answers and definitions to the guiding questions and vocabulary below. 

    Guiding Questions & Vocabulary:

    • Word 1

     

     

    2. Process Notes

    Take a moment the read through your notes and ensure that they make sense and answer the EQ. They should also include responses to the guiding questions and vocabulary. 

    3. Connecting Thinking

    Answer the following two prompts in the far right margin of your 2-page spread.

    1. How does this relate to what you've already learned? 
    2. What, if anything, about this concept that is confusing? (If something is confusing, ask during an appropriate time, email me, or find the answer to your question by communicating with peers or searching online. 

    4. Summarize & Reflect on Learning

    Think about how your understanding of this topic relates to your ability to answer the essential question for this lesson.  

    5. Apply Learning 

    Answer the following questions on looseleaf paper. (This does not go in your notes!) I encourage you to work with a partner. 

    1. Ex 1

    Process:

    Answer the essential question in the process section of your notebook. 


    Practice:

    Please complete as many as you feel you need to in order to master the standard. 

    1. Practice 1
    2. Practice 2
    3. Practice 3

     


    Check for Understanding:

    Remember, only submit 1 and wait for feedback before moving on to the next one. If you complete the first one with a rubric score of at least three, you will not be required to complete the other two. 

    1. Assessment 1 
    2. Assessment 2
    3. Assessment 3

Ratios IRL - Converting Measurements

  • Focused Standards Board

    Topic: Converting Measurements

    Standard: MAFS.6.RP.1.3 - 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. 

    1. 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.

    2. 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?

    3. 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.

    4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

    5. Understand the concept of Pi as the ratio of the circumference of a circle to its diameter.

    Essential Question: What strategies can I use to solve problems involving ratios. 

    Objective: I can use ratio reasoning to convert measurement units. 

    Check for Understanding: 5 Question Quiz

     

    Achievement Level Descriptors

    The rubric below shows the extent to which you can be assessed in the Limits column and summarizes the levels of ability you can demonstrate for the standard under each Achievement Level. Note: Our goal is to work towards achieving at least a Level 3 for all standards. 

     converting measurements descriptor


    Refresher

    In elementary school, we learned how to _____________________


    If you need a quick refresher on this concept, click here. {Insert link}

    Now we're going to move on to _________________________


    Lesson

    Preview: 
    (Note, the 2-page of your notebook should already be set up for this lesson. If it isn't, please go back to Focused Notes and then return to the lesson). 

    In the preview section of the first 2-page spread, answer the following two prompts:

    1. Question 1

    Notes:
    1. Take Notes

    You can write down the words, phrases, numbers, symbols, expressions, and equations that help you answer the Essential Question, as well as the answers and definitions to the guiding questions and vocabulary below. 

    Guiding Questions & Vocabulary:

    • Word 1

     

     

    2. Process Notes

    Take a moment the read through your notes and ensure that they make sense and answer the EQ. They should also include responses to the guiding questions and vocabulary. 

    3. Connecting Thinking

    Answer the following two prompts in the far right margin of your 2-page spread.

    1. How does this relate to what you've already learned? 
    2. What, if anything, about this concept that is confusing? (If something is confusing, ask during an appropriate time, email me, or find the answer to your question by communicating with peers or searching online. 

    4. Summarize & Reflect on Learning

    Think about how your understanding of this topic relates to your ability to answer the essential question for this lesson.  

    5. Apply Learning 

    Answer the following questions on looseleaf paper. (This does not go in your notes!) I encourage you to work with a partner. 

    1. Ex 1

    Process:

    Answer the essential question in the process section of your notebook. 


    Practice:

    Please complete as many as you feel you need to in order to master the standard. 

    1. Practice 1
    2. Practice 2
    3. Practice 3

     


    Check for Understanding:

    Remember, only submit 1 and wait for feedback before moving on to the next one. If you complete the first one with a rubric score of at least three, you will not be required to complete the other two. 

    1. Assessment 1 
    2. Assessment 2
    3. Assessment 3

Math IRL - Circles

  • Focused Standards Board

    Topic: Pi as it relates to Circles

    Standard: MAFS.6.RP.1.3 - 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. 

    1. 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.

    2. 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?

    3. 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.

    4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

    5. Understand the concept of Pi as the ratio of the circumference of a circle to its diameter.

    Essential Question: What strategies can I use to solve problems involving ratios. 

    Objective: I can use the ratio of Pi to compare the diameter of a circle to the circumference. 

    Check for Understanding: Gist Statement

     

    Achievement Level Descriptors

    The rubric below shows the extent to which you can be assessed in the Limits column and summarizes the levels of ability you can demonstrate for the standard under each Achievement Level. Note: Our goal is to work towards achieving at least a Level 3 for all standards. 

     pi ratio descriptor


    Refresher

    In elementary school, we learned how to _____________________


    If you need a quick refresher on this concept, click here. {Insert link}

    Now we're going to move on to _________________________


    Lesson

    Preview: 
    (Note, the 2-page of your notebook should already be set up for this lesson. If it isn't, please go back to Focused Notes and then return to the lesson). 

    In the preview section of the first 2-page spread, answer the following two prompts:

    1. Question 1

    Notes:
    1. Take Notes

    You can write down the words, phrases, numbers, symbols, expressions, and equations that help you answer the Essential Question, as well as the answers and definitions to the guiding questions and vocabulary below. 

    Guiding Questions & Vocabulary:

    • Word 1

     

     

    2. Process Notes

    Take a moment the read through your notes and ensure that they make sense and answer the EQ. They should also include responses to the guiding questions and vocabulary. 

    3. Connecting Thinking

    Answer the following two prompts in the far right margin of your 2-page spread.

    1. How does this relate to what you've already learned? 
    2. What, if anything, about this concept that is confusing? (If something is confusing, ask during an appropriate time, email me, or find the answer to your question by communicating with peers or searching online. 

    4. Summarize & Reflect on Learning

    Think about how your understanding of this topic relates to your ability to answer the essential question for this lesson.  

    5. Apply Learning 

    Answer the following questions on looseleaf paper. (This does not go in your notes!) I encourage you to work with a partner. 

    1. Ex 1

    Process:

    Answer the essential question in the process section of your notebook. 


    Practice:

    Please complete as many as you feel you need to in order to master the standard. 

    1. Practice 1
    2. Practice 2
    3. Practice 3

     


    Check for Understanding:

    Remember, only submit 1 and wait for feedback before moving on to the next one. If you complete the first one with a rubric score of at least three, you will not be required to complete the other two. 

    1. Assessment 1 
    2. Assessment 2
    3. Assessment 3

Advanced ONLY - Computing Unit Rates

  • Focused Standards Board

    Topic: Computing Unit Rates

    Standard: MAFS.7.RP.1.1 - Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. 

    Essential Question: How do I compute unit rates associated with ratios of fractions?

    Objective: I can use ratios of fractions to compute unit rates. 

    Check for Understanding: 5 Question Quiz

     

    Achievement Level Descriptors

    The rubric below shows the extent to which you can be assessed in the Limits column and summarizes the levels of ability you can demonstrate for the standard under each Achievement Level. Note: Our goal is to work towards achieving at least a Level 3 for all standards. 

     computing unit rates descriptor


    Refresher

    In elementary school, we learned how to _____________________


    If you need a quick refresher on this concept, click here. {Insert link}

    Now we're going to move on to _________________________


    Lesson

    Preview: 
    (Note, the 2-page of your notebook should already be set up for this lesson. If it isn't, please go back to Focused Notes and then return to the lesson). 

    In the preview section of the first 2-page spread, answer the following two prompts:

    1. Question 1

    Notes:
    1. Take Notes

    You can write down the words, phrases, numbers, symbols, expressions, and equations that help you answer the Essential Question, as well as the answers and definitions to the guiding questions and vocabulary below. 

    Guiding Questions & Vocabulary:

    • Word 1

     

     

    2. Process Notes

    Take a moment the read through your notes and ensure that they make sense and answer the EQ. They should also include responses to the guiding questions and vocabulary. 

    3. Connecting Thinking

    Answer the following two prompts in the far right margin of your 2-page spread.

    1. How does this relate to what you've already learned? 
    2. What, if anything, about this concept that is confusing? (If something is confusing, ask during an appropriate time, email me, or find the answer to your question by communicating with peers or searching online. 

    4. Summarize & Reflect on Learning

    Think about how your understanding of this topic relates to your ability to answer the essential question for this lesson.  

    5. Apply Learning 

    Answer the following questions on looseleaf paper. (This does not go in your notes!) I encourage you to work with a partner. 

    1. Ex 1

    Process:

    Answer the essential question in the process section of your notebook. 


    Practice:

    Please complete as many as you feel you need to in order to master the standard. 

    1. Practice 1
    2. Practice 2
    3. Practice 3

     


    Check for Understanding:

    Remember, only submit 1 and wait for feedback before moving on to the next one. If you complete the first one with a rubric score of at least three, you will not be required to complete the other two. 

    1. Assessment 1 
    2. Assessment 2
    3. Assessment 3

  • MAFS.6.RP.1.1

    Objective: I understand the concept of the ratio and use appropriate vocabulary to describe the relationship between two quantities. 


    Overview Video - with vocabulary and an example. 

    Application Video - Why are ratios important to understand?

    Activity 1 PDF - Use your understanding to make sense of these practice problems. Explanation and answers included. 

    Activity 2 PDF - Use your understanding to make sense of these practice problems. Explanation and answers included. 

     

     

  • MAFS.6.RP.1.2

    Objective - I understand the concept of a unit rate, and can describe a unit rate using appropriate vocabulary. 


    In-Depth Video - Check this video out to see a few examples of unit rate. 

    Application Video - See unit rate being used in a real-life situation. 

    Application Question - Try to answer this question to demonstrate mastery. 

     

  • MAFS.6.RP.1.3a-e

    Objective: I can use ratio and rate reasoning to solve real-world problems. 


    Real World Tutorial - Click here to work through a tutorial that outlines problems that could be answered under this standards. 

    Percent of a whole number video - Watch for a refresher on percentages. 

    Sales Tax - Determine the sales tax by creating a table. Solutions available. 

    Discounted Prices - Find out how much the shirt was originally given the discounted price.

    Mixing Concrete - Work to find out how much concrete is needed to make