1. Introduction to Ratio Tables
21st Century Lessons
Introduction to Ratio Tables
Primary Lesson Designer:
Lisa Schad

2. Warm Up Write the ratios as fractions in lowest terms.
OBJECTIVE: SWBAT solve ratio problems by using a ratio table. Language Objective: They will write about their understanding of ratio equivalence.
Write the ratios as fractions in lowest terms.
1. The number of red bears to all gummi bears.
2. There are 4 vans and 12 cars in a parking lot. Write the ratio of cars to vans.
Answer
(Time on this slide – 5 min) Time passed 5 min
In-Class Notes
Students will need to know how to write ratios in fraction form and to always simplify.
Encourage them to pay attention to the order of the ratio.
Preparation Notes
This should only take 3-5 minutes. It is a quick review.
3. There are 20 pens and 8 pencils in Li’s pencil box. Write the ratio of pencils to pens.
Answer
Answer
Agenda

3. Explore – Mini-Lesson
Let’s learn about another helpful tool for ratio problems.
Let’s say you love to make and eat cake. Your recipe calls for two eggs and one cup of flour for each batch.
If you have 6 eggs, how much flour would you need to make the maximum amount of cake?
(Time on this slide – 1 min) Time passed 13 min
In-Class Notes
Students may mention that you can use a tape diagram to solve this. Allow the student to demonstrate and let them know that they will also be learning a new tool today.
The benefit of a ratio table over a tape diagram is that you can see many equivalent ratios at the same time.
Preparation Notes
Agenda

4. Explore – Mini-Lesson
Let’s learn about another helpful tool for ratio problems.
Let’s say you love to make and eat cake. Your recipe calls for two eggs and one cup of flour for each batch.
If you have 6 eggs, how much flour would you need to make the maximum amount of cake?
You could draw a picture.
Then you could make copies until you get to six eggs.
(Time on this slide – 1 min) Time passed 14 min
In-Class Notes
The main idea that students should understand is that maintaining a ratio preserves the “flavor” in a recipe situation. Therefore equivalent ratios are not only equivalent because of math, but because in real life they are the same taste just more or less total quantity.
Preparation Notes
Agenda

5. New Tool: Ratio Table
Explore – Mini-Lesson
Seems like this takes a long time, don’t you think?
You could record the numbers for each batch in a table.
Eggs 2 4 6
Cups of flour 1 3
This table gives you the same information as the pictures. But faster!
(Time on this slide – 1 min) Time passed 15 min
In-Class Notes
Point out how the numbers correspond to the pictures.
Preparation Notes
We place a high value on efficiency in mathematics. Tables are more efficient than pictures.
(Later, equations will be more efficient than tables.)
Stress that this is the second tool for ratio problems. There is one more, double number lines.
This is a ratio table.
Agenda

6. New Tool: Ratio Table
Explore – Mini-Lesson
Question: Will 2 eggs and 1 cup of flour make a cake that tastes the same as one with 4 eggs and 2 cups of flour?
Eggs 2 4 6
Cups of flour 1 3
Will this
and this
make cake that has the same taste?
(Time on this slide – 4 min) Time passed 19 min
In-Class Notes
Next slide prompts a class share. Wait to click through to ask for responses.
Possible answers include a realization that if you double both the eggs and the flour it will taste the same because it is double the amount of cake.
Students can also realize that the ratios are equivalent when writing them as equivalent fractions.
Preparation Notes
We will come back to this question two more times in the lesson. The video addresses this idea. The summary question asks students to reflect on this idea in another problem.
Partners: Take turns asking each other this question and listening. Prove your answer.
Agenda

7. New Tool: Ratio Table
Explore – Mini-Lesson
Share Out: What do you think? Do these columns in the ratio table make the same tasting cake?
Eggs 2 4 6
Cups of flour 1 3
(Time on this slide – 1 min) Time passed 20 min
In-Class Notes
Short share. This idea will be revisited two more times in this lesson.
Hopefully students will make the connection between equivalent ratios and equivalent fractions. Try to find partners who have discovered this to share with the class.
Preparation Notes
Agenda

8. New Tool: Ratio Table
Explore – Mini-Lesson
It’s true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same.
Eggs 2 4 6
Cups of flour 1 3
How do you know the ratios are equivalent?
Discuss this with your partner. Prove that the ratios are equivalent.
(Time on this slide – 2 min) Time passed 22 min
In-Class Notes
Hopefully students will make the connection between equivalent ratios and equivalent fractions. Try to find partners who have discovered this to share with the class.
The next slide will explicitly show this connection.
Preparation Notes
Agenda

9. New Tool: Ratio Table
Explore – Mini-Lesson
It’s true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same.
Eggs 2 4 6
Cups of flour 1 3 2 1 = 4 2 = 6 3
Because …
(Time on this slide – 2 min) Time passed 24 min
In-Class Notes
Make the connection between this “fraction form” of a ratio and equivalent fractions.
They obey the same rules for simplifying.
Preparation Notes
What is different between ratios (in fraction form) and fractions?
Ratios may show a part to part relationship or a part to whole relationship while fractions show only a part to whole relationship. A fraction is a specific type of ratio.
Ratios will keep the one on the bottom to show the relationship between the two quantities.
A ratio shows a comparative relationship between two separate quantities.
A fraction is a quotient of numbers, the quantity obtained when the numerator is divided by the denominator.
Agenda

10. New Tool: Ratio Table
Explore – Mini-Lesson
It’s true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same.
Eggs 2 4 6
Cups of flour 1 3
A cake made with 2 eggs and 1 cup of flour will taste the same as…
(Time on this slide – 1 min) Time passed 25 min
In-Class Notes
This shows that not only are the first two columns equivalent ratios that make the same tasting cake, but all three columns, indeed any columns you make as you extend the table, will make the cake that tastes the same.
Preparation Notes
Agenda

11. New Tool: Ratio Table
Explore – Mini-Lesson
It’s true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same.
Eggs 2 4 6
Cups of flour 1 3
A cake made with 2 eggs and 1 cup of flour will taste the same as…
A cake made with 4 eggs and 2 cups of flour will taste the same as…
(Time on this slide - min) Time passed 25 min
In-Class Notes
This shows that not only are the first two columns equivalent ratios that make the same tasting cake, but all three columns, indeed any columns you make as you extend the table, will make the cake that tastes the same.
Preparation Notes
Agenda

12. New Tool: Ratio Table
Explore – Mini-Lesson
It’s true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same.
Eggs 2 4 6
Cups of flour 1 3
A cake made with 2 eggs and 1 cup of flour will taste the same as…
A cake made with 4 eggs and 2 cups of flour will taste the same as…
One made with 6 eggs and 3 cups of flour.
(Time on this slide - min) Time passed 25 min
In-Class Notes
This shows that not only are the first two columns equivalent ratios that make the same tasting cake, but all three columns, indeed any columns you make as you extend the table, will make the cake that tastes the same.
Preparation Notes
Agenda

13. Explore - video This video may help.
Here is a video about the taste of equivalent ratios.
(Time on this slide - 2 min) Time passed 27 min
In-Class Notes
If hyperlink doesn’t work find video at:
Or search Vimeo for “Taste of Ratios”
Preparation Notes
Agenda

14. Guided Practice Try this!
New Tool: Ratio Table
Guided Practice
Try this!
PB&J Trail Mix is made by combining 7 ounces of peanuts with 5 ounces of raisins. A ratio table has been started to show this relationship for different batches of trail mix.
Peanuts
(in ounces) 7 14 35
Raisins 5 15
(Time on this slide – 7 min) Time passed 34 min
In-Class Notes
Students may be prompted in the following way?
What do you notice about the numbers in the peanuts row?
Do you see a pattern? Can you continue the pattern?
What pattern can you find in the raisins row?
How can you figure out what is between 5 and 15? Does that help you to find the next missing numbers in the raisins row?
Preparation Notes
Copy the table. Work with your partner to fill in every box with the amounts to maintain the same flavor.
Agenda

15. Guided Practice Try this!
New Tool: Ratio Table
Guided Practice
Try this!
PB&J Trail Mix is made by combining 7 ounces of peanuts with 5 ounces of raisins. A ratio table has been started to show this relationship for different batches of trail mix.
Peanuts
(in ounces) 7 14 35
Raisins 5 15 21 28 10 20 25
(Time on this slide - 1 min) Time passed 35 min
In-Class Notes
The answers will auto-fill after initial click.
Students should check their work and correct any mistakes.
Preparation Notes
Let’s see how you did! Here are the missing values.
Agenda

16. Guided Practice Peanuts 7 14 35 Raisins 5 15 21 28 10 20 25
New Tool: Ratio Table
Guided Practice
What method did you and your partner use to fill in the table?
What do you notice about the numbers in the peanuts row?
What do you notice about the numbers in the raisins row?
Peanuts
(in ounces) 7 14 35
Raisins 5 15 21 28 10 20 25
(Time on this slide – 3 min) Time passed 38 min
In-Class Notes
Select students at random (calling sticks) to answer these questions.
Students are meant to discover the pattern of “counting by” the number in the original ratio. It is best if they recognize this as multiplication but they can continue to formulate this thought throughout future practice lessons when they will use ratio tables more.
Multiple methods may be highlighted.
Preparation Notes
Agenda

17. Guided Practice For every 7 oz of peanuts you have 5 oz of raisins.
New Tool: Ratio Table
Guided Practice
There are mathematical statements we can say with certainty about the trail mix based on this ratio table. We can say…
For every 7 oz of peanuts you have 5 oz of raisins.
or for every 10 oz of peanuts you have 14 oz of raisins.
Peanuts
(in ounces) 7 14 35
Raisins 5 15 21 28 10 20 25
(Time on this slide – 2 min) Time passed 40 min
In-Class Notes
Students should focus on speaking here, not writing.
Preparation Notes
This connects back to earlier lessons highlighting language usage for ratio situations.
Lefty: Tell Righty one more sentence based on the table.
Righty: Tell Lefty a different sentence using the table.
Agenda

18. Independent Practice
You will practice using your new tool, ratio tables, to solve ratio word problems. You will have 15 minutes to complete the class work. You will have a chance to check your work at the end of the work session.
(Time on this slide – 15 min) Time passed 55 min
In-Class Notes
Students may work independently or in pairs, if you think they need more scaffolding.
Preparation Notes
Answer slide follows.
Agenda

19. Independent Practice - Review
Here are the answers to the worksheet. Please check your work to make sure you have the correct answers. Put a question mark next to any problems you had wrong or you have a question about.
Problem #1
Problem #2
Problem #3
Problem #4
(Time on this slide – 5 min) Time passed 60 min
In-Class Notes
Teacher should take a poll for how many questions students had for each problem after showing the answers. This information can be used to choose problems to discuss in depth.
Preparation Notes
Agenda

20. Summary
Explain, in writing, why Trail Mix with 14 ounces of peanuts and 10 ounces of raisins tastes the same as one with 7 ounces of peanuts and 5 ounces of raisins.
PB&J Trail Mix
Peanuts
(in ounces) 7 14 21 28 35
Raisins 5 10 15 20 25
(Time on this slide – 5 min) Time passed 65 min
In-Class Notes
Remind students to think about the cake example in the mini-lesson and the Skittles example in the video. They can refer to their notes.
Similar responses would be anticipated.
Preparation Notes
Push students to write a response and to read their writing rather than to just think about the question. Many students like to skim over the requirement to write at the end of a lesson.
Explain why this
and this
will have the same taste.
Agenda

21. Summary PB&J Trail Mix Peanuts 7 14 21 28 35 Raisins 5 10 15 20 25
Read your writing to your partner. Will Trail Mix with 14 ounces of peanuts and 10 ounces of raisins tastes the same as one with 7 ounces of peanuts and 5 ounces of raisin?
PB&J Trail Mix
Peanuts
(in ounces) 7 14 21 28 35
Raisins 5 10 15 20 25
(Time on this slide – 3 min) Time passed 68 min
In-Class Notes
Encourage students to read their writing rather than speak from memory or show their writing.
Preparation Notes
Explain why this
and this
will have the same taste.
Agenda

22. Exit Ticket
Use the ratio table tool to figure out whose orange paint, Abby’s or Zack’s, is made with this “recipe.”
There is space on your worksheet.
1:3
15 cups of red & 25 cups of yellow paint
3:5
Hint
Solution
(Time on this slide – 5 min) Time passed 73 min
In-Class Notes
Encourage students to independently
Preparation Notes
Agenda

23. Assessment – Write your answers in your notes.
1) Which ratio table can be used to solve the problem below?
Jenny discovers that she has 8 shirts for every 5 pants. If she has 40 shirts, how many pants does she have?
shirts 5 10 15 20 25
pants 8 16 24 32 40 A.
shirts 8 16 24 32 40
pants 5 10 15 20 25 B.
(Time on this slide – 2 min) Time passed 75 min
In-Class Notes
This slide can be used as an optional assessment if the exit ticket does not sufficiently cover this purpose.
Preparation Notes
shirts 5 10 15 20 25 30 35 40
pants 8 16 24 32 48 56 64 C.
2) What is the correct answer to the problem?
Agenda