using tape diagrams with part- whole ratio problems 1
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Using Tape Diagrams with Part-Whole Ratio Problems
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Content Objective: SWBAT solve part-whole ratio problems by using a tape diagram. Learning Target: SWBAT identify the ratio in a word problem and translate the words into a tape diagram.
Lesson Target
Warm UpOBJECTIVE: SWBAT solve part-whole ratio problems by using a tape diagram. Language Objective: SWBAT identify the ratio in a word problem and translate the words into a tape diagram.
Agenda
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But I have 6.
But I have 6.
I have 9 cookies.I have 9 cookies.
Crystal and her brother Marcus have some cookies.
1. If there are 5 chocolate chips in each cookie, how many chips are in all the cookies?
2. What part of a dozen cookies does Crystal have?3. If Crystal ate one cookie each day, how many weeks would her cookies last?CrystalCrystal MarcusMarcus
Hint: A dozen is 12!Hint: A dozen is 12!
9 x 5 + 6 x 5 = 75 chips9 x 5 + 6 x 5 = 75 chips
¾ dozen¾ dozen
1 2/7 weeks1 2/7 weeks
Launch
Agenda
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Abby and Zack are mixing red and yellow paint to make an orange color to paint their kitchen table. They each think they have the perfect shade of orange.
Launch – Think, Pair, Share
Agenda
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Abby’s orange paint is made by mixing 1 cup of red for every 3 cups of yellow.
Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow.
Lefty – Tell Righty the ratio of yellow to total in Zack’s orange paint.
Righty – Tell Lefty the ratio of red to total in Abby’s orange paint.
Partner
SharePartner
Share
Explore – Predict
Agenda
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They will need a gallon of orange paint for the project.
1. How can Abby make enough of her orange paint for the project?
Hint: A gallon is 16 cups.Hint: A gallon is 16 cups.
2. How can Zack make enough of his orange paint for the project?
Write down in your notes any ideas you have about
how to answer these questions.
Explore – Mini-Lesson
Agenda
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Tape Diagram Tool Tape Diagram ToolFollow along by filling out the whiteboard as we go.
Explore – Mini-Lesson
Agenda
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Example 1) A recipe for fruit punch says to use 5 ounces of orange juice for every 3 ounces of grape juice. Janice’s punch bowl can hold 80 ounces of punch. How much orange juice is that? How much grape juice?
Now let’s look at what’s given.
New Tool: Tape Diagram New Tool: Tape Diagram
First, let’s draw the tapes.Orange
Grape
?
?
We don’t know the amounts of each juice so…
All of these boxes from both tapes make 80 ounces of punch.
80oz.
So, if 8 boxes equals 80 ounces, then each box is…
10 10 10 10 1010 10 10
Now we can see that the orange juice is…And the grape juice is …
50 oz30 oz
50
30
T O T A L
Why 10?Why 10?
Because 80 ÷ 8 = 10 Or algebraically: 8b = 80
So… b = 10
What is the ratio in the problem?Orange to grape is 5:3. So…
Explore – Guided Practice
Agenda
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Let’s practice this next one together.
Continue to put your work on
your whiteboard
Tape Diagram Tool Tape Diagram Tool
Explore – Guided Practice
Agenda
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A florist makes Mother’s Day bouquets of a dozen roses with a ratio of 1 pink rose to every 2 yellow roses. How many yellow roses are needed for 1 bouquet?
Vocabulary:
Here are the tapes: Now You:Label the tape diagram with
the information from the problem.
_____________
_____________
Let’s see how you did!
Hint: A dozen is 12.Guided Practice #1Guided Practice #1
What is the ratio in the problem?
Pink to yellow is 1:2.
What is a bouquet? What is a bouquet?
Tape Diagram Tool Tape Diagram Tool
Vocabulary
Agenda
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Bouquet - a pretty collection of flowers sometimes with a bow usually given as a gift to someone.
Roses
Back to LessonBack to Lesson
Explore – Guided Practice
Agenda
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A florist makes Mother’s Day bouquets of a dozen roses with a ratio of 1 pink rose to every 2 yellow roses. How many yellow roses are needed for 1 bouquet?
Vocabulary
pink
yellow
?
?
12
Hint: A dozen is 12.
I know that 3 boxes is equal to 12 roses so each box has… 4 roses
4
4 4
That makes the pink equal to
4 roses
And the answer: Yellow roses needed is...
Answer:8 roses
4
8
Guided Practice #1Guided Practice #1T O
T A L
Tape Diagram Tool Tape Diagram Tool
Explore – Guided Practice
Agenda
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Try the next one on your own.
Remember to put your
work on the
worksheet.
Tape Diagram Tool Tape Diagram Tool
Explore – Guided Practice
Agenda
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Mrs. Stanford is having a class pizza party. She has found that students prefer pepperoni pizza to cheese pizza in a ratio of 3 to 1. If she needs 48 slices of pizza in total, how many slices of pepperoni will she need?
____________
____________________
Let’s see how you did!Identify the ratio. Draw the tapes.Then fill out the diagram and find the answer.
Is there anyone who can draw the diagram and find the answer?Ok, let’s see what it should look like.
The ratio of pepperoni to cheese is 3:1.
Tape Diagram Tool Tape Diagram Tool
Explore – Guided Practice
Agenda
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Mrs. Stanford is having a class pizza party. She has found that students prefer pepperoni pizza to cheese pizza in a ratio of 3 to 1. If she needs 48 slices of pizza in total, how many slices of pepperoni will she need?
____________
____________________
pepperoni
cheese48 slices
If all four boxes equals 48 slices, then that means that each box is equal to …
12 12 1212
12 slices
So the amount of pepperoni pizza is…
Answer:36 slices
36
T O T A L
Tape Diagram Tool Tape Diagram Tool
Explore – Independent Practice
Agenda
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There are two more tape diagram ratio problems for you to solve on your own on your worksheet. Show your work. Circle your answer.
Answer #3 Answer #4 Challenge Answers
Tape Diagram Tape Diagram
orange
brown45
T O T A L
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Answer: 9 brown candies Answer: 9 brown candies
Explore – Independent Practice Answers
Agenda
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The ratio of orange to brown candies in a bag of M & Ms is 4:1. If there are 45 orange and brown candies in the bag of M & Ms altogether then how many brown candies are there?
Independent Practice #3
9 9 9 9
9
Ratio of orange to brown is 4:1Ratio of orange to brown is 4:1
Explore – Independent Practice Answers
Agenda
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For every eraser in a pencil box there are 2 pencils. If there are 14 pencils in the box, then how many pencils and erasers are there altogether?
Independent Practice #4
pencils
eraser?
T O T A L
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Answer: 21 pencils & erasers
Ratio of pencils to erasers is 2:1Ratio of pencils to erasers is 2:1
7 7
7
Explore – Independent Practice Challenge Answers
Agenda
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To make the Perfectly Pink paint color you use 8 parts of white paint for every one part of red paint. If 27 cups of Perfectly Pink paint is mixed up in a bucket, then how many cups of red paint were used?
Challenge Practice #5
Answer: 3 cups red paintAnswer: 3 cups red paint
The ratio of flour to sugar in a cake recipe is 7 to 5. If the recipe calls for 20 tablespoons of sugar, then how many tablespoons of flour and sugar will be required in total?
Challenge Practice #6
Answer: 48 tablespoons totalAnswer: 48 tablespoons total
Explore – Independent Practice Challenge Answers
Agenda
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A water molecule has a ratio of 2 Hydrogen atoms for every 1 Oxygen atom. If there are 27 atoms that make up some water, then how many Hydrogen atoms are there?
Challenge Practice #7
Answer: 18 atoms of HAnswer: 18 atoms of H
The ratio of flour to sugar in a cake recipe is 7 to 5. If the recipe calls for 20 tablespoons of sugar, then how many tablespoons of flour and sugar will be required in total? Extension: For the problem above: If 4 tablespoons equals ¼ cup, then how many cups of flour and how many cups of sugar are required for the cake?
Challenge Practice #8
Answer: 20 tbsp sugar ÷ 4 = 5 quarter cups or 1 ¼ cups sugar28 tbsp flour ÷ 4 = 7 quarter cups or 1 ¾ cups flour
Answer: 20 tbsp sugar ÷ 4 = 5 quarter cups or 1 ¼ cups sugar28 tbsp flour ÷ 4 = 7 quarter cups or 1 ¾ cups flour
Exit Ticket – use the half sheet of paper provided
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The painting project will require a gallon of orange paint . 1. How many cups of red paint and yellow paint will Abby need to make enough of her orange paint for the project?
Hint: A gallon is 16 cups.
2. How many cups of red paint and yellow paint will Zack need to make enough of her orange paint for the project?
Use tape diagrams to determine how much red and how much yellow paint each
child needs.
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