Problem Solving Graphic Organizer
Define the Problem
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What is the problem about? What is it asking you to do? Make a prediction for a solution.
The problem is about Mrs. Sutton and Mrs. Nomura opening a lemonade stand because it is a hot day.
The first part is asking us to find out if they have enough sugar and if not, then find out how much more they need.
The second part is asking us to find out how many more lemons they need to squeeze for the recipe.
The third part is asking us to find out how many of each ingredient do we need to sell lemonade to 13 people and have none left over.
The fourth part is asking us to find a price for the lemonade so that it is profitable and not unreasonable.
I think that they would need to squeeze around 1 1/10 more lemons.
I think that they would need around ½ more cups of sugar.
I think that they will need around 2 ½ cups of sugar, 17 cups of water, 4 ⅔ cups of lemon juice.
I think that they should charge around $1 per glass.
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Analyze the Problem
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What do you know from the problem scenario or lessons that can help solve the problem?
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What concepts or information do you need to know in order to solve the problem?
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Brainstorm Strategies for Solving the Problem
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What strategies might you use to solve the problem? How will you start the problem?
For part 1, I will find the common denominator for Mrs. Nomura’s total cups of sugar, and Mrs. Sutton’s total cups of sugar. Then, I could add them together. I will then find the common denominator for the amount of sugar you need for the recipe and the amount of sugar Mrs. Nomura and Mrs. Sutton have together. Then, I will subtract the two numbers. If it is negative, then I need to find out how much more sugar she needs.
For part 2, I will find the common denominator for Mrs. Nomura’’s and Mrs. Sutton’s total cups of lemon juice and the total amount of lemon juice needed for the recipe. I will then subtract the teachers lemon juice from the total juice needed. Whatever I have left, I will multiply that by 4 because 4 lemons make 1 cup of juice. I will start by finding the common denominator.
For part 3, I will begin by subtracting 12 by 7, and then I will subtract that number by the 13 people in line. The number I get will be how many people won’t get lemonade if no more is made. Then I will divide that number by 12. I will take this number and multiply it by each ingredient. (x * 1 ¾ or x * 8 ½ or x * 2 ⅓ )
I will start by subtracting 12 by 7.
For part 4, I will begin with thinking up of some prices that seem reasonable. Then, I will look online for average but profitable prices for a cup of lemonade and find the average between the two prices (My price and the online price). If one price matches with mine, I will use that.
I will start by thinking of a reasonable price.
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Your Work
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Mrs. Sutton’s sugar + Mrs. Nomura’s sugar = ⅝ + ⅔ = (⅝ * 3/3) + (⅔ * 8/8) = 15/24 + 16/24 = 31/24 = 1 7/24 (I found the common denominator and then added.)
1 7/24 - 1 ¾ = (1 7/24 * 4/4) - (1 ¾ * 24/24) = 1 28/96 - 1 72/96 = -44/96 sugar
-44/96 = 11/24 more sugar needs to be borrowed from their neighbours.
(First, I took Mrs. Nomura’s total amount of sugar and the number of sugar needed for the recipe and made an equation. Then, I found the common denominator for the fractions. Finally, I subtracted and got my answer of -44/96. I simplified that into -11/24, or 11/24 cups of sugar is needed.)
2) Teachers juice = 1 ½ cups of lemon juice
Total juice needed = 2 ⅓ cups of lemon juice
1 ½ * 3/3 = 1 3/6
2 ⅓ * 2/2 = 2 2/6
2 2/6 - 1 3/6 = 14/6 - 9/6 = ⅚
⅚ * 4 = 20/6 = 3 2/6 = 3 ⅓ more lemons need to be squeezed. If you can’t squeeze ⅓ of a lemon, then they need to squeeze 4 more lemons. You could also cut a lemon into thirds for the remainder.
(First, I found the common denominator of the amount of juice the teachers have, and the amount of juice they need for the total recipe. Then, I converted them into an irregular fraction. I subtracted the two numbers and then multiplied the number I got by 4. I did this because 4 lemons make 1 cup of lemon juice. Finally, I simplified the answer.)
3) 7 people have been served so far. The recipe serves 12 people. 12 - 7 = 5. 13 - 5 = 8. 8 / 12 = ⅔
1 ¾ * ⅔ = ⅔ + 6/12 = 8/12 + 6/12 = 14/12 = 1 2/12 = 1 ⅙
8 ½ * ⅔ = 16/3 + 2/6 = 16/3 + ⅓ = 17/6 = 2 ⅚
2 ⅓ * ⅔ = 4/3 + 2/9 = 12/9 + 2/9 = 14/9 = 1 5/9
1 ⅙ cups of sugar, 2 ⅚ cups of water, and 1 5/9 cups of lemon juice are needed.
(First, I subtracted 7 from 12. I got 5. Then, I subtracted 13 by 5, because 13 people are in line, and the teachers already have enough lemonade for 5 of them. I got 8, so 8 people won’t get juice if they don’t make more. So, I divided 8 by 12, and got ⅔. I did this to get the number I need to multiply by each ingredient to make enough lemonade for the people in line, and have none left over. I then multiplied each ingredient by ⅔.)
4) A reasonable price would be around $1 per cup.
Online Source:
It says that a reasonable price would be $1 to $1.25 per cup.
1 = 1
1 < 1.25
Final Answer: $1 per cup
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Reflective HW Section
Please answer honestly, thoughtfully, and in complete sentences.
- Which section of the PSGO was most helpful to you and why?
- Which section of the PSGO was the most challenging for you and why?
- How can we better help you to learn?
The Brainstorm Strategies for Solving the Problem section was the most helpful for me because it helped me take a certain approach to work, which made it easier.
The most challenging section was the work section, because that took the longest in doing the work, checking it, and correcting it.
You can better help us learn by maybe making a few questions harder. For example, the last question was very easy to answer and only took a few minutes to solve. Everything else, took much longer.
Lemonade Stand HW Practice Questions
1) 5 ½ + 3 ⅓ = 8 ⅚
5 ½ * 3/3 = 5 3/6
3 ⅓ * 2/2 = 3 2/6
5 3/6 + 3 2/6 = 8 ⅚
2) 5 ½ - 3 ⅓ = 2 ⅙
5 ½ * 3/3 = 5 3/6
3 ⅓ * 2/2 = 3 2/6
5 3/6 - 3 2/6 = 2 ⅙
3) 2 1/7 ⋅1 2/9 = 2 + 4/9 + 2/63 + 1/7 = 2 + 28/63 + 2/63 + 9/63 = 2 39/63
= 2 13/21
4) 3 ¼ ÷ 2/3 = 2 ⅜
3 ¼ / ⅔ = 2 + ⅜ = 2 ⅜
Copy the questions from ECHO and paste them below.
Luckily Mrs. Nomura has a lemon tree in her backyard. Here is the recipe they found online for one pitcher (12 servings):
1 3/4 cup sugar
8 1/2 cups of water
2 1/3 cups of lemon juice
Mrs. Sutton has 5/8 cup of sugar and Mrs. Nomura only has 2/3 cup of sugar. Do they have enough sugar to make a pitcher of lemonade? Will they need to borrow sugar from a neighbor? If so, how much?
When you have completed your work, please ask your teacher to check your work.
If complete, use the given password to open Lemonade Stand Part 2.
You can get about 1/4 cup of lemon juice from each lemon. Mrs. Sutton has juiced about 1 1/2 cups. How many lemons does she still need to juice in order to make enough lemon juice for the recipe?
When you have completed your work, please ask your teacher to check your work.
If complete, use the given password to open Lemonade Stand Part 3.
The lemonade stand is a success! Unfortunately we don’t have enough lemonade for all of our customers. We have served 7 customers and there are still 13 customers in line. How many ingredients of each type do we need to make enough lemonade with no lemonade left over?
When you have completed your work, please ask your teacher to check your work.
If complete, use the given password to open Lemonade Stand Part 4
Now that we have established how much of everything we need we need to think about how much all of this is going to cost. How much should we charge in order to make a profit that is good, while still charging a reasonable price?
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