Question

Emma made 3/4 of a quart of lemonade. She poured the lemonade into cups, filling each with 1/6 of a quart of lemonade. How many cups of lemonade did she have?

a. Write a mathematical expression to represent this situation.

Use the nonstandard algorithm to determine the desired amount.

Describe the whole situation with pictures, including your solution process. Make explicit connections between your picture process and the nonstandard algorithm.

Answer 1

To determine how many cups of lemonade Emma had, we can use a mathematical expression.

First, you convert the amount of lemonade Emma made (3/4 of a quart) into cups. Since there are 4 cups in a quart, we can multiply 3/4 by 4 to find the number of cups.

3/4 * 4 = 12/4 = 3 cups

So Emma made 3 cups of lemonade in total.

Next, you need to determine how many cups of lemonade were poured into each cup. The question tells us that each cup was filled with 1/6 of a quart of lemonade. Since there are 4 cups in a quart, we can multiply 1/6 by 4 to find the number of cups.

1/6 * 4 = 4/6 = 2/3 cups

Therefore, each cup was filled with 2/3 cups of lemonade.

Now, you can divide the total amount of lemonade Emma made (3 cups) by the amount poured into each cup (2/3 cups) to find the number of cups of lemonade she had.

3 cups ÷ (2/3 cups) = 3 cups * (3/2 cups) = 9/2 cups = 4.5 cups

Emma had 4.5 cups of lemonade.

To represent this situation mathematically, we can write:

Total cups of lemonade = (Amount of lemonade made) ÷ (Amount poured into each cup)

Total cups of lemonade = 3 cups ÷ (2/3 cups)

Additionally, we can visualize this situation with pictures:

Picture 1: Emma made 3/4 of a quart of lemonade. This can be represented by drawing a quart container and shading in 3/4 of it.

Picture 2: Each cup was filled with 1/6 of a quart of lemonade. This can be represented by drawing a cup and shading in 1/6 of it.

Picture 3: To find the number of cups of lemonade Emma had, we divide the total amount of lemonade made by the amount poured into each cup. This can be represented by drawing 3 cups and dividing each cup into 2/3 parts. Then we count the number of 2/3 parts in the 3 cups, which equals 4.5 cups.

The nonstandard algorithm, in this case, is using a visual representation to solve the problem. By drawing pictures and visually representing the lemonade quantities, we can easily determine the number of cups of lemonade Emma had. The pictures help us make explicit connections between the visual representation and the mathematical calculations involved.