standard_description: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
problem_activity: Narrative
The purpose of this activity is for students to match situations to expressions and then find the value of the expressions (MP2). Students see expressions that show both quotients of a whole number by a fraction and quotients of a fraction by a whole number. They need to think carefully about the situations to make sure the expression they choose matches the situation (MP2).
Launch
Groups of 2
Display the image from student book:
[IMG]
“What do you notice? What do you wonder?” (They look like seeds. How many are in the bowls? Why are there 2 bowls?)
“The small bowl is filled with
\(\frac {1}{4}\)
cup of kernels. That is one serving of popcorn kernels. What does ‘one serving’ mean?” (It is the amount you are supposed to eat at one time.)
“About how many servings are in the big bowl?” (Answers vary. Sample responses range from 10 to 15.)
Activity
1–2 minutes: independent think time
5–8 minutes: partner work time
Monitor for students who:
draw diagrams to represent the situations
describe the relationship between the dividend and divisor using language such as “groups of”
use the value of the expression to describe why the expression matches the situation
Student Facing
Match each problem to an expression that represents the problem. Some expressions will not have a match. Be prepared to explain your reasoning.
One serving of popcorn is
\(\frac {1}{4}\)
cup of kernels. There are 3 cups of kernels in the bowl. How many servings are in the bowl?
[IMG]
One serving of orange juice is
\(\frac {1}{4}\)
liter. The container of juice holds 2 liters. How many servings are in the container?
One serving of granola is
\(\frac {1}{2}\)
cup. The bag of granola holds 5 cups. How many servings are in the bag?
\(\frac {1}{4} \div 3 \)
\(\frac {1}{2} \div 5\)
\(3 \div \frac {1}{4}\)
\(\frac {1}{4} \div 2\)
\(5 \div \frac {1}{2}\)
\(2 \div \frac {1}{4}\)
Find the value of each expression.
Student Response
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Advancing Student Thinking
If students do not correctly match the situations to the expressions, refer to each situation and ask, “How does the situation represent division?”
Activity Synthesis
Ask previously selected students to share their solutions.
“How did you decide which expression matched which situation?” (I thought about the number of things being divided and whether it was a fraction or a whole number. I thought about the size of the pieces.)
Display:
\(3 \div \frac {1}{4}= 12\)
“Describe how this equation represents the situation in the first problem.” (There are 3 cups of kernels in the bowl and a serving is
\(\frac {1}{4}\)
a cup, so there are 12 servings in the bowl.)
Display:
\(\frac {1}{4} \div 3 = \frac {1}{12}\)
“How do you know that this equation does not match the situation?” (The answer is a fraction. That doesn’t make sense because there is more than 1 serving in 3 cups.)


aligns: no