standard_description: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about numeric expressions using what they know about operations with negative and positive numbers without actually computing anything.
Launch
Explain to students that we sometimes leave out the small dot that tells us that two numbers are being multiplied. So when a number, or a number and a variable, are next to each other without a symbol between them, that means we are finding their product. For example,
\((\text-5)\boldcdot (\text-10)\)
can be written
\((\text-5) (\text-10)\)
and
\(\text-5 \boldcdot x\)
can be written
\(\text-5x\)
.
Display one problem at a time. Give students 1 minute of quiet think time per problem and ask them to give a signal when they have an answer. Follow with a whole-class discussion.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
\((\text-38.76)(\text-15.6)\)
is negative
\(10,000 - 99,999 < 0\)
\(\left( \frac34 \right)\left( \text- \frac43 \right) = 0\)
\((30)(\text- 80) - 50 = 50 - (30)(\text- 80)\)
Student Response
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Activity Synthesis
Ask students to share their reasoning.


aligns: no