The purpose of this Estimation Exploration is for students to reason about the size of a complex fraction sum with large denominators. Students can see that 1 is a good estimate because one fraction is small and the other is close to 1. In the Activity Synthesis, students refine this estimate to explain why the value of the sum is a little greater than 1.
Launch
Groups of 2
Display the expression.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Task Statement
What is the value of the sum?
Record an estimate that is:
too low
about right
too high
Student Response
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Advancing Student Thinking
Activity Synthesis
“How do you know that the sum is greater than 1?” ( is short of a whole. Since 17ths are bigger than 19ths, adding makes it greater than 1.)
Activity 1
20 mins
Priya’s Salad Dressing
Standards Alignment
Building On
Addressing
5.NF.A.2
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result , by observing that .
The purpose of this activity is for students to add and subtract fractions and estimate sums and differences of fractions, using the context of a recipe. Students may have different responses and reasoning for the estimation questions. In both cases, they can calculate and compare fractions, but they may have different thoughts about how these differences would affect the recipe or what exactly it means for the recipe to make “about cups.” In the Activity Synthesis, students discuss the reasonableness of the estimates and how to make precise calculations (MP6). When students relate their calculations to Priya's salad dressing, they reason abstractly and quantitatively (MP2).
Reading: MLR6 Three Reads. Keep books or devices closed. Display only the problem stem, without revealing the questions. “We are going to read this question 3 times.”
After the 1st Read: “Tell your partner what this situation is about.”
After the 2nd Read: “List the quantities. What can be counted or measured?”
Reveal the question(s).
After the 3rd Read: “What strategies can we use to solve this problem?”
Advances: Reading, Representing
Launch
Groups of 2
“What kind of ingredients do you like to put in your salad?” (lettuce, cabbage, beans, seeds, beets, tomatoes, cheese)
“What kinds of dressings do you put on your salad?” (homemade, Italian, ranch, tamari)
Activity
1–2 minutes: quiet think time
6–8 minutes: small-group work time
Monitor for students who:
Estimate to determine that Priya’s recipe will make about cups of dressing.
Add to determine the precise amount of dressing Priya’s recipe will make.
Activity Synthesis
“If Priya borrows a tablespoon of olive oil from her neighbor and uses it to make dressing, will she be putting in more or less olive oil than the recipe calls for?” ( is smaller than so she will be putting in less olive oil.)
“Do you think 1 tablespoon is close enough?”
Poll the class.
“How might Priya’s decision to use 1 tablespoon of olive oil change the salad dressing?” (It won’t make a difference because the difference is so small. It might taste more lemony or more mustardy because there is not as much oil. It might affect the consistency of the dressing a little.)
Ask previously selected students to share their estimates for the amount of salad dressing in the given order.
“Why might Priya estimate that the recipe makes cups of salad dressing?” ( is away from 1 and is close to .)
“Does the recipe make more than or less than cups? How do you know?” (More, because is more than .)
“How many cups does Priya’s recipe make? How do you know?” (, I added , , and .)
Activity 2
15 mins
More Problems to Solve
Standards Alignment
Building On
Addressing
5.NF.A.2
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result