Interpreting Division Situations
10 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to carefully analyze and compare four situations involving equal-size groups. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology related to multiplication, division, and equal-size groups and how they talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the four items for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three items that go together and can explain why. Next, tell students to share their response with their group and then together to find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
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Jada fills 4 jars with salsa. Each jar has 10 ounces of salsa. How many ounces of salsa are in all the jars?
-
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Andre is filling 4-liter jugs with water. How many jugs can he fill if he has 10 liters of water?
Sample Response
Sample responses:
A, B, C go together because:
- There are 4 equal-size groups in each situation.
A, B, D go together because:
- We can tell what is happening in each situation and what the equal-size groups represent.
A, C, and D go together because:
- The total amount in each situation is 10 units.
- The unknown number can be found by finding 10÷4, which is 2.5.
- The situations can be represented with the equations 4⋅?=10 or 10÷4=?.
B, C, D go together because:
- The situations are about volume.
- The situations involve putting equal amounts of something into containers.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology that they use to describe equal-size groups, such as “4 times the same amount,“ “divide into 4 groups,” and “split into 4 equal parts.” Ask students to clarify their reasoning as needed. Consider asking:
- “How do you know . . . ?”
- “What do you mean by . . . ?”
- “Can you say that in another way?”
Standards
- 6.NS.1·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. <em>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?</em>
- 6.NS.A.1·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. <span>For example, create a story context for <span class="math">\((2/3) \div (3/4)\)</span> and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that <span class="math">\((2/3) \div (3/4) = 8/9\)</span> because <span class="math">\(3/4\)</span> of <span class="math">\(8/9\)</span> is <span class="math">\(2/3\)</span>. (In general, <span class="math">\((a/b) \div (c/d) = ad/bc\)</span>.) 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? </span>
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Interpreting Division Situations
10 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to carefully analyze and compare four situations involving equal-size groups. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology related to multiplication, division, and equal-size groups and how they talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the four items for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three items that go together and can explain why. Next, tell students to share their response with their group and then together to find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
-
-
Jada fills 4 jars with salsa. Each jar has 10 ounces of salsa. How many ounces of salsa are in all the jars?
-
-
Andre is filling 4-liter jugs with water. How many jugs can he fill if he has 10 liters of water?
Sample Response
Sample responses:
A, B, C go together because:
- There are 4 equal-size groups in each situation.
A, B, D go together because:
- We can tell what is happening in each situation and what the equal-size groups represent.
A, C, and D go together because:
- The total amount in each situation is 10 units.
- The unknown number can be found by finding 10÷4, which is 2.5.
- The situations can be represented with the equations 4⋅?=10 or 10÷4=?.
B, C, D go together because:
- The situations are about volume.
- The situations involve putting equal amounts of something into containers.
Activity Synthesis (Teacher Notes)
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology that they use to describe equal-size groups, such as “4 times the same amount,“ “divide into 4 groups,” and “split into 4 equal parts.” Ask students to clarify their reasoning as needed. Consider asking:
- “How do you know . . . ?”
- “What do you mean by . . . ?”
- “Can you say that in another way?”
Standards
- 6.NS.1·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. <em>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?</em>
- 6.NS.A.1·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. <span>For example, create a story context for <span class="math">\((2/3) \div (3/4)\)</span> and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that <span class="math">\((2/3) \div (3/4) = 8/9\)</span> because <span class="math">\(3/4\)</span> of <span class="math">\(8/9\)</span> is <span class="math">\(2/3\)</span>. (In general, <span class="math">\((a/b) \div (c/d) = ad/bc\)</span>.) 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? </span>