What Fraction of a Group?
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is twofold: to familiarize students with the quantities and representations they will see later in the lesson, and to elicit observations about the size of a quantity relative to the size of 1 group. The insights will be useful later when students interpret division situations involving quotients that are either greater than 1 or less than 1.
While students may notice and wonder many things about these diagrams, observations about whether the amount shown for each day represents more or less than 1 batch are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Display the two tape diagrams for all to see. Give students 1 minute of quiet think time, and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.
Student Task
What do you notice? What do you wonder?
Tuesday
Thursday
Sample Response
Students may notice:
- The tape diagrams show different numbers of cups of something on two days of the week.
- In each diagram, the size of 1 batch is 9 cups.
- On Tuesday, the number of cups is more than one batch.
- On Thursday, the number of cups is less than one batch. It is 96 of a batch.
Students may wonder:
- What is the situation about?
- Why is the amount for Thursday less than one batch?
- How many batches do 2221 cups each make?
- On Thursday, what fraction of a batch is being made?
- Why might someone want to make 96 of a batch?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the diagrams. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement
If the number of batches represented in each diagram does not come up during the conversation, ask students to discuss this idea.
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
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
What Fraction of a Group?
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is twofold: to familiarize students with the quantities and representations they will see later in the lesson, and to elicit observations about the size of a quantity relative to the size of 1 group. The insights will be useful later when students interpret division situations involving quotients that are either greater than 1 or less than 1.
While students may notice and wonder many things about these diagrams, observations about whether the amount shown for each day represents more or less than 1 batch are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Display the two tape diagrams for all to see. Give students 1 minute of quiet think time, and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.
Student Task
What do you notice? What do you wonder?
Tuesday
Thursday
Sample Response
Students may notice:
- The tape diagrams show different numbers of cups of something on two days of the week.
- In each diagram, the size of 1 batch is 9 cups.
- On Tuesday, the number of cups is more than one batch.
- On Thursday, the number of cups is less than one batch. It is 96 of a batch.
Students may wonder:
- What is the situation about?
- Why is the amount for Thursday less than one batch?
- How many batches do 2221 cups each make?
- On Thursday, what fraction of a batch is being made?
- Why might someone want to make 96 of a batch?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the diagrams. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement
If the number of batches represented in each diagram does not come up during the conversation, ask students to discuss this idea.
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>