Multiplying Rational Numbers (Part 2)
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students interpret negative time in the context of a person walking. This activity primes students to think about opposites and constant speeds, which will be useful in following activities.
Launch
Arrange students in groups of 2. Give students 30 seconds of quiet think time followed by time for partner discussion.
Student Task
- Where was the person 5 seconds after this picture was taken?
- Where was the person 5 seconds before this picture was taken?
Sample Response
- Students should mark a position to the right of the person's current position.
- Students should mark a position to the left of the person's current position. The marks on the left and right should be about equally distant from the person’s current position.
Activity Synthesis (Teacher Notes)
The purpose of this discussion is to get students thinking about constant speeds and negative times. Begin by displaying the image from the Task Statement for all to see. Invite students to share where they think the person was 5 seconds earlier and will be 5 seconds later.
If necessary, point out that if we assume the person is walking at a constant speed, their before and after locations should be equally far from their current position in the image. Ask students how they might represent time in this situation. (5 seconds before the picture was taken could be -5, while 5 seconds after the picture was taken would be +5. The picture was taken when the time was 0.)
Standards
- 6.RP.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <em>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</em>
- 6.RP.A.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <span>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</span>
- 7.NS.2.a·Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
- 7.NS.A.2.a·Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as <span class="math">\((-1)(-1) = 1\)</span> and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
15 min
Knowledge Components
All skills for this lesson
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Multiplying Rational Numbers (Part 2)
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students interpret negative time in the context of a person walking. This activity primes students to think about opposites and constant speeds, which will be useful in following activities.
Launch
Arrange students in groups of 2. Give students 30 seconds of quiet think time followed by time for partner discussion.
Student Task
- Where was the person 5 seconds after this picture was taken?
- Where was the person 5 seconds before this picture was taken?
Sample Response
- Students should mark a position to the right of the person's current position.
- Students should mark a position to the left of the person's current position. The marks on the left and right should be about equally distant from the person’s current position.
Activity Synthesis (Teacher Notes)
The purpose of this discussion is to get students thinking about constant speeds and negative times. Begin by displaying the image from the Task Statement for all to see. Invite students to share where they think the person was 5 seconds earlier and will be 5 seconds later.
If necessary, point out that if we assume the person is walking at a constant speed, their before and after locations should be equally far from their current position in the image. Ask students how they might represent time in this situation. (5 seconds before the picture was taken could be -5, while 5 seconds after the picture was taken would be +5. The picture was taken when the time was 0.)
Standards
- 6.RP.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <em>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</em>
- 6.RP.A.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <span>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</span>
- 7.NS.2.a·Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
- 7.NS.A.2.a·Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as <span class="math">\((-1)(-1) = 1\)</span> and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.