Keeping the Equation Balanced
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to give students an opportunity to ground their understanding of equality in the context of weight, which will be useful when students examine hanger representations throughout the lesson. While students may notice and wonder many things about this image, the idea that things that weigh the same are balanced and things that weigh different amounts are unbalanced 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
Arrange students in groups of 2. Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder about.
Student Task
What do you notice? What do you wonder?
Sample Response
Students might notice:
- There are four bags on two hangers.
- One hanger is hanging diagonally and one is balanced.
- The blue bag with the square looks heavier than the green bag with the triangle because it is weighing down that side of its hanger.
- The red bags have circles on them, the blue bag has a square on it, and the green bag has a triangle on it.
Students might wonder:
- How does the red bag’s weight compare to the weight of the other two bags?
- Is this representing an equation?
- How many green bags with triangles would it take to balance the hanger on the right?
- What is in each of the bags?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered about. Record and display, for all to see, their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. 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 reasoning behind the left hanger being balanced and the right hanger being unbalanced does not come up during the conversation, ask students to discuss this idea. Students should understand that a hanger will balance only if the weight of the unknown objects in both bags is the same. If they are not the same, then the heavier side is going to be lower than the lighter side.
Standards
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
10 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Keeping the Equation Balanced
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to give students an opportunity to ground their understanding of equality in the context of weight, which will be useful when students examine hanger representations throughout the lesson. While students may notice and wonder many things about this image, the idea that things that weigh the same are balanced and things that weigh different amounts are unbalanced 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
Arrange students in groups of 2. Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder about.
Student Task
What do you notice? What do you wonder?
Sample Response
Students might notice:
- There are four bags on two hangers.
- One hanger is hanging diagonally and one is balanced.
- The blue bag with the square looks heavier than the green bag with the triangle because it is weighing down that side of its hanger.
- The red bags have circles on them, the blue bag has a square on it, and the green bag has a triangle on it.
Students might wonder:
- How does the red bag’s weight compare to the weight of the other two bags?
- Is this representing an equation?
- How many green bags with triangles would it take to balance the hanger on the right?
- What is in each of the bags?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered about. Record and display, for all to see, their responses without editing or commentary. If possible, record the relevant reasoning on or near the image. 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 reasoning behind the left hanger being balanced and the right hanger being unbalanced does not come up during the conversation, ask students to discuss this idea. Students should understand that a hanger will balance only if the weight of the unknown objects in both bags is the same. If they are not the same, then the heavier side is going to be lower than the lighter side.
Standards
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
- 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.