Balancing Act

Learning Resource Type

Learning Activity

Subject Area

Digital Literacy and Computer Science
Mathematics

Grade(s)

7

Overview

In this activity, students will create equivalent expressions using an online tool. Students are provided two expressions and asked to find the value of the variable to make the two expressions equal. Then, students are provided an expression and a value of the variable and asked to generate a different expression equal to the original expression. Through the online digital tool, students are able to substitute values and develop strategies for creating equivalent expressions. This provides a great opportunity for students to investigate how to solve problems using multiple methods.

Balancing Act Student Response Page

Phase

Before/Engage
Digital Literacy and Computer Science (2018) Grade(s): 7

DLCS18.7.27

Identify data needed to create a model or simulation of a given event.

UP:DLCS18.7.27

Knowledge

Students know:
  • an event is comprised of a set of steps or processes that can be identified and then simulated.

Skills

Students are able to:
  • abstract the sequence of activities that make up an event.

Understanding

Students understand that:
  • dissecting the parts of an event can aid in understanding of and the simulation of the event.
Mathematics (2019) Grade(s): 7

MA19.7.7

Generate expressions in equivalent forms based on context and explain how the quantities are related.

UP:MA19.7.7

Vocabulary

  • like terms
  • Equivalent expressions
  • Distributive property
  • Factor

Knowledge

Students know:
  • properties of operations can be used to identify or create equivalent linear expressions.
  • Equivalent expressions can reveal real-world and mathematical relationships, and some forms of equivalent expressions can provide more insight than others.

Skills

Students are able to:
  • determine whether two expressions are equivalent.
  • Rewrite expressions into equivalent forms by combining like terms, using the distributive property, and factoring.

Understanding

Students understand that:
  • rewriting expressions in multiple equivalent forms allows for thinking about problems in different ways and highlights different aspects/relationships of quantities in problems.
Mathematics (2019) Grade(s): 7

MA19.7.13

Use a number from 0 to 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event.

UP:MA19.7.13

Vocabulary

  • probability
  • Event
  • Chance
  • likely
  • Unlikely
  • very unlikely
  • very likely
  • Equally likely
  • Impossible
  • Certain

Knowledge

Students know:
  • probability is equal to the ratio of favorable number of outcomes to total possible number of outcomes.
  • As a number for probability increases, so does the likelihood of the event occurring.
  • A probability near 0 indicates an unlikely event.
  • A probability around 1/2 indicates an event that is neither unlikely nor likely.
  • A probability near 1 indicates a likely event.

Skills

Students are able to:
  • approximate the probability of a chance event.
  • Use words like impossible, very unlikely, unlikely, equally likely/unlikely, likely, very likely, and certain to describe the probabilities of events.

Understanding

Students understand that:
  • the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
  • An event that is equally likely or equally unlikely has a probability of about 0.5 or ½.
  • The sum of the probabilities of an event and its complement must be 1.

Learning Objectives

Students will use an online tool to create equivalent expressions.

Students will determine the value of a variable to create equivalent expressions. 

When given the value of a variable and an expression, the student will generate a different expression equivalent to the original expression.

Activity Details

Students will begin by exploring the Illuminations Pan Balance-Expressions online tool with an example problem. They will develop strategies through this example of how to adjust the variable to generate equivalent expressions. The online tool also generates graphs for the two expressions. Students will observe what they notice about the two graphs. Then students are given five problems where they are given two expressions. They adjust the variable value to make the two expressions equivalent. Next students are provided one expression and a given variable value. They use this information to create an expression equivalent to the original expression. The expression they create must be different than the given expression. In this portion of the activity, some exponent and negative values are used to challenge the students. Finally, students are asked what strategies they used to create equivalent expressions, if set 1 or set 2 was more difficult to solve, and any observations about the two graphs they noticed while creating the equivalent expressions. At this point, the teacher should conduct a Think-Pair-Share with the class. Each student should have a partner. Ask the students to compare the expressions they generated in set 2 on their activity page. Are their expressions the same or are they different? Have them record their results and determine what they would like to share with the class. Allow each group to share their results and reasoning with the rest of the class. For more advanced students, this would be a great activity to begin exploring systems of equation problems.

Assessment Strategies

The teacher will review student answers in Set 1 and Set 2 on the response sheet to evaluate correct usage of the digital tool and to assess understanding of creating equivalent expressions.

Background / Preparation

Visit the Pan Balance-Expressions Tool to become familiar with how to use the tool. 

Students will need online access to the Pan Balance-Expressions Tool.

Copy the “Balancing Act” student response page.

Illuminations Pan Balance-Expressions
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Pan-Balance…

Approved Date

Owner (Author)

kdockery
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