Balancing Act
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engage students in learning a concept or skill using a digital tool/resource.
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This learning activity provided by:
Author:
Kimberly Dockery
System: Alabama Department of Education School: Alabama Department of Education
General Activity Information
Activity ID:
2706
Title: Balancing Act
Digital Tool/Resource: Illuminations Pan Balance-Expressions
Web Address – URL:
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
Associated Standards and Objectives
Content Standard(s):
Digital Literacy and Computer Science 27) Identify data needed to create a model or simulation of a given event.
Examples: When creating a random name generator, the program needs access to a list of possible names.
Unpacked Content
Evidence Of Student Attainment:
Students will:
select a process or system and then determine the data needed to create a model or simulation of the process or system. 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 7. Generate expressions in equivalent forms based on context and explain how the quantities are related.
Unpacked Content
Evidence Of Student Attainment:
Students:
Write an expression for a situation and determine equivalent expressions for the same situation. Teacher 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. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.7.7.1: Define expression, equivalent, and equivalent expressions.
M.7.7.2: Recall mathematical terms such as sum, difference, etc.
M.7.7.3: Recognize that a variable without a written coefficient is understood to have a coefficient of one.
M.7.7.4: Recall how to convert mathematical terms to mathematical symbols and numbers and vice versa.
M.7.7.5: Restate numerical expressions with words.
Prior Knowledge Skills:
Define equivalent expressions.
Recognize equivalent expressions.
Recognize that a variable without a written coefficient is understood to be one.
Convert mathematical terms to mathematical symbols and numbers (Ex. sum: +, difference: -; product: ·, quotient: ÷).
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 13. Generate expressions in equivalent forms based on context and explain how the quantities are related. [Grade 7, 7]
Unpacked Content
Evidence Of Student Attainment:
Students:
Write an expression for a situation and determine equivalent expressions for the same situation.
Interpret and apply problem solving strategies in solving multi-step real-world word problems. Teacher 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 an expression in different forms in a problem context can clarify the problem.
Rewriting an expression can clarify how the quantities in the problem are related. Diverse Learning Needs:
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.
Strategies, Preparations and Variations
Phase: Before/Engage
Activity: 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.
Advanced 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.
Variation Tips (optional):
Notes or Recommendations (optional): Students can write their own two expressions. The expressions can be exchanged with a classmate to determine the value of the variable.
More advanced students can begin to explore systems of equations with the concepts presented in this activity.
Keywords and Search Tags
Keywords and Search Tags:
equivalent expressions, negative numbers, positive numbers, seventh, seventh grade, variable
