ALEX Classroom Resource

  

Combining Like Terms (Part2)

  Classroom Resource Information  

Title:

 Combining Like Terms (Part2)

URL:

 https://aptv.pbslearningmedia.org/resource/our20-math-7621/combining-like-terms-part-2/

Content Source:

 PBS
Type: Audio/Video

Overview:

In this video lesson, students are working toward gaining fluency in writing equivalent expressions. The goal of this lesson is to highlight a particularly common error: mishandling the subtraction in an expression like 8–3(4+9x). To this end, students first analyze and explain the error in several incorrect ways of rewriting this expression. Then, they consider the effect of inserting parentheses in different places in an expression with four terms.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
8. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
  • Interpret solutions of problems with rational numbers in the context of the problem.
  • Assess the reasonableness of answers using mental computation and estimation strategies.
  • Use variables to represent quantities in a real-world or mathematical problem.
Teacher Vocabulary:
  • Rational numbers
  • Integers
  • Estimation
Knowledge:
Students know:
  • techniques for converting between fractions, decimals, and percents.
  • Techniques for estimation, mental computations, and how to assess the reasonableness of their answers.
Skills:
Students are able to:
  • convert between different forms of a rational number.
  • Add, subtract, multiply and divide rational numbers. -translate verbal forms of problems into algebraic symbols, expressions, and equations.
  • Use estimation and mental computation techniques to assess the reasonableness of their answers.
Understanding:
Students understand that:
  • One form of a number may be more advantageous than another form, based on the problem context.
  • Using estimation strategies helps to determine the reasonableness of answers.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.8.1: Define estimation, rational numbers, and reasonable.
M.7.8.2: Recall mental calculation strategies.
M.7.8.3: Recall estimation strategies.
M.7.8.4: Analyze the given word problem to set up a mathematical problem.
M.7.8.5: Recognize the mathematical operations of rational numbers in any form, including converting between forms. (Ex. 0.25=1/4 =25%).
M.7.8.6: Recognize the rules of operations of positive and negative numbers.
M.7.8.7: Recognize properties of numbers (Distributive, Associative, Commutative).
M.7.8.8: Recall problem solving methods.

Prior Knowledge Skills:
  • Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.
  • Define integers, positive and negative numbers.
  • Define rational number.
  • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.8 Add and subtract integers in a real-world situation.
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
21. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem. [Grade 8, 11]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Recognize and explain when linear equations have one solution, infinitely many solutions, or no solution with and without completing the solving process.
  • Solve one variable equations with the same variable on both sides and require use of the distributive property.
  • Analyze and explain solutions in the context of a real-world problem.
Teacher Vocabulary:
  • One solution
  • No solution
  • Infinitely many solutions
  • Like terms
  • Distributive property
Knowledge:
Students know:
  • How to solve one and two step equations with one variable.
  • Write linear equations given real-world contexts.
  • That a solution to an equation can represent a real-world quantity.
Skills:
Students are able to:
  • Apply the distributive property and combine like terms to simplify an equation.
  • Recognize a solution as representing one solution, no solution, or infinite solutions.
  • Analyze and solve a real-world problem and write an appropriate equation for it that leads to a solution that can be explained within the context of the problem.
Understanding:
Students understand that:
  • Equations can now have more than one solution in given real-world scenarios.
  • The distributive property and combining like terms are essential to simplifying an equation. therefore making it easier to solve.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 8
11. Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

a. Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

b. Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Recognize and explain when linear equations have one solution, infinitely many solutions, or no solution with and without completing the solving process.
  • Solve one variable equation with the same variable on both sides and require use of the distributive property.
  • Analyze and explain solutions in the context of a real-world problem.
Teacher Vocabulary:
  • one solution
  • no solution
  • Infinitely many solutions
  • like terms
  • Distributive property
Knowledge:
Students know:
  • how to solve one and two step equations with one variable.
  • Write linear equations given real-world contexts.
  • That a solution to an equation can represent a real-world quantity.
Skills:
Students are able to:
  • apply the distributive property and combine like terms to simplify an equation.
  • Recognize a solution as representing one solution, no solution, or infinite solutions.
  • Analyze and solve a real-world problem and write an appropriate equation for it that leads to a solution that can be explained within the context of the problem.
Understanding:
Students understand that:
  • equations can now have more than one solution in given real-world scenarios.
  • The distributive property and combining like terms are essential to simplifying an equation. therefore making it easier to solve.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.11.1: Define linear equation, coefficient, distributive property and variable.
M.8.11.2: Recall how to solve equations for a missing variable.
M.8.11.3: Recall properties of operation for addition and multiplication.
M.8.11.4: Solve multi-step equations.
M.8.11.5: Identify properties of operations.

a.
M.8.11.6: Identify how many solutions the linear equation may or may not have.
M.8.11.7: Recall how to solve equations by using substitution.

b.
M.8.11.8: Create an equation to represent a real-world situation or mathematical problem.
M.8.11.9: Analyze the solution in context of a real-world problem.

Prior Knowledge Skills:
  • Recognize properties of numbers (Distributive, Associative, Commutative).
  • Define equation, inequality, and variable.
  • Set up equations and inequalities to represent the given situation, using correct mathematical operations and variables.
  • Calculate a solution or solution set by combining like terms, isolating the variable, and/or using inverse operations.
  • Test the found number or number set for accuracy by substitution.
  • Recall solving one step equations and inequalities.
  • Recognize properties of numbers (Distributive, Associative, Commutative).
  • Define equation and variable.
  • Set up an equation to represent the given situation, using correct mathematical operations and variables.
  • Calculate a solution to an equation by combining like terms, isolating the variable, and/or using inverse operations.
  • Test the found number for accuracy by substitution.

  • Example: Is 5 an accurate solution of 2(x + 5)=12 .
  • Identify the unknown, in a given situation, as the variable.
  • List given information from the problem.
Tags: combining like terms, equations, expressions, linear
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
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AccessibilityVideo resources: includes closed captioning or subtitles
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  This resource provided by:  
Author: Kristy Lacks
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