Objective
Solve one-step equations with addition and subtraction.
Common Core Standards
Core Standards
The core standards covered in this lesson
6.EE.B.6— Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Expressions and Equations
6.EE.B.6— Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.B.7— Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Expressions and Equations
6.EE.B.7— Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Foundational Standards
The foundational standards covered in this lesson
5.NF.A.1
Number and Operations—Fractions
5.NF.A.1— Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
6.NS.B.3
The Number System
6.NS.B.3— Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand that in the process of solving for a variable, whatever is done to one side of the equation must also be done to the other side in order to maintain the balance.
- Use models and diagrams to solve for a variable.
- Solve one-step addition and subtraction equations algebraically.
- Write and solve one-step addition and subtraction problems for real-world contexts.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
Students first solve equations by using diagrams; they then generalize their actions to solve equations algebraically without diagrams. Though some students may find they can mentally solve these equations, encourage students to organize and show their thinking algebraically. This will support them later as the equations become more and more complex.
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Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Problem 1
The following three diagrams represent the equation $${x+2=6}$$.
a.Explain how you can use each diagram to find the value of $$x$$.
b.How can you solve the equation$${m+3.6=9.2}$$ without using a diagram?
Guiding Questions
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Problem 2
a.Draw a tape diagram to represent the equation $${d-5=7}$$; then use it to find the value of $$d$$.
b.How can you solve the equation $${p-{3\over4}=8}$$ without using a diagram?
Guiding Questions
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References
EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic G > Lesson 26—Exercise 2
Grade 6 Mathematics > Module 4 > Topic G > Lesson 26 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 3
At the grocery store, Martin uses some coupons and saves $5.75 off his total bill. His new bill comes to $21.36. Let $$x$$represent the amount of Martin’s grocery bill before using the coupons.
Write and solve an equation to find the amount of Martin’s bill before using the coupons.
Guiding Questions
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Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Fishtank Plus Content
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Problem 1
Solve the equations. Show or explain your thinking.
a.$${w+1.5=8.75}$$
b.$${z-12=9}$$
Student Response
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Problem 2
A large bowl holds$${5{2\over3}}$$ cups of punch. Some more punch is added to the bowl to make a total of 10 cups of punch. Let $$c$$represent the number of cups of punch that are added to the bowl.
Write and solve an equation to find the number of cups of punch that are added to the bowl.
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- Include problems with procedural practice in solving addition and subtraction equations, particularly those involving decimals or fractions.
- Include problems where students write an equation from a context (addition or subtraction only) and solve the equation.
- Include error analysis problems of mistakes made in solving equations.
- Open Up Resources Grade 6 Unit 6 Practice Problems—Lesson 3 (Do not include #3)
- Open Middle Solving One-Step Equations (Greatest Solution)—Challenge
- EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic G > Lesson 26—Exercises and Problem Set
Lesson 3
Lesson 5
