Curriculum / Math / 6th Grade / Unit 6: Equations and Inequalities / Lesson 2
Math
Unit 6
6th Grade
Lesson 2 of 14
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Define and identify solutions to equations.
The core standards covered in this lesson
6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
The foundational standards covered in this lesson
6.EE.A.1 — Write and evaluate numerical expressions involving whole-number exponents.
6.EE.A.2 — Write, read, and evaluate expressions in which letters stand for numbers.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Determine if the equations are true or false when the number given is used for the value of the variable.
a. $${12x=84}$$; for when $${x=7}$$
b. $${y-10=50}$$; for when $${y=40}$$
c. $${{1\over2}m=16}$$; for when $${ m=32}$$
d. $${3(x-1)=27}$$; for when $${x=9}$$
Which value of $$x$$ from the set below is the solution to the equation $$4x-14=38$$?
{6, 10, 12, 13, 15}
Below are some equations that each contain a variable. A list of values is also shown. Think about what each equation means to find its solution in the list of values.
List of Values:
$$\frac{1}{4}$$ $$\frac{3}{7}$$ $$\frac{1}{2}$$ $$\frac{4}{7}$$ $$\frac{3}{4}$$ $$0.8$$ $$1$$ $$2$$ $$4$$ $$8$$ $$600$$ $$1,400$$
Equations:
a. $$1,000-a=400$$
b. $$x^2=16$$
c. $$8c=8$$
d. $$2+x=2.8$$
e. $$2e=1$$
f. $$h+\frac{3}{7}=1$$
g. $$1-x=\frac{1}{4}$$
Grade 6 Unit 6 Lesson 2 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Feb. 27, 2018, 11:42 a.m..
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Which equations below have a solution $${x=4}$$?
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 1
Lesson 3
Topic A: Reasoning About and Solving Equations
Represent equations in the form $${ x+p=q }$$ and $${px=q}$$ using tape diagrams and balances.
6.EE.B.6 6.EE.B.7
6.EE.B.5
Write equations for real-world situations.
Solve one-step equations with addition and subtraction.
Solve one-step equations with multiplication and division.
Solve percent problems using equations.
6.EE.B.7 6.RP.A.3.C
Solve multi-part equations leading to the form $${x+p=q }$$ and $${px=q}$$.
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Topic B: Reasoning About and Solving Inequalities
Define and identify solutions to inequalities.
6.EE.B.5 6.EE.B.8
Write and graph inequalities for real-world conditions. (Part 1)
6.EE.B.8
Write and graph inequalities for real-world conditions. (Part 2)
Solve one-step inequalities.
6.EE.B.6 6.EE.B.8
Topic C: Representing and Analyzing Quantitative Relationships
Write equations for and graph ratio situations. Define independent and dependent variables.
6.EE.C.9 6.RP.A.3.A
Represent the relationship between two quantities in graphs, equations, and tables. (Part 1)
Represent the relationship between two quantities in graphs, equations, and tables. (Part 2)
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