Curriculum / Math / 6th Grade / Unit 6: Equations and Inequalities / Lesson 1
Math
Unit 6
6th Grade
Lesson 1 of 14
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Represent equations in the form $${ x+p=q }$$ and $${px=q}$$ using tape diagrams and balances.
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.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Students begin this unit by visually representing equations in diagrams, including familiar representations such as tape diagrams and some new ones such as balances and mobiles. This will help to support students’ understanding at a concrete level before they learn efficient ways to solve equations using inverse operations.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
There are nine small boxes. They all look exactly the same, but one is a bit heavier than the others. Jake says, “I can use the scales to find the heavy box in just two steps!”
a. This is what Jake does first. Explain what Jake now knows about the heavy box.
b. Then Jake does this. Which is the heavy box? Explain how you know.
Boxes of the Performance Assessment Tasks created by the by the Mathematics Assessment Resource Service (MARS) of the Shell Centre for Mathematical Education, University of Nottingham, England are made available by Inside Mathematics under a license from Shell Centre Publications. Accessed Feb. 27, 2018, 11:15 a.m..
Two tape diagrams are shown below. For each situation described in parts (a) and (b), choose the tape diagram that represents it. Explain your reasoning.
Tape Diagram 1:
Tape Diagram 2:
a. Situation A: As party favors, Stephanie makes 5 bags and puts an equal number of pieces of candy in each bag. Stephanie uses a total of 20 pieces of candy.
b. Situation B: At a restaurant, a glass holds some water in it. The waitress comes by and adds 5 ounces of water to the glass. There are now 20 ounces of water in the glass.
For each mobile, determine the missing value. Then write an equation to represent the situation, using the variable $${x }$$ to represent the missing value.
a.
b.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Draw a tape diagram or balance for each equation or situation below.
a. You purchase 4 gift cards, each in the same amount. You spend a total of $60.
b. $${x+6=18}$$
c. $${6x=18}$$
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 2
Topic A: Reasoning About and Solving Equations
6.EE.B.6 6.EE.B.7
Define and identify solutions to equations.
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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