Equations and Inequalities

Lesson 1

Math

Unit 6

6th Grade

Lesson 1 of 14

Objective


Represent equations in the form $${ x+p=q }$$ and $${px=q}$$ using tape diagrams and balances.

Common Core Standards


Core Standards

  • 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.

Criteria for Success


  1. Understand that an equation represents a statement of balance between two expressions. 
  2. Draw tape diagrams to represent situations and equations.
  3. Write equations to represent diagrams such as tape diagrams and balanced mobiles.

Tips for Teachers


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. 

Lesson Materials

  • Optional: Balance scale (Teacher set)
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Anchor Problems

25-30 minutes


Problem 1

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.

Guiding Questions

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Student Response

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References

Inside Mathematics Performance Assessment Tasks Grades 3-High School Boxes

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..

Modified by Fishtank Learning, Inc.

Problem 2

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. 

Guiding Questions

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Student Response

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Problem 3

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.   

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


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.   $${6x=18}$$

Student Response

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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 where students draw models for equations and vice versa; include equations in the form $${x+p=q}$$  and $${px=q}$$
  • SolveMe Mobiles (Stick to mobiles with one unknown and one tier of balances; others can be given as challenges)

Next

Define and identify solutions to equations.

Lesson 2
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Reasoning About and Solving Equations

Topic B: Reasoning About and Solving Inequalities

Topic C: Representing and Analyzing Quantitative Relationships

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