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Unit 2: Solving equations with one unknown

About this unit.

Let's take your equation-solving skills to the next level! You'll learn all the strategies you need to confidently tackle problems with variables on both sides, parentheses, and more. Plus, you'll get plenty of practice with word problems to really solidify your understanding.

Equations with variables on both sides

  • Intro to equations with variables on both sides (Opens a modal)
  • Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
  • Equation with variables on both sides: fractions (Opens a modal)
  • Equation with the variable in the denominator (Opens a modal)
  • Equations with variables on both sides Get 3 of 4 questions to level up!
  • Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!

Equations with parentheses

  • Equations with parentheses (Opens a modal)
  • Multi-step equations review (Opens a modal)
  • Equations with parentheses Get 3 of 4 questions to level up!
  • Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!

Number of solutions to equations

  • Number of solutions to equations (Opens a modal)
  • Worked example: number of solutions to equations (Opens a modal)
  • Creating an equation with no solutions (Opens a modal)
  • Creating an equation with infinitely many solutions (Opens a modal)
  • Number of solutions to equations Get 3 of 4 questions to level up!
  • Number of solutions to equations challenge Get 3 of 4 questions to level up!

Equations word problems

  • Sums of consecutive integers (Opens a modal)
  • Sum of integers challenge (Opens a modal)
  • Solving equations with one unknown: FAQ (Opens a modal)
  • Sums of consecutive integers Get 3 of 4 questions to level up!

lesson 1 8 problem solving answers

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Big Ideas Math Common Core 8th Grade, Grade: 8 Publisher: Holt McDougal; Student edition

Big ideas math common core 8th grade, title : big ideas math common core 8th grade, publisher : holt mcdougal; student edition, isbn : 1608402266, isbn-13 : 978-1608402267, use the table below to find videos, mobile apps, worksheets and lessons that supplement big ideas math common core 8th grade..

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lesson 1 8 problem solving answers

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Math Books - Grade 8

lesson 1 8 problem solving answers

Grade 8 HMH Go Math - Answer Keys

Year Published: 2017

Description: Florida Common Core Standard Practice

lesson 1 8 problem solving answers

Grade 8 McGraw Hill Glencoe - Answer Keys

Year Published: 2019

Description: Grade 8 McGraw Hill Glencoe - Answer Keys

lesson 1 8 problem solving answers

What is Common Core

The Common Core is a set of high-quality academic standards in mathematics and English language arts/literacy (ELA).

These learning goals outline what a student should know and be able to do at the end of each grade.

Learn more »

What Parents Should Know

Today’s students are preparing to enter a world in which colleges and businesses are demanding more than ever before.

To ensure all students are ready for success after high school, the Common Core State Standards establish clear, consistent guidelines for what every student should know and be able to do in math and English language arts from kindergarten through 12th grade.

Common core - Common mistakes

Use the repeated-addition strategy to solve 5x3.

If you answer the question with 5+5+5=15, you would be wrong.

The correct answer is 3+3+3+3+3.

Mathematically, both are correct. But under Common Core, you're supposed to read 5x3 as "five groups of three." So "three groups of five" is wrong.

Getting started

Math Practice 101 gives you a powerful, patterns-based way to learn and practice for the upcoming Common Core Standard Test

Get more didactic materials

We offer school books, library books, test and practice worksheets to help you sharpen your math skills.

Free Online Tutor

As a registered member, you have access to our online tutors that will help you with any questions you might have.

Featured problem of the day

Family passes to an amusement park cost $54 each.

Which expression can be used to find the cost in dollars of 8 family passes?

  • A. (8+50) + (8+4)
  • B. (8+50) x (8+4)
  • C. (8x50) + (8x4)
  • D. (8x50) x (8x4)

Explanation:

Explanation : to solve this problem, we use the distributive property of multiplication.

54 can be re-writen as (50+4), hence:

54x8=(50+4)x8=50x8+4x8






















































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Chapter 1, Lesson 1: A Plan for Problem Solving

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Curriculum  /  Math  /  8th Grade  /  Unit 2: Solving One-Variable Equations  /  Lesson 10

Solving One-Variable Equations

Lesson 10 of 12

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Use equations to model a business plan and determine the break-even point.

Common Core Standards

Core standards.

The core standards covered in this lesson

Expressions and Equations

8.EE.C.7 — Solve linear equations in one variable.

Foundational Standards

The foundational standards covered in this lesson

7.EE.B.4 — Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

  • De-contextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in context of the problem (MP.2).
  • Write and solve equations to represent a real-world business plan (MP.4).

Suggestions for teachers to help them teach this lesson

There is only one Anchor Problem for this lesson, however, it is longer than usual. It can be done with the whole class, or students can tackle it in small groups. The Target Task has students create their own problem similar to the Anchor Problem. The Problem Set Guidance includes a variety of resources that involve real-world applications.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

Corey and Akila are making small wooden tables to sell at the school fair. They have some fixed costs and some variable costs. The fixed costs come to $160 and include things that only need to be purchased once, like an electric saw, measuring tools, and a work station. The variable costs come to $3.50 for each table and include the wood, nails, and glue needed for each table. Corey and Akila plan to sell each table for $10.

a.   Fill in the chart below for different numbers of tables sold at the school fair.

 

         

 

         

 

         

 

         

b.   Write an equation to represent this situation. Explain what each part of your equation represents. 

c.   How many tables do Corey and Akila need to sell to break even?

d.   How many tables do Corey and Akila need to sell to make a profit of $150?

Guiding Questions

A set of suggested resources or problem types that teachers can turn into a 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.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

Create your own business model, similar to Anchor Problem 1. 

  • What are you selling?
  • What are your fixed costs? Your variable costs?
  • How much will you sell each item for?
  • How many do you need to sell to break even? 

Show all of your work clearly and include an equation in your answer.

Student Response

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.

  • EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 9 — Exercises 3-10, Problem Set 2-7
  • EngageNY Mathematics Grade 8 Mathematics > Module 4 — Mid-Module Assessment (1-2)

Topic A: Simplifying Expressions and Verifying Solutions

Write equivalent expressions using properties of operations and verify equivalence using substitution.

Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.

Create a free account to access thousands of lesson plans.

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Topic B: Analyzing and Solving Equations in One Variable

Justify each step in solving a multi-step equation with variables on one side of the equation.

8.EE.C.7.A 8.EE.C.7.B

Write and solve multi-step equations to represent situations, with variables on one side of the equation.

Model with equations using a three-act task.

Solve equations with variables on both sides of the equal sign.

Write and solve multi-step equations to represent situations, including variables on both sides of the equation.

Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.

Solve and reason with equations with three types of solutions.

Topic C: Analyzing and Solving Inequalities in One Variable

Solve and graph inequalities with variables on one side of the inequality (optional).

Solve and graph inequalities with variables on both sides of the inequality (optional).

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lesson 1 8 problem solving answers

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  3. Lesson 1-8 Practice + Problem Solving Part 1

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VIDEO

  1. Class 8 Math Chapter 1

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  5. NCERT Solutions for Class 8 Maths Chapter 1 Exercise 1.2

  6. Unit 4, Lesson 8 Practice Problems (7th Grade Illustrative Math) IM 7.4.8

COMMENTS

  1. 8th Grade Math

    8th grade 7 units · 121 skills. Unit 1 Numbers and operations. Unit 2 Solving equations with one unknown. Unit 3 Linear equations and functions. Unit 4 Systems of equations. Unit 5 Geometry. Unit 6 Geometric transformations. Unit 7 Data and modeling. Course challenge.

  2. 8th grade (Illustrative Mathematics)

    These materials enable personalized practice alongside the new Illustrative Mathematics 8th grade curriculum. They were created by Khan Academy math experts and reviewed for curriculum alignment by experts at both Illustrative Mathematics and Khan Academy.

  3. Ready Mathematics Practice and Problem Solving Grade 8

    Find step-by-step solutions and answers to Ready Mathematics Practice and Problem Solving Grade 8 - 9781495704857, as well as thousands of textbooks so you can move forward with confidence.

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    Lessons 8 and 9 introduce students to the three types of solutions that an equation can have. This lesson focuses on students understanding what each solution means about the equation, and on becoming familiar with arriving at solutions that look like 4 = 2 or − 8 = − 8 (MP.2). In the next lesson, students will reason with all three types ...

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    In grade 8, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students solve systems of linear equations and compare properties of functions provided in different forms.

  7. Unit 2: Solving equations with one unknown

    Let's take your equation-solving skills to the next level! You'll learn all the strategies you need to confidently tackle problems with variables on both sides, parentheses, and more. Plus, you'll get plenty of practice with word problems to really solidify your understanding.

  8. Big Ideas Math Common Core 8th Grade

    Use the table below to find videos, mobile apps, worksheets and lessons that supplement Big Ideas Math Common Core 8th Grade.

  9. PDF NAME DATE PERIOD Lesson 8 Homework Practice

    lopeFor Exercises 1. and 2, graph the data. Then find t. e. lope. Explain what the slope represents.1. ENVELOPES The table shows the nu. el. pes Stuffed306090120Time (min)2. ME. T There are 3 feet for every yard.Yards3. Use the graph that s. ows the number of laps comp.

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  13. MathPractice101 Answer Keys Grade 8

    Common core - Common mistakes. Use the repeated-addition strategy to solve 5x3. If you answer the question with 5+5+5=15, you would be wrong. The correct answer is 3+3+3+3+3. Mathematically, both are correct. But under Common Core, you're supposed to read 5x3 as "five groups of three." So "three groups of five" is wrong.

  14. PDF Lesson 1.1 Worksheets and Homework

    Topic 1: Exploring problem-solving strategies 1.1 CONSOLIDATION ACTIVITY For the following problems, work with your partner to rewrite the shape equations using letters as variables. You can decide which letters to use for your variables. Example: using shapes ax A -12 Equations using shapes o -13 7 Equations using shapes 0+0 = 24 Equations using letters Equations using letters Puzzle 1 Puzzle ...

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    Problem 3 (from Unit 1, Lesson 1) The rectangle seen in Frame 1 is rotated to a new position, seen in Frame 2. Select all the ways the rectangle could have been rotated to get from Frame 1 to Frame 2. 40 degrees clockwise. 40 degrees counterclockwise. 90 degrees clockwise. 90 degrees counterclockwise. 140 degrees clockwise.

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    GEOMETRY For Exercises 1-3, use the following information. = 6 2 models the area of a triangle with base 3x and height 4x. Graph the equation. Explain why you only need to graph the function in the upper right quadrant. 2. Explain how to find the area of the triangle when x = 3 inches. Then find the area. 3.

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  20. Lesson 10

    Topic B: Analyzing and Solving Equations in One Variable. Justify each step in solving a multi-step equation with variables on one side of the equation. Write and solve multi-step equations to represent situations, with variables on one side of the equation. Model with equations using a three-act task.

  21. PDF Part 1: Introduction Problem Solving with Angles

    a right angle. The sum of their measures is. 908. /FOE measures 58°, and /EOD measures 32°. Two angles wh. se measures add to 908 are complementary angles. omplementary angles don't have to. les.ABF 58° OC 58° S TED32°32°On the p.

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  23. PDF Solving Percent Problems

    19. about 1.2 billion 20. about 1.2 billion 21. about 0.3 in. Practice and Problem Solving: C 1. less than; 25% is equivalent to 25 or 100 1, a fraction less than 1 A number 4 multiplied by a fraction less than 1 gives a product less than the original number.