problem solving two step problems lesson 7.10 answer key

• Privacy Policy
• Terms of Use

Processing Request...

• AP Calculus
• AP Statistics
• Independent Study

Online Math Class

Mr. Math Blog

Thanks for your donation!  Every little bit helps me help you!  :-)

Problem Solving - Organize Data - Lesson 2.1

Use Picture Graphs - Lesson 2.2

Make Picture Graphs - Lesson 2.3

Use Bar Graphs - Lesson 2.4

Make a Bar Graph - Lesson 2.5

Solve Problems Using Data - Lesson 2.6

Use and Make Line Plots - Lesson 2.7

Number Patterns - Lesson 1.1

Round to Nearest Ten or Hundred - Lesson 1.2

Estimate Sums - Lesson 1.3

Mental Math Strategies for Addition - Lesson 1.4

Use Properties to Add - Lesson 1.5

Use the Break Apart Strategy to Add - Lesson 1.6

Use Place Value to Add - Lesson 1.7

Estimate Differences - Lesson 1.8

Mental Math Strategies for Subtraction - Lesson 1.9

Use Place Value to Subtract - Lesson 1.10

Combine Place Values to Subtract - Lesson 1.11

Describe Plane Shapes - Lesson 12.1

Describe Angles in Plane Shapes - Lesson 12.2

Identify Polygons - Lesson 12.3 ​

Describe Sides of Polygons - Lesson 12.4

​ Classify Quadrilaterals - Lesson 12.5

​Draw Quadrilaterals - Lesson 12.6

Describe Triangles - Lesson 12.7

Chapter 12 Performance Task Review For Test

Problem Solving - Compare Fractions - Lesson 9.1

Compare Fractions with the Same Denominator - Lesson 9.2

Compare Fractions with the Same Numerator - Lesson 9.3

Compare Fractions - Lesson 9.4

Compare and Order Fractions - Lesson 9.5

Model Equivalent Fractions - Lesson 9.6

Equivalent Fractions - Lesson 9.7

Divide by 2 - Lesson 7.1

Divide by 10 - Lesson 7.2

Divide by 5 - Lesson 7.3

Divide by 3 - Lesson 7.4

Divide by 4 - Lesson 7.5

Divide by 5 - Lesson 7.6

Mid-Chapter 7 Checkpoint on Division Facts and Strategies

Divide by 7 - Lesson 7.7

Divide by 8 - Lesson 7.8

Divide by 9 - Lesson 7.9

Problem Solving - Two-Step Problems - Lesson 7.10

Order of Operations - Lesson 7.11

Problem Solving - Model Division - Lesson 6.1

Size of Equal Groups - Lesson 6.2

Number of Equal Groups - Lesson 6.3

Model (Division) with Bar Model - Lesson 6.4

Relate Subtraction and Division - Lesson 6.5

Mid-Chapter 6 Checkpoint

Model (division) with Arrays - Lesson 6.6

Relate Multiplication and Division - Lesson 6.7

Write Related Facts - Lesson 6.8

Division Rules for 1 and 0 - Lesson 6.9

Chapter 6 Review for Test - Understanding Division

Multiply with 2 and 4 - Lesson 4.1

Multiply with 5 and 10 - Lesson 4.2

Multiply with 3 and 6 - Lesson 4.3

Distributive Property - Lesson 4.4

Multiply with 7 - Lesson 4.5

Associative Property of Multiplication - Lesson 4.6

Patterns on the Multiplication Table - Lesson 4.7

Multiply with 8 - Lesson 4.8

Multiply with 9 - Lesson 4.9

Review For Test on Chapter 4

Describe Patterns - Lesson 5.1

Find Unknown Factors - Lesson 5.2

Problem Solving: Using the Distributive Property - Lesson 5.3

Multiplication Strategies with Multiples of 10 - Lesson 5.4

Multiply Multiples of 10 by 1-Digit Numbers - Lesson 5.5

Chapter 5 Review on Multiplication Facts

Third Grade

      Math

• Second Grade Math
• Third Grade Math
• Fourth Grade Math
• Fifth Grade Math
• Sixth Grade Math
• Sixth Grade Math (CA)
• Seventh Grade Math (CA)
• Eighth Grade Math (CA)
• Integrated Math 1
• Integrated Math 2
• Integrated Math 3
• PreCalculus
• AP Statistics Exam Prep
• Elementary Statistics
• ELM Practice
• Percents and Decimals
• Sixth Grade Math (Big Ideas)

Model Perimeter - Lesson 11.1

Find Perimeter - Lesson 11.2

Find Unknown Side Lengths - Lesson 11.3

Understanding Area - Lesson 11.4

Measure Area - Lesson 11.5

Use Area Models - Lesson 11.6

Problem Solving - Area of Rectangles - Lesson 11.7

Area of Combined Rectangles - Lesson 11.8

Same Perimeter - Different Area - Lesson 11.9

Same Area - Different Perimeter - Lesson 11.10

Chapter 11 Review for Test on Perimeter and Area

Please Donate, if you're a regular!

The donate link is below. Thanks so much!!

Count Equal Groups - Lesson 3.1

Relate Addition and Multiplication - Lesson 3.2

Skip Count on a Number Line - Lesson 3.3

Problem Solving - Model Multiplication - Lesson 3.4

Model with Arrays - Lesson 3.5

Commutative Property of Multiplication - Lesson 3.6

Multiply with 1 and 0 - Lesson 3.7

Time to the Minute - Lesson 10.1

A.M. and P.M. - Lesson 10.2

Measure Time Intervals - Lesson 10.3

Use Time Intervals - Lesson 10.4

Problem Solving - Time Intervals - Lesson 10.5

Measure Length - Lesson 10.6

Estimate and Measure Liquid Volume - Lesson 10.7

Estimate and Measure Mass - Lesson 10.8

Equal Parts of a Whole - Lesson 8.1

Equal Shares - Lesson 8.2

Unit Fractions of a Whole - Lesson 8.3

Fractions of a Whole - Lesson 8.4

Fractions on a Number Line - Lesson 8.5

Relate Fractions and Whole Numbers - Lesson 8.6

Fractions of a Group - Lesson 8.7

Find Part of Group Using Unit Fractions - Lesson 8.8

Problem Solving: Find the Whole Using Unit Fractions - Lesson 8.9

Copyright 2013. All rights reserved.

GoMath! 7.10 Problem Solving - Multistep Fraction Problems

By heidi befort on jan 15, 2013.

About FAQ Contact Terms Privacy © 2024 Educreations, Inc.

Curriculum  /  Math  /  7th Grade  /  Unit 1: Proportional Relationships  /  Lesson 10

Proportional Relationships

Lesson 10 of 18

Criteria for Success

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

Make connections between the four representations of proportional relationships (Part 1).

Common Core Standards

Core standards.

The core standards covered in this lesson

Ratios and Proportional Relationships

7.RP.A.2 — Recognize and represent proportional relationships between quantities.

7.RP.A.2.A — Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Foundational Standards

The foundational standards covered in this lesson

6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

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

• Identify the constant of proportionality in graphs, equations, and tables.
• Represent and analyze proportional relationships in graphs, equations, and tables.

Suggestions for teachers to help them teach this lesson

Lessons 10 and 11 pull together all the representations of proportional relationships – written description, table, graph, and equation – that students have been studying since the beginning of the unit. As needed, review any one representation that students may be stuck on, but continue to engage them in looking at multiple representations at a time in order to strengthen the connections between them. 

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

A scientist plants a seed in a laboratory and tracks the growth of the plant. The height of the plant in centimeters is proportional to the number of days since it was planted.

a.   Explain what point B represents in context of the situation.

b.   At what rate is the plant growing? Indicate this as a point on the graph.

c.   Write an equation that represents the relationship between days and height. 

d.   If the plant continues to grow at this rate, how tall will it be after 12 days?

e.   If the plant continues to grow at this rate, when will it be 6 cm tall?

Guiding Questions

Match each table to its equation.

i.    $${y = {1 \over 2}x}$$

ii.    $${y = {2 \over 3}x}$$

iii.    $${y = 2x}$$

iv.    $${y=3x}$$

The cost you pay for limes is proportional to the number of limes you buy. Four different stores sell limes for different amounts, as shown in the graphs, table, and equation below. Which store should you go to if you want to pay the least amount for limes? Explain your answer.

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

The width of a small book measures 6 inches, or approximately 15 centimeters. You know that the relationship between inches and centimeters is proportional, but you can’t remember the conversion rate between them. 

Let $$y$$  represent the number of centimeters and   $$x$$   represent the number of inches. Represent the relationship in the coordinate plane below, and then write an equation that approximates the relationship between inches and centimeters.

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.

• MARS Summative Assessment Tasks for Middle School Buses
• SERP Poster Problems Drag Racer Dragonfly
• EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 8 — Example 2, Exit Ticket, Problem Set 5-6
• MARS Formative Assessment Lessons for Grade 7 Representing: Road Race

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Solve ratio and rate problems using double number lines, tables, and unit rate.

7.RP.A.1 7.RP.A.2

Represent proportional relationships in tables, and define the constant of proportionality.

7.RP.A.2 7.RP.A.2.B

Determine the constant of proportionality in tables, and use it to find missing values.

7.RP.A.2.A 7.RP.A.2.B

Write equations for proportional relationships presented in tables.

7.RP.A.2.B 7.RP.A.2.C

Write equations for proportional relationships from word problems.

7.RP.A.2 7.RP.A.2.C

Represent proportional relationships in graphs.

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.D

Interpret proportional relationships represented in graphs.

7.RP.A.2 7.RP.A.2.D

Create a free account to access thousands of lesson plans.

Already have an account? Sign In

Topic B: Non-Proportional Relationships

Compare proportional and non-proportional relationships.

Determine if relationships are proportional or non-proportional.

Topic C: Connecting Everything Together

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Make connections between the four representations of proportional relationships (Part 2).

Use different strategies to represent and recognize proportional relationships.

Topic D: Solving Ratio & Rate Problems with Fractions

Find the unit rate of ratios involving fractions.

Find the unit rate and use it to solve problems.

7.RP.A.1 7.RP.A.3

Solve ratio and rate problems by setting up a proportion.

Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.

Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.

Use proportional reasoning to solve real-world, multi-step problems.

7.RP.A.1 7.RP.A.2 7.RP.A.3

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School information, what courses are you interested in, are you interested in onboarding professional learning for your teachers and instructional leaders, any other information you would like to provide about your school.

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

1.7: Solving Multistep Conversion Problems

• Last updated
• Save as PDF
• Page ID 88316

Multiple Conversions

Sometimes you will have to perform more than one conversion to obtain the desired unit. For example, suppose you want to convert 54.7 km into millimeters. We will set up a series of conversion factors so that each conversion factor produces the next unit in the sequence. W e first convert the given amount in km to the base unit which is meters. We know that 1,000 m =1 km.

Then we convert meters to mm, remembering that \(1\; \rm{mm}\) = \( 10^{-3}\; \rm{m}\).

Concept Map

Calculation

\[ \begin{align} 54.7 \; \cancel{\rm{km}} \times \dfrac{1,000 \; \cancel{\rm{m}}}{1\; \cancel{\rm{km}}} \times \dfrac{1\; \cancel{\rm{mm}}}{\cancel{10^{-3} \rm{m}}} & = 54,700,000 \; \rm{mm} \\ &= 5.47 \times 10^7\; \rm{mm} \end{align}\]

In each step, the previous unit is canceled and the next unit in the sequence is produced, each successive unit canceling out until only the unit needed in the answer is left.

Example \(\PageIndex{1}\): Unit Conversion

Convert 58.2 ms to megaseconds in one multistep calculation.

Example \(\PageIndex{2}\): Unit Conversion

How many seconds are in a day?

Exercise \(\PageIndex{1}\)

Perform each conversion in one multistep calculation.

• 43.007 ng to kg
• 1005 in to ft
• 12 mi to km

Career Focus: Pharmacist

A pharmacist dispenses drugs that have been prescribed by a doctor. Although that may sound straightforward, pharmacists in the United States must hold a doctorate in pharmacy and be licensed by the state in which they work. Most pharmacy programs require four years of education in a specialty pharmacy school. Pharmacists must know a lot of chemistry and biology so they can understand the effects that drugs (which are chemicals, after all) have on the body. Pharmacists can advise physicians on the selection, dosage, interactions, and side effects of drugs. They can also advise patients on the proper use of their medications, including when and how to take specific drugs properly. Pharmacists can be found in drugstores, hospitals, and other medical facilities. Curiously, an outdated name for pharmacist is chemist , which was used when pharmacists formerly did a lot of drug preparation, or compounding . In modern times, pharmacists rarely compound their own drugs, but their knowledge of the sciences, including chemistry, helps them provide valuable services in support of everyone’s health.

A woman consulting with a pharmacist. This image was released by the National Cancer Institute, an agency part of the National Institutes of Health. Image used with permission (Public Domain; Rhoda Baer (Photographer) via NIH).

In multistep conversion problems, the previous unit is canceled for each step and the next unit in the sequence is produced, each successive unit canceling out until only the unit needed in the answer is left.

Contributors

Two Step Equations Puzzles TEKS 7.10 7.11 - Math Game - Math Activity

Learning Objective

Students will demonstrate an understanding of solving and understanding two-step equations.

Description

In this HANDS-ON activity, students will work to solve two-step equations. This low-prep, ready-to-print activity is a perfect addition to your classroom at any time.

In this activity, students will use all operations to solve two-step equations with one variable.

Included in this Download:

• Teacher Directions
• Student Directions
• Two-Step Equations Matching Puzzles (20 matches)
• Two-Step Equations Matching Puzzles Recording Sheet
• Two-Step Equations Matching Puzzles Answer Key

** Want to know more? Check out the video here to learn more about the Seventh Grade Math Workshop Concept-Based Activities !**

This activity, and SEVEN more, can be found in the Seventh Grade Unit Three Write, Model, and Solve Two-Step Equations Unit . The unit bundle also includes alignment guides and activity labels.

Interested in the Math Workshop FREE Sampler? Grab the Sampler and enjoy!

*************************

→ Did you know that you can get CREDITS for future purchases by leaving feedback on each of your purchases? Simply navigate to the My Purchases page and next to each download you will be able to leave a star rating and comments about the activities you have purchased. I truly value your feedback and consider each and every word left.

Personal Copyright: The purchase of this product allows you to use these activities in your personal classroom for your students. You may continue to use them each year but you may not share the activities with other teachers unless additional licenses are purchased. The license for this purchase is NON-TRANSFERABLE. Site and District Licenses are also available.

4mulaFun® , Flippables™ , and Solve and Snip™ are trademarks of Smith Curriculum and Consulting (formerly FormulaFun Inc. dba 4mulaFun), and are registered in the United States and abroad. The trademarks and names of other companies and products mentioned herein are the property of their respective owners. Copyright © Smith Curriculum and Consulting, Inc. All rights reserved.

DISCLAIMER: With the purchase of this file you understand that this file is not editable in any way. You will not be able to manipulate the lessons and/or activities inside to change numbers and/or words.

Questions & Answers

Smith curriculum and consulting.

• We're hiring
• Help & FAQ
• Privacy policy
• Student privacy
• Terms of service
• Tell us what you think