ALEX Classroom Resource

  

Grade 7 Mathematics Module 4, Topic B: Percent Problems Including More Than One Whole

  Classroom Resource Information  

Title:

 Grade 7 Mathematics Module 4, Topic B: Percent Problems Including More Than One Whole

URL:

 https://www.engageny.org/resource/grade-7-mathematics-module-4-topic-b-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Topic B, students create algebraic representations and apply their understanding of percent from Topic A to interpret and solve multi-step word problems related to markups or markdowns, simple interest, sales tax, commissions, fees, and percent error. They apply their understanding of proportional relationships from Module 1, creating an equation, graph, or table to model a tax or commission rate that is represented as a percent. Students solve problems related to changing percents and use their understanding of percent and proportional relationships to solve the following:  A soccer league has 300 players, 60% of whom are boys.  If some of the boys switch to baseball, leaving only 52% of the soccer players as boys, how many players remain in the soccer league?  Students determine that, initially, 100% = 60% = 40% of the players are girls and 40% of 300 equals 120.  Then, after some boys switched to baseball, 100% - 52% of the soccer players are girls, so 0.48p = 120, or p = 120/0.48.  Therefore, there are now 250 players in the soccer league. 

In Topic B, students also apply their understanding of absolute value from Module 2 when solving percent error problems. To determine the percent error for an estimated concert attendance of 5,000 people, when actually 6,372 people attended, students calculate the percent error as (|5000 - 6372|)/|6372|, which is about 21.5%. 

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
3. Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use proportional reasoning strategies including setting up and solving proportions to solve problems involving simple interest, tax, gratuities, commissions, fees, markups, percent increase, markdowns or percent decrease.

    • Example: Students might be asked to "order" from a menu for lunch then calculate the tax and gratuities to determine the total cost.
Teacher Vocabulary:
  • Proportion
  • Simple interest
  • Tax
  • Gratuities
  • Commissions
  • Fees
  • Markups and markdowns
  • percent increase and percent decrease
Knowledge:
Students know:
  • how to interpret a real-world problem to determine what is being asked.
  • Techniques for calculating and using percents to solve problems in context.
  • how to interpret the solution in the context of the problem.
Skills:
Students are able to:
  • Write and solve proportions to help them solve real-world problems involving percent.
  • Solve problems that require them to calculate: simple interest, tax, gratuities, commission, fees, mark ups, markdowns, percent increase and percent decrease.
Understanding:
Students understand that:
  • percents relate to real-world contexts, and how to determine the reasonableness of their answers based on that context.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.3.1: Define interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
M.7.3.2: Apply definitions to context in real-world problems.
M.7.3.3: Solve proportional problems.
M.7.3.4: Recall how to find percent and ratios.
M.7.3.5: Recall steps for solving multi-step problems.

Prior Knowledge Skills:
  • Define percent.
  • Calculate a proportion for missing information.
  • Identify a proportion from given information.
  • Solve a proportion using part over whole equals percent over 100.
  • Define equation and variable.
  • Set up an equation to represent the given situation, using correct mathematical operations and variables.
  • Identify the unknown, in a given situation, as the variable.
  • Solve the equation represented by the real-world situation.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.3 Calculate 10%, 20%, 25%, and 50% of a number up to 100.
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
3. Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease. [Grade 7, 3]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use proportional reasoning strategies including setting up and solving proportions to solve problems involving simple interest, tax, gratuities, commissions, fees, markups, percent increase, markdowns or percent decrease.

    • Example: Students might be asked to "order" from a menu for lunch then calculate the tax and gratuities to determine the total cost.
Teacher Vocabulary:
  • Proportion
  • Simple interest
  • Tax
  • Gratuities
  • Commissions
  • Fees
  • Markups and markdowns
  • Percent increase
  • Percent decrease
Knowledge:
Students know:
  • how to interpret a real-world problem to determine what is being asked.
  • how to interpret the solution in the context of the problem.
Skills:
Students are able to:
  • Write and solve proportions to help them solve real-world problems involving percent.
  • Solve problems that require them to calculate: simple interest, tax, gratuities, commission, fees, mark ups, markdowns, percent increase and percent decrease.
Understanding:
Students understand that:
  • proportional reasoning requires interpretation or making sense of percent problems.
  • Solving problems and determining their calculated answers may require further computation.
Diverse Learning Needs:
Tags: absolute value, algebra, commission, equation, fee, graph, gratuity, markdown, markup, percent, percent decrease, percent error, percent increase, proportion, simple interest, table, tax, tip, word problem
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Comments

There are five lessons in this topic.

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Author: Hannah Bradley
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