Standard #: MA.912.AR.10.1


This document was generated on CPALMS - www.cpalms.org



Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.


Examples


Tara is saving money to move out of her parent’s house. She opens the account with $250 and puts $100 into a savings account every month after that. Write the total amount of money she has in her account after each month as a sequence. In how many months will she have at least $3,000?

General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment


Terms from the K-12 Glossary

  • Arithmetic sequence
 

Vertical Alignment

Previous Benchmarks

Next Benchmarks

 

Purpose and Instructional Strategies

In Algebra I, students wrote and solved equations of linear functions. In Math for Data and Financial Literacy, students write and solve problems using arithmetic sequences. 
  • Instruction focuses on real-world contexts involving arithmetic sequences (MTR.7.1). 
  • Students may use a variety of representations to solve problems such as writing out the sequence using the explicit formula. The focus of the benchmark is to understand arithmetic sequences and how they relate to linear equations (MTR.2.1). 
    • In the example given in the benchmark, students are asked to write the total amount of money she has in her account after each month as a sequence. In how many months will she have at least $3,000? The sequence goes as follows: 350, 450, 550, 650, 750, 850, 950, 1050, 1150, 1250, 1350, 1450, 1550, 1650, 1750, 1850, 1950, 2050, 2150, 2250, 2350, 2450, 2550, 2650, 2750, 2850, 2950, 3050, ...
      Once students have written the sequence, they can simply count the number of months it takes to get to at least $3,000. It would take 28 months. 
    • Another method to solve this would be to use the explicit formula. In the case of using the explicit formula, students would not need to write as many terms in the sequence since solving the problem this way would not involve counting all the terms until getting to $3,000. When using the explicit formula, arithmetic sequences have a linear relationship where the constant change is the slope while the y-intercept is the starting amount. Students can use the equation y = 100x + 250, where x is the number of months and y is the amount of money in her account. To solve this problem students would substitute $3,000 with the y-value.
      3000 = 100x + 250
      2750 = 100x
      27.5 = x
  • Since she is only putting money in once per month, the x would need to be a whole number. She wouldn’t quite have $3,000 after 27 months so the solution would need to be rounded up to 28 months (MTR.6.1).
    • If the y-intercept is unknown, students can use point-slope form of a line and any term in the sequence to write the formula for the sequence. For example, in the second month she has $450. Using point-slope form of a line, students get y − 450 = 100(x − 2). 
      y  − 450 = 100(x − 2)
      3000 − 450 = 100x − 200
      2550 = 100x − 200
      2750 = 100x
      27.5 = x
 

Common Misconceptions or Errors

  • Students may have a hard time distinguishing between arithmetic sequences and geometric sequences. 
  • Students may have trouble using the equation by confusing the slope and y-intercept or not knowing to use point-slope form when the y-intercept is unknown. 
  • Students may not round correctly when needed depending on the context.
 

Instructional Tasks

Instructional Task 1 (MTR.2.1, MTR.7.1
  • Albuquerque boasts one of the longest aerial trams in the world. The tram transports people up to Sandia Peak. The table shows the elevation of the tram at various times during a particular ride. The tram increases elevation by 255 feet every minute. After 1 minute, the elevation of the tram is 6,814 feet.
    • Part A. What was the elevation at the beginning of the ride?
    • Part B. If the ride took 15 minutes, what was the elevation of the tram at the end of the ride?
 

Instructional Items

Instructional Item 1 
  • In a theater, there are 16 seats in the first row and the number of seats in each row after that increase by 2 successively. There are 35 rows in the theater. How many seats does the last row in the theater have?
    a. 65
    b. 78
    c. 84
    d. 86

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1202340: Precalculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1212300: Discrete Mathematics Honors (Specifically in versions: 2022 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))
1209315: Mathematics for ACT and SAT (Specifically in versions: 2022 and beyond (current))


Related Resources

Lesson Plan

Name Description
Plants versus Pollutants Model Eliciting Activity

The Plants versus Pollutants MEA provides students with an open-ended problem in which they must work as a team to design a procedure to select the best plants to clean up certain toxins. This MEA requires students to formulate a phytoremediation-based solution to a problem involving cleaning of a contaminated land site. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Printed On:3/29/2024 12:20:02 AM
Print Page | Close this window