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Standards-based assessment and Instruction

Instructional Task: Grade 5

Phoning New Friends

Task

Sarah becomes close friends with five other soccer players at soccer camp. Upon returning home, Sarah speaks to each new friend for five minutes three times a week. Sarah's parents need to decide on a phone plan. Below are two phone plans that the parents are considering.

  Flat Rate Cost Per Minute
Low Rate Phone Plan $15.00 Per Month  $0.15 Per Minute
Talk-A-Lot Phone Plan $30.00 per month $0.10 Per Minute

Sarah's parents want Sarah to determine which plan costs less because Sarah's parents want to spend as little as possible for all of Sarah's phone calls. Sarah decides to use the greater than, less than, equal to symbols on a paper to compare the plans. What could the paper show? Which plan should Sarah's family use? Show all of your mathematical thinking.

Alternative Versions of Task

More Accessible Version

Sarah becomes close friends with three other soccer players at soccer camp. Upon returning home, Sarah speaks to each new friend for five minutes three times a week. Sarah's parents need to decide on a phone plan. Below are two phone plans that the parents are considering.


Flat Rate
Cost Per Minute
Low Rate Phone Plan
$15.00 Per Month  $0.15 Per Minute
Talk-A-Lot Phone Plan
$30.00 per month $0.10 Per Minute

Sarah's parents want Sarah to determine which plan costs less because Sarah's parents want to spend as little as possible for all of Sarah's phone calls. Sarah decides to write the greater than, less than, equal to symbols on paper to compare the plans. What could the paper show? Which plan should Sarah's family use? Show all of your mathematical thinking.

More Challenging Version

Sarah becomes close friends with ten other soccer players at soccer camp. Upon returning home, Sarah speaks to each new friend for five minutes three times a week. Sarah's parents need to decide on a phone plan. Below are two phone plans that the parents are considering.


Flat Rate
Cost Per Minute
Low Rate Phone Plan
$15.00 Per Month  $0.15 Per Minute
Talk-A-Lot Phone Plan
$30.00 per month $0.10 Per Minute

Sarah's parents want Sarah to determine which plan costs less because Sarah's parents want to spend as little as possible for all of Sarah's phone calls. Sarah decides to write the greater than, less than, equal to symbols on paper to compare the plans. What could the paper show? Which plan should Sarah's family use? Show all of your mathematical thinking.

 

 

Decimal Place Value Unit

The Decimal Place Value Unit involves understanding and representing the relative position, magnitude and relationships within the numeration system in order to answer questions such as:

  • How can you use the additive property of place value to decompose this decimal number?
  • How can you use the multiplicative property of place value to describe the meaning of each digit in the number 0.123?
  • How can you use the base ten property of place value to explain the relationship between each of the digits in the number 5.555?
Standards covered in this Unit include: 5.2A, 5.2B, 5.2C

Exemplars Task-Specific Evidence

This task requires students to multiply and add money amounts. Students must also make a comparison of money values.

TEKS Mathematical Process Standards

  • 5.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
  • 5.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. 
  • 5.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
  • 5.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
  • 5.1E The student is expected to create and use representations to organize, record, and communicate mathematical ideas.
  • 5.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. 

Underlying Mathematical Concepts

  • Compare decimals
  • Inequality/Equality symbols
  • Money Notation
  • Addition/Multiplication of decimals

Possible Problem-Solving Strategies

  • Model (manipulatives)
  • Diagram/Key
  • Table
  • Number line

Possible Mathematical Vocabulary/Symbolic Representation

  • Model
  • Diagram/Key
  • Table
  • Number line
  • Money notation ($, .)
  • Per
  • Total/Sum
  • Product
  • Equivalent/Equal to
  • Greater than (>)/Less than (<)
  • Minute, hour
  • Pattern
  • Graph
  • Rate
  • Multiples

Possible Solutions

The cost of the Low Rate Phone Plan = the cost of the Talk-A-Lot Phone Plan. Both plans cost the same, so Sarah's family could select either plan.

 

 

 

 

 

 

 

 

 

 

 

 

More Accessible Version Solution

The cost of the Low Rate Phone Plan < the cost of the Talk-A-Lot Phone Plan. Sarah's family should select the Low Rate Phone Plan.

More Challenging Version Solution

The cost of the Talk-A-Lot Phone Plan < the cost of the Low Rate Phone Plan. Sarah's family should select the Talk-A-Lot Phone Plan.

Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

  • 75 minutes per week is 1 1/4 hours.
  • 15 minutes is 1/4 hour, or 0.25 of an hour.
  • If Sarah talks a total of 100 minutes per week, the Talk-A-Lot Phone Plan is less expensive than the Low Rate Phone Plan.
  • Patterns: Friends +1, Cost per week +$2.25 for Low Rate Phone Plan and +1.50 for Talk-A-Lot Phone Plan.
  • The Talk-A-Lot Phone Plan is $0.75 < the Low Rate Phone Plan per week.
  • Relate to a similar task and state a math link.

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Here's What People Are Saying

The Exemplars program is designed to assess students' problem-solving and mathematical-communication skills. It also supports higher-level thinking and extension of mathematical reasoning.

S. Dement
Teacher

Converse, TX

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