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Standards-based assessment and Instruction

Summative Assessment: Grade 4

A Computer Game

Task

Jaci and Emma are playing a game on their computer where a player earns points.

At the end of the first round:
Jaci has seventy-four thousand, two hundred sixteen points.
Emma has 70,000 + 4,000 + 100 + 80 + 9 points.

At the end of the second round:
Jaci has 52,000 + 200 + 30 + 1 points.
Emma has fifty-two thousand, sixty-eight points.

At the end of the third round:
Jaci has 62 thousand, 9 hundred seventy-nine points.
Emma has sixty-two thousand, nine hundred eighty-four points.

Jaci and Emma organize their points information together and use the greater than, less than, or equal sign to compare who made the most points in each round. How could Jaci and Emma organize their information and include the correct sign? Who made the most points in each round? Show all your mathematical thinking.

 

Whole Number and Decimal Place Value Unit

The Whole Number and 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 number?
  • How can you use the multiplicative property of place value to describe the meaning of each digit in the number 9,876,543.21?
  • How can you use the base ten property of place value to explain the relationship between each of the digits in the number 5,555,555.55?
  • How can you use base ten blocks or money to represent this decimal? What is ONE?
Standards covered in this Unit include: 4.2A, 4.2B, 4.2C, 4.2D, 4.2E, 4.2F, 4.2G, 4.2H, 4.3G

Exemplars Task-Specific Evidence

This task requires students to read and write multi-digit whole numbers in a variety of forms. Students will also use inequality symbols to compare multi-digit whole numbers.

TEKS Mathematical Process Standards

  • 4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
  • 4.1B 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.
  • 4.1E The student is expected to create and use representations to organize, record, and communicate mathematical ideas.
  • 4.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Underlying Mathematical Concepts

  • Base-10 place value system
  • Number sense to 74,216

Possible Problem-Solving Strategies

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

Possible Mathematical Vocabulary/Symbolic Representation

  • Model
  • Diagram/Key
  • Chart
  • Number line
  • Base-10 blocks
  • Greater than (>)/Less than (<)
  • Equivalent/Equal to
  • Inequality
  • Per
  • Place value
  • Ones, tens, hundreds, thousands, millions
  • Odd/Even
  • Expanded notation
  • Additive Property
  • Ordinal numbers: 1st, 2nd, 3rd

Possible Solutions

Round 1: 74,216 > 74,189
Round 2: 52,231 > 52,068
Round 3: 62,979 < 62,984

Jaci wins rounds 1 and 2. Emma wins round 3.

 

 

 

 

Possible Connections

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

  • Jaci and Emma had a total of 148,405 points in round 1; 104,299 points in round 2; and 125,963 points in round 3.
  • The total combined points of both girls is 378,667.
  • There is a 27 point difference between Emma and Jaci in round 1; 163 point difference in round 2; and a 5 point difference in round 3.
  • Jaci has a total of 189,426 points.
  • Emma has a total of 189,241 points.
  • Relate to a similar task and state a math link.
  • 3 point totals are even numbers and 3 are odd.
  • Round 1 could be easier for both girls than round 2 because they both scored the most points in round 1.

Scoring Rationales and Corresponding Anchor Papers

Novice

Apprentice

Expert

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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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