Standards-based assessment and Instruction

One Thousand Sea Shells

Emily and Kayla collect sea shells. Emily has 400 + 90 + 2 sea shells. Kayla has four hundred ninety-four sea shells. Emily and Kayla put all the sea shells on a large tray and start to count them. Emily wants to have a total of one thousand sea shells. After counting for a while, Kayla thinks they will each have to find seven more sea shells. Is Kayla correct? Show all your mathematical thinking.

Place Value Unit

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

• How could you use base-10 blocks to show what the numerals in this number mean?
• How can you use the additive property of place value to decompose this number?
• What other way(s) can you use thousands, hundreds, tens, and ones to show this number without changing its value?
Standards covered in this Unit include: 2.2B, 2.2C, 2.3A, 2.7B

Students are expected to use different representations of whole numbers to find sums and differences.

TEKS Mathematical Process Standards

• 2.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
• 2.1B 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.
• 2.1E The student is expected to create and use representations to organize, record, and communicate mathematical ideas.
• 2.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Underlying Mathematical Concepts

• Additive Property of the Base-10 Number System
• Finding sums when the parts are known and differences when the whole and one part is known.
• Number sense to 1,000
• Comparison

Possible Problem-Solving Strategies

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

Formal Mathematical Language and Symbolic Notation

• Model
• Table
• Diagram/Key
• Number line
• Total/Sum
• Part/Whole
• Odd/Even
• Subtrahend/Minuend
• Difference
• Amount
• Expanded notation/Standard notation
• Rule
• Per
• Equivalent/Equal to
• Equal share
• Ones, tens, hundreds, thousands

Possible Solutions

Yes, Kayla is correct.

Possible Connections

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

• Kayla has 2 more sea shells than Emily.
• Both girls have the same number of hundreds and tens, but different numbers in the ones place.
• They both have an even number of shells. Even + Even = Even
• 494 = 400 + 90 + 4
• Both girls had an estimation of 500 sea shells.
• Solve more than one way to verify the answer.

Scoring Rationales and Corresponding Anchor Papers

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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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