Standards-based assessment and Instruction

# Math K-2

## Insect Collecting

Mrs. Best's class collected 24 insects on the playground. They decided to put them in netted cages to study them and then they would return them back to the playground. They had just enough cages to put 4 insects in each. How many netted cages did they have?

### Alternative Versions of the Task

#### More Accessible Version:

Mrs. Best's class collected 10 insects on the playground. They decided to put them in netted cages to study them and then they would return them back to the playground. They had just enough cages to put 2 insects in each. How many netted cages did they have?

#### More Challenging Version:

Mrs. Best's class collected 27 insects on the playground. They decided to put them in netted cages to study them and then they would return them back to the playground. They wanted to put 4 insects in each cage. How many netted cages would they need for the insects that they collected?

### NCTM Content Standards and Evidence

#### Number and Operations Standard for Grades Pre K-2:

Instructional programs from pre-kindergarten through grade 12 should enable all students to ...

• Understand meanings of operations and how they relate to one another.
• NCTM Evidence: Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.
• Exemplars Task-Specific Evidence: This task requires students to devise a way of dividing a two-digit whole number by four.

### Common Strategies Used to Solve This Task

Many students drew cages and counted as they put four insects in each cage.

### Possible Solutions

#### Original Version:

24 insects ÷ 4 insects = 6 cages

#### More Accessible Version:

10 insects ÷ 2 insects = 5 cages

#### More Challenging Version:

Mrs. Best's class would need 7 cages. They could put 4 insects in 6 of the cages and they
would need an additional cage for the remaining 3 insects.

General Notes: This task will elicit a math representation but may be limited in math notation.

Click on a level for student example.
Novice The Novice will not be able to understand the idea of putting four insects in each cage. Arguments are made with no mathematical basis. Little or no math language will be used. Correct reasoning of justification for reasoning will not present.
Apprentice The Apprentice may use a partially correct strategy or a correct strategy for only solving part of the task. A mathematical error may be made somewhere in the solution. Or the solution may be correct but without the supporting labeled representation, connections or observations and mathematical language, the solution will not rise to a Practitioner level.
Practitioner The Practitioner will achieve a correct solution and have all the supporting work needed to communicate their strategy and mathematical reasoning. A connection or observation about the problem is needed (for example, the connection to counting by four). An accurate and appropriate mathematical representation will be constructed.
Expert The Expert will achieve a correct solution. Evidence will be used to justify and support decisions made and conclusions reached (for example, by solving the problem in more than one way to verify the solution). A sense of audience and purpose will be communicated by using precise math language to consolidate math thinking and to communicate ideas. Mathematical connections or observations will be made and mathematical representation will be used to extend thinking and clarify or interpret the solution.

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## Here's What People Are Saying

Our school subscribes to the Exemplars Library. I find the formative tasks aligned to the Common Core are strong and can be easily embedded in any curriculum. Having a more accessible and more challenging version of each task provides teachers' support as they have the resources to problem solve across different levels of understanding in their classrooms … Students are enjoying the tasks and are demonstrating a deeper understanding of the underlying concepts of the standards as they apply formal math language, accurate representations and connections.

C. Hemley

Principal

PS 94
New York

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