Chapter 4 work - Salisbury University



Number Theory PROJECT (100 PTS)

Handout #2

This project should be a culmination of the work you have been doing in class. You will need to sift through that work and class discussion to complete this assignment. Note that this project is worth as much as a test. The writing you do for this is similar to what you will be required to do for your final portfolio and the rest of the class material. This project will be placed in your final portfolio.

Chapter 4: Basic number theory concepts

multiple divisor/factor prime number composite number

greatest common factor common multiple least common multiple

even number odd number

This chapter covers some basic number theoretic concepts that are covered in the middle grades. These ideas can be developed intuitively at the lower grades without the formal definitions. With the nine concepts listed above, do the following:

A. Provide a conceptual explanation (description) for the concept.

The description/explanation of a concept should precede the formal definition (in most cases). Each conceptual explanation should use your own words to describe the important features of the concept. It should include the following:

• How to share the concept with a child using the rectangular arrays, tile sequences, skip counting, and/or the C. rods (make sure to explain with diagrams and words each method that works for the concept- for example, since multiple can be shared using rectangular arrays, skip counting, and the C. rods you would explain how each of these 3 methods models the concept). When explaining how the models work, make sure to include:

o at least 5 examples of the concept

o at least one “non-example” of the concept- explain why

o Diagrams that illustrate your ideas and support and are supported by explanations

• any subtleties about the concept that may cause difficulty in understanding or working with the concept

B. Provide a personal (unique) metaphor for the concept. You need to discuss what makes your metaphor work (the ground) and how it differs from the concept (the tension). You may share these with your group members but each individual needs to have their own.

Metaphor example “Prime numbers” are building blocks for the integers because I can use them to make ANY integer by multiplying the appropriate primes together. So if you give me a number I can find the building blocks (or primes) used to make it. The building blocks of 10 are 2 and 5 since 2x5=10 and the building blocks of 18 are 2 and 3 since 2x3x3 = 18.

C. Provide a definition (in your own words) of the concept. Your definition will be a “cliffs notes” version of your description from part A. Make sure that this definition:

1) Defines the concept completely so that someone else reading the definition

would come up with examples that work.

2) Is not just a book definition, but is one that you write.

D. Explain how these concepts are related to one another by using a “concept web”. I will explain what this is in class.

Project specifications

• Make sure that your work is either typed or very neatly written with NO cross-outs. You may do a mix of typing and hand-drawn diagrams.

• Diagrams should be included for each concept as the models are all visual models and hence their power will lie in their pictures. You should also make sure your diagrams go along with your explanations and vice versa. I would say a minimum of 5 diagrams per concept should be included.

• If one of the models (arrays, C. rods, skip counting, and tile sequences) can be used to explain the concept then it should be included in the conceptual explanation portion of the concept.

• Each concept should probably take up about 1.5-2 pages once you include all of the explanations and diagrams.

• The concept web will take about 1 page and should be included at the end of your packet.

• For each concept, you should first include part A, followed by part B, then part C. Part D should be done at the very end.

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Rubric

Level 4 – think “A”

This project contains all of the following:

• Plenty of diagrams that support and are supported by concise, mathematically correct verbal explanations of all of the concepts.

• Work that is well-organized

• Neatly written work or typed verbal explanations

• Examples and non-examples that support and are supported by the included diagrams and verbal explanations.

• Subtleties about the concepts are well-thought out and presented.

• If a model could be used to explain the concept then it was included.

Level 3 – think “B”

This project contains the following:

• Plenty of diagrams that support and are supported by concise, mathematically correct verbal explanations of all of the concepts.

• Work that is somewhat well-organized

• Neatly written work or typed verbal explanations

• Examples and non-examples that mostly support and are mostly supported by the included diagrams and verbal explanations.

• Subtleties about the concepts are well-thought out and presented.

• Most of the models that could be used to explain a concept were included.

Level 2 – think “C”

This project contains the following:

• Plenty of diagrams that support and are supported by concise, mathematically correct verbal explanations of most of the concepts.

• Work that is somewhat well-organized

• Neatly written work or typed verbal explanations

• Examples and non-examples that somewhat support and are somewhat supported by the included diagrams and verbal explanations.

• Subtleties about the concepts are presented.

• Most of the models that could be used to explain a concept were included.

Level 1 – think “D”

This project contains the following:

• Some diagrams that support and are supported by concise, mathematically correct verbal explanations of most of the concepts.

• Work that is not well-organized

• Messy written work or typed verbal explanations

• Examples and non-examples that somewhat support and are somewhat supported by the included diagrams and verbal explanations.

• Some subtleties about the concepts are presented.

• Most of the models that could be used to explain a concept were included.

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