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STATE GOAL 6.A: Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings. |
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Our ability to function in everyday life is increased by our ability to reason quantitatively. The intuitive feeling for handling quantitative information is what we often refer to as “number sense.” There are four aspects of number sense which form the foundation of this module and promote the ability to reason quantitatively. These four aspects are: Quantities—being able to deal comfortably with different types of quantities and extremely large or small numbers that are unfamiliar to us or uncomfortable to imagine; Representations—understanding the different quantities often require different labels and are best represented by different types of graphs, tables, or expressions; Relationships between quantities—being able to make comparisons, forming ratios and use proportional reasoning; Patterns—recognizing patterns in numbers and how these patterns can be displayed leads to recognition of trends in numerical data and the ability to reason inductively. Within the field of mathematics, these four aspects also indicate that increased number sense is a necessary foundation for understanding in other content areas and processes of mathematics, i.e., number sense promotes a deeper understanding of algebra, geometry, probability/statistics, problem-solving, communication, etc. |
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In this unit, we will explore the four aspects of number sense listed above. The main activity of the module is to build a theme-based poster that demonstrates those understandings through written communication, graphs, and illustrations of numerical facts about the chosen theme. |
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Part 1 |
Part 2 |
Part 3 |
Part 4 |
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Content/Topic |
Numbers as counts and as measures, appropriate labels, extremely large and small quantities |
Representing numerical facts graphically. |
Making comparisons of numbers, i.e., ratios. Equal ratios, proportions, and scaling. |
Recognizing numerical patterns. Visualization of numerical patterns. Recognition of trend data. |
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Opening |
Where do the numbers fit? |
Organization of data |
Scaling activity with GSP |
Mathematical Quilts |
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Module Activity |
Poster—Identification of a theme and numerical facts |
Poster—Creating graphs that illustrate theme |
Poster—Illustration of two types of comparisons in theme. |
Poster—Analytical Questions about theme, completion of entire poster. |
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Assessment |
Completeness, assessing writing in mathematics, holistic rubrics |
Appropriateness of types of graphs. |
Validity and reasonableness of comparisons, accuracy vs. estimation |
Assessing higher order thinking skills; completion of analytic rubric |
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Standard |
6A |
6A,6C |
6D, 6C |
6B, 6A |
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Instructors' page table of contents |
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Participant page table of contents |
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Important URL's |
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Support for the material |
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Contact information |
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Glossary |
