In the post CCSS Call for Rigor, we contemplated the necessity of implementing concept teaching that reveals the process in order to meet the standards.
Assuming students have prior knowledge of the definition of a rational number, how would you address the 7.NS.A.2d standards?
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.Since students have used the standard algorithm for division in 6th grade (6.NS.B.2), would you take a procedural approach or a conceptual approach?
Process...given fractions use long division to observe the results of decimals that terminate or repeat. Is that doable? Certainly. What's the problem? The students haven't learned why some fractions terminate and others repeat; which means the students haven't connected those results with the standard algorithm. And they would most likely be unable to discuss the results without trudging through long division every single time.
Concept...given fractions develop a geometric model.
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| Geometric Discovery Model |
Students then use the model to connect part-to-whole with the decimal expansion to determine which fractions terminate and which ones repeat, why, and how that connects to the standard algorithm for division.
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| Geometric Discovery Record Sheet |
This depth of knowledge enables students to strengthen their number sense and build critical thinking skills within the science of mathematics. This encourages students to reach mathematical practice standards while addressing mathematical content standards.
