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5.1 ConceptsOther [numerical] relationships can be seen by decomposing and composing area models. For example, a model for 20 x 6 can be split in half and the halves rearranged to form a 10 x 12 rectangle, showing the equivalence of 10 x 12 and 20 x 6. NCTM Standards 2000, page 152The above demonstration from the Standards is an example of the mental calculating technique called equal products which was illustrated for products of whole numbers in section 3.3. Will the equal products technique work for the product of integers? Explain why or why not and give examples. 5.1 Concepts Negative integers should be introduced at this level [3-5] through the use of familiar models such as temperature or owing money. The number line is also an appropriate and helpful model. NCTM Standards 2000, page 151Write an activity with questions which uses the model of temperature or owing money to introduce negative integers. Explain with diagrams how this model illustrates positive and negative integers, inequality, addition, and subtraction of these numbers. 5.1 Teaching Teachers need to understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected enterprise. Their decisions and their actions in the classroom - all of which affect how well their students learn mathematics - should be based on this knowledge. NCTM Standards 2000 page 17How would you respond to a concerned parent, who wants to know why students should learn about positive and negative numbers and how to add, subtract, multiply, and divide them? |