M7 Unit 4B Study Guide - Area, Surface Area, Volume

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This includes all of the problems from M7 Unit 4 Study Guide 4B with all steps to each problem worked out.

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M7 Unit 4B Study Guide - Area, Surface Area, Volume

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Os historiadores do século XIX dividiram o tempo dos seres humanos na terra em dois períodos:  Pré-história: Começou com o aparecimento dos humanos (há cerca de 2 milhões de anos) e teria fim com a invenção da escrita (por volta de 3000 a.C.).  História: Idade Antiga, Idade Média, Idade Moderna e Idade Contemporânea. Neste capítulo mostramos que para a ciência atual, todos os seres humanos fazem parte de uma mesma espécie que surgiu na África há cerca de 70 mil anos e foi fruto de uma longa evolução.

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In BC’s nearly-decade-old “new” curriculum, the curricular competencies describe the processes that students are expected to develop in areas of learning such as mathematics. They reflect the “Do” in the “Know-Do-Understand” model. Under the “Communicating” header falls the curricular competency “Explain and justify mathematical ideas and decisions.” Note that it contains two processes: “Explain mathematical ideas” and “Justify mathematical decisions.” I have broken it down into its separate parts in order to understand--or reveal--its meaning. The first part is commonplace in classrooms. By now, BC math teachers—and students—understand that “Explain mathematical ideas” means more than “Show your work.” Teachers consistently ask “What did you do?” and “How do you know?” This process is about retelling, not just of steps but of thinking. The second part happens less frequently. Think back to the last time that you observed a student make—a necessary precursor to justify—a mathematical decision. “Justify” is about defending. Like “explain,” it involves reasoning; unlike “explain,” it also involves opinion and debate. In order to reinterpret the curricular competency “Explain and justify mathematical ideas and decisions,” I will continue to take apart its constituent part “Justify mathematical decisions” and carefully examine the term “mathematical decisions.” What, exactly, is a “mathematical decision”? Below, I will categorize answers to this question. These categories, and the provided examples, may help to suggest new opportunities for students to justify.

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