to model the problem. What activity adheres to Guideline 7: Provide options for recruiting interest ,Checkpoint geometry might they be able to 7.2: Optimize relevance, value and authenticity. use? Can they set up an equation? SMP#1 Make of Activity 1 Materials problems and persevere in Part I of the Pennies” handout (pages 17) “Saving solving them. Implementation Place students in groups based on pre-assessment data. These groups While students can connect to could be based on ability, observed methods of solving problems, student a variety of Standards for learning preferences, or other grouping techniques. Mathematical Practice in this Groups should complete Part I of the Pennies” handout. Note that “Saving activity, try to focus on SMP#1. no scaffolding is provided for the students. Challenging students to It is natural to want to point complete unscaffolded problems provides opportunities to build their students in the correct proficiency with the Standards for Mathematical Practice. At this point, you direction, but the class has just are not looking for correct answers, but rather the realization that doubling considered a similar situation (tripling, etc) grows much faster than adding a specific amount each week. and students should be given a chance to choose a similar Possible teacher questions to facilitate (only use these questions if needed): method or devise their own For question #2: What if tomorrow I double the number of pennies you plan. Encourage students to already have in your box? demonstrate the following Do you want me to do this again the next day? Why? What would characteristics of happen? mathematically proficient students. Providing a rubric for Possible extension question for students who need enrichment and/or are moving this might be a way to faster: informally capture student Do you think it is reasonable to ask students to carry around a box of one progress towards proficiency. cubic foot? Hopefully students will consider the weight of the box in their response.
to model the problem. What geometry might they be able to use? Can they set up an equation? activity adheres to Guideline 7: Provide options for recruiting interest ,Checkpoint 7.2: Optimize relevance, value and authenticity. SMP#1 Make of problems and persevere in solving them. While students can connect to a variety of Standards for Mathematical Practice in this activity, try to focus on SMP#1. It is natural to want to point students in the correct direction, but the class has just considered a similar situation and students should be given a chance to choose a similar method or devise their own plan. Encourage students to demonstrate the following characteristics of mathematically proficient students. Providing a rubric for this might be a way to informally capture student progress towards proficiency. Activity 1 Materials Part I of the “Saving Pennies” handout (pages 17) Implementation Place students in groups based on pre-assessment data. These groups could be based on ability, observed methods of solving problems, student learning preferences, or other grouping techniques. Groups should complete Part I of the “Saving Pennies” handout. Note that no scaffolding is provided for the students. Challenging students to complete unscaffolded problems provides opportunities to build their proficiency with the Standards for Mathematical Practice. At this point, you are not looking for correct answers, but rather the realization that doubling (tripling, etc) grows much faster than adding a specific amount each week. Possible teacher questions to facilitate (only use these questions if needed): For question #2: What if tomorrow I double the number of pennies you already have in your box? Do you want me to do this again the next day? Why? What would happen? Possible extension question for students who need enrichment and/or are moving faster: Do you think it is reasonable to ask students to carry around a box of one cubic foot? Hopefully students will consider the weight of the box in their response.
AI_U1_LP_ExponentialRelationships.docx