SMP#8 Look for and express Activity 3 Developing the Concept regularity in repeated reasoning. Materials Students can connect to a Part III of the handout (pages 17) “Saving Pennies” variety of Standards for Implementation Mathematical Practice in this Groups should complete Part III of the handout. Part III “Saving Pennies” activity, try to focus on SMP#8. requires students to build the symbolic form of the relationships they’ve The accompanying worksheet examined in Parts I and II. Students will first look at the recursive provides some structure to the relationship relating the current term to the previous term. Students will process of relating the then build an explicit relationship, relating the independent variable (in this recursive representation of the case the number of days) to the dependent variable (in this case, total pattern to the explicit number of pennies). representation of the pattern. Using a Jigsaw approach, form new groups and have students compare Though it is difficult to see answers. Complete a whole class final debrief of problems 1-10 from Part students struggle, take the time III of the handout. “Savings Pennies” to allow them to process what Extension they are doing and ask Assign either problem 4, 5 or 6 to the student groups. questions of themselves and The group members should create a scatter plot of their assigned problem each other to discover the on the attached grid. ( page 23) After completing the scatter plot, instruct pattern and make students to sketch a curve which contains the points on the scatter plot. generalizations. Encourage Groups should display their scatter plots. students to demonstrate the Ask students to share their observations about the behavior of the following characteristics of displayed curves. Note: This is simply to make connections; students are mathematically proficient not expected to be able to graph an exponential function at this point. students. Characteristics Formative Assessment Notice if and when Provide students with several additional situations for which they will write an calculations are repeated. exponential expression. This could be done on individual white boards, with Look for general methods students at boards around the room, or simply on their paper for teacher
SMP#8 Look for and express regularity in repeated reasoning. Students can connect to a variety of Standards for Mathematical Practice in this activity, try to focus on SMP#8. The accompanying worksheet provides some structure to the process of relating the recursive representation of the pattern to the explicit representation of the pattern. Though it is difficult to see students struggle, take the time to allow them to process what they are doing and ask questions of themselves and each other to discover the pattern and make generalizations. Encourage students to demonstrate the following characteristics of mathematically proficient students. Characteristics Notice if and when calculations are repeated. Look for general methods Activity 3 Developing the Concept Materials Part III of the “Saving Pennies” handout (pages 17) Implementation Groups should complete Part III of the “Saving Pennies” handout. Part III requires students to build the symbolic form of the relationships they’ve examined in Parts I and II. Students will first look at the recursive relationship relating the current term to the previous term. Students will then build an explicit relationship, relating the independent variable (in this case the number of days) to the dependent variable (in this case, total number of pennies). Using a Jigsaw approach, form new groups and have students compare answers. Complete a whole class final debrief of problems 1-10 from Part III of the “Savings Pennies” handout. Extension Assign either problem 4, 5 or 6 to the student groups. The group members should create a scatter plot of their assigned problem on the attached grid. ( page 23) After completing the scatter plot, instruct students to sketch a curve which contains the points on the scatter plot. Groups should display their scatter plots. Ask students to share their observations about the behavior of the displayed curves. Note: This is simply to make connections; students are not expected to be able to graph an exponential function at this point. Formative Assessment Provide students with several additional situations for which they will write an exponential expression. This could be done on individual white boards, with students at boards around the room, or simply on their paper for teacher