MA.7.A. 1.6 Apply Measurement in Multiple Contexts, including scale drawings and constant speed

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MA.7.A. 1.6 Apply Measurement in Multiple Contexts, including scale drawings and constant speed. Block 29.

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### MA.7.A.1.6 Apply Measurement in Multiple Contexts, including scale drawings and constant speed

Block 29

"To believe that one can teach mathematics successfully by lectures, one must believe what most mathematicians know to be untrue--that mathematics can be learned by watching someone else do it correctly" National Research Council (NRC), 1991, p.24

Elements necessary to ensure quality mathematics instruction
• appropriate discourse
• reflective analysis of teaching & learning.

The following activities will allow participants to explore these three elements

### Real Life Drawing of a Doll

Activity 1

Barbie and G.I. Joe
• The extent to which people are considered beautiful depends on the similarity of their appearances with a viewer's preconceived image of beauty.
• Cultural standards of beauty are typically accepted without question by the members of the cultural group.
• Because the adolescent or near-adolescent is confronted by a changing body, coming to terms with this new body has long been considered one of the prime tasks of this age group.

Teachers of both male and female students in grades 5-8 are faced with young adults who are particularly critical of their own appearances and unhappy about how they look

• Comparison of their shape and facial characteristics with the prevailing standards of beauty often lead to a negative self-evaluation.
• Making such comparisons partially explains the connection to mathematical similarity where comparison is at the essence of the definition.
The Activity
• Review the concept of similarity
• Divide participants in groups of four
• Give each group either a Barbie doll or a G.I. Joe doll
• Participants collect measurements of the doll and of one of the members of the group and fill out the information of the Measurement worksheet
After measurements
• After measurements are collected for the dolls and for the member of the group, determine what measurement the group wants to match, example, do you want the drawing of the life-size doll to have the same height as the member of your group, or same foot size?
• Use the measurements they obtained to draw a "life-sized" Barbie or G.I. Joe on large sheets of newsprint paper
Final discussion
• Participants share comments about the activity and the mathematics involved in obtaining the results, addressing in particular the concept of similarity.
• Finally, participants consider the totality of the lesson experience, focusing on the importance of discourse during the activity, and reflection after the activity.

### Crumpled Foil

Activity 2

Foil Activity

Determine the total area of the crumpled foil without flattening out the ball.

You will have eight minutes to formulate a strategy and an alternative strategy for solving the problem.

Provide a rationale for each of the two strategies. During the eight minutes, you may NOT touch the materials.

Now do it…

You have 12 minutes to solve the problem.

Show all calculations in the proper section of the Crumpled Foil Activity worksheet.

Results

NSF Summer Institute 2005