# Three Middle School Activities Based on Problem 5

Based on AP* Calculus AB Problem 5, 1995

## Middle School Activity 1, Based on Problem #5

**TEKS addressed: (6.8)(A); (6.10)(D); (6.12)(A)**

This Pre-AP* activity introduces the calculus topic rate of change. It was conducted in a Pre-AP grade 6 classroom. Students began drawing graphs from data collected by pouring rice into containers and then moved to a more abstract level by drawing graphs from pictures of containers. The purpose of this activity was to have students think about the rate at which the height of rice in various containers changed depending upon the shape of the containers.

Sample A:

- Student Sample A, Graph
- Student Sample A, Graph Summary
- Student Sample A, Worksheet Part 1
- Student Sample A, Worksheet Part 2

Sample B:

**Middle School Activity 2, Based on Problem #5 **

**TEKS addressed: (6.2)(C); (6.3)(C); (6.8)(B); (7.3)(B); (8.8)(A); (8.9)(B); (8.10)(A); (8.10)(B)**

This is a good Pre-AP worksheet because it addresses the difficulty that students have with the similarity of three-dimensional figures. It addresses several TEKS simultaneously and goes well beyond what is covered in most textbooks. Notice that in problems 1-3, surface area and volume for each figure can be calculated directly. In problem 5, you can easily find surface area and volume of the first figure and then set up proportions to find values for the second figure.

Student Worksheet

Teacher Guide and Answer Key

**Middle School Activity 3, Based on Problem #5**

**TEKS addressed: (6.1)(B); (7.2)(F); (7.3)(B); (8.7)(A); (8.8)(C); (8.9)(B); (8.10)(B)**

This is a good Pre-AP worksheet because it builds upon and extends skills that students have developed in middle school and Algebra I (using geometric formulas, solving literal equations, symbolic manipulation, function notation) while simultaneously addressing some TEKS for high school geometry. It does so in a way very different from that seen in most textbooks. Most importantly, the context and wording is based upon an actual AP problem with which the students had difficulty.