Chapter 3 Feedback Exercise 2

## Exercise 2

Following are some examples of tenth grade students’ mathematical problem solving about measurement.

The learning goals and objectives for mathematics tasks are shown next.

#### Learning goals and objectives:

Goal 1: Students will learn the concepts and procedures of measurement.

¨  Students will understand how and why measurement units are organized into systems.

¨  Students will learn how to choose the appropriate level of measurement precision for a situation.

¨  Students will understand the usefulness of standard units of measurement.

Goal 2: Students will learn how to solve real-world problems.

¨  Students will learn to clarify a problem before beginning to solve the problem, including identifying known, missing, or extraneous information. Students will determine what is to be known through the problem solution.

¨  Students will learn to apply relevant tools, concepts, procedures, and tools to a problem.

¨  Students will learn to construct solutions that are viable, accurate, and complete.

Read the directions for students. Then, using the guidelines for feedback on pages 86 through 93 of your text, try providing some encouraging feedback that will (a) help each student learn more about measurement and mathematical problem solving, and (b) support their motivation to learn.

Once you have finished, exchange papers with a fellow student or colleague. Discuss why you provided the feedback you did.

Here are the directions that the students had for the activity.

##### Measuring Water on a Desert Planet

Today you will solve a problem about measurement. The problem does not have one solution, so you will be evaluated based on how well you think-through the problem and develop a reasonable solution.

Suppose you lived in a colony on the desert planet Dune. On Dune, water is precious and measurement of water is in terms of water drops. You have been given an eyedropper and a cup. You have the chore of deciding how much water will be needed for various aquariums the colony is using to grow underwater plants, fish, and animals. How can you estimate the number of drops of water needed to fill an aquarium of any size? Be sure to describe in detail:

¨  the problem in your own words

¨  the questions you need to ask to have more precise measurements

¨  the steps you will use to estimate the amount of water for the aquarium, using the eyedropper and the cup

¨  how you will account for the gravel in the bottom of the tank

You may use drawings, equations, or tables to support your description.

When you have finished describing the problem and your solution, think about how you could improve the efficiency of the water-measurement system on Dune. Write a paragraph telling the people of Dune:

¨  How your system can meet their need to account for every drop of water they use

¨  Why your system is more efficient than their current “eyedropper and cup” system

#### Keep the learning objectives in mind as you write encouraging and useful feedback for the following student work.

HINT: Use the first four criteria from Characteristics of Effective Feedback to guide and evaluate your feedback.