## Finding the Balance

In this lesson for grades 6‑8, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum. The focus of this lesson is the relationship between the length of the arm and the mass of the objects.

Prior
to this lesson, students should have experiences in using balances. In
particular, students should be able to balance objects in pans or cups,
identify the fulcrum, and be familiar with the term **mass**.

To begin the lesson, ask students:

When using a balance, what is the relationship between the length of the arm and the mass of the objects on the balance?

Tell students that they will be exploring the answer to this question during today's lesson.

Distribute the Finding the Balance Activity Sheet to each student.

Finding the Balance Activity Sheet

Give each group a thirty-centimeter ruler, two small paper cups,
a large crayon, tape, and a quantity of like-sized paper clips. Guide
the students as they label the paper cups **A** and **B**. Help the students to locate the center of balance of the ruler.

Direct the students to place two paper clips in cup **A** and three paper clips in cup **B**.

Guide the students as they experiment to locate positions at which the two cups balance. Ask the students to suggest other numbers of clips for experimentation. Help the groups to locate various positions at which the pair balance.

Elicit the relationship between the position of cup **A**
and the number of clips and the position of cup B and the number of
clips. Repeat the procedure when the fulcrum is repositioned.

As students are working, be sure to walk around the room and make observations. You may wish to use the Class Notes Recording Sheet for this purpose.

Lead a class discussion which focuses on the relationship between the length of the arm and the mass of the objects. Return to the question posed at the beginning of today's lesson, and ask students what conclusions they drew as a result of the experiments.

- Finding the Balance Activity Sheet
- A centimeter ruler for each group
- Crayons for each group
- 2 small paper cups for each group
- Tape
- Paper clips of like mass
- A collection of small, paired objects to be weighed

**Assessment Options**

- You may wish to use the Class Notes Recording Sheet to record observations about students.
- Collect the Finding the Balance Activity Sheet from each student and assess student understanding by checking their responses to the questions on the activity sheet.

**Extension**

Experiment with standard units of mass and with other balances.

**Questions for Students**

- Why was it important for each of the cups to be almost weightless?
- When using a balance, what is the relationship between the length of the arm and the mass of the objects on the balance?

**Teacher Reflection**

- Were students able to articulate the relationship between the length of the arm and the mass of the objects? If not, what further experiences do these students need?
- What observations about student understanding did I identify while walking around the classroom?
- Are students able to explain the difference between mass and weight?

### Keeping in Balance

### Maintaining the Balance

### Learning Objectives

Students will:

- Construct and use a two-pan balance.
- Record the results of weighing.
- Compare mass of two objects.
- Become familiar with the relationship in balancing between the length of the arm and the mass of the objects on either side.

### NCTM Standards and Expectations

- Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.

- Solve problems involving scale factors, using ratio and proportion.

### Common Core State Standards – Mathematics

-Kindergarten, Measurement & Data

- CCSS.Math.Content.K.MD.A.1

Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

-Kindergarten, Measurement & Data

- CCSS.Math.Content.K.MD.A.2

Directly compare two objects with a measurable attribute in common, to see which object has ''more of''/''less of'' the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

Grade 1, Measurement & Data

- CCSS.Math.Content.1.MD.C.4

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Grade 2, Measurement & Data

- CCSS.Math.Content.2.MD.A.1

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Grade 2, Measurement & Data

- CCSS.Math.Content.2.MD.D.9

Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

Grade 3, Measurement & Data

- CCSS.Math.Content.3.MD.B.4

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-- whole numbers, halves, or quarters.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP1

Make sense of problems and persevere in solving them.

- CCSS.Math.Practice.MP4

Model with mathematics.

- CCSS.Math.Practice.MP6

Attend to precision.

- CCSS.Math.Practice.MP7

Look for and make use of structure.

- CCSS.Math.Practice.MP8

Look for and express regularity in repeated reasoning.