Illuminations: Exploration of a Balance

# Exploration of a Balance

In this unit, 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. This unit includes an individual activity for three different levels: grades 1‑2, 3‑5, and 6‑8.

This unit was adapted from an article entitled "Ideas: Exploration of a Balance," by Mikki Weiss, which appeared in The Arithmetic Teacher, March 1990, pp 26-32.

### Math Content

Students will:

• balance pairs of like and unlike objects by changing distance from fulcrum
• record observation and identify patterns in their work
• construct and use a two-pan balance
• compare mass of two objects
• construct a bar graph showing the results of their measurement
• determine position necessary to balance uneven objects
• identify effect on balance of moving the fulcrum.
• become familiar with the relationship in balancing between the length of the mass arm and the mass of the objects on either side.

It is important that styrofoam cups are used in any of the balances for this unit, specifically lessons 2 and 3. The cups need to be almost weightless, and styrofoam cups will serve well in this capacity.

### Individual Lessons

Lesson 1 - Keeping in Balance

In this lesson for grades 1‑2, students balance pairs of like and unlike objects by changing distance from the fulcrum. Students use a crayon (as the fulcrum) and a ruler to represent the balance.

Lesson 2 - Maintaining the Balance

In this lesson for grades 3‑5, 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 determining the position necessary to balance uneven objects and the effect on balance of moving the fulcrum.

Lesson 3 - 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.

### NCTM Resources

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