Note: In this lesson, subtraction will be demonstrated using a pan balance. If you only have a balance with hanging weights, please modify the directions for that type of balance. You may wish to use large pasta shapes for this lesson so that the balance will clearly register the differences in weight. The pieces should be identical so that groups of the same size weigh the same amount.
Call on a volunteer to play the role of a pan balance. Ask the child to hold out his or her arms while you place a container in each hand. Tell the child to imagine that the container on the left side is very heavy and to act out what the balance would look like. Then ask him or her to imagine that the left side is much lighter than the right side, and act that out. Then ask the class to stand and stretch their arms out and show how a balance works.
Now display a pan balance and review with the students how it operates. Ask a volunteer to place eight pasta shapes in the left pan of the balance beam and then to put two pasta shapes on the other side. Write on the board: 8 - __ = 2. Say: "How many pasta shapes would we need to take away from the left side so that the scale balances?” Accept and model all the students' responses. When the
response "six" is given, select students to record this on the board using an equation [8 – 6 = 2]. Continue with other examples until the students are comfortable with the process, and then give them time to explore subtraction
with a pan balance.
Give each pair of students a number cube, and assign each student to one side of the pan balance. Tell the students to roll the number cube and place that many pasta shapes on their side of the balance. Then have them work with their partner to write the subtraction example as an equation, and then to make the scale balance by taking some pasta shapes away from the heavy side. Ask them to record the difference and to repeat the activity several times. Balancing with a pan
balance is concrete preparation for the algebraic procedure of balancing an equation.
Next, give the pairs of students a paper bag. Instruct students to not look in the bag. Assign one student to go first. Ask the student to take up to five pasta shapes from the bag and place it on the left side of the scale, and the
same or a different number (between 5 and 10) of pasta shapes on the right side. Tell the other student to take away pasta shapes from the heavier side until the scale balances. Then have each student write a subtraction equation to describe the situation. Have them repeat the activity several times, switching roles each time. Then call the class together and give the students time to share one of the ways they balanced the scale. If you wish, ask them to record it in words or pictures.
