Teach me how to balance equations
This lesson encourages the students to explore another meaning for operations of subtraction, the balance. This meaning leads naturally into recording with equations. The students will imitate the action of a pan balance and record the modeled subtraction facts in equation form.
Teacher Note: In this lesson, subtraction will be demonstrated using a pan balance. If you have only a balance with hanging weights, please modify the directions accordingly. You may wish to use heavy weights such as sinkers 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.
To review with the students how a pan balance operates, display one and call on a volunteer to "be" a pan balance. Ask the child to hold out his or her arms, then 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 will look like. (You might also place a heavy object in the hand that represents that left side of the balance.) Then ask him or her to imagine the left side is much lighter than the right side and act that out. Tell students they will “act out” the behavior of a pan balance. Then ask the whole class to stand, stretch their arms out and show how a pan balance works. [You may wish to suggest which side of the pan balance is heavier, lighter.]
Now ask a volunteer to place nine weights in the left pan of the balance and then put four weights on the other side. Ask: "How many more weights are on the left side than on the right side? What will we need to add to the left side so the pan balance is level?" Accept and model all the students' responses. When the response "five" is given, record this on the board using an equation [9 = 4 + 5] that models what was done with the weights to make the pan balance level. (Note that although the number sentence is an addition sentence, subtraction is used to find the missing addend.) Continue with other examples until the students are comfortable with the process. (Because this is an example of a missing addend problem, some students may have difficulty completing the equation correctly.) To continue the investigation, call on volunteers to pose problems and
model them on the pan balance.
Now give each pair of students some crackers and a copy of the Pan Balance Activity Sheet.
Pan Balance Activity Sheet
Tell students they will take turns choosing two numbers and acting out how a balance would look if there were that many crackers on the left and right sides. Ask students to determine how many more crackers would be needed to balance the pan and record that information on the recording sheet. Then ask them to write the number sentence that they modeled. Invite the students to select one of the resulting equations to illustrate by drawing a pan balance that models the equation.
- Pan balance with weights
- Resealable bags with fish-shaped crackers
- Pan Balance Activity Sheet
- Because a new and especially challenging meaning for subtraction has been added with this lesson, you may wish to make more entries on the Class Notes recording sheet begun earlier in this unit.
- Students may use the Pan Balance - Numbers Tool to model and solve additional subtraction equations, similar to those in this lesson.
Questions for Students
1. When you modeled comparison subtraction on the balance, what did you do first? Then what? How did you record this?
[Student responses may vary, but they should be able to model the steps followed in the lesson.]
2. Suppose you put seven fish-shaped crackers on the left side of the balance and three fish-shaped crackers on the right side. To balance the pan, which side should you add crackers to? How many more crackers should you add to balance the pan balance? What equation tells what you did?
[Right side; add 4 more; 7 = 3 + 4.]
3. How would you explain to a younger student how to make the sides balance?
[Student responses may vary, but they should be able to model the same steps used during the lesson.]
4. Choose one equation that you wrote when you acted like a pan balance. How does this equation show what you did?
5. How could you use the balance to complete this number sentence: 3 + _ = 5? Which numbers are the addends?
[Put 3 on one side, 5 on the other, and balance; 3 and 2 are the addends.]Source: illuminations.nctm.org