Balance: Equations
Pre-lab
Demonstration:
 Do this pre-lab as a teacher-led demonstration and discussion.
 You may choose to break students up into groups and give each group a
balance. This will help students test their predictions.
 Orientation: If you are facing the class, left and right will reversed for them. To
avoid confusion, refer to the sides of the balance using student’s left and right.
 The goal is to lead students to the equation DM = DM where D = distance and
M = mass.
 Use the following questions to lead students through a demonstration and
discussion. For each question, ask for student predictions before showing the
result with the balance.
 Start by showing the math balance and asking students:
- Did you ever use a balance or a scale in science class?
- What do you have to do to make it balance?
Answer the questions below as you watch the teacher demonstrate.
1. Label the different parts of the balance as the teacher points them out:
Fulcrum
Beam
Weights
Numbered Pegs

Point out the different parts of it and have students label the parts on their
sheet as reference:
- Fulcrum: Pivot point at the center of the balance
- Numbered Pegs: Indicate distance from the fulcrum. There are pegs on
each side of the beam.
- Weights: Weights can be hung on the numbered pegs. Several weights can
be placed on each peg, and on the corresponding peg on the back of the
beam.
Balance: Pre-lab
Teacher Notes
© 2004 The University of Texas at Austin and the GE Foundation
Page 1 of 4
2. If the same amount of weight is placed on the same numbered peg on
each side, will the beam be balanced? (yes)
Ask students for their predictions first. Then show that the beam will balance with
the same amount of weight on the same numbered peg on each side.
3. If the same amount of weight is placed on different numbered pegs on
each side, will the beam be balanced? (no)
Get student predictions first. If students predict that it will not balance, ask which
way the balance will tip. Then show that the balance tips down on the side where
the weight is farthest from the fulcrum.
4. If one weight is placed on peg 10 on one side, on which peg can you place
two weights on the other side to make the beam balance? Write a 2 in the
table below to show where you would put the two weights.
Peg #
10 9 8 7 6 5 4 3 2 1  1 2 3 4 5 6 7 8 9 10
Weights
1
X
2
Get student predictions. If students make incorrect predictions, test the
predictions with the balance. Show a couple of incorrect positions before showing
the correct position with two weights on peg 5.
There are several ways to make the beam balance with one weight at peg 10. A
person could put two weights at the 5 position or they could put five weights at
the 2 position. Even less obvious is the fact that you could put one weight at the 6
position and one weight at the 4 position and balance things also. However, for
this question, focus on putting two weights on peg 5 to balance one weight on
peg 10. This leads to the next question.
5. We see that the beam can balance with different amounts of weight on
each side, so weight is not the only factor involved in balancing the beam.
What other factor is involved in making the beam balance?
Getting the beam to balance involves both mass (weight) and distance from the
fulcrum (the number of the peg). A lighter amount of weight can balance a heavier
amount of weight if it is farther from the fulcrum.
6. The beam is balanced with twice as much weight on one side. Compare
the distance of the weights from the fulcrum on each side. (Hint: The
numbers on the beam can be used count the distance.)
The distance on the side with one weight is twice the distance on the side with
two weights. In other words, twice the mass is at half the distance, or half the
mass is at twice the distance.
Balance: Pre-lab
Teacher Notes
© 2004 The University of Texas at Austin and the GE Foundation
Page 2 of 4
7. How can we express the relationship between distance and weight on
each side of the balance in a mathematic equation?
Encourage students to formulate equations. If needed suggest using the variables
M for mass and D for distance. Answers will vary but you may get M+D=M+D. Do
some experimenting by filling in some numbers and see if you can get students
to:
MxD=MxD
8. If four weights are placed on peg 3 on the left side, how many weights
must you put on peg 6 on the right side to balance the beam? Show how
you solve the equation in the space provided below.
10 9 8 7 6 5 4 3 2 1  1 2 3 4 5 6 7 8 9 10
Peg #
Weights
4
X
Encourage students to solve the problem with the equation first, then test their
prediction with the balance.
MxD=MxD
4x3=Mx6
12 = M x 6
M=2
Follow up with other examples if needed to reinforce the relationship. If student
groups each have a balance, allow them some time to experiment.
When students have a firm understanding the basic equation, move on to the next
series of questions. By placing weights on more than one peg on each side of the
balance, the equation becomes more complex.
9. If one weight is placed on peg 7 on the left of the beam, how can you
balance the beam with two weights on the right side? Indicate where you
put the weights in the table below.
Peg #
10 9 8 7 6 5 4 3 2 1  1 2 3 4 5 6 7 8 9 10
Option 1
Weights
1
X
Option 2
Weights
1
X
Option 3
Weights
1
X
1
1
1
1
1 1
Give students time to work with the balance to figure out a solution.
Answer will vary. Any of the combinations shown above will work.
Balance: Pre-lab
Teacher Notes
© 2004 The University of Texas at Austin and the GE Foundation
Page 3 of 4
10. Three weights are placed on peg 6 and two weights on peg 2 on the left of
the beam. Find a way to balance the beam with three or more weights on
only two pegs on the right side. Indicate where you put the weights in the
table below.
Peg #
10 9 8 7 6 5 4 3 2 1  1 2 3 4 5 6 7 8 9 10
Option 1
Weights
3
2
X
Option 2
Weights
3
2
X
Option 3
Weights
3
2
X
1
2
2 1
1
3
There are numerous ways to solve this. Only three possibilities are shown
above.
11. The equation D x M = D x M works when only one peg is used on each
side of the beam. Rewrite the equation so it works when two pegs are
used either side of the beam.
Make sure they understand that the D x M for each peg is added together.
The pattern of adding (D x M) for each peg works for any number of pegs.
D x M = (D x M) + (D x M)
(D x M) + (D x M) = (D x M) + (D x M)
Follow up with other examples if needed to make sure students understand
the equations.
Explain that students will do some experimenting on their own with the
balance in the lab and then there will be a contest (game) using what they
have learned.
Balance: Pre-lab
Teacher Notes
© 2004 The University of Texas at Austin and the GE Foundation
Page 4 of 4