1. What do you think would happen to balance A if I put one more sphere on each side? Why?
[It would still be balanced because both sides will still weigh the same amount.]
2. What would happen if I took away one sphere from the right side of balance A? Why?
[The pans would not balance. The left side would be heavier and would tilt downward; the right side would go up.]
3. Which block is heavier — the cylinder or the sphere? How do you know?
[The cylinder is heavier. It takes two spheres to balance one cylinder.]
4. What could you put on the right side of balance B to make the pans balance? How do you know?
[I could put two cylinders or four spheres or
one cylinder and two spheres. I know because one cylinder is the same
weight as two spheres, so two cylinders would be the same weight as
1. Look at balance A in Figure 2. Which block is heavier — the sphere or the cylinder? How do you know?
[The cylinder is heavier. I know because it takes three spheres to balance one cylinder.]
2. What would happen to balance A if I took away one sphere from the right side? How do you know?
[The left side would tilt downward and the right side
would go up. The pans would be out of balance. One cylinder weighs the
same as three spheres, so it has to weigh more than two spheres.]
3. What would happen to balance A if I took away the cylinder from the left side of the scale? How do you know?
[The right side would tilt downward and the left side
would go up. The pans would be out of balance. Three spheres weigh more
than zero cylinders.]
4. How do you think balance A would look with one cylinder on the left and one sphere on the right?
[The cylinder side would tilt downward and the sphere side would be up because one cylinder weighs more than one sphere.]
5. If one cylinder weighs six pounds, how much would one sphere weigh?
[It weighs two pounds. If one cylinder is six pounds,
then the three spheres weigh six pounds, and each sphere weighs two
pounds since 2 + 2 + 2 = 6.]
6. Look at balance B. What can you put on the left side to make it balance? Can you think of another answer?
[I can put one cylinder and one sphere or four spheres.]
1. Look at both pan balances. Think about what they show. Which block on balance A is heavier? On balance B?
[The cube is heavier on balance A. The sphere is heavier on balance B.]
2. Which is heaviest - the sphere, the cylinder, or the cube? How do you know?
[The cube is heaviest because balance A shows that the
cube is heavier than the sphere, and balance B shows that the sphere is
heavier than the cylinder. Together they show that the cube is
heaviest, the sphere is next heaviest, and the cylinder is lightest.]
3. What would happen to balance A if I put one more sphere on each side?
[It would stay in the same position.]
4. If the cube weighs five pounds, could the sphere weigh six pounds? How do you know?
[No because balance A shows that the sphere must weigh less than the cube.]
5. What would a pan balance look like if the cube were on the left and the cylinder were on the right?
[The cube is heavier, so the left side would be tilted downward.]
- Were the materials appropriate? Did the materials allow you to assess student understanding?
- Were students able to associate the pictorial pan balances with the real pan balances successfully to check their answers?
- Were students able to solve balance problems on the Balancing
Act activity sheet independently? If not, what additional experiences
will you plan to give them more practice? If they did, what additional
algebra concepts are appropriate?
- Did students relate the mathematical term “equal” to an even pan balance?
- Did students explain their reasoning in ways that the rest of
the class could follow and understand? How can you help students
monitor this themselves?