Wednesday
Wednesday: Loft Lab, the Coat-Hanger Balance
Comet hangs a coat hanger from a hook and ties a paper cup to each end with string. "Lab day. A real balance."
Wren seals some dried beans in a small envelope and marks it x. "Nobody looks inside. That is the unknown."
He drops the envelope and 3 loose beans into the left cup and 8 beans into the right. The hanger levels out.
"x + 3 = 8," Comet says. "Take 3 beans off each side." The hanger stays level. "The envelope equals 5 beans."
Nova hovers above the hook, her light steady. "Would you like a hint? Open the envelope only after you solve."
"What do you notice?" Wren asks. "The hanger tips if you take beans from one side only."
"Both sides, every time," Comet says. "That is the rule, in cardboard and string."
What you need
- A wire or plastic coat hanger and a hook, doorknob or broom handle to hang it from.
- Two paper cups, string or tape to hang them from the hanger's two ends.
- A bag of dried beans or other small identical counters, and a few small envelopes.
- A marker to label each envelope with a letter, and your Loft Log.
Beans and small counters stay out of mouths and away from younger children and pets.
If the wire hanger has a sharp end, a grown-up bends it in or covers it with tape.
Cut string with scissors only with a grown-up present.
Run the lab
- Hang the hanger and tie a cup to each end. Check that it hangs level when both cups are empty.
- Have someone else seal a secret number of beans in an envelope and mark it x.
- Put the envelope plus a few loose beans in the left cup. Add beans to the right cup until it is level.
- Write the equation. Envelopes are x, loose beans are numbers, and level means equals.
- Take the same number of loose beans off both cups until only the envelope is left. Write each step.
- Open the envelope and count. Record whether your solution matched.
The crew's four balances
Here are the four balances the crew set up. The bean counts are their own, made up for the story.
| Balance | Left cup | Right cup | Equation | Beans per envelope |
|---|---|---|---|---|
| 1 | 1 envelope and 3 beans | 8 beans | x + 3 = 8 | 5 |
| 2 | 2 envelopes and 1 beans | 9 beans | 2x + 1 = 9 | 4 |
| 3 | 1 envelope and 5 beans | 12 beans | x + 5 = 12 | ? |
| 4 | 3 envelopes and 0 beans | 12 beans | 3x = 12 | ? |
- Read the question.
- Tap your answer.
Balance 3 shows x + 5 = 12. How many beans are in the envelope?
Balance 4 shows 3x = 12: three envelopes against 12 beans. How many beans are in each envelope?| Statement | True or false? |
|---|---|
| A level hanger shows that the two cups hold equal amounts. | ? |
| Taking 3 beans from one cup only keeps the hanger level. | ? |
| x = 7 is a solution of x + 5 = 12. | ? |
| x = 4 is a solution of 3x = 12. | ? |
| 2 × 4 + 1 = 9 | ? |
Try an envelope on each side, like x + 6 against x + 2 with more beans added. What happens?
Great lab work. Tomorrow the crew keeps a build under a mass limit with inequalities.