Investigating Standard Measures 3:

# Do very tiny things have weight?

## 2. Place small objects on a weight line

Small Groups 20 Mins Notebook

### Measure and explore

This is the heart of the investigation, where students consider the weight of ever–smaller pieces of plastic modeling clay. As the weights fall below 1 gram, students wrestle with the idea of fractional weights that approach zero on the weight line. As they cut smaller and smaller pieces, and can no longer feel the weight in their hands, they confront the question: Does weight disappear?

Students first weigh their undivided portions of plastic modeling clay in the pan balance, then work on their own to cut the material in halves, using a plastic knife. When groups have three pieces placed on their weight line. Check that the pieces are placed at the 4–gram, 2–gram, and 1–gram markers.

• How much does the remaining piece weigh?
• 1 gram
• Can you feel that weight in your hand?
• Yes, it feels the same as the red 1-gram weight or a large paper clip.

Note: Working with plastic modeling clay. Plastic modeling clay is a good material for this exercise because it can be manipulated between cuts. If the first piece is rolled to pencil thickness, it will be easy to estimate the middle and cut it into two 4-gram pieces. You might point out that cut pieces will be easier to halve if they are first rolled into a longer, thinner pieces; or help students to discover this on their own. By working with thinner and thinner rolls, students should be able to halve the original 8 grams at least six times, possibly more.

When students cut the 1-gram piece in half, and place one piece on the weight line, check to see where it is placed.

• How much does the remaining piece weigh?
• Half a gram
• Can you feel that weight in your hand?
• If I cut a 1/2-gram piece of plastic modeling clay into two equal parts, is there a place on the weight line to put one of the pieces? Does it still weigh something?

Continue this process one step at a time. Naming or writing the fractions below ¼ is not important to this work, but see if students develop a sense of where to place the quarter–gram, the eighth–gram, and subsequent pieces on the weight line. Do they see the pattern? They are moving half the distance toward zero each time.

Is the weight really disappearing? When students claim they can no longer feel the weight, suggest that they drop the piece 6 inches from one hand to the other. They should feel the piece of plastic modeling clay hit the hand. Do they agree that if they can feel something hit, it must have weight? When they can no longer feel a piece landing in a palm, ask them to drop the piece onto the back of the hand, which is more sensitive than the palm.

• Do you think objects have weight, even if we can't feel the weight?

Have students sketch their weight line with the pieces of plastic modeling clay placed on it in their notebooks. Students should also record their thoughts on the weight of the plastic modeling clay pieces.