Acknowledge that students have just finished some interesting work; they used mathematics to figure out the weight of something that was too light for the classroom scale to sense.

Purpose of the discussion

The purpose of this discussion is for students to jointly construct explanations for how objects such as a bucket of water or sand can have significant weight, given that a single drop of water or grain of sand has no perceptible weight.

Engage students in the focus question

If a drop of water weighs just 1/30th of a gram, how do you explain why a bucket of water is so heavy?

• There are many, many drops of water in a bucket full of water.
• Each drop contributes something to the total weight of the bucket of water.

Allow time for students to formulate responses. Engage all by asking for others to share their own explanations and to respond to the explanations of others.

Do you think a single grain of sand weighs anything? Explain your answer.

• If students claim "yes", what reasoning can they provide to support their claim?
• If students claim "no", ask for the explanation; it will help you determine whether students are focusing on whether a grain of sand will register any weight on the scale, or if students believe a grain of sand has no weight.

How does a bucket of sand get to be so heavy when a grain of sand weighs so little?

• There are many millions of grains of sand in a bucket, with each grain contributing a tiny bit of weight to the total weight of the bucket of sand.

Can you think of other examples of tiny bits that seem to have no weight individually, but that can be combined together to have significant weight?

• Grains of sugar or salt; particles of flour.

Summarize the discussion and recap the investigation

Using the same language students have used, summarize their main ideas. Include the following key ideas:

• If a large collection of grains of sand (or drops of water, etc.) have weight, then we can reason that each individual grain must have some weight, even if that weight is too small to sense or measure.
• Although individual grains of sand or drops of water may have imperceptible weight, combining millions or billions of them together can result in significant weight.

Recap the following:

• Tiny things, such as drops of water, are not heavy enough to register weight on the classroom scales.
• We've figured out how to calculate the weight of a water drop and concluded that tiny things such as single drops of water or grains of sand actually have weight.

When we think about how heavy a bucket of water feels, or a bucket of sand feels, it can make us wonder, "How many of those drops, or grains, are there in a bucket, to make it feel so heavy?"