## Thursday, November 8, 2012

### Density Gizmo

This week, with a Density Gizmo in Science, our students continued to deepening their understanding of matter, mass, and volume, and explored density. They first brainstormed objects that they think would sink in water and then those that would float, and formed a hypothesis for why the objects sink or float.

After that, they did a Gizmo warm-up which familiarized them with the virtual exploration by measuring the mass of objects on a scale, and measuring the volume of objects using water displacement in a graduated cylinder.

The essential question then focused their activity, How do mass and volume affect sinking and floating?

During the Gizmo, students filled in a chart with each object's mass and volume, and then whether the object would sink or float when placed in the beaker.  This is a sample of their chart.

 Object Prediction (sink or float?) Mass Volume Result (sink or float?) Ping pong ball F 3.0 g 36.0 mL Float Golf ball S 45.0 g 36.0 mL Sink Apple F 33.0 g 44.0 mL Float Chess piece S 40.0 g 80.0 mL Float Penny S 3.0 g 0.4 mL Sink Rock S 200.0 g 50.0 mL Sink

They analyzed their results and concluded that you could not predict whether an object would sink or float using the mass alone, because the mass of a ping pong ball and penny were both 3 grams and one floated while the other sank. Based on the volume alone, they concluded that you could not predict whether an object would float or sink, because the volume of a ping pong ball and golf ball were both 36 mL and one floated while the other sank.

However, mass and volume, when considered together could predict whether an object would sink or float. When an object's mass was less than the object's volume, the object floated.  When an object's mass was more than an objects volume, then the object would sink. Density refers to the mass found in a given volume of a substance.

These are third graders that I teach and they are taking it in like sponges! They even clapped when we said, "Today, we will be doing a Density Gizmo!" It doesn't get any better than that!

### Decomposing Arrays and Multiples of Ten

Our students' knowledge of multiplication has come so far in so little time. We worked on finding the total number of squares (or area) in an array. An array is a multiplication model used to work toward independence and mental math strategies.

Students discovered that by decomposing the array into smaller arrays, they could more easily find the product. We also encouraged them to record using correct algebraic notation. You'll notice in this piece of student work that 4 x 3, said, "four groups of three," can be decomposed into (2 x 3) + (2x3) = 12.

More recently, we've been exploring larger numbers, too, and recognizing relationships. The chart below was created by my co-teach partner, Ashley, during a lesson to emphasis why students have been seeing the pattern of a 0 in the ones place. Zeros aren't merely added to the ones place, rather they are in the ones place because they are a multiple of 10. Multiples of 10 have a 0 in the ones place. A student could see that 5 x 60 = 5 x 6 x 10. This helps them see why the pattern occurs.