## Chapter 9

### Part 1: Home and School Investigation

Send the Letter to Family (PDF file) home with each child. Once all of the children have brought in their folded pieces of paper, tell them that they are going to help you sort the papers into two groups. Arrange a place for each group: those pieces of paper that were folded into halves and those pieces of paper that were folded into fourths. Hold the pieces of paper up one-by-one and ask the children which group they belong to. As you do this, occasionally ask the children if the parts look equal. If you run into a piece of paper that is divided into parts that are obviously unequal, use this as an opportunity to talk about why that paper was not divided into halves or fourths.

It is possible that a child will point out that the papers divided into fourths are also divided into halves. Let the child know that is a very good comment and explain that the two groups are actually “divided into halves only” and “divided into both halves and fourths.” Using one of the pieces of paper that has been divided into fourths, show how it has also been divided into halves.

A good time to do this activity is after Lesson 3 on fourths.

### Part 2: Be an Investigator

A good time to do this investigation is after Lesson 5 on probability.

#### Materials

- counters of two colors
- two clear jars of the same size, one labeled Jar A and filled with nine “blue” (Color 1) counters and one “red” (Color 2) counter and the other labeled Jar B and filled with two “blue” (Color 1) counters and eight “red” (Color 2) counters
- paper bags

#### Introducing the Investigation

Show the two jars with the counters in them to the children. Ask, **If you were going to get a prize for picking a “red” counter when you reached into the jar blindfolded, which jar would you draw from?** Discuss why Jar B would be a good choice. You might even want to have children draw a counter from the jar a few times to see what happens. If you do that, be sure to put the counter back after each draw.

Now ask, **If you were going to get a prize for picking a “blue” counter when you reached into the jar blindfolded, which jar would you draw from?** Discuss why Jar A would be a good choice. Again, you might want to have children draw a counter from the jar a few times to see what happens.

#### Doing the Investigation

Put the children in pairs. Ask half of the groups to put 10 counters in a bag so that a person would be certain to draw “red.” Ask the other half of the groups to put 10 counters in a bag so that a person would be certain to draw “blue.”

When children have their bags ready, have all of the groups that created the “red” counter bags pour the counters out of the bag for all to see. Children should have put all “red” counters in the bags. If there are any bags that contain colors other than “red,” talk about why, with a bag like this, a person would not be sure to pick “red.”

Do the same with the groups that created the “blue” counter bags where a person would be sure to draw a “blue” counter.