## Chapter 12

### 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 counting pictures, create a “Counting Pictures” bulletin board display. You might want to have the children help you group the pictures into categories, those that show counting by fives and those that show counting by twos. A good time to do this activity is after Lesson 2 on counting by fives.

### Part 2: Be an Investigator

A good time to do this investigation is after Lesson 4 on even and odd numbers.

#### Materials

- Investigator Worksheet (PDF file) for each pair
- square tiles

#### Introducing the Investigation

Show the children a group of six tiles. Ask them if they could make a rectangle that is two units wide with those tiles. Have a volunteer show how by making a two by three unit rectangle.

Now take one of the tiles away. Ask the children if now they could make a rectangle that is two units wide with those tiles. Let the children try and discover it is impossible.

Put the children in pairs and give them the Investigator Worksheet. Tell them that they are going to try every number from four to 12 to see if they can make rectangles that are two units wide. They will write yes or no in the table to show if they could do it or not. When they can do it, they will draw a picture of what the rectangle looks like in the table.

#### Doing the Investigation

When the groups are finished doing the investigation, have a discussion about the results. Ask the following questions:

**What do you notice about all of the numbers that worked (where you could make a rectangle two units wide)?**(They are all even numbers, 4, 6, 8, 10, and 12.)**What do you notice about all of the numbers that did not work (where you could not make a rectangle two units wide)?**(They are all odd numbers, 5, 7, 9, and 11.)

#### Extending the Investigation

Have the children try this with numbers greater than 12 to confirm that you can always make a rectangle two units wide with an even number of square tiles and you can never do it with an odd number of square tiles.