#### Material

Four boxes of different colors, each containing a set of cylinders that match the dimensions of the four cylinder blocks.

Yellow box, three dimensions of variation, width, breadth and height decrease.

Green box, three dimensions of variation, width, breadth and height, cylinder diameter decreases while height increases.

Red box, two dimensions of variation, width and breadth, height remains constant while base decreases.

Blue box, one dimension of variation, height decreases, diameter remains constant.

#### Presentation

- Take red and yellow boxes to the table.
- Place red box in the top left corner of table, yellow box in the top right.
- Bring red box close to you, remove cylinders one at a time, randomize.
- Place the red box back to its corner, lid on, and order the cylinders in a row from widest to narrowest.
- Visually examine cylinders. Put the red cylinders up.
- Repeat process for yellow cylinders, ordering them from tallest to shortest, 1/3 of the way through, invite the child to finish ordering them.
- Once the child completes the yellow cylinders, keep them out and invite the child to get the red cylinders out and randomize the red cylinders.
- Align them in a row right behind the yellow cylinders, matching them by wideness and narrowness.
- Let the child explore, build, and stack the cylinders.
- For cleaning up, explain that it may work best to place the larger cylinders in the box first.

#### Exercises

##### Exercise 1: Presentation

The child performs the exercise as presented.

##### Exercise 2: Green and Yellow Boxes

- Take green and yellow boxes to the table.
- Place the yellow box in the top left corner of the table, the green box in the top right.
- Order the green cylinders from widest to narrowest, left to right.
- Behind the Green row, repeat this process for the yellow cylinders, widest to narrowest, left to right in a row.
- Invite the child to see if any green cylinders and yellow cylinders are the same height.
- After noticing that there are matches of height, invite the child to order them all based on corresponding height.
- Point out that each cylinder can fit on top of another cylinder.
- Demonstrate this by picking up a yellow cylinder and place it on a green cylinder. Invite the child to do this.
- Once all the cylinders are stacked with a corresponding match, invite the child to explore.

##### Exercise 3: Blue Box

- Bring only the blue box to the table.
- Randomize the blue cylinders from left to right, tall to short.
- Invite the child to bring another colored cylinder box of his/her choice to compare the cylinders.
- Let the child explore.

##### Exercise 4: Comparing any Two Sets

##### Exercise 5: Comparing Three and Four Sets

##### Exercise 6: Towers

The child may take two boxes to a rug, and build a tower on top of one of the boxes, using the lid as a platform. When the child is ready, he may take three or four boxes to a rug to perform this exercise.

#### Language

None.

#### Control of Error

The child’s ability.

#### Direct Purpose

Observe and compare the different sets of cylinders.

#### Indirect Purpose

Getting a clear idea about dimensions and their interplays.

Preparation for mathematics.

#### Age

4 1/2 to 5