**1. "How Many Are There?"**

Children love to count -- and they need practice to learn the correct sequence of numbers. But in order to develop an understanding of the meaning of numbers, they must learn about one-to-one correspondence -- counting objects one by one, pointing to them as they say the numbers in the sequence. And children must also grasp the concept of cardinality -- that the last number in the sequence tells how many objects there are.

**Activity Idea:** Play "How Many Buttons?" As children come to the front of the room one by one, have the class count how many buttons are on each child's shirt. This is a good way to introduce the idea that zero means none at all.

**2. "How Many of Each Kind?"**

Children develop classification and counting skills as they think about this question. "How many?" asks them to count the number of items -- but first they have to sort the items to determine "each kind." Children learn that different types of things belong to different groups.

**Activity Idea:** Provide collections of almost anything in your classroom -- from buttons to beads to bottle caps -- for children to sort and count.

**3. "How Are These the Same/Different?"**

To answer this question, children looks at two items and identify how they are alike or different. Answering the question requires children to observe, compare, analyze, and then reach a conclusion -- the basic skills of mathematical and scientific exploration.

**Activity Idea:** Gather children in a circle and have each child take off one shoe. Pick up two shoes and ask, "How are these the same?" Let children share their ideas. Then ask, "How are they different?"

**4. "Which Has More/Fewer?"**

Comparing quantities is key to setting the stage for chidlren's later thinking about subtraction.

**Activity Idea:** Play "Coin Toss." Give a child an odd number of pennies to toss -- five or seven to start. Ask,"Which are there more of -- heads or tails?" This is also good for helping children become familiar with coins.

**5. "Which Is Taller/Longer/Shorter?"**

Young children are most comfortable comparing lengths by using direct comparison -- matching up objects to see which is taller, longer, or shorter. When this isn't possible, such as when figuring out which table is longer when they're on different sides of the room, children can use a variety of nonstandard measures -- paper clips, pencils, baby steps. Making direct comparisons and using nonstandard measures help prepare children for learning standard units such as inches, centimeters, and feet.

**Activity Idea:** Choose one length of ribbon from a basket of ribbons, and have children sort the rest according to whether they're longer or shorter.

*This page is an excerpt from the January 1998 issue of Early Childhood Today. The author is Marilyn Burns, a leading mathematics educator and the creator of Math Solutions, a nationwide in-service training program.*