# From One to One Hundred, by Michael Naylor

*Math activities with a hundreds chart can be a great way to celebrate the 100th day of school!*

The 100th day of school usually occurs at some point in February. This month, let's take a look at activities for a hundreds chart.

A hundreds chart is simply a 10 x 10 grid with the numbers 1-100. (The chart can also be numbered 0-99.) They're easy to make on a computer, or you can download a grid here.

**Chart tour (Grades K-2)**

Provide copies of the hundreds chart to each of your students. Make a transparency of the chart to model the activity on the overhead projector. Ask your students to place a transparent chip (or other counter) on the 1. Call out commands, asking them to add or subtract single-digit numbers or add or subtract multiples of ten – "Add 3. Add 2. Add 10. Add 20." The idea is to get kids familiar with the relationships between numbers in the same row and column.

Once your students have the hang of this, hide your model on the overhead and call out more commands. After five or six moves, reveal your model and the students can check to see if they followed all of the instructions correctly.

**Mystery number (Grades 1-3)**

Create a "mystery box" for your classroom model by cutting a hole in the middle of a piece of construction paper so that it frames one number on the chart and hides the eight numbers surrounding it.

Next, place the mystery box on a number and then point to various spots that are hidden by the box and ask your students to figure out which number is in that spot. Be sure to elicit lots of responses – there are many ways to figure out what the number is, and each idea is worth thinking about!

Try this on several numbers, then place a sticky note over the opening so the entire 3 x 3 square is blocked. Can your students figure out what number is in the center of the square?

**Missing numbers (Grades 1-3)**

Provide hundreds charts that have 20 or 30 missing numbers. Working in small groups, have students complete the chart. Discuss the different strategies students used to fill in the charts.

**Multiple patterns (Grades 3-5)**

Ask your students to choose a number from 2-12. Then ask the class to color in the squares on their hundreds chart that are multiples of that number. Display different multiples in the classroom and discuss any patterns the students find. Which numbers make straight lines? (multiples of 2 make five lines, multiples of 5 make two lines, and multiples of 10 make one line…what is the relationship between those numbers?) Which numbers make diagonals? (9 and 11) What patterns are there in other multiples?

Have students hang their charts in groups in the hallway or in the classroom. These fun and colorful patterns can develop number sense long after the activity is done.

**Least common multiples (Grades 5-8)**

Use this as a follow-up to the above activity. Have your students choose a second number from 2-12 and color multiples of those numbers a different color. Students should circle any numbers where the two colors overlap.

Place the students in small groups and ask them to find as many patterns as they can. During discussion, introduce the notion that the circled numbers are multiples of both numbers, so they are called common multiples. In this example, 28, 56 and 84 are common multiples of 4 and 7. Give your students a minute or two to find as many other common multiples of their two numbers as they can. Notice that there is no greatest common multiple!

There is a least common multiple – and it usually is the product of the two numbers (4 x 7 = 28 in the above example), but not always! If the starting numbers are 4 and 6, for example, the first common multiple occurs at 12.

Introduce the notation LCM (a,b) to stand for the least common multiple of a and b. LCM (4,7) = 28 and LCM (4,6) = 12.

There is a mystery here – when does the least common multiple of two numbers equal the product of the two numbers? This makes for an excellent problem-solving activity with older students. The main idea is that if a and b have any factors in common, then LCM (a,b) ? ab. 4 and 6 both have 2 as a factor. Divide by 2 from the product 4 and 6, and you'll have 12, which is LCM (4,6). This can lead into a unit about prime factorization and number theory. Have fun!

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.