As long as my grandson has been willing to play around with graphs recently, we have been trying to come up with more things to graph.

After we graphed the number of letters in state names and the size of states in area and population, we turned to rivers and created scatter plots.

One of the things I found out in all this graphing activity is that you have to figure out how many lines you have available on your graph paper, in both directions, across the top and up the side.

Then, find out the highest numbers you will need.

That way, you can figure out what numbers to put on the left side, or vertical or y-axis, of your graph, or across the bottom, the horizontal or x-axis.

For example, what is the longest river in the United States?

If you had said the Missouri, you’d be right (2,341 miles).

If you’d said the Mississippi, you’d be close (2,202 miles). It is the second longest river.

Then, come the Yukon (1,979 miles) and the Rio Grande rivers (1,759 miles).

Let’s get graphing!

**Materials:**

- Graph paper
- Pencil or pen
- A reference book, such as an atlas or almanac, or the Internet to find the lengths of the top 15 longest rivers in the U.S.
- Click here to get a list of the longest rivers in the U.S.

- Pick the top 15 longest rivers in the U.S.
- Optional: Pick the 20 longest rivers in the world
- Click here to get a list of the 20 longest rivers in the world

**Instructions:**** **

- Have your grandchild write the title of the graph across the top: 15 Longest Rivers in the U.S.
- Count the number of lines across the bottom and up the side of the graph paper.
- My paper had 8 large boxes across the bottom, the short side, and 10 boxes up the left side, the long side. Each box had 4 lines inside, in addition to the dark lines marking the sides of the boxes.
- You will need 15 lines across for the 15 rivers. Label lines or spaces an equal distance apart across the bottom edge with river names or 2-letter abbreviations.
- I found it easier to make the graph if I started on the left corner at the bottom of the page with the shortest of the 15 rivers, continuing across the bottom of the page and ending with the longest river to be labeled, even though your list probably starts with the longest river.
- Normally, the bottom left of a graph shows the lowest number, rising to the top right corner for the highest number.
- You or your grandchildren can label the middle of every other line with river names or abbreviations, across the bottom.
- You or your grandchild can label each of the lines going up the side of the graph paper. I labeled mine in 100s, thus, 0 on the bottom line on the left of the page, 100 on the line above it, 200 on the line above that. You have to get to at least 2,400, because the longest river in the U.S. is the Missouri, at 2,341 miles.
- Have your grandchild find the spot above the first river, in my case, the shortest, the Green River, at 760 miles long, where the column above the river name is about the same height as the number nearest to the length of the river. Since you have labeled the lines by 100s, the 7
^{th}line up is 700. To show 760 miles, put a dot about half-way between the 700 line and the 800 line. - The next shortest of the 15 rivers is the Brazos, at 860 miles. Have your grandchild find the spot above where the Brazos River is labeled, and put a dot between the 800 and 900 lines.
- They are making a scatter plot!
- Continue looking for the spot that represents the length of the river and put a dot above where the river is labeled, until you have all 15 dots.
- Optional: Make a scatter plot for the 20 longest rivers in the world.
- Since the Nile is 6,650 miles long, the graph you made for the U.S. rivers won’t be big enough.
- Either tape a piece of graph paper to the top of the U.S. rivers graph and continue labeling the lines by 100s up the left side, or start a new graph and label the lines by 200s.

**Why Is This Useful?**

One of the first things you will notice when you have all 15 dots on your U.S. river graph, or all 20 on your world river graph, is that the dots tend to cluster.

Seven of the U.S. rivers lie between the 800-mile and 1,200-mile lengths.

No other 400-mile range has so many rivers.

Similarly, six of the longest rivers in the world lie in the 3,200-mile to 3,800-mile range and six lie in the 4,200 to 4,700-mile range.

Scatter plots make it easy to see patterns like this.

One of the best examples comes from statistician Edward Tufte, who specializes in making information easy to understand with graphs.

One of his most dramatic examples is a scatter plot showing how much more often a critical component of a rocket ship, the O-ring, failed as the temperature dropped.

He argues that had the information been displayed in a scatter plot instead of the timeline that was used, it would have been easy for engineers and managers to see how unsafe it was to allow the Challenger to launch when the temperature was below freezing, and avert what came to be the Challenger disaster.

Instead, they were left with the fact that sometimes an O-ring didn’t fail at temperatures below freezing, instead of seeing that the cluster of successful launches were well above freezing and very few successful launches were below freezing.

On January 28, 1986, the Space Shuttle Challenger was given permission to launch, broke up 73 seconds into its flight and seven astronauts died.

For lack of a scatter plot.

** This article first appeared on grandmotherdiaries.com**

Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers”

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Very impressive. I appreciate any and all assistance when it comes to helping grandkids with their math because I definitely have to work so hard at it. Thank you 🙂

I’ve always loved math, Kaye, but I know that’s not true for everyone. What’s fun about finding these activities is that they demonstrate fundamental math concepts in the physical world, not just the abstract world where most math education lives.

Wow! Another remarkable and well researched idea for sharing with kids as enrichment! I think of all the extra self confidence your grandson is building as a result of his time with you and these unique activities. Lots of critical thinking skills being developed as you play these games together!

Thanks, Joyce. I like to think of it as sneaky education. Even though I’m not a teacher, as a grandmother, I can help prepare the educational ground and have fun at the same time.

You really do make learning fun for them!

Thanks, Grandma KC! I’m on a math jag now and look for concepts that can be explained in simple terms. So far, I haven’t found a way to explain Planck’s Constant!

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