Mom's 1st Grade Graphing Unit

Mom and Me
In 1993, my mom won one of the Presidential Awards for Excellence in Mathematics Teaching (PAEMST). Sadly, she no longer remembers this extraordinary accomplishment. Like so much else, Alzheimer's has robbed this happy memory from her. In order to commemorate the end of Teacher Appreciation Week and Mother's Day, I thought I would share part of her award winning unit with you in order to keep this memory alive. With the exception of adding hyperlinks and some spacing and editing, I have tried to keep much of the original formatting.

A developmentally Appropriate, Hands-On, Spiraled,
Integrated Graphing Unit

This unit was developed during the '91-'92 school year. It was the result of my second year of experience with the Everyday Mathematics Curriculum-University of Chicago School Mathematics Project (EMC-UCSMP) and the Michigan Mathematics Inservice Project (M2IP) trainer sessions I attended at Northern Michigan University (NMU).

We are beginning to look at outcomes-based education. Thus, I will write the unit goals as exit outcomes.

Exit Outcomes
  • Students will be able to gather data for graphs, report the data, and construct graphs.
  • Students will recognize different kinds of graphs.
  • Students will be able to read and interpret graphs.
  • Students will see the value of graphs as a means of communication in all areas of the curriculum.
These are skills we adults use. We find it beneficial to be able to read and interpret graphs in newspapers, magazines and other written material.


September: "What bus do you ride?"
  1. A first grade "people" graph
  2. A large, yellow-circle, floor graph
  3. A small, yellow-circle, chalk board graph
  4. A yellow-circle graph on graph paper
  5. A yellow, vertical, bar graph on graph paper
October: "What's your favorite kind of gum?"
  1. object (sticks of gum) graph
  2. vertical, bar graph on graph paper
November: Weather (Math./Science)
  1. A horizontal pictograph
  2. A horizontal tally graph
  3. A horizontal, bar graph on graph paper
December: Our favorite animals (Science/Reading)
  1. vertical bar graph using "post-its" (names on)
  2. vertical bar graph on graph paper
January: The Temperature (Math./Science)

  • symbol pictograph

January (continued): Birthdays (Soc. Studies/Math)
  1. vertical bar graph using large post its, with name, and picture if they wish
  2. vertical bar graph in Math. Journal
February: The U. P. 200 Sled Dog Race (Soc. Studies/Math./Language Arts)
  • Graph 1 - Number of times each alphabet letter is used in "Midnight Musher Sled Dog Race"
  • Graph 2 - Distance in miles between check points in The U.P. 200
(both graphs are vertical bar graphs)

March: "Are you 6, or 7, or 8?" (Language Arts)
  • Using A. A. Milne's poem "The End" (When I Was One...), children graph their present age using a vertical bar graph
(this poem is in our reading curriculum)

April: "How many students in each grade level at Vandenboom?" (Social Studies)
  • line graph
  • I make copies (black) of the graphs we have made on graph paper during the year. These then resemble graphs the students see in magazines and newspapers. We look at these graphs, one at a time, over several weeks, reviewing how we gathered the data what information the graph contains, and how we read and explain the graph.
  • We continue to review the graphs we made during the year. I bring in simple graphs from newspapers and magazines to use with the children.
  • If possible we make a Stem and Leaf Plot, using our class Birth-Month Graph. (Two years ago the first graders handled this easily. Last year the class had no difficulty with pictographs and bar graphs. Line graphs were manageable. However, it was a class that was easily frustrated by a difficult concept. They had enjoyed the graphing unit throughout the year and so I decided not to attempt a Stem and Leaf Plot which might have changed their positive feelings about graphing. I think I can do a Stem and Leaf Plot again this year.)
  • We close the year-long unit by discussing all the different kinds of graphs we constructed during the year. This year I may ask them to decide which graphs were their favorites, and then graph the results.
I'm only providing one example in an effort to conserve space.
You can find a link to the entire document at the end of this page.

The February graphing experience is built around the U.P. 200 Sled Dog Race, a big community event!! The media covers this event thoroughly, and some first graders even attend the beginning of the race and the finish. Our classroom is filled with pictures of previous races, newspaper clippings, stories and legends about the Iditarod, sled dogs and sled dog races. We include art and music in this thoroughly integrated unit. Our school adopts a Musher, who then visits the school with some of his sled dogs. He presents an assembly program and then each class has an opportunity to spend some time outside with the Musher and his sled dogs, and sometimes ride on the sled. As a result of the excitement surrounding this event, the graphing we do is always fun for the children and includes some advanced (for first graders) map reading skills.

Graph 1 is titled "Midnight Musher Sled Dog Race". Across the bottom are the letters of the alphabet. We gave the number of times each letter of the alphabet occurs in the title - Midnight Musher Sled Dog Race.

Graph 2 is titled "U.P. Sled Dog Race". Across the bottom of the graph are the 5 checkpoints. We graph (vertically) the distance in miles between each of the check points.

UP 200 Start February 18, 2011


From the research I have seen (M2IP), I believe this unit provides a developmentally appropriate progression from concrete (people and objects) representation to the abstract. After hands-on activities I find first graders have a much improved understanding of bar graphs and line graphs.

I believe this unit prepares the children to intelligently and confidently construct and interpret simple graphs. They see how graphs can clearly and easily communicate information. We share some of our graph information with students and parents at our school. The skills the first graders acquire now will be useful in their adult life. Parents and teachers in our school, and in our school district, want to see students develop a strong and meaningful foundation for skills they will use as successful adults. This unit addresses that goal.


The Everyday Mathematics Curriculum uses Performance Assessment. I am a firm believer in this type of evaluation and have been very happy with the results in our classroom.

I liten to the students do the problem solving needed when we begin to make graphs. I note this on an assessment chart. I continue to assess through-out the unit. I listen to their verbal responses in whole group discussions and in their small group work. I talk with them in groups and individually as they construct graphs, and listen to their responses to questions. I watch them work and I question them about the data on their graphs. They sometimes write brief statements about what information the graphs contain. By questions and observations I assess their knowledge of the different kinds of graphs. I also do some individual assessments in areas I feel necessary. I find that I can track the process students are using much more accurately with performance assessment than with the "tests" I formally used. I am able to interact with the students, and thus better see where they are having problems. I try to find time to do reassessments when it seems necessary. I strive to make my assessments congruent with my expected exit outcomes.


Here is a PDF of the First Grade Graphing Unit submitted by my mom at the insistence of NMU Math Education Professor John Van Beynen. Unfortunately, a sample assessment chart and example performance assessments described in the submission were not included in the file that I found. I fear that they have been lost, just as my mom's memory of the entire episode has been lost. If you download the unit and find it useful, I would encourage you to consider making a small donation to the Alzheimer's Association. With your help, we can work toward making sure that the happy memories of mothers and teachers everywhere are no longer stolen by this terrible disease.

Update: On August 30, 2012, my mom died from complications related to Alzheimer's.


  1. Thank you, David, for sharing your mom's great lesson. I will share it with our 1st and 2nd grade teachers.

  2. First of all, my deepest condolences on the loss of your mother. She was not only a great Mathematician but also one of the best I've ever seen in my life. Thank you David for sharing this priceless gem from your mothers closet. May her soul rest in peace and I'd be ever grateful to have learnt and seen such a remarkable educator like your mother and obviously yourself.


  3. I feel very lucky to have come across this website. Thank you for sharing your mothers work with the rest of the teaching community. You have done a great thing in continuing on her legacy while bringing attention to the sad disease of Alzheimers .. my step-father has been recently diagnosed at the young age of 60.