Yarn, Tape, and Scratch Paper: Creatively Estimating the Dimensions of the Reflecting Pool

In this LILI mini-lesson students visit the Reflecting Pool to think creatively about how to measure and estimate length to help them determine a value.

Developing expeditionary math lessons can be difficult, but real-life examples of math concepts are everywhere in Washington, DC! They are in the curves of our Capitol’s dome, in the sound waves at the Opera House of the Kennedy Center, in WMATA’s data on Metro riders. Getting your students out of the classroom for math-focused field trips requires solid planning, but it is critical that students experience and see the relevance of mathematics in the real world!

My brother, an audio engineer, has spent a lot of time at (and sometimes IN) the Reflecting Pool, setting up and striking (taking-down) shows in front of the Lincoln Memorial. When chatting with him about potential math-based field experiences in DC, he immediately suggested a student-driven discovery of the measurements of the Reflecting Pool. It was brilliant!

Live It Learn It spends a lot of time at the Reflecting Pool during our March on Washington unit. It is a wonderful space for field trips with older elementary school students – giving them a bit more autonomy for self-discovery, while also being open enough to ensure that you can keep tabs on all your students at once. It is also less visually distracting than other field destinations, allowing for deep project-based focus.

This lesson encourages students to creatively problem solve. There is no singular correct answer for this activity – the goal is that students are making educated estimates (rather than guesses) of area and/or volume by inventing a way to measure a length. By giving your students an odd assortment of materials, groups will have to work collaboratively and creatively to measure distance!

Here’s how to lead an expeditionary STEM-based lesson on area/volume at the Reflecting Pool!

Objective: Students will be able to estimate the area/volume of the Reflecting Pool through designing a measurement system and calculating the area and/or volume of rectangular and triangular prisms.

Grade Level: Please adapt this lesson to suit your class’ needs (i.e. running the first steps before the field trip or saving the calculations for after the field trip)! While this field experience aligns with most 4th and 5th grade standards for calculating volume, you can easily adjust this lesson for students learning area or estimation of length. You can also adapt it for older grade levels learning liquid volume or the order of operations (by adapting the formulas for volume). Please note that students should have experience measuring lengths, and calculating either area or the volume of prisms (depending on which extension you choose).

Time: ~60 minutes at the Reflecting Pool

  • Printed photos of the aerial view of the Reflecting Pool to show while teaching at the site
  • Materials for each group of 4-5 students:

A clipboard
A ball of yarn or string
A roll of scotch tape
Scratch paper
Pair of children’s-sized scissors
A yardstick or ruler
Handout Part I (Word or PDF)
Handout Part II – EITHER: Area (Word or PDF) OR Volume (Word or PDF)

Notes about the space:

  • Review where they are and the importance and significance of the Reflecting Pool (this will help students be mindful of their actions while at the Memorial).
  • Explain to your students the importance of keeping the space clean and point out an accessible recycling bin and trash can.
  • If possible, give the Park Service an advance warning that your class will be at the Reflecting Pool. They may be able to greet your class and/or provide additional support while at the Memorial. Contact Jennifer Rudnick at Jennifer_epstein@nps.gov.

Notes about the field experience:

  • This lesson is best conducted in groups of 4 or 5 (each accompanied by a chaperone). Each group should have either a student leader or chaperone who is comfortable making measurements and estimates.
  • Students are practicing estimations, there is no singular correct answer. This field experience is about ensuring that students can think critically and show their work.


  1. After arriving at the Reflecting Pool, find a good spot to gather your class.

  2. Warm-up:
  • Ask students to guess the length of a pencil – don’t discourage answers that are way off!
  • Then discuss the difference between guessing and estimating, an estimate being an educated guess, backed up by a process or method.
  • Finally, ask students how they might estimate the length of a pencil without having a ruler. What tools could they use instead? Look for students to explain their method, (i.e. “I know that the top of my thumb is about an inch, and a pencil is about 8 thumb-tops long, so I think the pencil is 8 inches long.”). If students are stuck, ask them if they have a general idea of what an inch looks like.
  1. Explain the shape of the Reflecting Pool: The pool is not a perfect rectangle – it has two little flanges/wings extruding at either end. Ask students if any of the sides appear to be even in length (this should help prevent them from measuring the entire perimeter).

  1. Investigation:
  • Split the class into groups, each accompanied by a chaperone. Give each group an activity sheet and have them sketch out the shape of the Reflecting Pool.
  • Give each group a yardstick, small kid-sized scissors, scratch paper, tape, and a ball of string or yarn. The idea is that the students can use all or some of these materials to creatively estimate length.
  • Send the groups to different corners of the pool to start their measurements in order to ensure that they have creative space.
  • Allow students to work collaboratively to invent ways to estimate length using the tools they’ve been given. The idea is for students to invent a more efficient way to find length than measuring yard-by-yard. Encourage chaperones beforehand to push students to think beyond the yardstick. Students might measure out a length of 10 yards of string and then use it to measure stretches of 10 yards, or they might invent a way to incorporate tape and scratch paper in their technique.
  • Make sure students are tracking their measurements on their activity sheets and/or scratch paper.  
  • When students are finished, have them meet back at a given location. You may also want to give chaperones a final cut-off time.
  1. Analyze and Connect: Allow students to use their measurements of length and width to calculate an estimate of either area or volume.
For classes determining area: use this worksheet.
–   Hand out the second activity sheet. Have students separate the Reflecting Pool into rectangular segments.

–   Have students explain how they might calculate area using these rectangles and the formula for calculating the area of a rectangle.

–   Make sure students show their work as they calculate their estimate of the area of the Reflecting Pool.

For classes determining volume: use this worksheet.
–   Hand out the second activity sheet. Have students determine which shapes they recognize in the 3D image of the Reflecting Pool (as seen below). Allow students to take their time finding both rectangular prisms and triangular prisms in the graphics. The idea is that they will determine that the Reflecting Pool is made up of two rectangular prisms and two triangular prisms. (Note: We have chosen to ignore the shallow edge that faces the Washington Monument.)

–   Have students use their activity sheets to determine an estimated volume of the Reflecting Pool. (Note: Students may notice that the pool is not filled to the brim – remind students that the volume will give them the maximum capacity of the pool.)

For Early-Finishers:
Once they’ve found their measurements and have shown their work, have students discuss what they would like to fill the pool with instead of water. Then have them draw their filling of choice on scratch paper until the other groups are finished!

Share your photos and sketches with @liveitlearnitdc – we would love to see them! Happy estimating!


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