# Pumpkin Math Part 1

## Curriculum Goal

#### Junior: Geometry and Spatial Sense/Measurement

• Use appropriate metric units to estimate and measure length.
• Solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units.

## Context

• This lesson is Part 1 of 2. It explores circumference and height using non-standard measurements. It also introduces the relationship between various units of measure. Part 2 allows students to build on their knowledge from Part 1 by having students measure and convert between units.
• Students face the educator in a circle with the pumpkins in the center.

## Materials

In-person version

• 3-6 pumpkins of varying sizes
• Whiteboard and erasable markers
• Ribbons (plastic or fabric)
• Scissors
• Rulers
• Cube blocks
• Practice conversion worksheets, teacher reference chart (Appendix A)

Online version

• Video conference capabilities

## Lesson

Introduction

• Have students organize the pumpkins from the smallest to the largest. Make sure they arrange them in that sequence so their classmates can see.
• Label each of the pumpkins with a permanent marker as “A”, “B”, “C”, etc.
• Ask students: What are different ways that we can measure these pumpkins?
• Students may suggest looking at the weight of pumpkins, their volume, their height, etc.
• Note students’ suggestions on the whiteboard.
• Tell students that we will focus on measuring and comparing the pumpkins’ circumference and height.

Lesson

• Have students share their ideas about how to measure the circumference of one of the pumpkins.
• Ask: How can we measure the circumference of Pumpkin A using this piece of ribbon? Where would we place our ribbon?
• After giving students time to discuss their ideas, inform them that the circumference must be measured at the widest part of the pumpkin.
• Choose one of the larger pumpkins and set it in the middle for all students to see.
• Have each student cut a piece of ribbon that they think will match the circumference of the pumpkin.
• When everyone is ready, ask each child to compare their ribbon to the circumference of the pumpkin.
• Support students if they need help aligning their ribbon in the middle of the pumpkin.
• Repeat this activity with a smaller pumpkin: have students observe the pumpkin, cut a ribbon that they think fits the circumference, and then compare to see how close they got to the pumpkin’s actual circumference.
• Ask students to explain how they were visualizing the circumference of the pumpkin in order to cut out the matching ribbon length.
• After students explore with their ribbons, share that they could measure the pumpkin’s circumference by wrapping a measuring tape around its middle, just the way they have been working with their ribbons.
• When exploring the pumpkin’s height, ask students to estimate how many stacked cube blocks would be equivalent to the pumpkin’s height. Have them use cube blocks to represent their estimates and share with the class. For example, a student might stack 12 cube blocks and say: I think the height of Pumpkin C is 12 cube blocks.
• Students may line up their stacked cube blocks beside the pumpkin to see how close they were.
• When measuring the pumpkin’s height, show students how they can place their rulers in a position to most accurately determine the measurement. Have one ruler measuring vertically, while a second ruler is held horizontally across the top to determine where the two rulers intersect (see Image 1A).
• Inform students that the height of the pumpkin would be measured from its base to top, not including the pumpkin’s stem, and also in the center of the pumpkin.
• Tell students that the weight of a pumpkin can be measured using a weighing scale, which they will use in Part 2 of this exploration.

Class Discussion: Measurement

• Briefly review measurement if required by your students.
• Emphasize the relationship between different units of measure.
• Write the relationship between the units on the whiteboard. For example, “100 cm = 1m”.
• When discussing circumference and height, ask students to explain the relationship between millimeters (mm) and centimeters (cm), cm and meters (m), and m and kilometers (km).
• When talking about units of measurement, it is also important to discuss place value so students can understand the base ten relationships among metric units. This helps to build a foundation to fluently convert between units. For example, 27mm is 2.7cm, or 2 and 7 tenths of a centimeter. This highlights the relationship between mm and cm (10mm = 1cm).
• Prepare some examples for students to practice noticing the base ten relationships where they convert between bigger and smaller units. For example, ask students: How many mm is 27.2 cm equivalent to? Practicing conversions this way allows for exploration of decimals.
• Write the key relationships between units of measure on the whiteboard for length (Appendix A).
• If time permits, work through practice conversions with students to help solidify the knowledge of the relationships between the units of measure (Appendix A).
• Depending on the capabilities of your students, you may choose to omit the weight in pounds. We have included this because, here in Canada, weight is often measured in pounds even though we use the metric system. You may wish to challenge your students to convert the weight from metric to imperial.

## Look Fors

• Are students able to accurately measure the height and circumference of the pumpkins using standard and non-standard units of measurement?
• Can students recognize the relationships between units of measure and convert between them?
• Can students describe the base ten relationships among the metric units?

## Acknowledgment

We thank educator Zoe Donoahue for inspiring us with this lesson. This lesson is an adaptation of an activity Zoe conducts with her Grade 5 students at The Dr. Eric Jackman Institute of Child Study Lab School at the Ontario Institute for Studies in EducationUniversity of Toronto.