Pumpkin Math! Introduction to Metric Units

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Objective

SWBAT measure circumference, diameter, & length using centimeters/meters, liters and grams.

Big Idea

Students get introduced to metric units using pumpkins.

Introduction: Capacity

10 minutes

 We will study measurement later in the year, but this lesson is a fun way to introduce the metric system ahead of studying a whole unit on measurement. We are focusing mainly on the introduction of using the meter tape, a gram scale and a liter. The goal of this whole lesson is just exposure, experimentation with metric measurement tools, and motivating their interest in learning more about measurement. Our MAP data ( benchmark scores) showed lowest scores in measurement and so I hope to spark their interest so that it continues when the actual metrics unit starts.

Materials: Pumpkins of various sizes with the lids cut, one pumpkin per two students. Worksheet, two 1000ml & 100 ml graduated cylinders, beaker, metric scale that can weigh a good sized pumpkin (not a balance scale), newspapers, scoops or spoons, metric tape measure and lots of newspapers. ( I cut all of the tops prior to the lesson, set up the science lab with newspapers and enough pumpkins per pair of students.

Introducing Metric Concepts: I opened up the lesson by asking students if they knew about metric units. I asked them if they knew what a millimeter was. I explained that it was about the size of a hair. They were so surprised. I continued by talking about centimeters. I showed them that a centimeter is just about the size between the tip of our index fingers to the first knuckle. They all looked at their fingers and then I showed them how to use the thumb and index finger to show a centimeter size. I asked them if they could tell me what they thought a meter was. One student said that it was about the size of a yardstick. We were supporting the standard by discussing relative sizes.

Meters: I drew stair steps for a visual mode (that they will see again later in the year), on the white board and placed the meter at the top ( we would not be going above a meter today) and then wrote mm on the bottom step. I then explained that if I multiplied by 10 that I would get the next unit...so 1m would be 10 dm, 10 dm would be a 100 cm and then 100 cm would be a 1000mm. This served as visual model only at this point and introduction as we will study this stair step model and conversion methods in depth later on.

Grams: I moved into grams, explaining that  mass or weight works the same way, except that we have a different name, much like we have different names for inches and feet vs. pounds and ounces. I explained that grams were the base unit for mass, and placed each of the units on the stair steps above the meter units. This develops their real world connection to understanding that different categories of objects to measure have explicit units that are assigned.

Liters: I explained that we now had unit for length and weight...but what about measuring liquids? I asked if they knew the metric unit for measuring liquids? . Relative size: Liters vs. Millilters I used the graduated cylinder so they could understand the concept of what a liter looked like and the tool we would use to measure the liquid capacity of the pumpkin.

After the introduction, we were ready to begin using our pumpkins to measure using meters, grams and liters.


 

 

 

 

Working in Pairs to Measure

20 minutes

I partnered up my students according to their levels to assure learning support. I paired low/mid with high end students. I had lots of help today with a parent and an aide! I would suggest other adults in the room the day you do this lesson! Extra help is necessary.

Students found their lab site complete with a tape measure and an activity sheet. Pumpkin Math Worksheet. We examined the tape measure to discover it has both inches and centimeters. I told student we would be using only the centimeter side of the tape. I wanted them to measure to the nearest centimeter.

We started with circumference. I explained what that was and demonstrated on a pumpkin. I also asked them what word they could see in circumference, as I emphasized the "cir". One student said, "Circle". I made a circular motion with my finger and had them do the same as they said "circumference" three times in order to reinforce this vocabulary word.

They knew how to measure height easily, but asked if they should include the stem. I told them to include the highest point of the pumpkin, meaning the stem. 

When it came to measuring diameter, several students had trouble.Measuring diameter of a pumpkin is a little tricky... I had to stop and explain what it was. I realized that when we converted the worksheet to metrics, we had forgotten to label the diameter in centimeters. I corrected that error and moved on. The sample worksheet included has been corrected.

I told them we needed to just do all the measuring and recording in the lab and that we would do all the calculations back in the classroom. Students continued to work. They estimated the weight, and then weighed it with the seeds. I had them put their sheets on another counter away from the pumpkin so they wouldn't get them all gooey. Then, they gutted their pumpkin, (gutting the pumpkin) estimated the weight again and weighed it again. We didn't have a metric scale, so a bathroom scale had to do. If I would do this lesson again, I would be sure we had a metric scale on hand.

I stopped and talked about grams once more, making sure they knew that these were pounds they were measuring in and that belonged to a different system. I apologized about the scale and told them it was important to have the right tools to measure the right system. They would have a chance to use a gram balance scale later in the year.

They all were able to measure everything independently and they filled out their sheets easily. We cleaned up and returned to class to finish.

 

Pumpkin Pi

10 minutes

 

I asked students to calculate the measurements on their worksheets and compare their estimations with the actual measurements and weight. I told them to hold off on figuring out pi. We would discover what pi means later in the lesson.

I roved and talked with them about whether or not they were surprised at their answers. I checked for their understanding as they shared their data. Calculation . We discovered that the seeds and guts on average weighed about a pound.

An Extra Concept: For fun, I decided to expose students to the concept of pi. This is not included in the standard, but if we look at MP7, looking for and making use of structure, we can understand that students need exposure to using reasoning and understanding where mathematical formulas come from. Pi is just interesting and the thinking involved is rigorous for this grade level. It will lay a foundation for later on. CCSS demands that we create lessons that are rigorous and so I try to stretch my students when I can with relative concepts. Pi relates to the circumference and diameter and I thought it would be fun to infuse this in with discovery. Many of my students know that pi exists from older brothers and sisters.  I asked them to use their iPad calculator and divide the circumference by the diameter. I told them to check 3 others answers and compare. They got busy and soon were roving around looking at answers.

I stopped them and asked for volunteers to give me their calculations. Sure enough, even though the pumpkins were measured at the middle for circumference and we fudged a little on the diameter, the calculations came out between 2.75 and 3.25. I wrote 3.14 on the board and explained that it was the number for Pi.  I drew a circle on the board and a line for the diameter. I told them that any circle's circumference divided by its diameter will produce a number that is 3.14. I asked why our numbers were a little off? We discussed how hard it was to accurately measure the pumpkin's circumference and diameter because where you placed the tape would change the measurements a little. This work opened up their minds to understanding that we derive formulas from specific phenomena and that math doesn't just "happen". This is underlying  theme and thread that continually runs through CCSS that makes mastering standards so wonderful. I know as I extend and expand on their current thinking that it supports standards down the road. Many of my students heard the word pi from their older siblings. The pi idea was fun and they were amused by this numerical consequence involving measurement of a pumpkin's circumference and diameter.

 

 

Closure

10 minutes

I moved toward closure by touching on the ideas involving capacity using liters.  I wanted them to ponder the different liter units we would use in relation to the size of what we were measuring. For example, we talked about bathtubs vs coffee cups. I lead them to think about how the units would be different for measuring the amounts of liquid in these two containers. We talked about how size of objects being measured would affect which units we would use. We talked about not measuring miles in inches because it was silly to use such large numbers when a larger unit will express it simply. This reinforces again the standard as we try to grasp relative sizes and the relationship to units as I introduce thinking and conceptualizing using real world examples to support Math Practice Standard 4.

This little movie clip shows you the energy and how they still were not completely understanding the meaning or size of the units yet. They will understand when we work with it again. I wasn't worried about mastery because it was intended for an introduction. Relative size and units  (Note the bouncy little guy who keeps blurting out numbers. He was so excited about the whole experience.

We closed our lesson with summarizing that metric measurement is in meters, grams and liters. Students stated one thing they liked about their lesson today. The comment that I heard the most was that they thought using a pumpkin to measure was great and their favorite part was pouring water inside of it. Imagine that?!