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Lesson 2 – How To Measure Quantities – Discussion
Give an example of an object that could be measured in more than one way depending on the attribute you are measuring.
Share:
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The object you will be measuring;
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The specific attribute you plan to measure;
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The unit you will use to measure that attribute; and,
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Describe how you will use the unit to compare with the quantity to measure.
Share your reflection below along with any wonders you still have.
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48 Replies
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An object that could be measured in more than one way in a math unit I teach are the model buildings we create for our Volumeville. We hope the kids measure the volume, but they could just as well measure the height, the surface area, the weight, the time to make the building, etc. It’s a very good reminder to be incredibly clear and on the same page about what is being measured and how else we could measure the object.
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I know I’m not answering the prompt, but as I watched this, I thought back to my programming days with object-oriented programming (OOP). We used attributes and properties as well, with the same definitions.
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3 or 4 years ago, I taught math to a group of 3 gr. 8 boys ( yes, the smallest class in our small school) I tried to make Math more interesting while teaching surface area (before I had stumbled onto Christina Tondevold and Kyle and Jon’s nontraditional ways of teaching Math – I wish I would’ve had these experiences long ago!!) I had them measure the surface areas of various sizes of boxes. One of the boxes was even a triangular prism. Woo-hoo. We measured using centimetres as our unit. My students were very diligent and worked hard at measuring and using the formulas as espoused by the text (and, ahem…me) So. First of all, do I think they retained the formulas? Probably not. Did we discuss how they arrived at answers? Nope. Did I spend hours measuring and figuring out the “answers” myself. Yup.
This upcoming year, the students will be working together to answer the questions re total surface area of an object and we will be sharing how we arrived at our answers. It will probably take longer to do but I have the feeling it will be more beneficial for all in the long run.
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A swimming pool could definitely be measured in more than one way.
1. Surface area (sqr metres)
2. Volume of the pool (cubic metres)
3. Capacity of the pool (kilolitres)
4. The perimeter of the pool (mm – needs accuracy if you are going to tile around the edge, so a small unit of measurement is important)
5. The depth of the pool (metres)
I wonder how many people could fit in the pool without it overflowing?
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The object you will be measuring: What if I gave students pattern blocks?
a) ten green triangles, b) ten yellow hexigon, c) ten red trapiods, d) a mixture of ten different block.
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The specific attribute you plan to measure:
-Ask students to list what their collection have in common.
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The unit you will use to measure that attribute:
-Ask class whose are larger, smaller, ask students for attributes to compare, (harder to find in a dark room, pointer edges, sharper edges, easier to package in a group….) -
Describe how you will use the unit to compare with the quantity to measure.
– ask class to brainstorm what rules of measure (types of measure) can we use to justify your answer.
-which groups block make the longest chain (touching)
-which groups blocks can cover the most surface of a 81/2 by 11 paper?
-Which group can stack their’s higher
I didn’t quite know were we are going with properties. Until considering what makes a rectangle?
What makes a triangle? I am going to keep thinking. I can’t wait to see how my class can come up with ways to brag what attributes their collection has. (maybe I will not have a mixed collection for grade 5)
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We measure the floor of the classroom
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We measure the area of the classroom floor
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The unit we use is square feet.
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The tiles on the classroom floor are conveniently one foot squares.
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Nice example!
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We can measure a bunch of bananas. The specific attribute to measure is …. the number of bananas. The unit of measure will be – each banana, and I’ll compare the quantities by purchasing the bunch that has the MOST bananas in it! 🍌
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A person can be measured in more than one way.
Height, weight, body mass, temperature, and blood pressure are a few measurable attributes.
The attribute to measure is temperature.
The unit used will be degrees Fahrenheit.
(I was not sure how to answer #4) Degrees Fahrenheit is the standard unit to measure temperature in this region.
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Nice example and yes trying to articulate how you’d use Fahrenheit to compare to the actual temperature is super abstract!! 🙂
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The object being measured is “BMI” or body mass index. The specific attributes being measured are weight and height. The units used to measure each attribute will be Kilograms or pounds to measure weight divided by the height in meters squared or inches squared times 703. Since the U.S. uses customary units, I will be using pounds divided by inches squared times 703. This could be a cross-curricular connections between math and Physical Ed./health. Since there is a high incidence of obesity among children in the U.S. this measurement task would be beneficial. Here is a link for finding BMI https://www.youtube.com/watch?v=4LfANanF0Dg
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I really like how this task can relate to everyone. Oftentimes we present math problems to kids and they don’t see how it relates to “real life.” Thanks for sharing this one.
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In the classroom, I would start off simple with rectangular prisms, shoe boxes, game boxes, anything we could get our hands on. I would have students measure surface area and volume, using square inches and cubic inches (or square cm and cubic cm). I would have students make estimates first– how many 1 inch squares would cover the box? How many cubes would fit inside the box.
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Awesome example.
Alternatively, or I should say prior to using standard units, you could consider using square tiles for area and some other non standard cube.
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My class is just starting to focus on multiplication, which starts with area & perimeter. If we measure the area and perimeter of a flat figure now, later we can use similar figures (in 3D) to also measure volume.
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Street hockey balls. The guys I play hockey with are very particular about the balls we use to play with. We could measure their:
– height of bounce
– squishiness (not sure what unit of measure I would use for this. Something that measures pressure?)
– color
Not sure what else.
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These are great ideas… and I’m sure there is much more that could be measured (but maybe not that you’d necessarily WANT to measure it). Now that I think about it, I’m struggling to think of others as well… maybe temperature? (is it room temp at room temp or a little warmer/colder? etc.)
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I am fortune to have the school courtyard attached to my classroom and it is square.
1. School Courtyard
2. Measure the surface area of walls and ground. I have also measured the volume/capacity (It is fun to have students try to figure out how many starburst they would need to cover the walls and ground or fill the courtyard)
3. Usually meters to measure need lengths then used those measurements to calculate approximate surface area and volume. Some students will choose to measure in feet and inches.
4. Students need to be able to relate how many centimetres are in a meter to achieve a greater accuracy in their measurement.
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Convenient indeed! Are you going to get the students out there?
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If weather permits, we will definitely head outside.
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Recently, I did a lesson that showed me stacking books. What was funny is I was looking for one answer and thought it was obvious. I wanted them to think about at what rate the tower of books was increasing however I got a list of other ideas. The students thought I was looking for the following: the weight and change of the tower with each book, how fast I can stack books, the volume of tower and how it changes with each book, and how many edges are shown when placing another book on the tower. When hearing these answers, I realized that we could actually solve for all of these and that with each situation that proportional reasoning could be used.
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Isn’t it fascinating what seems obvious to us, but may be completely hidden to students? I’m constantly fascinated by this.
As for stacking books, have you checked out the Stacking Paper series of tasks?
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My first thought was measuring a book. One could measure the number of pages, the length of time it would take to read it, the weight of it (if we were going to mail it), or the size, height of it and whether it would fit on a certain shelf on my book shelf.
I will measure the height of the spine when the spine is vertical and facing out! (I had to be real specific there when describing it!) I will use inches because I know the height of the shelf.
Cool exercise that contributed to my understanding of measurement and the need to be explicit/ specific given the context.
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To help learn the metric system of measuring length, we had Metric Olympics Day where students predicted, estimated, and then measured different Olympic events. Example event: Long jump – how far can you jump with two feet together from a standing position? Students predicted how many centimeters they could jump, then they would jump and estimate how far they jumped, and finally they would measure how far they actually jumped. On a day prior to this activity, the students made up their own unit of measure, defined it’s length and measure things around the room to learn about the reason for a standardized way to measure.
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My 8th grade students learn about volume of solids but must also know the surface area of those same solids. We also talk about the origins of the formulas for solids and how they are based on the area of the bottom of the shape multiplied by the heights of the solid and how this makes sense when, “filling up an object”.
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I live in a rural, ranching area and I think it would be fun to use a cow or horse and ask the students what attributes they could measure. I’m sure they come up with things I would not have thought of that would have practical value to them in ranching and would make connections far better that way.
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That’d be great! Keep us posted if you do decide to go that approach. I’d be curious to hear what they come up with as well!!
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A smartphone has a wide variety of ways in which it could be measured. I could measure its storage capacity. I will use gigabytes to measure it. I can use the information to see how much storage I have left on my phone.
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Great example and it might be a really good one to use with students if asking them about measurable attributes!
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An object that could be measured in more than one way could be a classroom. You can measure length, width, height, area and volume. Depending on what your goal is, you could find the dimensions and create a scale drawing, or redesign the layout of the desks based on the available area. Talk about which unit the students will use or assign some students one unit and other a different unit, then they could discuss the pros and cons of different units.
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Love this idea. Thanks for sharing your thinking!
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One year I was preparing to paint the cabinet doors in my classroom and I asked the students to help me figure out how much paint we needed. The students measured the height and width of the cabinet doors, some in centimetres and some in metres. We talked about which measurement was easier to use when subsequently finding the surface area. Here in Grade 5, students haven’t been exposed to multiplying decimal numbers yet, so that posed a problem if they measured in meters…so we needed to either convert or learn to multiply decimals a little early!
All of the doors were congruent rectangles, which meant the students were able to add or multiply to find the total. Other attributes that we could have measured, but didn’t are: the volume of the cupboards, the height from the floor, the color density before and after, the approximate fraction of paint that was peeling off 😂
I’m still struggling a little with distinguishing between an attribute and a property. If I had asked the students to study the cabinets and classify them between which ones closed properly and which ones didn’t, would we be looking at a property, whereas an attribute would be that each cupboard had a metal closer (whether it worked or not?). Could a property also be that the cabinet doors are all rectangles with 4 right angles and the opposite sides congruent? Or are those attributes? Or both?
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I’d love to “measure” a knitted or crocheted scarf. This could be measured in length, width, area, or even number of stitches.
1. Crocheted/Knitted Scarf
2. Number of Loops/Stitches
3. I guess the unit would be 1 stitch, though you could look at scale of a centimeter being equivalent to a certain number of stitches if you want to get more complicated.
4. I would love to see students expanding their thinking via multiplicative reasoning to talk about how a longer scarf has more stitches – how many more, etc…
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Great example!
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Although circumference and area of circles are traditionally taught in our 7th grade curriculum, I find that we have to review this in some depth in Math 8. To do so, we do a Pi Day challenge where students measure the diameter, radius, circumference and area of different pies. After watching this (and the previous video), I am thinking we need to add height, volume and some sort of cost or financial value of the ingredients.
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I will check that out! Thank you!
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The object you will be measuring: pumpkins
The specific attribute you plan to measure: circumference around the outside surface
The unit you will use to measure that attribute: inches and centimeters
Describe how you will use the unit to compare with the quantity to measure: Depending on what part of the pumpkin you are measuring, you would get a different measurement. Aim for the middle of the pumpkin and measure around the widest part (as opposed to bottom to top). Compare different sized pumpkins.
Other things you could measure would be as follows:
numbers of seeds in each pumpkin
diameter of the inside of the pumpkin once it has been opened
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Thanks for the great (and timely) example 🙂
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1. In Math 8 we typically do some Pi Day activities where we measure pies.
2. We measure circumference and area, but after watching your video, I am realizing we could also measure volume and some sort of economic value.
3. We use centimeters to give our students more experience with metric units. If we estimated the cost of ingredients, we would use US dollars.
4. We would use centimeter which would be more accurate than a larger unit.
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Love this.
To assist in your Pi day activities, be sure to check out the problem based unit: Going In Circles!
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1. Bottle of wine.
2. Volume.
3. Ounces.
4. Number of 8 ounce glasses in it.
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1. I would give them a box to wrap for a gift.
2. We would measure surface area.
3. We would measure in square inches.
4. How big of a surface area of wrapping paper do I need to wrap the box and why? Is it helpful to estimate before I wrap? Do we actually do this already but you didn’t realize it before?
I wonder how the students will connect the idea of when we wrap that we estimate using the visual of the object for easier wrapping? Too much paper and the extra makes it a difficult task. Too little and you have a hint to the gift. This is one thing I would like students to realize. They use estimation and math often they just don’t recognize it.
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I am thinking about cookies with bites out of them. Maybe talk about area, angles, chocolate chips, etc.
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Love it. Always remember to get clear on the learning goal/intentionality. If it is area, are you good with area of a circle or did you want area of a rectangle first? Maybe instead of cookies, it is brownies (rectangular)… etc. Just some thoughts to think about!
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We measured our desks
We measured height, width and length
We found the area of the top of our desks
We used sticky notes which we also use to measure various things throughout the year
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The object you will be measuring: mason jar, shape of cylinder
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The specific attribute you plan to measure: surface area
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The unit you will use to measure that attribute; centimeters
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Determine how big to make the label for the outside of the jar.
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Measurements were determined by what you wanted for the outcome. Using a real life object for measuring makes it more meaningful.
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Awesome work here. Thanks for sharing with the group!
How is your comfort level with these concepts?
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