Make Math Moments Academy › Forums › MiniCourse Reflections › The Concept Holding Your Students Back › Lesson 3 – Why The Unit Of Measure Matters – Discussion

Lesson 3 – Why The Unit Of Measure Matters – Discussion
Posted by Kyle Pearce on December 6, 2019 at 5:20 amWhat resonated with you from this lesson?
How does unitizing apply to one (1) or more concepts from a grade or course you teach?
Share your reflection below along with any wonders you still have.
Kyle Pearce replied 4 months, 1 week ago 31 Members · 50 Replies 
50 Replies

What resonated with me was making sure students are exposed to the different units that could be used since different units can represent different quantities.
 This reply was modified 2 years, 8 months ago by Hayley Anderson.
 This reply was modified 2 years, 8 months ago by Hayley Anderson.

Thanks for sharing! I’m trying my best to always be explicit about the unit of measure when describing quantities and working with them through problems. Hard habit to get into, but worth it!

The thing that resonated with me was the idea that a unit could have 2 or more items in it. I never used to think of a unit that way. To me, a unit was always made up of only 1 thing. So, It becomes sort of a brainbender. How can I put together a unit to count – but then, if you expect someone else to use the same unit, you must explicitly tell them what the unit is comprised of.
Very interesting and enlightening!

Definitely an idea that I was not aware of until more recently. This idea is so important and permeates mathematics at so many levels – it is crazy that ideas like this are sort of “hidden” or in disguise from us when we learn things too procedurally without meaning.


Like @marianne I too related a unit of measure to only being one thing as we have always related the word unit to one of something. By being more explicit with the definition of a unit, it opens up so many more options for students to visually connect with problems and see them in different ways.

What resonated with me is importance of being clear about the unit being used – before measuring. In traditional mathematics teaching, I think about all the points given/lost for “labeling” the answer to a word problem. However, it seems like so much of an afterthought a that point. Problem solving needs to start with selecting an appropriate unit with which to do the measuring.

As a grade 5 teacher, I am charged with introducing French language to BC kids for the first time. “Sonn” or “cent” was an uhha moment. I always impress upon the french spelling of metre and the pronunciation: Keelometer, and not Killometer. I totally, went a different direction in finding squares. I found 38, 20ones, 12fours, 4nines, and 2sixteens. Each year, I give the kids adding machine paper to create individual height strips. We go around the school measuring the hall in “Alice’s” and the gym in “Jame’s”. To be more accurate we have to sometimes include 1/2 an Alice. Confusion with dramatically taller students lead to discussions of common units.

I really like this idea of having students create their own unit, it help them develop a much better and more personal understanding of why the unit of measure matters… especially since you’re using their units to measure a standard distance (the hallway for example) … they would all have similar but different answers. This is a great idea, thanks so much for sharing!

I agree that creating your “own” units and calling them by a name is a genius idea.
One of my favorite math literature books for measuring is, “Measuring Penny” by Loreen Leedy. She uses some clever units of measure such as qtips, etc. Here is the link: https://www.youtube.com/watch?v=kH1Qh6bgq0 Certainly gets students thinking about why different units are necessary depending on the attributes of a dog: ears, paw width, tail length, weight, how high they can jump etc.

Awesome!
Common language for making our own units is “non standard units” which is used a lot in our Ontario math curriculum. It can really help us serve the purpose of exposing why the unit of measure really does matter!

Thanks for sharing this book! A great connection!


That is awesome to hear. Clearly you’re already putting the importance of the unit of measure into play during your math block. Fantastic!


In an earlier reflection I shared about a project where students are designing a conservation area for endangered species and how student completely misjudged the size of their designs because of the unit. They were using the grid squares on their maps to design without paying attention to the scale – 1 grid square = 20 m…. this caused a lot of confusion because the unit of measure matters. This ties perfectly into spatial reasoning and the idea that students need a conceptual understanding of measurement in order to make sense of unitizing! Great lesson!

That’s a great comparison (no pun intended) to help connect your learning from this lesson to the learning opportunity your students stumbled upon with that project. Nice work.


I, like many who have already commented, always thought of the unit as ONLY 1.
I am so excited with the idea of students creating their own units! I envision my kiddos counting their items using different units, and the great discussions that will ensue because students LOVE it when they can all have a different, yet correct, answer. How rich a conversation it will be too, when we talk about the fractional parts of their units!

So awesome to hear. Be sure to keep us posted on this!


So the unit of measure matters because children are wired with a intuitive sense to measure quantities by selecting units they are comfortable working with. Unless we are crystal clear about the unit of measure, we cannot be sure if our students are correct or not.

The idea of defining the unit in order to measure the quantity really resonates with me. This concept came to life for me when I took Graham Fletcher’s Foundations of Fraction course. When we can encourage students to measure a quantity of something but in different ways( changing the size of the unit) when can move them to think more flexibly.
I never realized before that I did this back when I taught fractions in Grade 4 (910 year olds) using pattern blocks. When we defined one as being the yellow hexagon we limited ourselves to just working with halves, thirds and sixths but when we defined our unit as 2 hexagons, then we were able to explore fourths and eighths.
It’s the same thing with using base10 blocks. If the cube is always “one” then we can only use that resource in just one way. But if the hundreds flat is defined as “one” then we can use those materials to explore decimals.
 This reply was modified 2 years, 3 months ago by Aaron Davis.

Great reflection and great course that Graham has there!
We too often had a limited view of what was possible with our students simply because we were unaware. The flexibility you speak of is hard to achieve for students if we aren’t more flexible in our own thinking regarding the questions we ask. Thanks for making some connections for us.

What resonated with me is the importance of being explicit with students. Also, we should vary what we present and include units that are more than one. That could lead to an interesting inquiry lesson.

It is so easy to forget about how important being explicit is when we try to shift our teaching away from a more traditional approach. Sometimes we trick ourselves into thinking students should discover everything which is simply not true. Thanks for highlighting this!


Unitizing applies to my grade 9 course when they are encouraged to make referents with their body. Before they can make referents they need to be able to understand the linear measurement. I’ve had many students over the year who do not even understand how to read the rule and how to use it to measure lengths.
I also think more students need to be exposed to the idea that they choosing their own units to use are acceptable as long as they can explain why behind it.

So true! That struggle to read a ruler often stems from students not spending enough time measuring with non standard units and doing so concretely (such as creating a concrete ruler out of linking cubes). They get tripped up on counting the “ticks” on the ruler rather than the “spaces between” ticks, etc.


This just shows again that we need to get the reasoning for each answer from the students. The reason being is because if they give correct reasoning for their answer it could be right especially if we as teachers never gave a criteria for the question.
I also enjoy that it good idea to share the multiple answers and compare them to each other to show how the thinking can be similar or be worked together to solve the problem. For example, how can measure a bigger line with smaller lines and how you can take that number to change into fraction, percent, or decimal answer. This can lead to better understanding of other forms of measurement (unit conversions in metric etc).

Great points here. The whole idea of unit conversion is something I think of completely different to how I used to think of it just a few short years ago. I like your ideas on how using those different measuring units can help solidify some of this thinking!


“Numeral responses alone are not enough.”
Quantity has a context…
The idea of iterating and partitioning in fractions is something I learned from Marian Small’s work and it has helped me a great deal when working with teachers and students.
Division of fractions! You need to have a firm grasp of unit to be able to think through these problems. One half divided by threefourths? How many units of three fourths are in onehalf? Two thirds of a unit that is threefourths. The language gets messy to write/type, but you have to be clear when expressing the relationship.

I think it is important to use the precise language when referring to units. When teaching the concept, I have even used objects such as paper clip to measure a piece of yarn of certain length. I encourage students to describe the dimensions in terms of units. Once students have good understanding of the concept, they can visualize to make better predictions of the quantities in a given problem.

I love the idea of having the students explaining their reasoning and then connecting with the units that way. It shows that math doesn’t have to be strictly black and white but that there is some creativity in it as well

Love it! So true. Math is so much more than steps and procedures!


I like this gave me more ideas for encouraging students to see units in different ways. It opens up their minds to different perspectives which tends to get them more excited about learning and sharing their ideas.

I think what resonated with me is the idea of being clear about the unit and what it is representing. I have my students write the unit in their answers and it is clear that they don’t know the difference between inches, square inches, and cubic inches. They make no differentiation with these three so I’m not sure if they are really understanding the meaning of their answers.

Two things resonated with me. First using fractions to define the relationship of metric units might help some students who struggle with the relationships between them. Second, the comment above about how dividing fractions is partitioning units. I had not thought of it that way but it makes perfect sense. If I can help help students understand this, it might make more sense to them.

Love it. Thanks for sharing your reflections and what your next steps might be!


The thing that resonated with me is the idea that the unit can change when measuring something. I recall using this idea when I taught 4th grade. I said I would give everyone a candy bar but realized that I didn’t have enough so I asked if someone was willing to take a half of a bar. Once someone volunteered I took out a King size bar and broke it in half. Oh the groans!

Ha! The unit of measure truly does matter and the kids experienced it first hand in that case 🙂


I love how unitizing links so many mathematical concepts together. This lesson is a great reminder to use specific language when asking students to measure, count or calculate sets, quantities etc if you’re looking for a certain answer. I often ask openended questions on purpose however, to push students to think differently about the same image and then ask them to demonstrate their thinking to me and to each other.
I teach the metric system here in Canada and have the advantage of doing so in French. It is true that using the words to help inform and understanding of units is helpful for those who intuitively link the language and the mathematical concept together. Some students still struggle with conversions of course, even when we talk about fractions such as hundredths or thousandths. I’m still thinking about how/if I could use a more single unit language to refer to fractional amounts (such as 2 onefouths) in French. It doesn’t seem to fit the linguistic aspect of teaching math in the students’ second language and I have to be careful in a French Immersion context not to make up words that the students will then try to use in the real world!!

I particularly appreciate the attention to the specificity of the unit that you are measuring. As someone who works in middle school, I find this helpful when trying to help my students understand fraction division conceptually — rather than just the algorithm they have been taught, I try to help them realize that they’re partitioning into units that are just fraction amounts. This precision to language is also a great connection beyond our content area into ELA, Science, etc… where we want students to be precise with their choice of words in their written expression!

I think the thing that stood out to me what how the unit of measurement doesn’t always have to be one. We do a lot of work with fractions in my grade 6 course and getting the students to think more flexibly about fractions is a major goal of mine. I think incorporating units of different sizes and amount will be a huge help.

While my students should be able to convert fluently between decimals, fractions and percents, few can actually do so. I think they don’t actually understand the meaning of “percent.” I loved your explanation of this.
I also really like the concept of creating your own units of measurement. I think this would give students a solid foundation to then understand different units of measure.

Agreed! We need students to have repeated opportunities to explore conceptually in order to build that fluency and flexibility we are looking for.
Glad you found this learning impactful!


Something that resonated with me is how specific we need to be with kids, even with vocabulary in math, because a slip in the correct vocabulary could lead them into misunderstandings. Or the proper vocabulary/terminology could help them understand better (for example, the two onefourths, three onefourths, etc)
As I work with junior high teachers they need to be aware of this as well.

I do my best to teach my 7th graders to be specific about what ideas they are sharing. I often misinterpret their words to encourage more specific responses. Using measurements is another good way to foster this practice. I also like how being specific about the number of fractions, like 3 onefourths can help increase their fraction sense.

I teach sixth grade. My brotherinlaw is a professor of math and math education students so I often go to him with wonders and questions in order for me to help teach my students. I picked up that when he made a fractional model with a rectangle he said, “Can we agree this is a whole?” I understood that if we don’t agree it is a whole it could change our whole division of the rectangle to mean something else. This was an AHa for me, so I started incorporating that phrasing with my students. There have been a few times when I have said this one on one with a student and have students look at me like, “Ok, whatever.” I just no understood that this is an indication that they are seeing that it isn’t inherently a whole unless we agree it is. I wonder if students have been given models before without this consideration of unitizing? Could we be creating confusion with models when we think we are trying to clear up a misconception? I think we underestimate the power of a model to create understanding or misunderstanding depending upon how the discussion around it goes.

I like that phrasing as well. The unit of measure is so important otherwise you are speaking a different language.


The “5 fours” reminds me of visual models of distributive property I use . Many students do not see the way 2(2x+3) is 2 groups of 2x+3.Example–https://illinois.pbslearningmedia.org/resource/mgbh.math.ns.distprop/distributivepropertywithvariables/

This lesson reminds me of a book I read “The problem with Math is English” It resonates because we tend to use “naked numbers” or numbers that have no specific representation. One of the examples from the book was 2 times 3 is really 2 sets of 3 each or 2(y3) is 2 sets of (y3) or (y3) + (y3).
This lesson brought that all back.

I’m going to have to give that book a read. It is so true… we tend to teach kids “how” to deal with math symbolically, but don’t always start with the language first then work towards the symbol. We are constantly starting symbolic and working backwards. Later, we will show you how to “be more prince” and that’ll drive this point home yet again.


I resonated with the French words cen that means 100. I always knew that, but it really jumped out and how beneficial that information would help students have a deeper understanding of how smaller units make up bigger units.
I recently used the task Making Hot Chocolate. My students are unitizing as they count be threes adding scoops of chocolate every time they add one cup.
I also having students use a dot grid to determine area. They are counting the number of squares inside 2D figures.

Giving students the tools they need to help (like dot grids for area) is important. Consider nudging them away here and there to see if they can visualize and or apply the strategy of multiplying rows and columns. Sometimes we get “stuck” at a stage if we don’t push them a bit to see if they are ready to move on.
