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Lesson 71: Hot Chocolate Task – Discussion
Posted by Kyle Pearce on December 6, 2019 at 6:36 amHow might you use the context of the Hot Chocolate task to help you address learning for your students at their grade or course level? What modifications might you make to lower the floor even further or extend the problem?
Share your reflection below along with any wonders you still have.
Luke Albrecht replied 7 months, 3 weeks ago 18 Members · 25 Replies 
25 Replies

In my gr. 7 and 8 combined classroom, there will be one or two students who will benefit from, basically, the type of concrete work that is shown in the video of gr. 1s. Others will be ready to tackle higher numbers using more abstract thinking such as a table of values. Many will be somewhere in between. The diversity is quite extreme in this group. I love how one task can be differentiated for individual students!

Amazing to hear that you are seeing that built in differentiation that is possible. When we pay attention to how the math develops, differentiating becomes so much more easy!


Since I’m responding to this discussion question after watching the entire series, it would definitely depend on my objective and grade level as well as the 3 teacher moves: Knowing where my students are coming from; knowing where they’re going and anticipating what my students will do. Now applying those ideas to 5th grade, I would definitely look at multiplicative comparison and quotative division using the double number line.

I just want to repeat again here how amazingly helpful it is to my learning to see students actually interacting with the material, and hear the inthemoment questions to lead them forward. It was incredibly helpful to see students struggling and have a path opened, and then hearing the post analysis of what might have been the hang up for each one. More of this please! 😀

Watching the student videos makes me miss working in the classroom with students! Distance learning is so difficult and, well… distant!
I could use this activity with my fourth grade students in several different ways. At the beginning of the year, we could use it to introduce discourse. It could also be used to introduce the notice/wonder technique as this would be an activity all students would have access to. In class, students could begin to become comfortable using studentchosen manipulatives and defending their choice.

Agreed! Distance learning canâ€™t end soon enough!
I love this unit in particular to help reveal the double number line and the importance of scaling in tandem.


From these site, the one thing that I have learned is that I need to be ready for what kids might answer in order to help them. When offering task I need be more prepared. However it is somewhat hard because 8th graders try to provide the “I don’t know” answer – part of this is due to previous classes allowing them to work in this manner.
One way I could incorporate this in to my class is for them to represent this on a graph. This could then lead to slope, rate, and scale factor. A table could also be made which students would then be able to see the relationship between the two. Linear relationship is what we are working on currently and this would be a good task to begin with since it is simple.

I did this lesson with my 6th, 7th and 8th graders. The problem was accessible to all, and it was really interesting to question and push students into explaining their thinking– everyone was able to come to a correct answer, but it was more difficult for them to really show their reasoning. I used this lesson as an introduction to how we can represent ratio thinking (i.e. ratio tables, double number lines, graphs, tape diagrams) in multiple ways.
The extension was interesting as well– how many cups of hot cocoa can you make with 55 scoops. It was very gratifying to see students using their representations to solve the problem, and of course the discussions that occurred around the extra scoop– what does that extra scoop mean? what could you do with it? can you have just a part of a cup of hot cocoa or does it always have to be a full cup?

So happy to hear that you found the task accessible for all students. Iâ€™d agree that from my experience all students can enter the task and the approaches vary from one to one counting all the way to thinking multiplicatively. It certainly will take a lot of time and effort to get students into the routine of showing their thinking – as this is a metacognitive process and requires a lot of thinking on their part! Keep It up!


Working in a middle school, I could see this lesson being used as an introduction for the concept of unit rate, as in 3 scoops per ONE glass of hot chocolate. It would be interesting to ask students what their idea of one means. In other words, see which students might state that each scoop would make 1/3 of a cup of hot chocolate. Instead of teaching old fashioned algorithms, once students recognize the multiplicative relationship between each glass and 3, they would be able to answer questions of how many scoops per glass AND how many glasses per 1/3 scoop.

I agree – great place for this task. Super low floor, but easy to extend and start getting more complexity. What about another brand with 3 scoops to 2 glasses? Now what? Etc!


I would extend this activity to talk about the constant of proportionality and linear equations. The students could do and undo math with the information given. For example, if I had to make 55 glasses of hot chocolate how many scoops would I use. Extend that to how many containers of hot chocolate would that be. Or if I used 300 scoops of hot chocolate then how many cups of hot chocolate did I make? You could also graph this and make predictions. There are all kinds of ways you could push their thinking with this activity.
 This reply was modified 1 year, 5 months ago by Robin Bergen.

The Hot Chocolate task could be used to solve one step problems involving multiplication by calculating the answer using concrete manipulatives or visual representations.
To lower the floor for this activity, I could use a smaller, even quantity such as the number 2 as the number of scoops needed per glass.
To extend this problem, I could ask how many glasses of hot chocolate could be prepared using [number of] scoops.

for sixth grade I might have 2 1/3 scoops per glass or conversely I want to fill 4 1/2 glasses. To lower the floor you could have one scoop per glass and have differing numbers of glasses, getting one to one correspondence.

In my sixth grade class I was wondering about using this task to introduce a part to part ratios by including the amount of water that accompanies the hot chocolate scoops.
I am wondering about how to lower the floor with linking cubes. If I put 3 of one color to represent the scoops and 8 cubes to represent 8 fluid ounces. It looks like a total of 11 but the scoops and water wouldn’t be measured as 11 total because it is a solution. Would that be confusing example of part to part or a good one because you really need to focus on the part to part not the part to whole?

For 7th grade, I would have them start to think about higher numbers of hot chocolates, or maybe I would start with showing them something like 15 scoops = 5 glasses and ask them how many scoops are needed for 7 glasses.
For 8th grade, I would love to use this to write an equation, graph, and table for a proportional relationship and perhaps have them compare it to another brand of hot chocolate (provided in one of those forms), where I would ask them to say which one is “more chocolatey” to push towards the idea of comparing slopes/unit rates.

Fantastic ideas for stretching the thinking while leveraging the same context. Would love to hear how it goes if / when you try it!


I think it would be a great task for introducing proportional relationships. Giving the students an opportunity to all join in and create their representations, which also underscores the idea that there is more than one way to get to the answer. Many of my students think what they are doing is wrong because the ‘smart’ kid did it differently. Turning each of the representations into a gallery walk for all to view can really reinforce that what/how they are thinking is correct.

I teach Math 8 and plan on using this task this week! Because of remote learning my students just donâ€™t have the experience working with composed units that Math 8 students normally have. We are going to make ratio tables and practice scaling up and down. We will talk about making 1/2 of a glass or 1/3 as well as larger measures.
I also will use our estimates at the beginning to review range, mean, median and mode.

Love it. Many of these tasks are low floor which is great, but then can easily be modified as youâ€™ve mentioned to raise the ceiling. Keep it up!


This is a fun task. My students really enjoy doing tasks like this, so I am sure that they’ll be really engaged. We’re concentrating on multiplication at the moment, (although there are many other aspects of problemsolving thrown in!), so this fits perfectly. In grade 5, however, this will be too easy. They’ll have the answer in a snap, even those who are more concrete thinkers. But it would be fun to extend it to ask them to calculate how many scoops would be needed to make hot chocolate for everyone in the class, and then to ensure that there would be enough containers of hot chocolate, for next week’s pyjama day. The more realworld, the better I think!
Since we’ve also been working with converting units, I may also ask them to think about how many mL are in each glass and then calculate how many litres of hot chocolate we would need. We have Carnaval coming up where we serve hot chocolate to all the students, so we could contexualize this in that way to help the committee who is buying supplies ensure they make enough and have enough mix. Different groups could calculate different aspects and then present their findings to the Carnaval committee. Which is perfect because it would be in French (the students are in French Immersion) and the Carnaval committee is French speaking. So there would be the expressive piece, which is super important for showing understanding!
Something that just occurred to me is that older students (or maybe even mine) might calculate the ratio of hot chocolate mix to water…how many parts of each? Or you could use fractions to describe how much of the container of mix is used in every cup or 3 cups…or however difficult you want it to be. Or could you go smaller and ask how many scoops would be used if you had a cup that was 2/3 the size of the one in the video or 1/2 the size…
I’ll stop and go see what other people said!

Great points and so true about the low floor ness of this task. On its own, it wouldnâ€™t be that helpful for grade 5 students out of the gate. However, as a means to explicitly introduce concepts like ratio and rates as well as to have them working flexibly to find fractional scoops for glasses, etc can be helpful! Sounds like youâ€™ve got some ideas in mind to extend. Good luck!


Seeing the kids in action in this one is soooooo powerful. They are getting access to ratio content without even knowing it or without it being in their grade level curriculum. I’d use it for multiplication, obviously, and then expose them to the ration aspect.

This reminds me of a task in Illustrative Mathematics that is strength of mixtures. 3 scoops in each glass. If we keep the liquid amount the same and change the # of scoops–how does that change the mixture and how it might taste. What is we did 4 scoops with more liquid in a different sized glass? Can we find equivalent ratios of hot chocolate mixture in other sized containers?