This post and task was written and created by both Jon Orr and Kyle Pearce.
In those live workshops we’ve been using a task without a name. On the first anniversary after creating that task we wanted to share it here with you and give it a name.
We’re all about creating tasks and then thinking about how they might be modified for use across a variety of grade levels. With a few modifications, you can successfully run this task in classrooms from K through 10. In particular, you could address the following expectations:
- building estimation skills;
- building multiplicative thinking and proportional reasoning using arrays;
- building multiplicative thinking and proportional reasoning using double number lines;
- making connections to the inverse relationship between multiplication and division;
- connecting double number lines and ratio tables to creating and solving proportions through algebraic reasoning;
- highlighting the value of the constant of proportionality (i.e.: unit rates) so students can “own” every problem possible in a proportional relationship;
- determining rates of change;
- representing linear relations in various ways;
- solving problems using the four representations of linear relations; and,
- many more.
Here is Chocolate Mania:
Act 1: Sparking Curiosity
Ask your students to write down anything they notice and anything they wonder while viewing this video:
Note: There is no audio. Can’t see the video because you’re viewing this post in a rss reader? Click here to go to the post page.
Here are possible notice and wonders from our workshop participants and also some from our students:
- They’re both wearing plaid.
- The video is in reverse.
- How many chocolates will they eat?
- Did they get sick?
- How long did it take to eat all the chocolate?
- It looks like they’re spitting it out.
- Kyle is eating Kisses.
At this point the students’ responses are listed on the board during the class discussion.
After capturing all the notice and wonders on the board steer the class to working on the problem:
“How many chocolate did Kyle eat? How many did Jon eat?”
Have your students estimate how many each of us ate. What is too high? What is too low? Your students may be feeling uneasy about their estimates; that’s okay! The point here is we don’t have enough information. To help with estimates at this stage we disclose that all the wrappers of all the chocolates we ate are showing in the image above.
We encourage you to record many of the estimates in a chart as a class. This will put some pressure on making those estimates carefully.
Act 2: Revealing Information to Fuel Sense-Making
To avoid rushing to the algorithm we’ll push down the curiosity path some more. Instead of just handing over all the necessary information to solve a problem ask the students what they want to know more about. This process is key; student anticipation of what is needed is a gold mine for understanding where they are in their thinking. By having them ask for information they have to start problem solving!
Students may ask for the time it takes for the whole video and you as the teacher can then say, “And what would you do with that if I gave it to you?” Listen to how they answer this. You’ll gain valuable information about where that student is on this problem solving journey. You will know after that answer if the student is thinking proportionally or not.
Here is some information to share:
Ask students to share what this series of photos tells them. What do they notice? What do they wonder? Then share this photo. It reveals the total amount of ml each of us consumed.
At this point students will have enough information to determine how many pieces of chocolate each of us ate. Let them go at it!
Fuel Sense-Making to Consolidate Learning.
Note: You or your students may want to work with more familiar numbers compared to what you see above. For example, to get a close prediction to the actual number of chocolates each of us ate a student may round the 111.8 ml to 110 ml and similarly round the 17 ml for 3 chocolates to 20 ml.
Depending on the grade level or skill level of your students we can expect to see some of these strategies
- Counting with familiar numbers;
- Using arrays;
- Number line counting;
- Tables of value counting;
- Long division;
- Unit rates;
- Solving Proportions;
- Creating and solving equations.
Here are some of those strategies:
Counting Up Chocolates and ml.
Students may count up 17 ml every 3 pumpkins until they reach close to the total amount of ml. If they go over the total amount they may want to subtract a cup of chocolates so they can get more accurate.
Here’s that strategy in action
Working with Fractions:
To get more precise answers we can encourage students to work with parts of chocolates in decimals or fractions. Many teachers would be inclined to stay away from fractions because they feel it may “de-rail” the lesson. We say use this context to reinforce fraction work and understanding.
Counting/Multiplying/Dividing Using Arrays:
Students may organize their counting strategy in a double array model. Simultaneously counting in groups of 3 pumpkins and 17 ml will allow them to see that they will need just over 6 cups of pumpkins, while showing the proportional relationship between the pumpkins and volume.
Double Number Line:
Students who solve the problem with a proportion will benefit from seeing it laid out on a double number line. By showing how to solve a proportion on a double number line we take a familiar concept (counting on the number line) and extend it to work multiplicatively. Students who solved the problem with an additive strategy will see the benefit of greater precision of using a scale factor.
Many students may use a unit rate to help solve this problem.
Note: This student will benefit from a conversation on notation, units and order of division.
You may choose to use this problem to either introduce or practice linear relations. I used this task to link the idea of finding the unit rate to determining the rate of change (slope) in a linear relation and then use it to build an equation to help solve the problem.
Reveal the Answer:
After consolidating the learning goals you wanted to bring out into the open for discussion with your class show them this reveal video of the actual number of chocolates each of us ate. Be sure to go back and validate those students who estimated the closest early in this task.
Is there a Volume relationship?
We want to leave you with some thinking here. We chose these chocolates for a very specific reason. In fact we hunted down the spherical chocolate that has the same height and diameter of that Hershey’s Kiss.
Your Task: What volume relationships can we pull from this image?
Did you notice the relationship between the amount of chocolate by volume Jon ate versus Kyle?
Look for an upcoming post on how we used this task to teach volume. But before we do that we want to know how you see a lesson on volume forming with this information. Use the comment section below to share your ideas, questions, comments, or even just snippets of what a lesson could look like.
DOWNLOAD THE TASK AND RESOURCES
New to Using 3 Act Math Tasks?
One common misconception around how we should plan our lessons is that planning and creating lessons, course outlines, and assessments is all done in isolation.
There’s an iconic image of famous Fiction authors shutting themselves up in a cabin in the woods for months at a time and then emerge with this great manuscript.
This is actually a false image.
Most authors go through intense iterations of their books with many editors and audiences that provide feedback.
You many have this image that math lesson creators also lock themselves up in the teacher prep room to think up great lesson ideas only to miraculously emerge with perfect lessons. Or maybe you believe that we have magically created spiralled course outlines all by ourselves with little input from anyone else.
These things can’t be further from the truth. Every one of the lessons shared on this site and also any unit or course plans were all created in consultation with other teachers.
In fact, when Kyle Pearce and I first decided to change our course plans from the traditional textbook order to mixing up topics so we can maximize student retention through spiralling our math lessons, we created a joint outline with Google Sheets that we could each have input to. Planning lessons and courses should be collaborative effort.
In January 2018 I asked the twitter community “Your colleague is thinking of trying to teach through spiralling the curriculum. What are some SMALL changes they can make NOW so that’s it’s not overwhelming?”
Many teachers gave their suggestions but one comment really stuck with me, It was from Mary Bourassa,
“Lots of great replies but I would argue that most are not small changes. Switching to spiralling is a big change! My best advice is to plan a meeting with someone who has spiralled so that you can talk through your plan together. And make sure you know the curriculum really well.”
We need other people on our same teaching journey as we learn to create new lessons that meet our students need.
A book I highly recommend reading because it’s interesting with many great real-life stories and examples is The Creative Curve, How to develop the right idea at the right time. By Allan Gannett.
The main idea of this book is, and quoting from the publisher,
“We have been spoon-fed the notion that creativity is the province of genius — of those favoured, brilliant few whose moments of insight arrive in unpredictable flashes of divine inspiration. And if we are not a genius, we might as well pack it in and give up. Either we have that gift, or we don’t. But Allen shows that simply isn’t true. Recent research has shown that there is a predictable science behind achieving commercial success in any creative endeavour, from writing a popular novel to starting up a successful company to creating an effective marketing campaign.”
One of Gannett’s Laws of creativity is the law of creative communities. He argues that creatives leaders like Paul McCartney, Steve Jobs, and J.K. Rowling, didn’t create their great works in isolation, but were surrounded by a community of people. Gannett’s also argues that if you don’t have a community of supporting people around you then your chances for creating something is drastically reduced.
So, if you want to make math moments that matter for your students on a regular basis then you will need a community of supportive people!
Alex Overwijk is a high school math teacher in Ottawa Ontario Canada. What I admire so much about Al, is that after teaching math the “traditional way” for over 25 years he realized that he had been robbing his students of great thinking and made significant changes in his classroom routines with an emphasis on “Uncovering curriculum instead of covering curriculum”.
Basically, lesson study in a nutshell is a group of educators, teachers, and administrators who will together plan a lesson for a teacher to deliver. They will all observe to witness how the students respond to the questioning and tasks included in the lesson, then they debrief to make changes. Then this process repeats. The group will plan, observe, and debrief for another teacher, and so on.
The group is planning lessons collaboratively, not in solitary isolation. The success/ or failure of the lesson is felt by the whole group and not just from the teacher delivery it.
When responding to teachers who say “I can’t afford to be out of my classroom that many times”…. Al says, “How can you not afford it? Your classroom will become a different place-a place you’re not familiar with. Your instructional practices will be challenged and will probably change as a result. Your belief in what students can do will change. You need to try this!”
Al and so many other teachers know that the success of great lessons and course plans can hinge on your access to a community.
What can you do? —- Find one or two teachers who also want to plan, talk ideas through, and collaborate on lessons or course designs. Please. Don’t do this alone. We need to avoid isolation. Sharing ideas, strategies and resources is how plans not only get created but how we stick to them.
Your next step to avoid Teacher Isolation → Join our closed Facebook group: Math Teaching & Learning K-12. It’s closed so that you can feel comfortable asking math lesson related questions on Facebook without bothering your Aunt or your college friends with math related stuff. It’s a place just for us! It’s a place where if you’re feeling teacher isolation in your school come here and share your question or even just to vent.
For example, a group member asked the following question….and other group members jumped in to help out.
Or here’s another example of a team effort
So, I’m hoping to see you in group! Remember, don’t do this alone! We can create better things together.