Make Math Moments Academy › Forums › Full Workshop Reflections › Module 5: Planning Your Problem Based Lessons › Lesson 54: Before Move #3 Anticipate › Lesson 54: Question

Lesson 54: Question
Posted by Jon on May 1, 2019 at 11:59 amChoose a lesson from our curated list or choose another task and use the Anticipating template to anticipate what your students will do to solve the problem.
As a bonus you can use the Making Math Moments That matter planner to anticipate.
Share your thoughts, questions, and comments here.
Joseph Barnas replied 1 month, 3 weeks ago 27 Members · 33 Replies 
33 Replies


Often times we model things proportionally, when in real life they are not perfectly proportional. For example, phones don’t necessarily charge at an exact constant rate, but we make that assumption. This could be why the values aren’t 100% the same.



I chose the Charge It problem. I did not read to the end and made the same assumptions that students would make. I like the idea of using this to model a piecewise function as my students have typically had trouble with these. I anticipated that the students would solve this using a table and looking for the average rate of change, by estimating that it is close to 1% per minute, by making a linear graph and then by solving a proportion. It took me a while to think of the different ways that students would do it since as a math teacher, I tend to jump right to the “mathiest” way!

That is common as we are much further along the developmental continuum so it can be hard to think at earlier stages. Practice will get you there!


Some potential moves by students with regards to the Trashketball task. I’m trying to think of other possibilities if anyone thinks of other ones that are different.

I want to do the popcorn problem with the primary goal of understanding changing rates and their connection to graphical models, equations and tables of values. The future goal would be to understand the meaning of the point of intersection in a linear system.
possible student representations:
1 create tables of values
2 – use unit rates
3 – graph it(although unlikely)
4 – Additive Stategy
5 – create pattern rules then solve each
This will be a great activity to push students to make multple connections with the various representations of linear relations

Great work here!
Wondering what the additive strategy might look like/consist of?

I guess I was thinking they would start with the initial value and use a rate to keep adding until they arrive at the answer.



Anticipating a problem that becomes much more manageable with a transition matrix.
 This reply was modified 10 months, 1 week ago by Jonathan Lind.

I chose the Solar Panel lesson. My students are coming into it with a background of using ratios and unit rates and really don’t have experience with linear relationships. Of course, some kids with extensive background may decide to graph this or derive a linear function. Based on my students I think that below are the strategies they’d use in order from most likely to least likely. Of course, I’m ofter surprised by my students and I would be willing to bet that at least one group would use another strategy that I haven’t thought of.



Awesome stuff here. I love how “real” your solutions are … I believe firmly that we need to be “messier” so that students can see that we don’t always know exactly what to do before we start a problem either! Share it with pride 🙂


Hey Jon, one thing I noticed from your video is that in the first anticipation you showed an answer of 22 minutes and 45 seconds, and for the rest you showed answers of 22.75 minutes. I was wondering if that caused confusion for your students, because I know it would for mine, as most of my high school students cannot tell time on an analog clock and also don’t do very well with fractions and decimals. If it did cause confusion, how did you go about explaining to your students?

I noticed the same thing! and wondered the same thing!

@terryhill @colegiomarkham In this case we took a minute to discuss this. It may have taken longer than a minute or two if the number of minutes was 43 minutes instead of 45, but since it was 3/4 of an hour students grasped writing 3/4 as 0.75 easily .
This brings about a good point when designing problems or when working on anticipating student solutions.
We often design problems so that we can build our number sense skills along the way. This means anticipating dedicating a portion of the lesson time to addressing or discussing these ideas.
It’s a great talking point when you come upon a group who is working on this problem. How did they handle the time conversion? Did they convert the same way? Did they convert to minutes? Did they keep fractional units? Groups will handle this differently. Plan to discuss these differences in the connect stage.
 This reply was modified 7 months, 1 week ago by Jon Orr.


I did the Solar Panel 3 Act Math. I would anticipate proportions along with the unit rate being found. I like how the 3 ACT webpage shows other solutions so that I am more prepared as to what I might see and if I don’t get that solution I can show it as an option to broaden their thinking toolbox.

The active starting is process is a bit scary for me. I have seen most of my students in co taught classes in the past. They will wait for the correct work to be put up on the board. When approached 1:1 the first thing they say is, “I don’t know.” Often before I even ask a question, which may not even be about the math problem…. I am going to have to really work on building an intentional learning community that is safe and show what it looks like to productively struggle.

I chose Corner to Corner. I think I have trouble seeing more than two solutions (both similar) in this task. I guess I don’t know my students well enough to see how they might solve this problem.
1. I see the students drawing an illustration labelling the measurements of the classroom. Applying the pythagorean theorem, students will find either the diagonal of the area of the width and length of the classroom. They will then substitute to find the intended diagonal.
2. Maybe some students will add all three squared lengths together and then square root to find the intended diagonal.

I used the trashketball problem. I love this one because it is so simple. The concept is really simple at least. I know I will have students, because I did, who marvel at the consistency of the paper balls. Well done.

Great anticipation here Jared. I’d love to know the distribution of students who attempt each solution.


I chose Sowing Seeds to see how students would have 78 seeds and split into 6 different pots. Some students drew 6 circles and started putting 5 seeds per pot, found they could do it again, then added 2 more per pot finally 1 more per pot to make 13 seeds per pot. Another group started with 10 seeds per pot for 60 seeds, saw they had 18 seeds left over so they divided that into 3 seeds per pot. Another group started putting 6 seeds per pot for 36 then they doubled that for 72 and only needed 1 more seed per pot for a total of 13 seeds/pot. I showed them the area model to represent their multiplication. I really enjoyed seeing all the students work with multiplication opposed to long division with this problem.

Sounds like an awesome experience that gave you an opportunity to see where students were at in their own learning journeys! Glad you enjoyed the experience.


I chose the Soup du Jour problem. The three representations/solutions I worked out are attached.

I chose to plan out student responses to the grade 2 “Cover the Floor” task. I feel like I probably missed some strategies so I like that the sheet has blanks for the unexpected student thinking that I am sure I will notice each day that surprises me.
*students draw the entire 12×9 and count one by one on their picture
*students repeatedly add 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9
*students add 12 repeatedly 9 times
*students repeatedly add 10 12 times, then take away 12
*students may use some multiplication 10 x 9 and 10 x 2?
*students may model with blocks and then skip count to find the total
*students may use a number line and show jumps for each row or column


This lesson has caused a bit of conflict in my thinking as I have been doing lots of reading about not solving tasks before the students so as to not guide them in their thinking or nudge/prod them along with hints instead of asking probing questions to get them to stretch their thinking. I have done tasks in the past where I have told the students I don’t know the answer or I don’t remember from the previous year and they are initially distressed to hear this but then move forward to “show me” that they can figure out if I don’t know. I do see the benefit to having the work already done out for some of the ways students might approach a task, but I doubt that I would be able to come up with a comprehensive list as students think in so many different ways. I imagine that the place on the template for students/groups names is going to be extremely beneficial to identifying where students are in their understanding potentially based on the means by which they tackled the problem. I am looking forward to seeing how this all comes together.

I chose a problem from Jon’s Math is Visual site about growing geometric patterns. I took a screenshot and added below.
I am anticipating that in order to find what is next or further down the line, students might:
Draw the next few images (which even how they add on the “eggs” might be different for all.
Some may set up a proportion (although, we haven’t used this word yet so they may see it more like equivalent fractions).
Someone might do a double number line. (I don’t anticipate this one to be a popular strategy as it is not modeled much in the previous grades)
Someone may make a table
And someone will definitely write an equation (those are usually the ones who take math classes outside of school).
My goal of the lesson is to create the equation to go with this pattern (and ones that follow), but after giving them time to solve first what comes next in the sequence and then what comes further down the line, I would review the strategies, ending with the equation strategy. If, maybe in one particular class, no one uses the equation method, I would actually add on to the questions giving ones that might not be as easy to “skip count” into and help the class get to the equation.
I do love the mathisvisual.com site. And I see some 3act tasks, but when googled, I get many older 3act tasks that I am struggling to find the purpose for (although, I do realize that each one probably has many purposes). My concern is the research time…is there an organized place to go for ideas for 3act tasks?

This week I’m going to circle back to support my students with solving two step equations.
I’m planning to use the Planning Flowers Revisited Task from MMM.
Honestly, I’m a bit unsure about what strategies that they might try to use as I’m still struggling to determine the “where they came from” portion of their understanding. Given their vast and varied learning experiences of the past few years, there are definitely some gaps in conceptual understanding.
If I know my students, I think they might use the concrete manipulatives with groups of three to model the solution. Others might try a skip counting method.
I’m planning on highlighting the double number line and then exploring the algebraic representation during the consolidation.

I will be teaching writing linear equations when given two points of data. I plan to not “teach” this directly by starting with notes this year. I am going to give students word problems first and see what they do. I think some students will take what I have given them, example: number of pillows and cost and divide and find that they get two different rates. They will be confused by this and I will have to give them a push to have them wonder why they are different and how we could make the cost the same. I think there may be a second level of students who will make a table or two coordinate points and calculate the slope but then get stuck. They will find the difference of the rate they found and the leftover and consider the to be the yintercept. It will be my job to gently guide them along to think about y=mx+b and what information they know and what they want to know. They will have to grapple with this but I think there may be a third group that will go straight to the equation to substitute in the (x,y) and the slope to find the “b”.

I am going to try something, not on the list (it is fun to find ideas from within our own life experiences).
I found a website that shows the value of an automobile over time. In this case, I used my truck as an example. For the students, I will remove the label for the xaxis along with the “Ford F150 Depreciation” label. I am sparking curiosity by leaving those essential tidbits out. The question we will be answering is when my truck reaches 0% value (knowing full well that it will not necessarily do that in real life).
I can see students taking many different routes to the solution:
1. Students could simply choose two points that fairly mimic the data and calculate the change in % compared to the time in years. Essentially determining the slope of the line between two points. Then use repeated subtraction or division to calculate when y is 0%.
2. My truck appears to be at about 75% value after five years. So another 15 years (every five years is a reduction of 25%) will put my value at 0%.
3. In that same fashion, at about 9 years my truck is about 50% value, so an additional 9 years is 0% value.
4. Another student may just extend the line until it hits the xaxis (xintercept).
I am sure a student will surprise me and come up with something entirely unique (at least I hope so).
 This reply was modified 2 months ago by Noel McMillin.

I am intrigued to debrief with student about this activity at different times to see if they feel the most efficient and accurate strategies are the same strategy or different. Also, if their idea of the most efficient or accurate strategy changes throughout the lesson.