Make Math Moments Academy › Forums › Full Workshop Reflections › Module 3: Teaching Through Problem Solving to Build Grit and Perseverance › Lesson 32: How we can reshape our lessons around the Hero’s Journey? › Lesson 32: Question & Discussion

How will you use the Hero’s Journey Template to plan a lesson this week?
OPTION 1
Choose any problem from the textbook or any other lesson you like and map it out on another copy of the Hero’s Journey Lesson Template to include elements, teacher moves, questions, tasks fit onto the Hero’s Journey.
OPTION 2
Choose a task from the list by grade level, map the lesson out to include elements, teacher moves, questions, and tasks fit onto the Hero’s Journey curve.
Share your lesson choice and any comments or questions here or with your community partners.

Thinking about using physical tiles for this, I have the game Blokus which will be great for providing the tiles, just need to print a 100s board. Using physical tiles, will be interesting to see about pieces that are not symmetric. The L shape could be in 8 different orientations! Does that mean 8 different equations to solve?
Fun!
Also, what happens if the grid is not 10×10, maybe 20×20, how does that change things?

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I created a desmos activity from the worksheet you provided based on the trig example, which is so cool. Thanks to whoever made those videos. I am using this to start the module on day 1.
https://teacher.desmos.com/activitybuilder/custom/6024329ae29fd8430d1615cd

Super awesome! I think it was Andrew Stadel who put those videos together… but I’m not certain.


One problem I think I could us a hero’s journey task for is working with scatter plots – we used to make paper bridges between two red cups and ssee how many pennies it could hold. Then we would and add layers and see how many more pennies each layer could hold. I walked them through it and defined words like slope and yintercept and such. It was good because it was hands on and tactile.
If I were to do it again, I think I would start with a video or a picture of me placing pennies on a bridge made of paper with an indeterminate number of layers and then go to a visual of a bunch of pieces of paper and do a notice and wonder, withholding the information. Then when they ask, I would give them cups and pennies but only 8 pieces of paper or a limited number of pennies. Eventually at the climax we would look at y=mx+b and then ask them things like “what if I needed a brige to hold 500 pennies” or “how many pennies would 200 papers hold.

That sounds fantastic! Can’t wait to hear more about how that goes!
Another scatter plot friendly task is Candle Burning:


I really like the trashketball activity for my grade 7 & 8 students and see it working really well with the Hero Journey format. Volume of a sphere is not part of the elementary curriculum which offers an interesting opportunity for differentiation with this task which is great!

I agreed! You could have a great exploration with that activity to extend beyond what the curriculum demands of us.


I found a lesson on Desmos called Chance Experiments (Probability) that aligns perfectly with what my students are learning right now. The teacher moves are all laid out for me and I’ve tried it as a student. I plan on printing it off and using the teacher guide when I run the lesson for my notes. I have not used Desmos in my classroom yet so this will be a great way to introduce it.

Task: Corner to Corner
https://mrorrisageek.com/cornertocorner3actlesson/
I like this activity because it is straightforward to adapt to my classroom. I like the idea of giving each group a meter stick and asking them to provide me with the exact length of string I will need to cut to get the line tight to fit from the lower corner to the opposite upper corner {beginning}. I can see the struggle at the beginning where students will try to measure the diagonal distance with their meter sticks {rising tension}. After about 2 minutes, I will notice and wonder about this process of measuring. Students’ hope to see measuring in space will not be an accurate measurement and have the students decide what other measures they can use to help get the diagonal size {Level Tension}.
Hoping the students will say that it would be more accurate to measure horizontal and vertical surfaces {More Rising Tension}. Reveal the dimensions of my classroom and discuss/teach the Pythagorean theorem {Rising Tension}. Once students use calculations, we will consolidate student solutions and methods to agree on a distance and cut the string length {Climax}. Discuss why the string was too long, short, or exact. Falling climax, find the diagonal of different rectangular prisms using the Pythagorean Theorem.

I chose Fletcher’s Fish Tank 3 – Act Task as I thought it would connect well as our 6th grade learners approach rate.
The Spark occurs at the beginning: the video shows the increasing volume with the small dribble coming from the hose and a stopwatch advancing; Notice and Wonder at this place will peak curiosity; Estimating creates crisis and introduces productive struggle as students start to mentally examine what is wanted to solve the problem; Curiosity continues with the establishment of a measured quantity within a timeframe and with the screenshot of the cup conversion to cubic inches; Another dimention of productive struggle occurs with the release of the measurements of the tank through the photo.
This is a challenging problem in my perspective as I have students who struggle with multiplying decimals and perhaps one of my question techniques to maintain engagement would be, “Are there friendlier numbers a person could use to explore here?”
The solutions provided by groups of students is the climax and would allow for consolidation, along with the idea of which answers are reasonable? When would using friendly numbers be adequate? When need to be exact? What would happen if there had been a kink in the hose and someone straightened it out…
Keeping in mind that the slow climb builds anticipation and intrigue, and ultimately student investment, will help me hold off on “giving it all away.” Further, I anticipate students will be more likely to share their solutions since they spent more time building up to the conclusion. Focusing on consolidation with students discussing strategies will also remind me to plan for adequate time so I don’t do the “telling.” I looking forward to the time when I can adequately facilitate the different methods through the learning progression.

I love how these examples are directly highlighting stages of the Curiosity Path starting at withholding information. The words used to describe the mystery, intrigue and wonder are great indicators that you are all reflecting and planning with these key ideas in mind.
Keep on Sparking, Math Moment Makers!

I chose the Krispy Kreme donuts lesson. The beginning and estimation are low struggle. The picture gives some sense of the number of doughnuts in an area, but the box obscures the data needed. The email with some info given and some blocked out give all that is necessary to calculate, and the student’s choice of workable strategies is where the productive struggle begins.

Love it! Are you able to try this out with a group of students sometime in the near future? If so, be sure to share some student thinking with us 🙂


Tomorrow I am teaching how to convert measurement with the milk jug prompt. I anticipate walking through the hero’s journey with the notice and wonder, make a prediction and when the numbers are introduced that is where I will see the struggle. We will see how they solve it as we just finished input/output tables so that could be applied or ratios or basic modelling skills. This will introduce measurement conversations for the week.

I created a lesson to introduce and begin to work with trigonometric ratios. I hope it will follow the hero’s curve!!!!
 This reply was modified 7 months, 1 week ago by Laura Las Heras Ruiz.

I used a problem from nrich called “reach 100” with a large group of year 8 students.
Stage 1
We started basically pick any 4 numbers put in a grid, add the rows and columns
eg. 1 2
3 4
Add 12 + 34 + 13 + 24 = 83
Pupils then pick their own numbers and add
Stage 2
Then we see who got an odd number and who got an even number.
Students who got an odd answer try to get an even.
Why do we get odd or even?
Stage 3
Challenge is to pick 4 digits that make 100
The most challenging part was to ensure other members of staff do not give too much information to students. The important thing here was ensuring a productive challenge, and promoting discussion. Not all pupils managed 100 but that was intended.
Stage 4
Those pupils who managed to reach 100 to find other ways of reaching 100 and to develop conjectures to why some numbers work.
This problem followed the hero’s curve but after each challenge another larger challenge was developed. As mentioned earlier the biggest obstacle was to ensure pupils continued to be resilient and productive at each level of the challenge without giving too much away as “you can always add but you can’t subtract”.

I choose the Trashketball Volume lesson by Stadel. I’m about to teach volume for 8th graders and this is such an exciting lesson. As I built the Hero’s Journey, I had two noticings. One, that when I give information is fluid and dependent on the students. That I need to be ready when they are for certain types of information. That may also mean I may prompt with information they don’t know they need. Also the idea of refining their estimation with a lesson like this may be really helpful as they get more information. So plotting 2 points of estimation could be useful. Finally, I was trained to prepare prompts for students to execute throughout a lesson and the hero’s journey gives that skill a nice arc for me. It is a different way for me to thoughtfully plot the questions I already had prepared.

I chose to do a lesson on constructing triangles using poly strips. Other materials such as string, paper, or wooden dowels, could also be used. At the start I am going to control the numbers used and ask students to try to construct a triangle using the given side lengths. Students will then complete a Notice/Wonder table and I will then ask students to try and predict sets of numbers that will build triangles, and will not. Students will continue working with random sets of numbers independently. Admittedly some students are going to notice the rule quickly, but others are going to struggle and build up that tension, which will become productive struggle. After providing adequate time for a solution, I will allow students to collaborate in small groups and discuss which groups of side lengths construct triangles and which do not. As the tension starts releasing students will begin to establish the rule for constructing triangles and will no longer need to build them to determine if given side lengths can construct a triangle.
 This reply was modified 4 months, 3 weeks ago by Jeremiah Barrett.


I took a lesson about creating a regression line. Because the unit was on investing the data sets were closing prices of 3 different stocks over a period of 12 days each. The worksheet gave explicit steps how to input the data set into the TI84 and derive the coefficients and rvalue for regression line. I completely changed the activity to a notice in wonder with one unnamed stock. Since our class size was small I acted as another student and we each added a notice to the shared document. Ss did not fully understand what I meant by wonder so I added the first, “I wonder why the dots go up and down.” Then students quickly caught on and added their own. We discussed some of the ideas that students wondered about. Only one related to mathematical calculations and I thought it was too early to reveal the direction of the lesson. I put up another scatter plot of a second Stock and asked would you rather invest in this company or the other? Why. It brought out the idea of seeing trends. I added a third scatterplot in which a trend line would be hard to visualize. I asked the same question about would you rather invest in this stock over your last choice? Ss recognized that the trend was hard to identify so they were not confident that the stock would increase or decrease.
Then I asked students to draw in a line that reflects the trend. Each student added in their own line of different colors. I added in one that shared their starting point and asked why they did not draw it as such so we could bring in the idea of needing a measure for determine the fit.
I also added in a graph with a line of best fit and asked which of 4 equations would connect to information given in the graph. How?
Once they saw the need for an equation of this line and a measure of “fitness” then they were ready to understand why we should use
After reflecting on this activity, I liked that Ss were still engaged in the activity even though there are only a few days left of school and many teachers are not requiring much engagement. Although it took longer to get to the calculator aspect of the lesson, I am feeling confident that Ss had greater understanding of what the coefficients of the linear function and rvalue mean. I also realized how important the phrasing of my questions are to move student thinking on the journey.

Fantastic approach!
Glad to hear that the small tweaks made it curious enough for students to engage even at the very end of the year when engagement is awfully low!
I’m curious which stocks you had shown! 🙂


I Created a Lego task about area and perimeter. I started with just a picture of some Legos and said today we are going to use some Legos. Students started calling out ideas of what we might do with the Legos. We made a list of things we know about Legos and questions (Wonders) about Legos. Next I stated that we were going to make a house foundation with the Legos. Students began predicting how many Legos we would use, what shape the foundation might be and how tall it would be. Next I gave them the perimeter of the Lego house. Students began to draw possible Lego foundations. If we were in person I would have provided actual Legos for students to use. Next I provided students with 1 side length of the foundation. We continued to predict and draw possible foundations. I then gave another side length, students know realized that 2 of the sides were the same size and began to use that to determine that it was either a rectangle of square. Then I gave a third side length. Students continued to predict and figure out the fourth side. I finally asked them what the fourth side length must be. The purpose of this lesson was for students to solve for the missing side length. By using this task instead of just drawing a shape and giving three side lengths and the perimeter students were able to see how adding the 3 sides and subtracting from the total perimeter would give them the length of the missing side without me even teaching anything. We repeated with two more examples using the same method but giving them the area and then providing the side lengths. By the time we got to the test on Friday and students saw a shape with a perimeter or area and some given sides lengths they were quickly and easily able to find the missing side length. I was very impressed with the thinking skills and problem solving that students did. I was amazed at the different possibilities they came up with along the way. So much more meaningful that shapes on a paper.

@gerilynstolberg I love your progression in this task. Super low floor but then we raise it a little each time!


For this assignment, I borrowed the pentomino puzzle idea to teach subtracting a negative numbers, such 9(4)..
From a specially populated square grid, for example, the students will determine sum of two digits across right or two digits down.
For part two, the students will now work backwards to determine the difference between the sum an the addend.
For part 3, three of the entries are entered wrongly or ommitted and the students are challenged to fish out the wrong entries or complete the table.


Sure. Any example you can share that models this concept?

I’ve got a bunch of visuals for integers on mathisvisual.com



I looked at the corner to corner activity. Showing the video starts the curiosity, which is built as you ask the students what they notice and wonder. Have them give estimates of the distance, too low and too high and best estimate. Give students the dimensions of the room and ask them to try to find the distance from corner to corner. The productive struggle comes as they try to use the information that is given to find the distance. Giving them the Pythagorean Theorem part way through will help, and eventually I can explain how the Pythagorean Theorem can be used in 3 dimensions by calculating the diagonal distance across the floor and using that with the height of the room to find the total distance. Students should then be ready to do some practice problems.

@marjorie.allred you might want to have a peek at the new Unit/Task Squares To Triangles https://learn.makemathmoments.com/task/squarestriangles/ We’ve incorporated Corner to Corner in this unit.


I also was drawn to the corner to corner lesson. The Pythagorean Theorem is such a common part of units I my grade 8 class, so I’m very interested. I concur with Marjorie that there is a clear opportunity for productive struggle and anticipation, however I felt like with just corner to corner (without first doing triangles and squares) there was a hard jump to giving the theorem. I appreciate how triangles/squares gives more of an inquiry into the theorem for the students to discover. I usually use graph paper and have students draw given right triangles, like one with a side of 3 and 4 or 5 and 12 and draw the squares of each around the triangle.

The activity I choose was the 3 Acts Coca Cola Pool from Dan Meyers. I adapted it to draw out the productive struggle and only give students one dimension of the pool at a time. The potential problem will be some students will forget how to calculate the volume of a cylinder. I have an applet that decomposes the shape to get them thinking about how they could solve the problem. The applet and the proceeding questions I intend to be part of the consolidation but depending on how students respond it might be the push they need to scaffold the problem. Please check out the Hero’s Story Arch, it has all the questions and moves there. I also created a Desmos with some cool polling features I adapted.
Desmos Coca Cola Pool: https://student.desmos.com/join/zmfbqc



In our high school, we have a very active agriculture department and they spend a lot of time outside. This year, as we were clearing farm land, the ag teacher wondered how tall some of the trees were. We turned this into a geometry lesson by measuring shadows of a human and the tree, setting up a proportion, and solving to find the height of the tree. I did a lot of the mental load during this lesson and I can see a transformation to the hero’s journey. I can present the problem to the students as a need to ensure the falling tree doesn’t knock over power lines or fall into a road or onto a house. We need to measure the height of the tree without actually climbing the tree.
To begin, we can present the problem and/or show a picture/video of the tree and farmland and do a notice and wonder. I can give smaller models using different sized building blocks and figure out ways to use those blocks with maybe a flashlight to symbolize the sun shining to create a shadow.

Fantastic. Loving the creativity and connections to the things that are relevant and available in your school community.


I worked through the Charge! task and found that it fit pretty well into the Hero’s Journey template. Staring with the picture of the almost dead phone, noticing & wondering, posing a question, and then estimating all flow nicely. Follow that with productive struggle as the kids come up with questions and use new information and prior knowledge to build skillsets as they work to find a reasonable answer to the question posed. The ‘climax’ would be when the answer is finally shared. Because the answer is not what one would expect when ‘doing the math,’ the end portion of the lesson would be given to discussion regarding why the correct answer was so far off from the answers that came up using 7thgrade math strategies that seemed to have made perfect sense. I think this end discussion has the potential to create more curiosity – which is a good thing.
Wanting to try to turn some of the activities I already use with students around using this format so there is more curiosity and engagement. Thinking following this structure will become easier after consciously working through it and presenting this way over time.


One of my favorite lessons to which I could apply the Hero’s Journey planning strategy is to challenge kids to figure out whether a rectangle with a given perimeter will always have the same area. One of our standards in fourth grade is to use the standard formulas for finding Area and Perimeter of rectangles, including squares. Students who have decent addition and multiplication skills are able to learn this skill pretty easily, but just giving them the formulas takes away their chance for exploring this topic in a fun way. After all, it is one of the most lifeapplicable geometry concepts we teach!
So, to allow kids to use their curiosity and productive struggle, I would introduce it in a fun and engaging way. I would pose the question, “If I had 48 yards of fencing, what would be the best rectangle to arrange my fence in so that my three dogs could have the biggest area to play in?” Remembering what area and perimeter are will be a struggle for some at first, but since they do work on it in third grade, I believe that in cooperative groups, they could get started.
I would provide square tiles and dry erasers for them to explore on their dryerase desktops, or they could have graph paper and markers if they prefer. I would challenge them to create their first configuration and then to think of a different way to arrange with the same perimeter. What do you notice? What do you wonder?
What do you think would happen to the area as you keep changing the length of the sides?
At some point they would begin to see that as the lengths of the sides get closer to forming a square, the area increases. Why do you think that works? Will that always work? By now, they will start to create their own generalizations about the relationship between Areas and Perimeters when the Perimeter is the same.
When they are ready I will introduce the formulas for Perimeter and Area, and challenge them to try their newfound generalization to other numbers like 18, 24, 100, etc.

I chose “Shark Bait” for first grade:
Open with Act 1 video and notice/wonder…estimation “How long is the worm/how many cubes long is the worm” and think pair share
Act 2: verify and pose…”but then he grew 2 more orange cubes” /think pair share
Act 3: verify
For the Hero’s Journey I asked a friend for help and this is what we came up with (thanks Terri): challenge them by giving them Playdoh to create their own worms and ask…”How many cubes long could two worms be?” or “How many cubes could four worms be?” Since it is a “could be” students could have different answers based on how much Playdoh they choose to use (this would invite discourse and allow for an informal assessment).

Awesome job. Thanks for sharing your breakdown of how you’d apply the curiosity path to this problem.


I teach a sixth/seventh special education math class. My students range from close to gradelevel students and students who are working on 13 grade standards. I love that some of these activities will be great for everyone depending….I looked at the worm activity and tried to figure out ways to extend it…the low floor is what I need to include everyone. Since all my kids seem to have issues with number sense and thinking, we need these activities to include everyone. My goal for all the students is to extend their thinking to as close to grade level as possible.

I am using the heroes journey template to help plan my lesson(s) to introduce and build on the concept of growing patterns in grade 3. Not having a defined textbook, Though I find these patterns easy to do, I went web surfing for a deeper understanding of what is involved in teaching this concept so that students are minds on. After learning more than I knew before, I landed upon a research site called What Will Your Math be today? (https://researchideas.ca/wmt/c2b1.html) which gave me an idea of how to use bingo dappers, large graph paper, and locking cubes to explore growing patterns.
Since it will be the beginning of the year, I do plan on doing some work with repeated patterns to bring their grade 2 knowledge forward. How much do you think will this influence the curiosity aspect of what I want to do?

@Linda Andres, the link you shared doesn’t seem to work and I’d love to take a look at where you got those ideas!


I used the link “Mathalicious” which brought me to “citizenmath.com/lessons” and I chose: “Happy Meal” Probability Level: Algebra1 – Probability (Beg)
Act 1: Watching the commercial about “Happy Meals” up to a part where someone has a choice in picking from the list of Meals with her child “Johnny” beside her.
Estimation: Share & discuss: ideas, experiences.
Q prompt: “How many times do you have to buy a Happy Meal to get 1 toy?” and maybe when more comfortable “2 toys?”Act 2: Rewatch the commercial maybe this time the part where there is a children’s menu (lower number of choices) and mother chooses “Happy Meal” where Johnny indicates something about toys. Students ask more questions to help in their estimation.
Get “High”, “Low”, and “Convinced” estimations.Productive Struggle: Use die and record – They are motivated to prove their estimation is right/wrong.
Leads to Max (but not quite there): Use Aggregate trials to create histogram.
Beyond Max (confident but new information): Calculate how many added meals EXPECTED before obtaining another toy? (Review the data with a different perspective)
Act 3: More Calculations, with students, discovering and looking at formulas/ideas to relay lesson intended. “How much do the toys really cost?”
Conclusion: Discuss reasonable fees and Debate other options on how McDonalds could distribute toys related to “Happy Meals”
 This reply was modified 3 months ago by Velia Kearns.

I have always wanted to get more creative with the introduction of algebraic equations.
I will create task cards with variables, some with coefficients, and some with constants, and equal signs.
As students enter class they pick a card. Then I would build a human concept attainment lesson using the students, yes examples and no examples, use think pair share to get students discussing.
All ideas would be recorded on chalkboard or under the document camera.
As students start to see patterns, and begin to develop strategies I would move to more challenging equations as students are ready for them. This may take a few classes but it would build and grow based on student discovery…

I worked on a Scaled copy lesson from my text book. The main thing looking at this helps me to remember is to let students struggle. Do more allowing them to struggle and share with each other. Facilitate discussion and eventually get to the solution. It might take a bit for me to change the culture of the students I had last year to encourage struggle and discussion. I do like what the previous section suggested in that if students struggle with decimals just use friendly numbers to start with so that decimals don’t get in the way of the other concepts. Obviously, we’ll need to use decimals in class but depending on my group of students I don’t necessarily want to cover too many things at once with them.

I would like to use “Hero’s Journey” With the introduction of Transformations
I will create task cards with Different Transformations
As students enter class they pick a card. Then I will show examples of each type of transformation – which will also be added as Anchor Charts Across the room. Students will work independently to create a different transformation, do think pair share with their shoulder partners and then will go to vertical surfaces to draw their solutions. Students will do a gallery walk to view other students work and to add examples to their notes.
All ideas would be recorded on the class whiteboard or on the mobi board and projector.
As students start to see patterns, and begin to develop strategies I would move to more challenging transformations and how we write them algebraically as students are ready for them. This may take several classes but it would build and grow based on student inquiry…

Although I think this is great for nearly all of my standards, the first activity that comes to mind is determining when three lengths form a triangle.
To set up for this lesson I would take wooden sticks, such as dowels or skewers, and cut them to specific lengths with whole number measurements. I would then color code the sticks with paint, stain, or tape to represent those specific lengths.
I would begin with asking about the attributes of a triangle. How many sides? How many angles. What are the names of the classifications?
I would then give each student three random sticks and ask them to make a triangle without altering the lengths of the sticks. The students would then work individually to attempt to create their own triangle. I will then ask the students to share in their groups who was able to make a triangle and who was not. They will also be prompted to discuss their thoughts on why some students were able to make a triangle and some weren’t. For those who could make a triangle what did they notice in comparison to those who couldn’t.
If length was not discussed I may casually prompt that discussion as well.
After discovering any connections the students may have found (as a whole group) I would then read the theorem of side lengths of a triangle: The Sum of two side lengths must be greater than the third side length. I would then ask the students to discuss this theorem with their group and how it connects to the triangles they did or did not make.
After sharing their thought in a whole group I would introduce the formulas:
A + B > C; A + C > B; B + C > A
From here I would have the students use the lengths of their triangles and nontriangles to see if this theorem holds true.
Extension:
Give students triangles of different classifications with two lengths labeled on each triangle (whole numbers are preferable). Ask students to list all possible measurements on the third side length (whole numbers are preferable).
This will make students think through all possible inequalities of each triangle.
Ex. The given triangle has two of the three sides labeled. What are the possible whole number lengths of the third side?
Answers: 2 ft; 3 ft; 4 ft; 5 ft; 6 ft
Remediation:
Continue using the random measured side lengths and the following template to help understand how the theorem is working. Ask the question below.
“Once an incorrect inequality is found do you need to continue with all three?” (no)
“Do you always have to set up the inequalities in the same order?” (no)
“What lengths would be the best to add first?” (the two longest lengths)
“Why would the two longest lengths be the best?” (If the two longest lengths is a true inequality then it will LIKELY be a triangle. If this does not make a triangle it will LIKELY be proven with the first two longest lengths.)
Measure of side length A: __________
Measure of side length B: __________
Measure of side length C: __________
________ + ________ > ________
Length A Length B Length C
________ + ________ > ________
Length A Length C Length B
________ + ________ > ________
Length B Length C Length A
Closure:
Spiral back to adding decimals and fractions by having students find the correct side length combinations and then find the perimeter of the triangle with the given side lengths.
Determine which of these combinations will form a triangle.
What is the perimeter(s) of the triangle(s) that can be formed?
(Answer: Combination D; 20 3/4 or 20.75)
 This reply was modified 2 months, 3 weeks ago by Holly Dybvig.

Using the Krispy Kreme task for grade 4.NBT.4 & 5, I would just show the three images provided, maybe turning it into a Google doc for students who might want to see closer than projecting on the board or who wanted more time with it and have both options. I would ask the students what they notice and what they wonder. I would write this down so students could see one another’s responses. I would ask them to estimate how many donuts are in the box, including too high and too low. I would let them productively struggle with this question and walk around listening to their discourse after timing a think/pair/share. When the class as a whole had a detectable level of frustration I would reveal the email information. Then I would give students time to discuss what this meant and what new clues they were given. I would hand out rulers that had mm on them so that students could use this as a tangible reference with the email information. I might use the 25 x 35 pic if students needed another entry point into the problem which is likely after the covid learning gaps. I would walk around listening to student answers and ask if there are any other things they wonder. I would notice aloud any strategies I saw in the room and allow groups of students to work together if pairs alone were reaching too high of a frustration level. Then I would ask for solutions and visuals to prove their mathematical reasoning. We could also do a gallery walk of posters if I gave each grouping chart paper to work out their problems on. Then I would reveal the second email after all ideas had been shared and we had a chance to ask questions and dialogue. Lastly I would show the video that contains the answer. Then we would talk about it and look back at our own solutions and visuals. Then I could do extension activities off of the task such as “if the box had of donuts had a total of a half million calories, what activities could you do to expend that energy, how long would it take?” etc.

I will be using the Hero’s Journey Template by using Esti Mysteries : https://stevewyborney.com/2019/09/51estimysteries/
Giving them lots of time at the beginning and doing one a week to keep them practicing their skills!

I chose to work with the Trashketball problembased lesson for my Hero’s Journey assignment.
First, show the video of letter sized paper being used to make trashketballs to be thrown into a garbage can. This will peak students’ curiosity. All other information is withheld at this point.
Next, I will have students show what they Notice and what they Wonder from the video. This will occur early on in the hero’s journey curve. ThinkPairShare will occur during this stage. What I expect to see as one of the wonders is ‘How many paper balls (trasketballs) will fit in the can?’
Once the problem to be resolved is identified, I will ask students to predict how many trasketballs will fit into the garbage can (we will have our own can similar to the one in the video). They should make a best guess, as well as choose a number that is too small and one that is too big. Students will work independently before discussing with a partner and then whole class.
At this point, students will need to think about what information they require to solve this problem. Many or most will want to jump in and begin constructing trasketballs right away to throw in the can. We will go this route to find their test result and move towards calculating volume later on (the learning goal); however, students should think more about the trasketball construction. This could be a point of struggle if they have forgotten their work in science. Prompting may be required initially to get them thinking about what is particular about the size of these trasketballs. Each one should be approximately the same size and ideally, they should be compact. If more than one person is making the trasketballs, they should try to keep all very close in size. When students have filled the garbage can, they should compare the count with their estimation. Who has a good eye for predictions? 😊
For the next stage of the process, I will ask students if there is another way to solve this problem with more precision. ThinkPairShare will be used to give students time to think it through and feel a little more confident about their ideas. I believe there will be students who will suggest finding the volume of the garbage can and the trasketballs. If it does not come up, then I will let them know that finding volume is our goal. We will complete the activity again using volume to find the number of trashketballs that will fit in the garbage can (theoretical result).
Before providing students with the required formulas, I will need them to name the shape for the garbage can. Now I will show the formula to find volume for the cylinder. I will ask them to look at the parts of the formula before asking them what they notice…what is familiar to them. They should recognize that we are working with the area of a circle (the base) and the height of the container. Students should already know pi and how to find height and radius. We will also review the formula for finding radius as it will be easier for them to measure diameter. From a previous unit, students should know how to calculate r<sup>2</sup>. Now they can find the measurements of the garbage can, and finally, substitute their values for the variables used in the formula (may be a struggle for some students). Students will need to know that units for volume are required and should be cubed.
The process for finding the volume of the trashketballs will be similar to that above. Students will name the shape – a sphere – and I will show them the volume formula. I will ask them to look at the parts of the formula to see what is familiar to them. Again, students should already know pi and how to find radius. Calculating r<sup>3</sup> means multiplying by one more radius than for volume of a cylinder. Since we have already reviewed how to find radius using a formula, students will have discovered that it is easier to measure the diameter to find radius. But what we do when we are measuring diameter of spheres that are not all identical and which are numerous? Potential struggle: ThinkPairShare…hopefully students will determine that they should find an average diameter by measuring the diameter of a few spheres. Also, to measure the diameter, we will look at the strategies suggested by students. Now students can substitute their values for the variables in the formula to find volume of a sphere which may be a struggle for some students. Again, students should recognize the units need to be cubed.
To find the response to the question (How many trasketballs can fit in the can?), students should realize that the volume of the can will be divided by the volume of the sphere. This answer is our theoretical response as it is based on formulas. As a supplemental activity to take the problem a further, students might think about how they might get their test result (practical solution) to be closer to the theoretical solution.
This is a long procedure to follow, but if students can bravely struggle through it, most certainly they will show resilience, grit, perseverance, and become better problem solvers. Hallelujah! I am really looking forward to running this activity with students this year!!
