Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 24: How to transform textbook problems into captivating tasks › Lesson 24 Question & Sharing
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Lesson 24 Question & Sharing
Kyle Pearce updated 1 week, 6 days ago 60 Members · 111 Posts 
Select one textbook problem you plan to use with your students in an upcoming unit. Use the blank 2.4 Curiosity Path Template to plan how you will use the Curiosity Path to transform your problem into a curious challenge kids will want to solve.
Share your result here.
What problem did you choose?
How did you change it?
How did your students respond?

I have a question about the “growing blocks” problem Kyle uses as his example. What if your students themselves “rush to the algorithm”? When I did this problem, the kids did not come up with the creative patterns Kyle mentions; they ALL saw it the same way — times 2 plus 1. At that point, do you just move on, or do you push kids to come up with multiple ways to think about a problem, when the way they have thought about it is already effective? When I do that, they look at me as if to say, why are you wasting my time asking me to do something less efficient?

I tend to think of the big picture in this case — representing linear relations in multiple ways. So, yes, I would push for other ways to represent the pattern. I have found the phrase helpful: “I saw another student in another class represent this relation in a different way. How might they have represented it?” Or rephrase it as a challenge “how many ways can you represent this linear relation pattern?” The big picture is to have they recognize the connections among representations.

I think you could also just give a more complicated pattern next that more easily lends itself to multiple representations. Either way, the key is to make them understand that there are different ways to do the same problem. I find so many students that think there is only 1 correct method to solve the problem, I love any time I can highlight a different approach.


I’m thinking about my Linear Programming unit. A typical problem would be something like:
“Sally makes gingersnaps and snickerdoodles to sell. She has 20 eggs and 15 cups of sugar. A dozen gingersnaps requires 3 eggs and 2 cups of sugar. A dozen snickerdoodles requires 2 eggs and 3 cups of sugar. She can sell 1 dozen cookies for $5 each. How can she maximize her sales?”
Students really tend to struggle with the many steps in these problems. I always work hard to break down the steps and have them really understand, but they struggle. So, I’m trying to think through the process in this way.
“Sally is making cookies to sell at the fair.” – What do you wonder? (What kind? How much do they cost? How much will she earn?)
“How can she maximize her sales?” – (Advertise! Make more cookies!)
“She makes snickerdoodles and gingersnaps and sells them for $5 per dozen.” – What do you notice/wonder? (What is keeping her from making as much as she wants? If she sells 100 dozen, that is $500!)
“She has plenty of most ingredients, but only has 20 eggs and 15 cups of sugar.” – (I wonder how many eggs and how much sugar it takes to make those cookies.)
“It takes 3 eggs and 2 cups of sugar for a dozen gingersnaps. It takes 2 eggs and 3 cups of sugar for a dozen snickerdoodles.”
Now they have all the information, but will they be able to work out an answer? They could do it via some trial and error, but I’m not convinced this will get them to the correct answer.
This is really thinking about next year. I always introduce the unit by having them create some lego furniture and working through the process that way, but they always get hung up on the constraints and the graphing part of the solution.
https://teacher.desmos.com/activitybuilder/custom/563870954871f4bb4c18ac45
 This reply was modified 1 year, 11 months ago by Kyle Pearce.

The textbook question I have adapted is, “Matthew’s bed takes up ⅓ of the width of his bedroom and ⅗ of the length. What fraction of the area of the floor does Matthew’s bed take up?”
I think I will show the following three pictures for a three act lesson:

That can certainly help to invite all learners into this discussion. I wonder how we might introduce this image in order to get them noticing and wondering?


I will be teaching scale factor. I am going to show the students the 2 triangles and ask them to notice and wonder. Then, hopefully someone wonders “how much bigger/smaller” is one figure compared to the other, then we can move into scale factor.

Let us know how it goes!
You might want to check out @jon’s Trees lesson on his site: https://mrorrisageek.com


One problem I had done in the past for systems of equations was have students solve a problem about a race between two people but one had a head start and one ran faster – something like Usain Bolt ran at 10mps and Mr. Diehl ran at 3 mps. Mr. Bolt gave Mr. Diehl a 30 foot head start. How long will it take Mr. Bolt ot catch up to Mr. Diehl.
To withold information and create anticipation, I could show them two videos – one of me running and a clip of Usain Bolt. Students might notice some numbers on Mr. Bolt’s track or know from their own track and field experiences different lengths of races. They could hopefully ask questions like how fast are they both, how much of a head start would Mr. Diehl need to win the race, how long is the race.
I would then eventually ask student to estimate how long it would take both of us to run across the field next to our playground, then aks if they thought Mr. Bolt would give me a head start and we could get to how big it should be to create a “fair” race. This would allow for more discussion about what “fair” would be. We could also introduce the diea of linear vs. non lienar (i.e. will both of us be able to keep the same pace the whole time).

Great idea @david.diehl you may want to check out this activity from Desmos https://teacher.desmos.com/activitybuilder/custom/56d139907e51c4ed1014b51f


I pulled a question from the 7th grape CPM textbook the reads.
“Gracie loves to talk on the phone, but her parents try to limit the amount of time she talks. They decided to record the number of minutes that she spends on the phone each day. Here are the data for the past nine days: 120, 60, 0, 30, 15, 0, 0, 10, and 20
Find the mean and median for the information.
Which of the two measures in part (a) would give Gracie’s parents the most accurate information about her phone use? Why do you think so?”
I would start by just revealing the first line, “Gracie loves to talk on the phone, but her parents try to limit the amount of time she talks.” By withholding the information, the students can start noticing the dilemma they are probably accustomed to and wonder about what they feel is too much and how to collect it. Have them anticipate what information will be needed for the parents to justify their argument.
After that, I would have the students look at the quantitative information given in the problem.” The parents decided to keep a record of the number of minutes that she spends on the phone each day. Here is the data for the past nine days: 120, 60, 0, 30, 15, 0, 0, 10, and 20” And ask without any calculations, How would you describe how much Stacy talks on the phone in one sentence? (Estimation)
Next, I would reveal the question, “Find the mean and median for the information.” Do the students discuss the meaning is? What is the Median? How are the two different? Also, discuss what information students will need to get and how much to get a fair comparison of how much Gracie talks on the phone.
Finally, I would bring out the last question, “Which of the two measures would give Gracie’s parents the most accurate information about her phone use? Why do you think so? “and of course the question, “Do you think Gracie talks on the phone too much? Please Justify.

@scott.mcnutt I’m really liking this. I think it’s super simple and effective! Let us know how this goes.


In a lesson on bearings, I gave the questions without the questions.
“what do you see?”
“what can you find out?”
Then we had a look at some questions and found out we had answered them already!
 This reply was modified 11 months, 1 week ago by Stephen Prince.

I found this problem, Peter was very thirsty and drank 2 glasses of water. There was 3/8 litre of water in the 1st
glass and 3/5 litre In the 2nd glass. How much water did Peter drink altogether? and tried to transform it.I would start with Peter was thirsty, and have students notice and wonder and anticipate where the problem is going. Then I would reveal that he drank 2 glasses of water. Now I would have students estimate what volume he drank and have them share their estimates. Next, I’d reveal that there was 3/8 litre of water in the first glass. Students could then estimate the total one more time with that new information. Finally, I’d reveal that his second glass was 3/5 litre and have them solve for the total without a calculator and they must show their thinking.

Great problem and use of the curiosity path!
Now that you mention it, think how easy it would be to show a photo of the glass full then some missing. . (Or a video even better)
Seems like some good opportunity there.

This is a great way to spark curiosity and build in a problem based learning scenario that you can come back to in multiple units (fractions, measurement, etc).

Glad you think so! The more we can cycle back to ideas, the more likely it’ll stick!



I am working on the probability unit and determining theoretical probability. The problem was: The bag holds 2 red cubes, 2 blue cubes and one green cube. The number cube shows the numbers 1 to 6. You roll the number cube and draw a coloured cube without looking. What is the probability that each situation could occur? Use a model to show your thinking. a) You roll an even number and draw a blue cube b) You roll an odd number and draw the green cube c) You roll either 3 or 5 and draw a red cube or blue cube d) You roll 6 and draw the green cube.
I decided to use a Notice and Wonder with the picture of the paper bag with the cubes and the die from the MathUp online textbook. The only information I gave my students was the picture and information about the bag and die, not that they were being used for probability. There was a lot observations and statements of probability to do with bag and die individually. Fractions were used to describe the probabilities. There were questions about why there was only one green cube and not 2. I left off for the weekend with the Notice and Wonder and plan on having my groups determine the probabilities they want to find using the bag of cubes and die for an occurrence they decide on. I can use the textbook questions once the groups are comfortable with determining the probability for their occurrence. I think this strategy will be more engaging and the end goal is the same.

Love it! It doesn’t have to take much to flip how we introduce a problem to students to spark curiosity. Thanks for sharing!


Raoul has 72 wristbands and 96 movie passes to put in gift bags. The greatest common factor for the number of wristbands and the number of movie passes is equal to the number of gift bags Raoul needs to make. Find the number of gift bags that Raoul needs to make. Then find how many wristbands and how many movie passes roll can put in each gift bag if he evenly distribute the items.
Raoul is making gift bags.
{NOTICE/WONDER} then add “for a charity event.”
He has wristbands and movie passes to put in the gift bags.
{NOTICE/WONDER} {ESTIMATE}
There are 72 wristbands and 96 movie passes.
{NOTICE/WONDER} {ESTIMATE}
Raoul wants to use all the materials.
{ESTIMATE}
He also wants each person who gets a bag to get the same things, in the same quantity..
{ESTIMATE}
How many people will get a gift bag? What’s in each gift bag?
Extend:
How would you change the bags when 36 baseball hats were also to be included? How would you change the bags if there were 29 Itunes gift cards to be included?

I like how to withheld information here @maryannabiedermann I’m eager to hear how this will go in your classroom.


Here’s the original textbook problem I’m using with my grade 2s and 3s in a unit of mixed operations story problems: “Kelso had two dogs. Each dog eats one and a half cups of dog food each day. There are 75 cups in one bag of food. How many days does one bag of food last?”
For anticipation and withholding information: This problem seems perfect for a video! My students are already familiar with my dog, as she appears frequently in our lessons. I might start by introducing a video of her at breakfast and at dinner time over a few days. Then open the floor for notice & wonder.
Notice & Wonder is already a common activity in our classroom, but we usually do it as a whole class. We also have established Think/Pair/Share routines, so it’s funny that I’ve never thought to put these two practices together! For this problem, I plan to let kids work with their partner/small table groups first before sharing out with the class and zeroing in on the question: “how long will a bag of food last?” and hoping that students will ask me how much she eats each day.
My grade 2 students have not done much work with fractions yet, and are building fluency with multiplication. I know that they can handle “halves”, and can think of this problem as repeated addition. However, their primary math instruction is based on the Chinese national curriculum and relies heavily on the algorithm, so I anticipate they will experience some frustration. I might modify the problem to only be about 1 dog, and have the introduction of a second dog as a challenge problem.

Withholding information for the win!
Keep in mind that while videos are always fun, there are ways you can get a similar effect from the curiosity path without a video. However, if you’re geeked to try it out, then by all means! 🙂

yes! I agree that there’s definitely other ways of hooking them in without videos, but they ALWAYS love seeing my dog 🐶



Maxine is moving into a new apartment. Before moving day, she wants to decide where to place her furniture in her new living room. When she visited the apartment, she drew this rough sketch of the room’s layout and recorded some measurements. She has also measured her large furniture, which she wants placed by the movers. These measurements are shown in the table below.
Furniture Dimensions (width by length)
couch 40 in. by 90 in.
loveseat 40 in. by 66 in.
wall unit 20 in. by 60 in.
How can you use a scale diagram of this room, on an 8.5 in. by 11 in. sheet of paper, to determine where to place these pieces of furniture?
A. Determine a scale you can use to create a scale diagram of the living room on an 8.5 in. by 11 in. sheet of paper.
B. Use your scale to determine what the lengths of walls and openings in your scale diagram should be.
C. Create your scale diagram of the living room.
D. Use your scale to determine the dimensions of each piece of furniture that needs to be placed.
E. Select a strategy to determine a good location for each piece of furniture. Add the three pieces of furniture to your scale diagram.
This could instead be:
Maxine is moving into a new apartment. She drew this rough sketch of the living room’s layout and recorded some measurements.
<insert photo>
She wants her couch, loveseat, and wall unit to be placed by the movers.
WDYN? WDYW?
*reveal*
couch: 40 in. x 90 in.
loveseat: 40 in. x 66 in.
wall unit: 20 in. x 60 in.
Where should the movers place these pieces of furniture?
Inches to feet? or Feet to inches? 12 in = 1 ft (careful for 0.5′ = 5″)
couch: 3’4″ x 7’6″
loveseat: 3’4″ x 5’6″
wall unit: 1’8″ x 5′
 Create a scale diagram of the living room, including furniture.
 Compare your diagram with your classmates’ diagrams. How are they the same, and how are they different?

Original Problem: Shari had 24 charms on her bracelet. The bracelet broke and the charms fell off. Shari found 17 of the charms. How many were lost?
Changed Problem: Show a picture of the bracelet and don’t say anything. After some time, show a picture of the broken
bracelet with some of the charms missing? Ask students what they notice and wonder.Estimation: I could show a close up of the charms on the floor. Students could how
many charms are on the floor. I could also show the bracelet after the charms are put back on. I could ask whether or not the charms are
identical. Did Shari find them or did she purchase some more?I think this is a little harder to do with younger age groups, but I can see the point in expanding the imagination of our learners.

The younger students are, the more willing they will be to share. This also means huge tangents that will need to be managed without discounting any of the voices in the room.
One thing I think is so key is listening to their estimates. We quickly realize that student perception and their understanding of magnitude is much more underdeveloped than we may realize. This process can be huge to help them develop their number sense.
