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
Tagged: @jon, @jon @kyle, @kyle, @kyle @jon, #halfwaythere, #math, Algebra 2, based, context, desmos, lessons, Linear Programming, naked, no, problem

Lesson 24 Question & Sharing
Dawn Oliver updated 3 weeks, 3 days ago 58 Members · 107 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, 8 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 8 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?

I’ve tried but i’m still thinking that is not as open as I wold like to.

I like this!
I wonder if initially just googling a big stadium or festival or something and having them estimate the number of people from the picture might help that spark?


Here’s the question:
Rafi has a savings account that earns 9.2% simple
interest each year. The account contains $47,000.
If Rafi does not add or take out any money, how
much will be in the account in 7 years?
We’ve done some simple interest work already, but I noticed that lots of students can’t remember the info they need to use from the problem (not too much there, I think) or they only use part of the info (for example, 47000 x 9.2) and forget that the % needs to be converted to a decimal.
I think I might use this with a small group, since we’ve gone online now and the ones who know the formula and understand what to do will railroad those who are more hesitant.
I think I would start with: Rafi has a savings account. (N/W time) Hard to T/P/S online, so far in break out rooms they stay on mute (I’ve got a quiet group).
How much will be in the account in 7 years? (They are always forgetting the time factor, so I figure reveal that first as important?) Estimate? (they might talk about whether he’s going to access the funds at all, add more in, etc.)
Some might remember that there are two kinds of interest, so I might reveal that next. This might draw out what they still need to know (Principal and Interest rate).
He has 47000 in it right now. (Refine estimates) Some might take 47000 and multiply by 7, so seeing answers on a number line may help them see some highs and lows. Does it seem reasonable that each year you can add another full amount? (100%) Draw out the third “need” %.
Let them figure and then plot some answers (high and low) on a number line to discuss the “does that seem reasonable” Why are some so far apart? Can we see a connection between the highs and lows (perhaps the 2 decimal places’ difference?)
Open to suggestions! Thanks.

Existing problem:
Reworked problem:
Jasmine is a caterer. This weekend she needs to provide the food for a corporate lunch
(What kind of food might she be serving? Does she cook the food? How many people are coming to the lunch?)
The company has requested BBQ sausages, salad and bread. Jasmine knows she catered a similar event a few months ago, and she always takes notes on how well her events go. Here are her notes from that earlier event:
Note: Sausages: 2 – 3 per person, Salad: 1 large bowl feeds approx 8 ppl. Small bowl = 4 – 5 people, ALWAYS HAVE 10 SPARE SAUSAGES! Last minute guests – argh!!, Bread: 1 slice per sausage plus 1 extra slice per person (12 slices per loaf)
(N & W: sausages are listed in 2 places, there’s 2 sizes of salad bowl, the formula for bread is in 2 parts, there’s no exact number of sausages per person, bread comes in loaves, are sausages bought individually?)
How many sausages, bowls of salad and loaves of bread should Jasmine order for the estimated 50 guests?
(Do we have to minimise wastage?)
Can you generalise Jasmine’s notes into formulae which will help her plan her next Sausage Sizzle & Salad event?
Here is Jasmine’s world famous salad recipe:
Large bowl: 1 cos lettuce, 4 roma tomatoes, 2 lebanese cucumber, 1 carrot (grated), ¼ jar kalamata olives, 50g feta cheese, 100ml salad dressing<div>
Add to Jasmine’s shopping list for this weekend’s event
Generalise Jasmine’s salad recipe into a formula which will help her plan for future events
</div>

Great revamp here! I’m also wondering how we might take this context and initially present it with less words? Maybe some details on a slide with a visual of some sort? This might help more students enter the problem. Nice job!


original Problem: Mr. Walthour is building a storage shed in a conical shape. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed?
I will only provide the following information when presenting this question.
Mr. Walthour is building a storage shed. What is the volume of the shed?
I will then provide time for a notice/wonder followed by a think, pair, share.
Next, I will disclose that the shed is a conical shape.
I will ask students to estimate.
Finally, I will reveal the diameter of the base and the height of the shed.
 This reply was modified 4 months, 3 weeks ago by Jeremiah Barrett.

@jeremiah.barrett Nice. It looks like you’ve got the handle on transforming those textbook problems!

I am a third grade teacher.
Original Problem: Aanya and Vish wanted to build a house out of Legos. The wall has a perimeter of 150 feet. One side measures 24 feet. A different side measures 24 feet. A third side measures 51 feet.
a. Draw and label a diagram of the wall. Use a letter to represent the unknown side.
b. What is the unknown side. Show your work and explain how you know.
c. What is the area of the house? Show your work and explain how you know.
To spark curiosity I would start with the first sentence and an image of Legos. I would allow the students to talk about what they know about Legos, experiences building with Legos, shapes, sizes and wonder what the house might look like.
Next I would give them the information that the perimeter is 150 feet. Talk about what that means (hopefully students will remember that perimeter is the distance around the shape). Estimate what the sides could possibly be and draw these diagrams.
Give them the first side measurement and adjust our diagram and predictions/estimations.
Continue with the next side measurement and encourage students to draw and change their thinking. If students don’t bring it up talk about what shape it could possibly be now that we know two sides are the same size. Estimate the possible length of the other sides.
Continue with the third side measurement and adjust our diagram and calculations.
Give students the question: What is the unknown side length and how to do you?
Now that we have this information: What is the area? Explain how you know?
This is actually easier than I thought it would be and much more interesting of a problem. It allows students to think instead of me solving the problem and showing them the steps.

Fantastic work. I love that you’ve realized that transforming the problems you already use isn’t a huge task, but rather just requiring a small shift in perspective when planning it out. Curious to hear how this translates in your classroom!


TEXTBOOK PROBLEM:
Julie’s bathtub has 84 L of water. She pulls the plug and lets the water drain. Due to a clog, the water drains slowly at a constant rate. After 3 minutes, there were still 36 L of water left in the tub.
a)Write the linear equation that represents this situation.
b)How long will it take for the bathtub to empty?
Grade 9 – LESSON GOAL: To make sense of and model a linear situation using a graph.
Note: Problem is given before rate of change equations are introduced.
<WITHHOLDING INFORMATION> Show: Julie’s bathtub has 84 L of water
<NOTICE WONDER> done individually, then ThinkPairShare and whole group
I’m assuming lots of interesting questions and opinions will come up.
<WITHHOLDING INFORMATION>
<ANTICIPATION> Show: How long after Julie pulled out the plug will it take for the bathtub to empty?
<NOTICE WONDER> discuss all the possible factors involve here and questions the students have.
<ESTIMATE> ask for too low, too high and best guess. Collect answers visually
<WITHHOLDING INFORMATION> Show: Due to a clog, the water was draining slowly, and at a constant rate. After 3 minutes there were still 36 L of water left in the tub.
<NOTICE/WONDER>
<ASK IF ESTIMATES CHANGE>
<STUDENTS WORK>
Say: Make sense of this situation on a graph. (students work in small groups). Provide graph paper.
*I do not want to constrain the thinking here. But choosing a model to focus on will help streamline the discussion. Students are still doing the thinking.
Teacher circulates and observes. Then teacher invites students to share their thinking. Teacher selects solutions that are correct and incorrect to spur discussion and for students to validate their thinking and bring misconceptions to light.
We will likely get into a conversation about unit rate since it’s easier to talk about how the water is draining per minute rather than per 3 minutes, but it comes from the students. We’re not so focused on the actual answer here, more on the correct modelling of the situation on a graph.

Nice lesson here. You’re right, we don’t want to constrain the thinking but we do want a learning goal and outcome in mind. Sometimes this might be a particular way to model the solution (using a graph or using an equation). I’m eager to know how your class does.

This looks great! I like how you are planning on leading your students into modeling with a graph after giving more information.


Begin with the statement:
Jonathan and Lucas are each allowed to play video games after they complete their homework and reading.What do you notice and wonder?
Next:
If both boys spend the same amount of time on homework and reading this week, which boy gets more time playing video games?Students will need to seek out the additional information about the time spent completing homework in order to earn the time playing video games.

I like this question because it is very open, students who arrive at an answer quickly can be given an extension: Lucas wants to create a counter offer to his parents so he can have the more time than Jonathan. What did Sally’s parents offer if she has less time than Jonathan but more time than Lucas?


To start with, I’ll draw a quarter of a circle and ask the students, while in a group, to generate more shapes to the initial quarter of a circle. Then I’ll ask them to assign values to each part. Using a gallery walk strategy, each group get to share their art work. The intention here is to get them to generate a full circle.
While withholding info about the corner shelf is a quarter of a cicle and the dimension of the radius, students will be asked to estimate the area of the gallery art presented.

Original problem: Pam bought 80 shares of Netmark Associated stocks @ $24/share. The company paid annual dividends of $0.38/share. What is the total annual dividend? What is the annual yield to the nearest hundredth of a percent?
OPENER: Display wallet with bills sticking out along side 2 different stocks. On top of 1 stock I would display 38 cents.
Anticipate: Why is there 38 cents on top of that one stock? How much did it cost to buy the stock?
After wonderings were presented, I would focus on what are factors to consider when buying stock?
I would share that stock A is higher priced but has a dividend and stock B does not and ask if this changes their decision. After students share out, I would reveal the stock price of $24/share.
Finally I would ask if students would rather earn the 1.5% interest in savings account or buy the stocks which earn $0.38/share? I would expect them to justify their answer with math calculations.

I do a unit on dimensional analysis and have a problem that says, “Four students want to take a road trip but they have limited funds. Genny’s car holds 4 people and gets 35 miles per gallon (mpg). They want to go to San Francisco for the day. The distance for them is 180 miles one way and fuel is $4.25/gallon. How much money would each student have to pitch in order for them to make it to San Francisco and back home again?”
Since we live almost 800 miles from San Francisco, I would probably change it to some place closer to home. We could start with “Four students wanted to go to a play at the Utah Shakespeare Festival in Cedar City and, since they had limited funds they decided to drive down, see a matinee, and come home the same night. How much money would each student have to pitch in for gas to make it to Cedar City and back home again?”
Have students give notices and wonders. I can tell them that I have actually made that trip and it wasn’t as bad as I thought it would be.
Hopefully their wonders have included the gas mileage, distance to Cedar City (270 miles), and cost of gas. If not, I will ask them what information they need to find the cost. They will have to take into account that the total distance travelled will be 540 miles and the cost will be divided into 4 equal parts.

I would only tell the students the first statement. As the students notice and wonder, I hope they will wonder where the scouts are going and if the trip will cost anything. When I tell them where and yes, they have to pay 5% of the land value, students may ask what is the land value and how much land will the scouts be using. I can then ask the question How much will the scouts be charged for their camping trip.
 This reply was modified 4 months, 1 week ago by Kristina Hill.

Nice @kristina.hill You’ve withheld some information here but I’m wondering if you can withhold a bit more. Ask What do you notice / What do you wonder here instead of “will it cost anything?”

@JonOrr…thank you for the feedback. I’m wondering if I wrote this correctly. I would only tell the students the scout leaders were planning for the upcoming year. What do you notice? What do you wonder? My wish would be the students would wonder “Are they planning any trips?” “Where are they going?” “If they are scouts, they are probably going to go camping. Where would they go camping?” The last wonder would lead me to tell the students the scouts are planning camping trips to Cherokee National Forest. I’m hoping the students would start talking about camping trips and the students would ask if the scouts have to pay to camp. Would this be more in line with anticipation and curiosity?

Yes those would be some great prompts to start with. Note that it is a grind at first if students are new to the notice and wonder protocol. Stick with it. Also, if students are slow to share, you can share some of what you notice and wonder and eventually start a context by telling a story… slowly giving more information informally… then you can shift to a prompt for the intentionality of the problem. Think of it as a drawing them in process.


For the fourth graders – Original Problem If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?
Will begin by showing a heap of wheat grains and ask the students what do they notice and wonder?
Reveal that there is 9975 KGs of wheat in total.
Then add pictures of bags, let them estimate how much wheat will go in each bag, and based on that how many bags of wheat can be made?
Will then reveal that 95 bags were filled and then let them find out how much each bag could hold.

Nice work here. You will want to also include a prompt after your estimation: What information will you need to know to improve your estimation?
This can help students formulate strategies.


I will be teaching 1st grade again next year (I looped with my class this past year and taught 2nd grade because, well, Covid and virtual teaching). Our school is finished for a few weeks now but I chose a lesson from our school’s required curriculum. The original problem is: Bobby found shells at the beach. He found 10 shells each day for 6 days. How many shells did he find in 6 days. And the curriculum has a “table” provided to help solve this problem.
So, what I will do next time I teach this lesson is: #1Bobbly found shells at the beach. (Notice / Wonder/Record student thinking). #2 How many shells did he find in 6 days? (Discuss / wonder/ record student thinking). #3 He found 10 shells each day. Record/discuss thinking.
I would also like to take this further by asking, what if he continued to find the same amount for 7 days? How many shells will he find? On to 10 days.
Along with this kind of thinking, I’m wondering about how to represent this – my students will be familiar with using a 10 frame – would it be appropriate to use this tool to help clarify their thinking?
At some point, because it is in the text book, I feel like I need to use the table that is with this problem. In first grade, arrays are not taught, but it seems like this might be another interesting way of representing this information before taking it to the table for representation.
Thank you for your help with this!

Love it. Also consider just having an image of a beach and shells possibly. You can even hold off on the story of Bobby until after students share what they notice / wonder. Maybe their favourite thing to do at the beach, etc.
As for the table, I’d argue that you want to emerge that model after students solve the problem. The textbook is trying to push students to use a specific model – which is too narrow. Rather, allow students to solve and use their thinking to organize in a table and then consolidate why the table might be helpful.
Of course this is only if you’re using this problem as a part of your lesson. If it is just for students to do purposeful practice, then leaving the problem “as is” might be the way to go.


My original question was “ Thomas is ordering tacos for his party. The table shows the cost for ordering a certain number of tacos. What is the value of X the cost is proportional to the number of tacos ordered?” Do you know the problem there was a table showing that the two tacos it cost $2.60, for three tacos it cost $3.90, and for four tacos it cost $5.20. Then there is a column, where are you have six tacos cost X number of dollars.
I first would just introduce the statement that Thomas is ordering tacos for his party, I would also probably show some delicious tacos. That would hopefully build anticipation for the question. We would begin a “what do you notice / what do you wonder” where I would assume the following contributions:
 how many tacos he would need
 how many people are at the party
 why is he ordering tacos
 what kind of tacos
 where are you from
 how much do they cost
I would circle the cost question ask for some estimate of how much it would cost for a taco party. Discuss the best place to get tacos, and look up their menu online for the price.
I could get a little information that I have been holding, I could share that for one taco it costs $1.30 and then we could have a moment to think/pair/share for the cost of 2, 3, etc. .. We could discuss how this would be a proportional relationship.
We could ask Thomas how many people are invited to this party, and find a final answer for the cost.

My original question was “ Thomas is ordering tacos for his party. The table shows the cost for ordering a certain number of tacos. What is the value of X the cost is proportional to the number of tacos ordered?” Do you know the problem there was a table showing that the two tacos it cost $2.60, for three tacos it cost $3.90, and for four tacos it cost $5.20. Then there is a column, where are you have six tacos cost X number of dollars.
I first would just introduce the statement that Thomas is ordering tacos for his party, I would also probably show some delicious tacos. That would hopefully build anticipation for the question. We would begin a “what do you notice / what do you wonder” where I would assume the following contributions:
how many tacos he would needhow many people are at the partywhy is he ordering tacoswhat kind of tacoswhere are you fromhow much do they costI would circle the cost question ask for some estimate of how much it would cost for a taco party. Discuss the best place to get tacos, and look up their menu online for the price.
I could get a little information that I have been holding, I could share that for one taco it costs $1.30 and then we could have a moment to think/pair/share for the cost of 2, 3, etc. .. We could discuss how this would be a proportional relationship.
We could ask Thomas how many people are invited to this party, and find a final answer for the cost.

Algebra 1 textbook problem on setting up equations and solving:
“The Buffalo Bills scored 24 more than twice the number of points that the Miami Dolphins scored. Altogether, the teams scored 66 points. How many points did each team score individually?”
To begin, I could show the football team logos or even a clip of them playing from a past football game. I would be looking for them to ask questions like, “Who won?” “By how much did they win?” “What was the total score?” “The Bills are better than the dolphins.” “The weather is nicer in Miami.”
Once we land on a question around scoring, I could reveal that total points scored. Next, students could come up with different combinations of points that could total 66. They may come up with the idea that a touchdown is 6 points, extra point is 1, twopoint conversion, a field goal is 3 points, and a safety is 2 points. This is where students could do estimation to come up with points that each team scored.
I’m looking for them to ask who won the game. I’m a little stuck here…. would you deviate from the problem verbage and state the Bills won before revealing the “24 more than twice the number”? Or, reveal the “24 more than twice the number” and let them wrestle with figuring out who won the game. From there, they could use the information to determine each team’s individual score.
The goal here is for a student to write an equation to solve, so, would you work on deriving an equation after the students solve the problem?

Loving these everyone!
Noticing the key is withholding information and trying to keep it visual some way, some how. Curious to hear how it goes after implementing!


A baker determined the annual profit in dollars from selling pies using p(n) = 52n − 0.05n^2 , where n is the number of pies sold. What is the annual profit if the baker sells 400 pies?
From the 2019 Algebra I Texas STAAR
Withhold information by revealing only “A baker determined the annual profit in dollars from…” Ask students about what they notice and wonder about the problem? Maybe they notice the word annual and that the baker sells something related to his occupation for a profit. We might ask students in 2 minutes to make an estimation about the profit based on the occupation of a baker that is too low or too high and just right. Allow the students to share in their group before a class discussion. Maybe the baker is Paul Hollywood and has his own TV show. Maybe the estimates might be higher because students notice the prices behind the showcase are sometimes really high. There is interest and anticipation because students still are unsure where this is going to go.
Then reveal the question, “what is the annual profit if the baker sells 400 pies?” Allow students to think about this in the same think, pair, share format. Now is there anything you notice or wonder about the problem? Students might think pies are not wedding cakes, they might not be that expensive. Knowing there are only 400 pies changes the estimate because maybe the pies couldn’t be less than a dollar. Students may wonder how large are these pies because more ingredients will drive the cost of the pies. If students need to determine annual profit, students will be looking for the cost of the pie, a table of values, some additional information that will allow them to determine profit.
Next I would reveal 52n0.05n^2, ask students how they might interpret the expression with the story of the baker’s profit? Do they think there is enough information to answer the question about the annual profit after selling 400 pies? If we return to the notice and wonder, students may notice n and wonder what does it mean in the story? Why are we subtracting 0.05n^2? What is it about this problem that makes it a quadratic if we talked about quadratics already? Finally reveal p(n)=520.05n^2 and discuss n might represent the number of pies and p might be the profit. Students may recall the function notation and determine the number of pies is the domain of the function.
I might push students to try instead of algebraically how would the solution look graphically if that was my learning target. Spiral in the domain and range of the function.

I love the withholding of information and heading down the path towards an estimate. I wonder if you might have some sort of visual as well? Maybe a short clip of a baker or something… or just a pie being pulled out of the oven?
These little edits you’ve made to how you present the context can go a long way. Excited for you to put these ideas to practice! 


Okay, I have general questions about adapting this lesson cycle. Algebra I in Texas is very computational, here is what I mean:
https://tea.texas.gov/sites/default/files/2019_staar_algebra_i_test_tagged.pdf
When I created the curiosity path for this activity, I noticed some of the test questions were straight math problems with no context. For example, solve this equation with variables on both sides for x. Then some questions were systems where they needed to choose elimination or substitution. There are no words only equations to these problems.
How do you approach this in the classroom and is there any additional practice afforded to students to ensure they have the necessary skills to answer these types of questions? I feel like one problem and a deep conversation may not be enough to say I know my kids will do well on the assessment, but I haven’t taught problembased lessons before either?
 This reply was modified 3 months, 3 weeks ago by Anthony Waslaske.

My last district used a scripted curriculum where I didn’t necessarily have the freedom to redefine what was given to me. When I think about teaching Domain, Range, Discrete, and Continuous Functions in Algebra 1, I felt it was more a vocabulary lesson than anything requiring a strategy. I am thinking to myself how will I make a problembased lesson out of that? I wonder if a textbook creates an entire lesson for something that may just as well be taught along with another topic. Exponent rules to me seem to fit the same category. How do you teach these concepts in your class?

Jon and Kyle have a great task for beginning exponents: https://tapintoteenminds.com/3actmath/pennyaday/
Jo Boaler also has some rule making activities
https://www.youcubed.org/tasks/exploringexponents/
Andrew Stadel has a great activity for kids learning from mistakes
http://mrstadel.blogspot.com/2013/04/thankyoumathmistakes.html


A few more questions, vertical whiteboards, are we just trying to get students out of their seats and moving?
Also, when you slowly reveal information in a problem to students, does every piece of new information require another thinkpairshare, or after the first thinkpairshare can you just have a classroom conversation? For example, the Baker selling pies problem I created for this lesson has about 5 pieces of information I want students to process. If I tried a thinkpairshare for each piece of information I shared the strategy might get old. At some point do you all just skip the pair and share, and just have a class discussion?
Along this vein of thought is cold calling considered poor practice in the classroom? I usually use it to draw students back in when they were bored with the lesson. I guess changing to problembased lessons might resolve that.
 This reply was modified 3 months, 3 weeks ago by Anthony Waslaske.

The lesson target for this problem is using equations to solve word problems.

Third Grade Teacher
Original Problem: Ann is learning to play the trumpet. She practices 30 minutes every day.
A) How many minutes does she practice in 6 days?
B) How many hours is that?
Rework:
1. “Ann is learning to play the trumpet”
WDYN/WDYW (think, pair, share)
2. “She practices every day.”
WDYN/WDYW (think, pair, share)
Estimate, too low, too high, best guess
3. “She practices 30 minutes every day.”
WDYN/WDYW (think, pair, share)
(hopefully a student wonders how much she practices in a week/month/year)
4. “How many minutes does she practice in 2 days… 3….”
Estimate, too low, too high, best guess
5. “How many minutes does she practice in 6 days?”
6. “Is there another way to represent the time she spends practicing?”
hours, days, other forms of time

Distance Formula—on the heals of Pythagorean theorem unit.
Working with the problem below, I would first remove all the numbers—coordinates and field measures. I would make my player and her goalie (behind her) one color and opposing goalie another color. May change to soccer players…
N/W, TPS, discuss as class. My athletes will get to “how far to the goal.” At least one student will ask for numbers or suggest layering coordinate plane on the field.
Reveal numbers as students request, add player to increase understanding (at right angle position) or increase complexity at other field locations.
My goal is to avoid making this all about the distance formula, and allow students to discover and extend their use of Pythagorean theorem.

In my school the constant concern is, “Students don’t know what the question is asking, so they don’t know how to solve it.” So I think this is a very good way to begin to help alleviate this problem.
I most recently taught 4th grade, and next year I will be in a new role as an Interventionist, so here is a problem that I would like to go back and transform or use with students as I help them learn to break apart problems.
Original Problem: Each Saturday Mr. Franklin teaches 3 piano lessons at his music school and 4 piano lessons in students’ homes.
For each lesson at his music school, he charges $15.
For each lesson in a student’s home, he charges $20.
What is the amount of money in dollars that Mr. Franklin earns from piano lessons each Saturday?
Here’s how I would transform it into a Curious Challenge:
Show a video of a piano teacher instructing a student, either from a movie clip, or a clip from YouTube so that students without any background about pianos or music lessons can understand and visualize what’s going on in the problem.
Reveal only the first part, but withhold the information about how many lessons and how much he charges.
Each Saturday, Mr. Franklin teaches some piano lessons at his music school, and some piano lessons in his student’s homes.
What do you notice? What do you wonder? Have students think and jot on their own, share with a partner, then share with the class. Record students’ ideas.
Next, reveal the question that goes with the prompt, and ask students to estimate the amount Mr. Franklin can earn, but still withhold how many of each type of lesson and the amount he gets for each.
How much does Mr. Franklin earn each Saturday?
Ask students to estimate an amount that would be too high, an amount that would be too low, and their best estimate. Allow them to spend two minutes to think about what their own estimate would be, and write it down. Then give three minutes to pair up with a partner and explain their estimates for reasonableness. Finally, have students share with the whole group.
Ask students if there is any information they would like me to give them so that they could get a more concise estimate.. Perhaps they will ask for how many lessons he gives, and / or how much he gets paid.
Reveal the number of lessons. Each Saturday, Mr. Franklin teaches 3 piano lessons at his music school, and 4 piano lessons in student’s homes.
Allow students time to revise their estimates, using think, pair, share again. Most students might realize that he should get paid more for going to students’ homes than he does for having them come to his music school. Once they realize this, I will reveal the following: For each lesson at his music school, he charges $15, but he gets more if he goes to their homes.
Allow time to revise estimates again. Make sure that students record their best and final estimate, share it with a partner, then record final answers.
Reveal the last piece of information: For each lesson at a student’s home, he charges $20.
Give students time to solve the problem using all the pertinent information. Share final answers.
 This reply was modified 3 months, 2 weeks ago by Terri Bond.

Nice work here. I also agree that this is a great way to ensure all students understand the context and can enter the problem. Without ensuring all students can access the problem from the start, we risk losing out on opportunities for some to engage in the learning.

The original problem is attached.
Starting with a blank slate, here is what I am thinking:
Option 1:
1) Tito saw a flyer asking for donations to the local food pantry. On the flyer was a list of the top three items requested. (What do you think are the top three items?)
2) The items listed as most needed were (in no order): tuna, peanut butter, bread. Tito doesn’t want to purchase a little of each item; instead, he thinks it would be better to buy as much of one of the items as possible to donate. (Your thoughts on the best item to buy/donate)
3) For various reasons – share some given by students who selected PB as the item they would give – Tito decided to buy peanut butter to donate. Because Tito wants to donate as much peanut butter as possible with the amount of money he has to spend, he wants to find the best deal. At the store, he sees several different brands and prices. The lowestpriced container of peanut butter (Nutty) costs $2.19. The highest price for a container of peanut butter (SaveaLot) is $6.60. There are two other brands on the shelf, Grandma’s peanut butter costs $2.79 per container and Bee’s peanut butter costs $4.69 per container. (Notice & Wonder)
Option 2:
1) At the store, Tito is looking to buy peanut butter. He sees several different brands and prices. The lowestpriced container of peanut butter (Nutty) costs $2.19. The highest price for a container of peanut butter (SaveaLot) is $6.60. There are two other brands on the shelf, Grandma’s peanut butter costs $2.79 per container and Bee’s peanut butter costs $4.69 per container. (Notice & Wonder)
2) Tito saw a flyer asking for donations to the local food pantry. He decided to donate peanut butter. Because Tito wants to donate as much peanut butter as possible with the amount of money he has to spend, he wants to find the best deal. (Estimate)
Options 1 & 2 continue:
1) As Tito is loading several Nutty peanut butter containers into his cart, he notices something that makes him think that buying the lowest priced peanut butter container might not end up getting him the most peanut butter for his money. (Thoughts)
2) Tito takes a closer look at his choices. [post the table with size $ cost of each from original problem]
3) Which peanut butter should Tito buy to get the most peanut butter for his money to donate to the food pantry?
I can come back to this problem and throw in sales & taxes, coupons, etc. at a later time. It could be used for many other concepts – maybe even something with the volume of cylinders eventually.

@andrea.cadman You’re definitely transforming this with the curiosity path! Have a peek at the Sugar Sugar lesson I built in Desmos that is similar in standards https://teacher.desmos.com/activitybuilder/custom/56d766ebf260b18c09188aa5 Let me know if you see some similarities.


Original problem from a first grade textbook:
Tori counts the toys in her toy box. She has 3 bears and 3 cars. The rest are dolls. She has 12 toys in her toy box. How many dolls does Tori have?
Curiosity Path:
Show an image or video clip of a child taking toys out of their toy box. (Thinking that a reenactment of the first 2 sentences would be best for this age group.)
Notice and wonder
Think Pair Share
Record student responses on an anchor chart/board. Circle a response that mirrors the target question…how many dolls does Tori have (take estimations)
Ask students what information would you like to help you with your estimation (provide the total number of toys and/or manipulatives)…have students turn and talk to refine estimate

Fantastic work my friend! The more you put the Curiosity Path into action, the more natural and automatic this process will feel, too!

Nice work here. Your task reminds me of our Gummy Worms task. Give it a gander https://learn.makemathmoments.com/task/gummyworms/

@lisamarie.barnes I am encouraged by your posts. Thank you, again, for helping me apply the lesson to primary students. I’m not sure why I’m struggling with this so much. I am grateful to you and for you. Andrea


Not having a textbook handy at home, I chose a problem for salamander math (https://www.mathsalamanders.com/imagefiles/3rdgrademathchallengesbikesandtrikes.gif).

Nice work here @linda.andres I’d even insert some questions after you reveal there are 25 wheels…..What are some combinations that will work here? Show me what that will look like? How many combinations can we come up with?


Original problem:
Ann’s fish bowl holds 5 liters of water. If she used a scoop that
holds 1/6 of a liter, how many scoops will she need in order to
fill the entire bowl?
Curiosity Path:
First, remove a LOT to withhold info and create a level of anticipation.
Perhaps just show pics of a fish bowl that is empty and then one that is full. I could even do a video of me with an empty fish bowl and then show me starting to add a scoop or two of water to the bowl. I could also have a fish in a bag, as they come from a pet store, off to the side.
Second, I would have students think/pair/share and create a class list of what they notice and wonder.
Finally, from there I would follow down the path to get students to look at the actual problem of how much water the fish bowl can hold, and how many scoops it would take using the scoop that I had in the video.
As Terri mentioned in her reply, I have the majority of my students who see long word problems and automatically say, “I don’t get it. What do I do?” They have also learned to look at the tests we give, see what standard it says at the top to narrow down what operation to do. This definitely does not help them in life as we don’t get those clues about how to solve each problem we encounter in life. Boy would that be nice! I really like how we are getting to see how students are thinking, what they are understanding, what is possible, etc. for each scenario we present. Awesome strategies!

“The height of a skydiver during a free fall is given by y= – 4.9x² + 5100. x is the time, in seconds, since leaving the plane and y is the height above the ground, in meters.
a) What is the altitude of the plane when the skydiver jumps?
b) If skydiver plans to open the parachute at 3000m, how many seconds of free fall does the person have?”Curiosity Path:
1) Show video of someone standing at the open door of an airplane.
*Students notice and wonder, anticipating what will come forth2) Show them the person free falling and opening a parachute
*Student notice and wonder3) Estimate how long it took for them to open their parachute (Prompt)
*Thinkpairshare
4) Add fact that parachute has to open at 3000m
*Thinkpairshare, revising estimation
5) Add model of graph (formula)
*Thinkpairshare, revising estimation6) Reveal after math talk and discussing the different directions that the conversation took and could be addressed.
 This reply was modified 3 months, 1 week ago by Velia Kearns.

Love this.
Just thinking about how after they notice and wonder … and even estimate height etc, we could share a scale drawing to help them spatially update their estimates, and then slowly reveal more information.
Love it.

We’ve just adopted a new textbook for the 20212022 year and have been told to “focus on fidelity” to the program. Rather than hunt through for a problem that I though would lend itself to some curiosityrevision, I went with the first problem my grade 4’s would see in this new textbook. Ugh.
Objective: Read and write numbers through one million in expanded form, with numerals, and using number names.
Original Problem: “Mrs. Darcy saved ten $100 bills. How much money did Mrs. Darcy save?”
I have been staring at this problem for about 15 minutes. I have thought about at least three different ways to approach this problem, and I keep rejecting them because I feel like the moment it starts to feel curious and engaging to me it also deviates too much from the original problem.
Inviting Notice and Wonder: a jumbled pile of play $10 bills equal to $1,000.
After notice and wonder, invite estimates. How much do you think is there?
Layer in other images, bundling the $10 bills into stacks of 10, allowing students to revise their estimates After each image.
Final image would be trying to fit that entire stack into a wallet. Will it work? What else could we do?
Maybe students will come up with ten $100 bills as a solution? I really don’t know. I really wanted to do something that would move them into other ways to find a 1,000, like fifty sets of $20 or twenty sets of $50. But like I said, that moves them away from the original intent of the lesson.

Original textbook question
It’s time to pick up a few items at the grocery store this week. You need to buy at least two fruits or vegetables. You have a $10 bill. You need to figure out what your total will be and how much change you will get. (Table of items given with their prices. Items on the table are using dollars and cents)
Changes
Start out with a picture of a grocery sack where they can’t tell what is inside. Also, let them know, it’s time to pick up a few items at the grocery store this week.
Let the students complete the notice and wonder.
Hand them a $10(fake) and tell them this is all you have to spend. Give them a tub with change manipulatives to work with.
Let them brainstorm things that they think they could get for $10 using estimation.
Give them the list of items that are options on the price sheet without the prices. Have the student create a list of items they believe they could buy with their $10.
Add in that they need to buy at least two fruits or vegetables. Have them think about if they will need to remove something from their list in order to afford the fruit or vegetable.
Then give the students the price chart. Ask them what is the total of the items they chose to buy. Were you able to buy everything you wanted?
Next, I would ask them if they could buy anything else and how do they know if they will have enough money. That should bring us into a conversation about what is their change.

What problem did you choose?
(From expressing Remainders as Decimals) Bianca is making necklaces for her friends. She has 6.3 m of leather cord. Bianca cuts the cord into 14 equal pieces, one for each necklace. How long is each piece? Show your work.
How did you change it?
1. Bianca is making necklaces for her friends using leather cord.
2. How long is each piece if s<strong style=”fontfamily: inherit; fontsize: inherit;”>he wants the pieces to be equal in length?
4. Give students a piece of string 6.3 m in length
5. She has 14 friends.
How did your students respond?
We are not running school right now…

A lot of the integer textbook problems from my campus’s textbook are about golf. I teach in the dual language program and my students play soccer, not golf, so there is a lot of background knowledge missing to make sense of the problem. I think something my students would understand universally is working for money, spending money, and borrowing money from their parents or savings account for a big purchase.
Here is a word problem I would work up to:
Claudia walks her neighbor’s dogs everyday after school for $10 a day, five days a week. At the end of the week Claudia puts $5 in her savings account. This Saturday Claudia hung out with her friends at the mall where she bought her favorite food court pizza and a drink for $8. One of her friends remembered she owed Claudia $25 from their trip to the movies a week ago. While browsing at the mall Claudia found a tshirt for $20 and a pair of blue jeans for $35. Will Claudia have enough money for her day at the mall or will she need to borrow money from her savings account?
I could either create (or find) a video of someone working and she shopping at the mall. Or create a comic strip of someone doing the same thing, but with images only (blank word bubbles maybe?).
We could slowly add the context in such as her earning money (money coming into her pocket) and spending/saving money (money leaving her pocket), then a friend paying back a debt (money back in her pocket). We could then discuss that the money in her pocket is constantly changing. Would the amount of money added/leaving her pocket be “good” or “bad” changes? In terms of good or bad, which experience would be a positive/negative experience for her pocket? This could lead to changes being represented by addition and the type of change to the amount would be positive or negative (being an integer). This could also lead to the discussing that subtraction does NOT exist. They are just negative and positive changes.

Great ideas @holly.dybvig you may want to explore this new task we released in the last week. https://learn.makemathmoments.com/task/piggybankrevisited/ Be sure to explore all 5 days as they will dive into adding negative integers.


Grade 8 Introduction to Transformations.
 This reply was modified 3 months ago by Mary Jackson. Reason: Inserted blank template initially
 This reply was modified 3 months ago by Mary Jackson.


Thanks so much for sharing this. I have been having trouble getting my files to upload. Would you please check to see if I was successful adding my file this time? I am trying to upload this file.


Original Problem:
Tara can bench press 130 pounds. Each week of training, she wants to increase the weight by 3%. The function models the weight Tara can lift w(x)=130(1.03)x where x represents the number of weeks of training.
Describe the transformation in w(x) as it relates to the parent function f(x)=(1.03)x
Robert is also increasing the weight he can lift by 3% each week. The function v(x)=95(1.03)x represents the weight he can lift after x weeks. What is his starting weight?
Compare w(x) and v(x)
My changes:
Learning Goal: Explore transformations of exponential functions.
Notice and Wonder/With holding Information:
Tara can bench press 130 pounds. Maybe create an image or video clip to present this data.
Notice and Wonder/Anticipation:
Each week of training, she wants to increase the weight.
Looking for this wonder/Estimate: How much could she try benching in the first week? Too low, too high, best guess
Give more information: Each week of training, she wants to increase the weight by 3%.
How much would she need to bench press the first week? (think pair share)
Extend by asking:
How much would she need to bench press the second week? (think pair share)How much would she need to bench press the third week? (think pair share)
How much would she need to bench press after x weeks? (think pair share)
Reveal:
The function models the weight Tara can lift w(x)=130(1.03)x where x represents the number of weeks of training.
Ask: Graph this function on Desmos
Ask: Can you give a similar, but simpler function (parent function)? Looking for the parent function.
Ask: Graph this function on Desmos.
Ask: Describe the transformation from the parent function. How did it change? [Describe the transformation in w(x) as it relates to the parent function f(x)=(1.03)x]
Extension or next day (since I’m not sure how long this problem would take in a 50 minute block):
Notice and Wonder:
Robert is also increasing the weight he can lift by 3% each week. (Include an image or video)
Looking for wonder/ Estimate: How much can he currently bench?/What is his starting weight? Too low, too high, best guess
Give more information/Reveal: The function v(x)=95(1.03)x represents the weight he can lift after x weeks.
Ask: Compare w(x) and v(x)
 This reply was modified 3 months ago by Serina Signorello.

This is the original problem, from a 6th grade unit on area of twodimensional figures:
*I would start out by showing a picture of a green space (possibly even one in our area, to increase their buyin) with a rectangle “marked off” in the middle. Ask them what they notice and wonder. Try to get to the question about how large the green space is.
*Ask them for an estimate (at this point, providing no actual dimensional information). Record/display the range of estimates. Then, provide the 13m x 13m dimensions, and ask them to revise their estimates. Hopefully they are able to identify that the green space would be smaller than the 13 x 13 (169m squared). Finally, give the dimensions of the 5m x 4m rectangle in the center, and ask for a “final” estimate.
Something I am “figuring out” in regards to how to start out: the less information we give students, the more room they have to notice and wonder, especially for those students (many of mine especially) who really struggle with math. I really like the idea of taking a word problem from a simple picture or sentence at the beginning to the actual math problem at the conclusion and bringing as many students as possible (hopefully all!) along the way using the curiosity path. I am very excited to get started with this in September!

You might want to have a look at day 1 of the Squares To Triangle task. https://learn.makemathmoments.com/task/squarestriangles/
You can use it for area of rectangles and triangles but eventually bump into Pythagorean Theorem. If the PT isn’t apart of your standards you can just leave that part out in the connect stage.


For my 8th grade Unit 5 Lesson 13.2
https://access.openupresources.org/curricula/our68math/en/grade8/unit5/lesson13/index.html This link is for the student version of the problem.
There is a lesson trying to have students compare the volume of a rectangular prism that is 3 units high with a cylinder that is one unit high and the same cylinder that is the same 3 units high. The pictures are clearly labeled with many specific questions that follow.
Instead I could take pictures of peanut butter and a box of granola bars. I can clone the picture to show it is three high. If I was ambitious I could take a picture in the store of each one three high. To start with nothing would be labeled. I’m thinking simply compare one box to the one jar to start with for the notice and wonder followed by thinkpair and of course share.
I’m not sure of the next step. I could have the picture of the 3 boxes, one jar, and 3 jar as the original problem had. In the original they happen to have approximately the same volume for the larger ones. Or if I’m feeling brave I could go off of one of their wonders. I’m not sure much student input I can get to change where we take it as a class.
 This reply was modified 3 months ago by Denny Nelson. Reason: I didn't include the link to the original problem. I'm linking the student version

A table with the lengths of four hiking trails in Joshua Park. How much longer is the Lost Palms Oasis trail than the Skull Rock trail. Instead, I would snip pictures of the four hiking trails and ask for notice and wonderings. The question could be one like the one posed in the book or any variation of computing with rational numbers. The students could give their estimates to the question selected. Eventually I would need to reveal the lengths of each of the four trails.

While looking at word problems for the Fourth Graders and the curiosity template, I am stopped in my tracks by the lack of wonder and excitement these problems create! As I need more time to really work on this I must say I am excited by the task!

Original Question (from Grade 10 Trig): A tree casts a shadow 9.3 m long when the angle of the sun is 43 degrees. How tall is the tree?
I would start by showing a timelapse video of a tree and it’s shadow changing length, and ask the students what they know and wonder. I would hope that it would lead to some comments about the length of the shadow changing, and the height of the tree not changing. The discussion could move to what caused the shadow to be different lengths, and could we determine the height of the tree. What information do they need? If someone asks about the length of the hypotenuse, so that they can use the Pythagorean Thm, we can then discuss what measurements are possible to physically measure and what are not. If I could physically measure the hypotenuse, then I would be able to physically measure the height of the tree at the same time.😉 We could then discuss clinometers, and how they measure the angle. Then make some predictions, and do some calculations, before I give them the numbers in the question and they finish that.

It is summer so I do not have student feedback yet. Before this activity, I was still unsure how to create a rich question from the textbook. By using your steps, it makes more sense to me now.

This is a 5th grade multiplication problem: A bakery bakes 15 batches of 29 cupcakes each week. How many individual cupcakes do they make each week?
I think I could start with showing a picture of a local bakery and asking students to notice and wonder. Then I would ask, “how many cupcakes do they make each week” and do a think, pair share. Then we would discuss what they know and what they wonder again. I could ask them to estimate: what is a number that is too big, what is a number that is too small. Then reveal that they make 15 batches of cupcakes and let students anticipate how many cupcakes per batch after asking a student to define what a batch is for the students who don’t know. Then I would reveal there are 29 cupcakes per batch and ask them to revisit the problem, encouraging use of visuals problem solving & multiple methods and then have the students share out the different methods they used to solve.

There is a spinner question in my textbook for grade 7 which is very direct for our probability unit. I am thinking I can use my actual spinner and just leave it on my desk at the front of the classroom. Let them chat about it as they come in. Then I can ask them what they think/wonder. Hopefully they would wonder things such as: what are the odds they spin a certain number, colour, shape. I would give students the opportunity to guess how many times/the probability one of these things happen.Then we can actually do it a few times and I could give them a bit more information. Continue to do this for a little longer and even integrate a talk about theoretical probability vs practice. Then I could let them go to work on some problems!

That is a great idea. Also, consider checking out our problem based games called “Spin It To Win It” in the tasks area!


I forgot to hit post 😩, so I’ve returned to retype my Action plan.
Grade 8 Textbook Problem: The grade 8 class wants to go skating at the town rink. It will cost $150 to rent the ice and $3 to rent each pair of skates. The total bill will be $294. How many students will go skating?
a) Write the equation to solve the problem.
b) Solve the problem.
I will show an image of middle school students skating at an indoor arena and will include the first statement of the problem to frame it – The grade 8 class wants to go skating at the town rink. This will get students worked up immediately as they will likely believe this is for real.😀 All other information will be withheld at this point.
Next, as anticipation is already building, I will ask students what they Notice and what they Wonder about the photo and the statement. Students will work independently first, jotting down their thoughts, then they will join their elbow partner to share their ideas (1 minute share) before sharing whole class. I will post their results for everyone to see. For Notice, I expect to see some of the following: Students are skating. They are in an arena. The look like middle school kids. They look like they are having fun. For Wonder, I expect to see some of the following: I wonder if we will get to go skating this year. I wonder if we’ll have to wear helmets. I wonder if it will be only our grade 8 class that goes. I wonder if we have to pay. I wonder if everyone will want to go.
If no one has landed on the question about how many grade 8 students will go, then I will add it to the list and put it out there. How many students will go skating? Everyone will be asked to estimate independently how many grade 8 students will skate. They should pick 3 numbers that represent the students going: one that is too low, one that is too high, and a best guess. There can be some discourse following this with other students to check their reasoning.
Now I am ready to reveal more information to students. I will let them know the total cost for this event – $294. Based on this number, they will look at their prediction for the number of students who will go skating and reevaluate. Students can make assumptions about the number attending as they may hear some students grumbling because they are not interested in going and vow they will stay home that day or others who say if they have to pay then they won’t go. Student estimates should be reasonable. For example, if students think there will only be 15 kids who want to go, then based on the new information given, those students would be paying almost $20 each. There will likely be a very low turnout if that is the case.
While the discussions continue between students, they will certainly ask more questions. They may wonder if the school is going to cover some of the cost. They may want to know if there is an ice rental fee or if there are other costs not yet considered. Here is where I let them know that the ice rental fee is $150, and the school will pay it. It’s time for students to reevaluate their predictions again. With each new piece of information, student predictions should be moving closer to the solution for the problem. The level of anticipation is probably escalating…I’m sure there will be a buzz in the air. Students will continue to share their thinking with one another as we move through.
The final piece of information is now presented. Students will have to rent their skates from the arena – groooaaaannnn – for a cost of $3 each. With this final reveal, students should be able to achieve the actual solution to the problem or be very close. We will have an opportunity to see who our best estimators were from the getgo.
To wrap up, I will want students to think of the math statement that could be written to solve this problem now that they have all the parts. This is a good way for them to see how it can be represented in a linear relationship equation.
*I have been away from school since midFebruary but will return in September, so I have not had the opportunity to try this activity with my students. I do look forward to using the curiosity path when I return. Our math periods are only 45 minutes long, so I’m not certain if this will be enough time to complete an activity such as this; however, I am game to try.
**I apologize for the length. Unfortunately, I am a little anal about detail.

I would take out the left image and the bottom image, leaving the one on the upper right to clean it up and to add some curiosity. I would also leave out the the fact that the ratio for the hypotenuse is n(squareroot)2 and the n’s on both sides. Since 2 of the angles are the same, they should be able to figure out the two legs (sides) are the same, then they can use the Pythagorean Theorem to find the missing side and see it is nSquareroot2.

Fantastic! Open questions are great to incorporate, too! Love it!