Make Math Moments Academy › Forums › Full Workshop Reflections › Module 2: Engaging Students Using Problems That Spark Curiosity › Lesson 2-4: How to transform textbook problems into captivating tasks › Lesson 2-4 Question & Sharing
Lesson 2-4 Question & SharingPosted by Jon on May 1, 2019 at 11:46 am
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?Sean Campbell replied 2 months, 4 weeks ago 38 Members · 51 Replies
Katrien VanceMemberJune 25, 2019 at 7:30 pm
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?
JonAdministratorJune 25, 2019 at 7:58 pm
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.
Daniel WhittakerMemberJuly 3, 2019 at 9:01 pm
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.
Daniel WhittakerMemberJuly 3, 2019 at 9:17 pm
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.
- This reply was modified 3 years, 1 month ago by Kyle Pearce.
Patricia SchelerMemberJanuary 4, 2022 at 12:39 pm
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.
Kyle PearceAdministratorJanuary 5, 2022 at 7:22 am
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.
Stephanie PritchettMemberFebruary 18, 2022 at 12:46 pm
The original problem is looking at a positive exponential function and having students make observations in regards to the negative x values. It also asks students to complete a related table that matches the graph. Students are asked to look for patterns in the graph and to use fractions so they can see those patterns.
I decided to remove the prompt about looking at x when it became negative. I just asked students to notice and wonder. Removing a specific focus, opened it up for all students to engage in any way that was possible for them.
My goal was to add in small small pieces of information that would engage my students further into the problem. I asked them to look at the points on the graph and determine inputs and outputs and to gather that information into a table and to notice and wonder about patterns that emerged.
My special ed students needed a lot of guidance on completing the table. I did want them to use fractions, so they could compare positive and negative exponents.
After the initial notice and wonder my students really struggled connecting the relationships and completing the table.
I’m wondering if I needed to back off and go over reciprocals and fractions to strengthen their overall concept of fractions.
After the lesson, my gut response was “good attempt.” My students who struggle with math were engaged initially. I struggled with keeping their curiosity through the process of the lesson.
- This reply was modified 1 year, 1 month ago by Stephanie Pritchett.
Tarini ArteMemberFebruary 20, 2022 at 1:41 am
JonAdministratorFebruary 25, 2022 at 6:24 am
Great job here Tarini! Love the slow reveal you’ve created here.
Is this your introduction to systems of equations? Our next step would be to anticipate how students will solve this problem!
Tarini ArteMemberMarch 9, 2022 at 6:29 pm
Hey Jon, thanks! Yes I thought it could be a nice way to ease into systems with having them use their strategies first and then get into how we can represent it with equations.
Lizann “Lizzie” HerreraMemberFebruary 24, 2022 at 12:17 am
The original text book problem is attached below. I would modify this problem to be delivered in the following order:
1. Han is planning to ride his bike 24 miles.
3. How long will it take? (hopefully comes up in the wonder)
4. Ask, what do we need to know to answer this question? Make an assumption (how fast Han goes) and an estimate (how long it will take)
5. Give info: If Han goes 3 mph?
8. Can we make a graph that represents this? (use Desmos)
9. Generalize an equation that Han can use to find the time it takes to ride 24 miles at r (any) mph
10. consolidate – t=24/r where t is the time it will take, r is the rate Han rides the bike, and 24 is the miles (how far) Han rides.
Jonathan LindMemberFebruary 26, 2022 at 12:13 am
My before and after of a typical goat on a rope problem is below; first round I left the general question in, but then realized that it wasn’t really necessary and not having the question would really open up the exploration and questioning phase.
When an 11th grade IB class was presented with this problem and asked to notice and wonder, they (having probably seen similar questions before) came up with the classic questions that could be asked here, but also came up with much more interesting questions, and we decided to answer one of those instead:
How long would the rope have to be so that the goat could reach the entire field if it was tied to the opposite corner.
This also gave students an opportunity to estimate the length of the rope after they asked for and were given the dimensions of the field.
IB questions are often very scaffolded, which is great if you’re taking a test, but pretty lame for classroom explorations. This exercise helped the class have a much richer discussion than we would have solving the original problem.
JonAdministratorFebruary 28, 2022 at 6:21 am
Love this @jonathan.lind Great withholding information here. The question the students posed is very clever! I might be borrowing this for my classes.
Kerri BrodieMemberFebruary 28, 2022 at 9:17 pm
This is my textbook problem:
gymnasium is being remodeled. The basketball court
will be similar to an NCAA basketball court, which
has a length of 94 feet and a width of 50 feet. The
school plans to make the width of the new court
45 feet. Find the perimeters of an NCAA court and of
the new court in the school.
I changed it as shown in the PDF (Google Slide) shown.
I am planning to use this problem on Friday in my class so I don’t know how the students will respond yet but I will post after I use it in class.
David McKnightMemberMarch 1, 2022 at 1:35 am
I have a question related to quadratic modelling. I happen to be near the end of the unit, though this might work anywhere in the unit. This is for my Honors Mathematics Class and generally look for the most “mathematical” approach. I sort of wish I could turn back the clock and do this earlier in the unit.
Gwyneth McIntoshMemberMarch 8, 2022 at 12:50 pm
In the modified question, we withheld most info and gradually released it. We noticed/wondered as well as did high/low/best estimates. It wasn’t the most interesting prompt to begin with (we actually modified this lesson on the fly – right before class), but the lesson went really well. Even though the prompt wasn’t that interesting, following the curiosity path helped our students buy in and get engaged in the question. It was pretty cool to see that we were able to transform the question quickly, easily and effectively. And…the prompt didn’t actually have to be amazing. Withholding, notice/wonder, as well as estimating were really enough to get them into the question.
Kyle PearceAdministratorMarch 9, 2022 at 6:43 am
So happy you shared this and also articulated the importance of the curiosity path itself (not the visual itself). The visual is a support for a great prompt – not the other way around. Glad it worked out well and didn’t take you a ton of time to get started with it.
Terry HillMemberMarch 19, 2022 at 10:30 pm
I have attached a PDF that shows the original problem and the PowerPoint that I used to do the problem following the Curiosity Path. I started them out with Notice and Wonder, and wrote down everything everyone said. This seemed to really start off very well. I made sure to get at least one notice or one wonder from every student, and while a couple simply said theirs was the same as another student’s answer, most of them gave some very good answers. As we worked through the problem, gradually releasing information, it seemed to go pretty good as well. (The blank page in the PowerPoint was so we could draw the three fields and then try to first guess, and then second, figure out their dimensions.) Overall I thought the lesson went very well and I did see more participation than usual. However, it did seem like it took a very, very long time to cover one problem, and there still seemed to be some confusion about what the problem was really all about.
I did show the students the original problem after we had completed it using the gradual release of information, and most agreed they liked the way we did it better than just being given the problem. Some even stated that it helped them to understand what the question was actually asking them, which was great.
Kyle PearceAdministratorMarch 22, 2022 at 6:52 am
Fantastic to hear!
Note that at first, this process can be a bit confusing to students as they are not used to the process. However, remember that we do need to be explicit in the consolidation to ensure students understand why we did what we did… some students will have made connections on their own, but others will not.
Glad that your first go was a success!
Fernando PerezMemberApril 12, 2022 at 2:41 am
An original question asked whether a plane could fit underneath an arch, the information given was the plane dimensions and the arch dimensions as well as the high at which the plane needed to fly. This question didn’t open much room to imagination so this is what I did:
The question title slightly changed to “Can the Qatar Airways Airbus 380 fit underneath Al-Wakra bridge?” This way, the question was about a local company and a local bridge in the city (Doha, Qatar). Students were lost a the beginning and realized they needed to find information about the plane, and also about the bridge, indeed, they were required to find that information online and no more info was given to them, they even have to think about the height at which the plane should fly and whether it was realistic or not. There was a great deal of noticing and wondering, anticipation, estimation and, of course, withholding information.
Kami FeveryMemberMay 7, 2022 at 12:35 pm
So I found this problem that to me with a quick glance would seem (on the spectrum of curiosity creating) maybe a bit more on the full curiosity side as anything with a picture seems to do so. However, I realized how limiting this question became when the words were added. I can see now what you mean how most text book questions function in a way to tell the student how to think. I decided to get rid of all the words and keep just the picture.
Here I came up with a list of notices my student would perhaps come up with. While I don’t think the highlighted ones would come up first, I have found doing more curiosity creating tasks, that each student’s response rolls off the previous, gradually thinking deeper and more mathematically.
Kyle PearceAdministratorMay 10, 2022 at 6:51 am
I’m also a fan of not “titling” the activity. No need to reference curiosity or what your intent is… they figure that out eventually vs sort of trying to encourage them (or give away) what you’re trying to do (spark their curiosity).
Colegio MarkhamMemberJune 4, 2022 at 2:31 pm
1- video of penguinarium feeding time. Notice and wonder – Withhold info/anticipation- discuss data needed to solve some of the wonders
2- How much fish is needed to feed all the penguins?
Eliciting data needed, estimation of these: how many penguins there are in the video, how much does one penguin eat (can google that). Share with neighbours and class.
In this aquarium, penguins are fed 3 times a day. Breakfast is 5/12 kg of fish, mid afternoon 1 ¼ kg and supper is ⅚ kg. See how students solve for how many does one penguin eat. They know equivalent fractions by now, but may use braining camp fraction tools
Reveal 2 – there are 20 penguins. <i style=”background-color: var(–bb-content-background-color); font-family: inherit; font-size: inherit; color: inherit;”>Again see how they solve, may multiply by ten first and the double, may double first and then multiply by ten, may add 2 and ½ in in groups etc.
Karl HirschmannMemberJune 10, 2022 at 12:37 pm
This is the original problem from the first unit of my 9th grade algebra curriculum. I used this problem in August of 2021 and it didn’t work very well. The question [as written] did not encourage spark curiosity, nor did it ask my students to think about the math.
Who got the better deal?
Both Larry and Linda bought the same value meal deal.
The menu price for the meal deal was $4.99.
Larry had a $1 off coupon he used first and then got a 10% student discount.
Linda used her 10% student discount first, and then used the $1 off coupon.
Who got the better deal?
 Both Larry and Linda used discounts to buy the same value meal deal … [I deleted the title and set the scene. I also added “used discounts” to the wording of the original problem for clarification].
 Who got the better deal? … [I ask the question].
 Estimations … [I encourage students to make estimations based on what they know].
 Release of more information … [In response to student questions, I release more information].
[a] The menu price for the meal deal was $4.99.
[b] Larry used a $1 off coupon he used first and then got a 10% student discount.
[c] Linda used her 10% student discount first, and then used the $1 off coupon.
While I haven’t used the revised problem in class [yet], I believe that my students will find it more interesting in its revised form.
Christine PomattoMemberJune 12, 2022 at 4:07 pm
Many of the word problems we use for area & circumference of a circle have room for some GREAT math, but they are so boring the way they’re provided. Here is how I reworked one of them (attached).
Renee HolmquistMemberJune 20, 2022 at 1:40 pm
Deanna SemyonMemberJune 22, 2022 at 1:57 pm
What problem did you choose?
A 30 foot tree casts a shadow of 12 feet. What is the length from tip of tree to the shadow tip?
How did you change it?
Show pictures of 3 or 4 trees casting shadows. Ask students what they notice and wonder. Have students partner share notice and wonder and then share to class. (why are all the tree shadows going left? why do I care about tree shadows? What do you need the shade for? What are you going to do under the trees? There are only 2 trees… we need more trees to have shade. Are all the trees the same height? How far does that shadow go now? Does it change. I wonder if we can make a zip line?)
Ask students what they need in order to make a zip line. (the supplies: wire, stake, ladder to get to top, etc)
Ask students to estimate the length of zip line. (students may state that they do not have enough information and then students may discuss what is needed.)
Inform students that the height of the one tree is 30 feet. (students may then discuss what else is needed to make a zip line to the shadow tree tip). Allow discussion and guide students to ask for additional measurement. (If I am lucky a student may recall something learned about a triangle.) Provide the shadow length and for practical purposes allow students to work with the right triangle concepts.
Ask for updated estimations. Allow students to work in pairs to come up with answers. (hopefully closer estimations).
Kyle PearceAdministratorJune 23, 2022 at 6:44 am
Nice work here!
Reney McAteeMemberJune 26, 2022 at 3:48 pm
Kyle PearceAdministratorJune 27, 2022 at 6:38 am
Nice. What specifically are you feeling needs adjusting?
Stefania LambustaMemberJune 27, 2022 at 11:18 am
In our first unit we introduce GCF and LCM. A textbook problem says find the LCM of 3 numbers, for example 2,3,and 5. I found this activity that I want to try with my students. It starts with a video of 3 different hour glasses. Students can notice and wonder and I can guide the thinking to when will the timers all be empty together again.
Julie GonzalesMemberJune 29, 2022 at 6:56 pm
As a math specialist/coach for the district I am really excited to have teachers experience a way to turn a textbook problem into a notice and wonder. I will try this at the beginning of next school year during our professional development in-service days. I will have to be deliberate in how I set up groups of teachers because I will have K – 12 teachers during in-service and I want all teachers to be able to access the question. Once I go through this activity, I will actually show the problem from the book and ask teachers to discuss their experience with a partner and then discuss as a whole group. It is my hopes that teachers will bring out their level of engagement/curiosity compared to what it would have been with just giving the original problem. I have found in my job that I have to challenge teachers’ thinking about their own routines in the classroom before they will consider changing what they do. The best way is through their own experience.
Original problem from Geometry: The tallest building in the world is Burj Khalifa in Dubai (as of April 2019). If you are standing on a bridge 250 m from the bottom of the building, you have to look up at a 73 degree angle to see the top of the building. How tall is the building.
First I would just show a picture of this building and ask teachers what they notice and wonder. There are many different notices and wonderings the teachers will come up with! After sharing with a partner and then with the group, I would then ask them “how tall is the building” (I believe this will be a natural wondering teachers will have). I would ask them to talk with a partner what they might need to know in order to answer this question. Once the group brainstorms some ideas, I would show the picture again but with a person standing 250 m from the base of the building and the 73 degree angle looking up to the top and ask them to solve. (I am considering changing the base length and angle to make it even more accessible for elementary teachers!)
- This reply was modified 9 months ago by Julie Gonzales.
Anna ClarkMemberJuly 1, 2022 at 5:10 pm
Original Problem taken from 8th grade math (pre-algebra) unit on solving systems of equations: A taxi ride costs $3 plus $2 for each mile driven. You spend $39 on a taxi. This can be modeled by the equations 2m+3=39, where m represents the number of miles driven. How long was your taxi ride?
Step 1: My mom is taking a taxi ride.
Step 2: WDYN&W? Maybe they wonder where she’s going. She must not have her own car OR she’s in an unfamiliar place (my Alabamian students will immediately go to NYC!). How long is the ride? How much money is she going to spend?
Step 3: Pick the wonder about how far she traveled and make an estimation. Allow students to google the average cost of a taxi and come up with a reasonable distance for a taxi to be taken. Ask students, what questions do you have that would help you make your estimate better?
Step 4: Slowly introduce information. The equation that models the cost of the ride is 2m+3=39. What does this tell us? WDYN&W now? Can you update your estimate?
ALTERNATIVELY for Step 4: First say that the taxi driver charges $3 up front. Update estimate. Then say the taxi driver also charges $2 per mile. Update estimate. Then say the total cost of the drive. Update estimate.
Would love for someone to weigh in here and critique this! I’m wondering which information is best to give them since the goal of the word problem is to give them an equation in hopes they solve it with inverse operations…but is that really necessary here? I feel like as an extension (if using my alternative step 4) I could ask the students to write a linear equation that shows the relationship between miles and cost, but then I’m not really asking the same thing this question is asking. To be fair, I really don’t think this question is asking something practically applicable to the real world!
Marion MulgrewMemberJuly 11, 2022 at 12:31 pm
I like this!
Nicolle RistowMemberJuly 5, 2022 at 8:57 pm
Algebra Use the diagram at the right for Exercises 29–32.
29. If AD = 20 and AC = 3x + 4 Then find AC and DC. (the diagram is at the end of the post)
A) I would start by just showing the class the diagram of the segments and ask what they notice about the picture. Then I would ask them to come up with some possible questions that could be asked about the diagram.
B) Along with the type of questions that could be asked about the diagram what type of information might be need to answer these questions.
C) Next, give them AD = 20 and have the students come up with all the answers they can answer based on using just this information
D) Finally, I would give the last bit of information about AC = 3x + 4.
E) I might ask the class with this given information is there any way to find the length of ED?
- This reply was modified 8 months, 3 weeks ago by Nicolle Ristow.
JonAdministratorJuly 9, 2022 at 7:30 am
Great start here Nicolle,
I wonder if your follow up could be related to having them create their own problem for the other line segment.
or another variation before you reveal the expressions for AC is to have students create expressions that would be equivalent to AC.
Some students might say AC = 10 + 10 or AC = 25 – 5 or some might say AC = 2*5 + 10 .
Having them create expressions can make the transition to solving the equation a little easier and intuitive.
Marion MulgrewMemberJuly 11, 2022 at 12:27 pm
I’m teaching 7th grade (again) in the Fall. This is from our curriculum, Big Ideas. I started with thinking about the problem on absolute value. I know this is a boring problem and the video I made is not very exciting either. However, I think it can be used to get kids to first notice that the zero is missing and hopefully wonder why. They can anticipate what may happen, then be shown the video up to where -1 and 1 have the dot. They can make predictions and then see the video from there, or it can be stopped again and they can make their own patterns as guesses, or just see if they can make patterns that fit the “rule” (which is the opposite values for any rational number set).
- This reply was modified 8 months, 2 weeks ago by Marion Mulgrew.
Lisette PoindexterMemberJuly 30, 2022 at 5:38 pm
Problem: If the room is 20 ft long and 3 feet wide, what is the area of the whole room?
Change it into this multi-step problem:
Draw a rectangular building which is 20 ft long and 3 feet wide. Imagine the whole room is filled with inflatable balls. What is the area that the balls will have to take up in order to fill the whole room?
Rose FriedmanMemberJuly 31, 2022 at 10:55 pm
Hey! I’ve been working on transforming my textbook problems and am pretty ok with them. However, I’m having an issue transforming the one I attached below. The reason I think it is so difficult is that the goal is to teach the students a relationship. Any ideas of how to go about doing it?
Alexis PerezMemberJuly 31, 2022 at 10:57 pm
Instead of showing the entire problem as the text book does below, I would gradually introduce parts. I would withhold information by picking just one of the squares with a number to start with. I would have students notice and wonder as I reveal each square. There will be anticipation and estimation present as students try to figure out the pattern or what number is coming next. They may be surprised when I reveal my pattern increasing, but then decreasing, which way will they choose to go next?
Heather AldenMemberAugust 1, 2022 at 10:02 am
Here is the original textbook problem (2nd grade):
Tammy and Martha both built fences around their properties. Tammy’s fence is 54 yards long. Martha’s fence is 29 yards longer than Tammy’s. (shows picture of 2 different sized rectangle yards labeled as Tammy’s Yard and Martha’s yard)
a.How long is Martha’s fence?_________ yards
b.What is the total length of both fences?_________ yards
Sparking Curiosity Instead:
Tammy and Martha built fences around their yards. (show a visual of fences being built)
What do you notice? What do you wonder?
Share that Martha’s fence is 29 yards longer than Tammy’s.
Estimate too low, too high
Share that Tammy’s fence is 54 yards long.
Revise estimates for too low, too high, and best guess.
Ask students to find out what the total length of both fences is? (multistep challenge for grade 2… support kids in groups who may need to solve a explicitly before trying to solve b)
Kristie D’ArcangeloMemberAugust 5, 2022 at 10:23 pm
Using description of the proportional relationship and the table, identify the constant of proportionality and then write the equation to represent the situation in the table.
Alison earned $24 by stocking shelves at the grocery store for 3 hours.
Time (h), x 1 2 3 6
Total Pay ($), y 8 16 24 48
1. Spark curiosity with a photo of a girl stocking shelves
What do you notice? What do you wonder? Discuss
2. Share that the girl, Alison, made $24 for the time she worked
Estimate too high, too low, and best guess. Discuss
3. Show the table and ask students to check their estimates and discuss how they know if their estimate is correct.
4. Follow up with prompt to identify the constant of proportionality and write an equation to represent the situation.
I am going to try this with my seventh graders when we head back to school at the end of the month.
Mary OlsenMemberSeptember 1, 2022 at 11:54 am
Problem: Arturo paid $8 in tax on a purchase of $200. At that rate, what would the tax be on a purchase or $150?
Changed to : Arturo paid $8 in tax on a purchase. WDYN? WDYW?
I thought then students should make estimates on how much the item he purchased cost to have $8 in taxes. Having students partner share and then share with the class.
Eventually I will reveal he spent $200.
Then I can have students find out how much tax he would spend on other purchases if the rate was the same. Or I can give them another tax amount and have them estimate how much was spent before moving onto how much tax it would be for a specific purchase.Problem: Arturo paid $8 in tax on a purchase of $200. At that rate, what would the tax be on a purchase or $150?
Changed to : Arturo paid $8 in tax on a purchase. WDYN? WDYW?
I thought then students should make estimates on how much the item he purchased cost to have $8 in taxes. Having students partner share and then share with the class.
Eventually I will reveal he spent $200.
Then I can have students find out how much tax he would spend on other purchases if the rate was the same. Or I can give them another tax amount and have them estimate how much was spent before moving onto how much tax it would be for a specific purchase.
Craig PolzenMemberOctober 30, 2022 at 6:48 pm
I’m thinking about my G10 group and revising this problem to have a hands on component.
“The construction plans for a ramp show that it rises 3.5 metres over a horizontal distance of 10.5 metres. How long will the ramp surface be?”
Creativity Path version:
1. Notice & Wonder – Find an image of a doorway or entrance that is raised above the ground with no stair or ramp, just a drop straight down.
2. Anticipation – introduce a 2.5 metre height from ground to the doorway (change from 3.5 so a standard ruler can be used in next step)
3. Guiding Question 1 – If we wanted to build a ramp from the doorway down to the ground, how long would it be?
4. Explore – build a scaled version (1m = 10cm) of this scenario with a ruler, tape and string for the ramp.
5. Guiding Question 2 – Explore different ramp lengths. What length would you suggest? Why?
6. Guiding Question 3 – If we wanted our ramp to land at 10.5 metres from the wall, how long would it have to be?
Alison PeternellMemberNovember 5, 2022 at 3:01 pm
I have attached a document of how I changed a textbook problem about sea level rising since a student’s birth on the Atlantic Ocean.
I have broken the problem down to not ask a question first but to give information before I ask the question. I have also included a graph to make the problem more inviting. I would have the students discuss this first before asking the question.
- This reply was modified 4 months, 3 weeks ago by Alison Peternell.
Alison PeternellMemberNovember 5, 2022 at 3:09 pm
See above reply
Noel McMillinMemberNovember 9, 2022 at 9:07 am
Triangle Angle Sum
Traditionally, one of two lessons happens with this theorem. Some teachers will have the students cut out triangles of varying sizes and shapes. Then the students, with the teacher leading, snip each of the three corners lining them up to construct a straight line. The other lesson is simply the teacher telling the students that the interior angles of a triangle add to 180 degrees – like the textbook picture I attached. I know this because I have done both of these lessons.
Taking inspiration from this class, I plan to project this picture on the screen and then see what happens. My plan is to do this on Monday so I will post the results of the lesson early next week. I am excited to see where this takes us. I have an idea, as a 25-year math teacher, but I’m hoping it goes places I never anticipated, honestly.
In the not-too-distant future, we will tackle the interior angle sum of all polygons and I think this will be a great anchor problem to use over and over.
Noel McMillinMemberNovember 16, 2022 at 4:00 pm
I did the angle sum theorem lesson today. I attached the students’ observations via Padlet. I, of course, wanted the students to see the angle position for each of the three triangles but we just did not get there. I was happy to see the students recognized how all three were congruent but we did not get much further. I decided to punt. I instructed the kids to open Google slides and make their own triangles, copy and paste them two times, and construct their own straight line. It became a little more teacher-directed, but the connections started to happen without me stating that the angles inside a triangle always equal 180 degrees.
Upon reflection, I think maybe next time I might show them the construction of the straight line rather than simply starting with the picture already put together.
On a side note, my 8th-grade lesson involving proportions and indirect measurement started with a picture and two simple (but powerful) questions – “What do you notice?” and “What do you wonder?”. Two questions that I did not ask prior to this class.
Victoria MurphyMemberNovember 11, 2022 at 7:21 pm
Here is my revised problem taken from our 7th grade textbook. This example was, as you can see, to get kids to write an expression to represent a word problem. I was toying with should the question be “How much to they spend?” or “How much change should they get?” I may still change it to the second when I do it after the Thanksgiving holiday. My images here are a slideshow. The goal is to write an expression representing their total amount and talk about the different ways groups wrote those expressions.
- This reply was modified 4 months, 2 weeks ago by Victoria Murphy.
Rebekah SchofieldMemberNovember 29, 2022 at 6:04 pm
I have attached the slide show that I used to present my problem. The original textbook problem is the last slide. When I presented to my 3rd hour class, I realized that I had not given them enough information to be successful. It only caused confusion, so I changed a few slides and the other three classes did much better. I really like this method of teaching, but it takes so long; I’m hoping that it is because the students aren’t as used to it as they could be.
It did grab all my students attention, and it was a great “low floor, high ceiling” problem. I just ran out of time and will have to continue tomorrow.
I will definitely try this again.
Sean CampbellMemberDecember 30, 2022 at 12:38 am
I am doing rates and ratios with grade 8s.
A snail travelled 48 cm in 2/3 hour. Suppose the snail moved at a constant speed and made no stops. How far would the snail travel in 1 hour?
Prompt: 1 minute video of snail moving along paving stones: https://youtu.be/eZsWJbmCItI
What do you notice? What do you wonder? – Think-Pair-Share
I think they will mostly wonder about speed of snail if not I will steer them toward how fast is snail moving? Discuss what speed is: a rate of distance over time.
Estimate: How far did it travel in one minute.
Estimate: How far would it travel in one hour.
Release of more information: Diagram of dimensions of paving stone. Review of how far along paving stones the snail moved in 1 minute in the video.
Go to whiteboards in small groups to determine the distance snail travelled in the video and calculate how far it would travel in an hour. Compare these values to original estimates.
Weird Note: The values from original question have no connection to the video I found on youtube. However, when I calculated the speed of snail in video and compared it to speed of snail from textbook question the video snail was exactly 10 times faster than textbook snail.