Make Math Moments Academy › Forums › Full Workshop Reflections › Module 6: LongRange Planning and Assessment to Make Math Moments That Matter › Lesson 61: Long Range Planning For Learning That Lasts › Lesson 61: Question

Lesson 61: Question
Posted by Jon on May 1, 2019 at 12:03 pmPick a lesson you are planning to teach this week.
Then, reflect on how you can ensure that YOU are incorporating the elements of the AGES Learning Model in that lesson to help your gain attention, promote students generating new connections from the new learning to their prior knowledge, somehow ensuring that positive emotion is included to help make it a true math moment that matters and finally, how can you space the learning and practice to help ensure the learning sticks?
Then, share out your reflection here in the message board and comment on at least one (1) other participant’s reflection.
Craig Polzen replied 1 month, 3 weeks ago 36 Members · 60 Replies 
60 Replies

<div>I will be using the following problem called Bubble Madness from CPM.</div>
I think this problem will get student’s attention because they get to play with bubbles (that is fun for even 7th graders). Although the problem is laid out in a pretty structured way, I think working with a team, and this handson approach to discovering pi, not just being lectured on it, will lead to a memorable lesson.
The idea of the circumference of a circle is similar to the idea of the perimeter for other shapes; it is the distance around the circle. Wrapping a string around a circular object is one way to measure its circumference. In this activity, you will investigate the relationship of the circumference of a circle to its diameter. The diameter is the length from one side of the circle to the other, through its center.

Follow the directions below.

Obtain a bubble wand, some bubble solution, and construction paper from your teacher.

Blow a bubble and allow it to land and pop on your construction paper. You will see a circle on your paper. (If this does not produce a clear circle, try catching the bubble you blow with your bubble wand and then placing it on the construction paper.)

Wrap a string carefully around this circle and then stretch it along a meter stick to measure the circumference of the circle. Make your measurement accurate to the nearest tenth of a centimeter.

Then use a string and ruler to find the longest measurement across the circle (also accurate to the nearest tenth of a centimeter). This is the diameter.
Share tasks so that each person has a chance to blow some bubbles and to measure their circumference and diameter. Take data for at least 8 circles of different sizes.


Organize your data in a table and then work with your team to decide on an appropriate scale to graph the data carefully on graph paper.

Discuss the following questions with your team and be prepared to explain your ideas to the class.

How can you use your graph to show that the circumference and diameter are related proportionally? (Remember that these are measurements and will thus have some degree of error.)

Approximately what is the multiplier between the diameter and the circumference?


This does sound like a fun way of generating random circles, and I agree that trying to make one of those huge bubbles that a person can stand in would be interesting!


Distance learning has made it tough to follow the AGES learning model. I have used a mix of wodb, splat, and cube connections for warm ups to get their attention. Each lesson I pick a problem to withhold information and have students share in the chat. I have found that I don’t get through nearly as many samples in distance learning as I would in class. For the turn and talks I have students pair up and private message each other then share their thinking. I’m a huge growth mindset fan and have all year trained my students to positively state their questions and difficulties, so that by the end of the year they correct each other, and me!

With distance learning it is hard to incorporate the AGES model especially with the grade 2’s. But when I am back in September I need to work more on time management in order to make learning enjoyable rather than rush through the lesson and move to the next topic. Allowing more time for social interaction during the notice and wonder or the think/pair/share. With my long range plans I will try to space and break the lessons into smaller chunks where it makes more sense to the students. I have been using lots of games at the start of this year and students really enjoyed!
 This reply was modified 2 years, 7 months ago by Premila Goorye.

A lesson I’ll teach near the beginning of next year is about proportional linear relationships.
To gain attention, I’ll make sure that the problem is an interesting one, like a notice and wonder – maybe using Dan Meyer’s “Nana’s Chocolate Milk” task
For generation, I’ll ask students to create their own strategies for figuring out how to fix Nana’s milk, and share these out to highlight multiple representations.
For emotion, making sure I’m valuing all of the different responses and fostering a positive, welcoming environment that allows students to feel heard. (Also, something about solving problems for Nana seems to make the room warm and fuzzy.)
Spacing is the one I struggle with the most. Bringing this idea of proportional relationships up throughout the year, when studying linear relationships that are not proportional, would help solidify this concept.

Hi Ericka, I wonder if students can look at linear proportional in unexpected places, for spacing. For example, if you are teaching circles next year or reviewing circles for volume of cylinder or something, students could measure diameter and circumference and plot them as an ordered pair to see the the relationship is proportional with pi being the constant of proportion.


I have been looking deeply at my current grade level standards and have created a document that shows how the different concepts connect or link with each other. I have worked with the two other teachers at my grade level. We are now thinking about how we can create engaging lessons to ensure students receive the lessons from missed lesson of the previous school year and still learn everything they need to learn for this upcoming current school year.

One of the lessons we usually teach at the beginning of the school year is rational vs irrational numbers, comparing irrational numbers, and understanding that every number has a decimal expansion. I’m still thinking through and searching for lessons that can help me approach the learning goals for these skills from a problembased approach. However, my plan will be to find a task that starts a few learning goals before the target goals that really grabs the Attention of students. Nothing gimmicky, but something definitely geared toward sparking curiosity by following the curiosity path. To provide for the Generation of student ideas and ownership, we will Notice and Wonder and make predictions that will allow us to reflect on what we’re observing and create new learning. I will create positive Emotions out of this experience for my students by giving them clear feedback and helping them know they can and will learn what they need to know. Finally, the Social Interaction students will enjoy will come from the the turn and talk, math fights, and conversations around sharing their math thinking. I know that this is not very precise but as I refine learning goals and search for appropriate tasks, this is how I plan to keep AGES in mind.

Did you find something amazing for rational and irrational?


Given that we are in break, I’m thinking towards the start of the year when I reflect on a lesson. I’m considering how I want to start building conceptual understanding of isometries in the plane (reflections, rotations, and reflections) and how congruency is related to them.
Attention: I plan on getting students attention by having them look at various visualizations of these isometries in the real world. I will have them notice and wonder about the things happening. I also plan on having them follow some “dance” moves with me to experience the various isometries, without naming any of them.
Generalization: I want to provide students with two images that seem to be congruent, by looking at them, and notice and wonder about them. Then they will have to prove, using the various methods we have begun to experience and name (probably at this point with more student generated language — like turn, flip, and move) how to get from one to the other. This will require students to think about the ways that things move to get from one place to another, to prove congruency. There will be multiple ways of doing it as well, but they have to figure that out. Students will be working in groups to determine the series of steps it takes to get from one spot to the other, using a set of rigid transformations.
Emotion: By having students work with an open ended problem, they are given choice in the way that they solve. Activation through the use of visuals and dancing is also a way to build emotions in the math space — I don’t like them having to stay in their seats for long periods of time. I will provide feedback as I walk around to groups at their vertical white boards who are trying to prove the two shapes are the same, as they figure out a “dance” that gets them from one to the other. And this builds fairness in that they are constructing their own conceptual knowledge of transformational geometry without me having frontloaded any information.
Spacing: This work will be just the beginning of the transformational geometry concept. We will return to this concept later in the year when we look at slope and slope triangles, and when we examine angles from transversals. I want to try and connect it to as many different topics as possible. When we talk about the yintercept, we will explore how that is a manifestation of a translation in the plane.

This sounds awesome! I like the isometric introduction and how you will piece it with transformations later. The movement aspect will definitely be appreciated by a large group of students that sit in their desks most of the day or are in dance. You might get some super creative movements which are a great way to build relationships with your students and among themselves. Thanks for sharing!


For this reflection I am using an exploration I wrote (trying to!) following the Curiosity Pathway called “How to win at fetes”, based on a task called Counting Sweets from the nRich website. The learning goals are related to the concept of Estimation.
Learning Intention: To explore estimating concepts, using the example of the fairground favourite, “Guess how many lollies are in the jar?”
* Explore rounding, and consider the effect of rounding to different place value
* Explore how rounding makes estimation easier, but prevents us from getting an exact answer
* Explore a 3D array as a way of calculating volume
I’m happy to provide the full lesson plan but rather than write it all out here, the lesson basically explores ways of estimating how many lollies are in a jar.
A: Attention: I find anything involving food is already an attention grabber for Year 7s! There’s an element of competition and reward involved too. I also hope to get their attention through the use of the curiosity Pathway – withholding info, partial reveal etc.
G: Generation: All students will have some prior knowledge or experiences to connect to. Almost everyone has entered a ‘guess the lollies in the jar’ competition at some point, and students will be keen to share their experiences and their ‘winning strategies’ with each other. The task starts off easily enough that all students will feel like they have a strategy that would be good enough to get them within a reasonable ballpark figure.
E: Emotion: as previously mentioned, the idea of maybe winning a jar of lollies will create pleasurable excitement and anticipation for most students. Element of reward and a bit of competition. Feeling like they can have at least some success in getting close to the ‘answer’ – feeling of competency. Feeling of familiarity with the situation. Positive feedback from teacher and peers as they work on their strategies can build feelings of confidence and competency. Autonomy is provided in letting them choose their own methods of working & representing. Social interaction – lots of chances to engage in maths talk with teacher & peers.
Spacing – this is the first exploration in this mini unit on specifically presenting and discussing estimation techniques and the other concepts listed in the learning intention, but estimation is used throughout the year so will be many opportunities to cycle back. Also opportunity to informally introduce the concept of volume using a 3D array which will be returned to in Term 4.

I think your lesson sounds very interesting and estimation is such an important skill. It is so crucial for students so they can “reality check” their solutions to problems as well as developing number sense. I think that this concept will be woven throughout their learning from year to year. Nice job with getting students’ attention.


For this reflection I am using an exploration I wrote (trying to!) following the Curiosity Pathway called “How to win at fetes”, based on a task called Counting Sweets from the nRich website. The learning goals are related to the concept of Estimation.
Learning Intention: To explore estimating concepts, using the example of the fairground favourite, “Guess how many lollies are in the jar?”
Explore rounding, and consider the effect of rounding to different place value
Explore how rounding makes estimation easier, but prevents us from getting an exact answer
Explore a 3D array as a way of calculating volumeI’m happy to provide the full lesson plan but rather than write it all out here, the lesson basically explores ways of estimating how many lollies are in a jar.
A: Attention: I find anything involving food is already an attention grabber for Year 7s! There’s an element of competition and reward involved too. I also hope to get their attention through the use of the curiosity Pathway – withholding info, partial reveal etc.
G: Generation: All students will have some prior knowledge or experiences to connect to. Almost everyone has entered a ‘guess the lollies in the jar’ competition at some point, and students will be keen to share their experiences and their ‘winning strategies’ with each other. The task starts off easily enough that all students will feel like they have a strategy that would be good enough to get them within a reasonable ballpark figure.
E: Emotion: as previously mentioned, the idea of maybe winning a jar of lollies will create pleasurable excitement and anticipation for most students. Element of reward and a bit of competition. Feeling like they can have at least some success in getting close to the ‘answer’ – feeling of competency. Feeling of familiarity with the situation. Positive feedback from teacher and peers as they work on their strategies can build feelings of confidence and competency. Autonomy is provided in letting them choose their own methods of working & representing. Social interaction – lots of chances to engage in maths talk with teacher & peers.
Spacing – this is the first exploration in this mini unit on specifically presenting and discussing estimation techniques and the other concepts listed in the learning intention, but estimation is used throughout the year so will be many opportunities to cycle back. Also opportunity to informally introduce the concept of volume using a 3D array which will be returned to in Term 4.

I love this! I will be teaching volumes of spheres and cylinders soon; what a great way to introduce that concept.

This is such a great simple way to set the framework for volume. I find a lot of students forget what volume is or mix up with area. Providing tasks such as these which create joy and excitement and potentially bring up memories of Jar Guesses is like the picture perfect way of developing emotion. I know myself I can’t help bring up a memory as a kid about asking my teacher to run a jelly bean jar guessing contest within the school. If only my teacher had used an activity like this to help me understand volume, I feel it would have prevented lots of confusion over measurement.
Thanks for bringing forth a great idea!


This week I will be teaching a lesson on graphing sine functions. In order to grab the students’ attention, I will show them a video of a ferris wheel with images of me and my dog (who they love hearing about) in a cart. We will do a notice and wonder. Then I will ask them to generate data regarding what they see. The will have a choice of using a graph, a table or a diagram. Our height off the ground as a function of time will be highlighted when I pause the video at intervals. They will work in groups which we are finally able to do again! To create those graphs. Students will do a “gallery walk” to see what the other groups have created and then we will discuss this as a class. This connection with peers should elicit some emotion and discussion with the the students to address that part of the learning. Since we have been studying the unit circle and trig ratios, I think this lesson will fit nicely in order to allow them to make connections with their prior learning.

This sounds great.
If you need some video or pictures, you can use the ones from day 1 of the Niagara Falls unit and simply modify your prompt after showing the video:
Let us know how it goes!

Thankyou for giving this idea. I have been focusing on changing my teaching practices in my grade 9 course. What a great way to introduce trig functions in my gr 12 College tech! This group especially needs a reason to connect the math they are learning with a real world context.

Isn’t it great to be able to work in groups again?
This sounds engaging. Using yourself (and your dog) is a great way of making some connection to the material. I’ve never used data generation to get into trig functions, but it sounds like a nice way to make them see how the functions work.


After returning to inperson learning this past month, one of my SEL activities for students has been to play “Sticky Ball”, with a target of points on the whiteboard and a suction cup ball to throw onto it. Our Math 8 Honors happened to also be in our Quadratics unit. I think a great use of the AGES model could be to incorporate problems with Sticky Ball directly into the math curriculum standards of quadratics. This game hooks student attention like nothing else. A problem with it could definitely gain their attention. I could use goals like where should we launch the ball to consistently get the most points. Would it hit the ceiling and break the lights? How far would you need to stand, how tall a height would be beneficial? Which students might perform the best knowing this information, which classes? An adaptation of it for my Standard Gr. 8 sections could be to model it with linear functions but be aware we are making assumptions (this can push them to think about various functions too). I can only imagine such a project bringing positive associations. Hope I can implement it next year or even as an activity or competition end of this year!

This week I will be introducing adding and subtracting polynomials.
Attention: I am using the Burger shack clip from Jon Orr to introduce the idea of grouping like items to create a simpler expression.
Gernerate: Students will then need to generate a solution to the Question “How much will the order cost?” After looking at Student representations of the solution we will look at which method was faster. Students typically collect the like items together naturally, they just don’t express it in algebraic form. We will then be able to give purpose to variables as opposed to some abstract thing that has no meaning. Students will then work on creating their own representations of various “orders” .
Emotion: This is a tough one. I don’t really know how to create an emotional connection here. Help?!
Spacing: This is not the first time we have discused variables so we are revisiting a concepts previously discussed. I will also be bringing the concept of collecting like terms up in a later lesson in linear relations and again in solving equations. I am kinda flying by the seat of my pants this year with the new curriculum and no long range spiralled plan. Unfortunately I had to dive in the deep end, so I am trying to adjust my Silo as I go….

Katrina, I think an emotional connection will naturally develop in this task as many students will connect with the video with strong feelings towards ordering in this way!
Let us know how it turns out!


Introducing matrices this week
Attention: Using transition diagrams to create or show a natural need for matrices. It’s a class of curious students, and this is a brand new format for presenting info, so I think it will graph their attention.
Generation: Students will turn the diagram into an organized table, which we’ll start referring to as a “matrix”
Emotion: I think when we can get students to see that something they have experience with (tables) is already the new content we’re going to talk about, especially if they can come up with it themselves, that creates an emotional connection.
We’ll see about spacing…

My plan:
A – Attention: find a video or image that represents a system of equations that is relatable to the class. For example: a budgeting question for a party with pizzas and donuts.
You have a budget of $125 for a party. You are responsible for buying pizza and donuts. Each pizza costs $9 and a dozen of donuts cost $5. Which would be best with your budget: Twice as many pizzas per donut? Or Twice as many donuts per pizza?
G – Generate: Hopefully this situation will ignite some discussion and/or arguments about which option would be better to have twice as more than the other item.
E – Emotions: I think the emotions would be high, because the problem is relatable, and most people love donuts or pizza and possibly both like I do. This will hopefully help them remember this problem in their memory.
S – Spacing: The topic of Systems of Equations could be taught over a few weeks and extended to Systems of Inequalities.

Dawn Oliver, maybe you could get a little more emotional attachment by offering a choice of donuts or pizza either to the whole class, or to those who attained mastery, or to those who made an A on the exam.


Our school district has set forth a plan for the year that includes all of the objectives we must teach as well as a timeline. Therefore, I am somewhat obligated to work within that timeframe. That being said, teachers have input, annually, as to whether or not the plan is adequate in terms of time allowance and flow. Thankfully, we have just about created a “perfect plan” (if you will) to establish pacing that stands the best chance of meeting most students’ needs. It also seems to scaffold student learning rather than teaching topics in isolation.
In my lessons, my colleagues and I include a warmup that spirals in topics that have already been learned. From that, students are continually practicing concepts they have already been taught.
My lesson for next week is a continuation of personal finance. Using the AGES plan, I can implement the following:
A Attention I will start with a problem that gets students excited and triggers their curiosity. We use “clickers.” They love it and are happy to get the question right.
GGeneration Since even students in 2nd grade are interested in money, I can gain enthusiasm for the topic when asking questions that are pertinent to them: video games, toys, and favorite books. Once I have their buyin, they will be more apt to pay attention.
EEmotion Status – Value all student input and encourage every student with positive feedback./ Certainty will help build confidence. / Autonomy can be achieved by allowing students to choose their centers./Relatedness must be proved so students will know that the topic applies to them. / Fairness allows students to get what they need in the way of extra tools and/or support.
SSpacing Students will have had time to absorb the topic since this is the 2nd week of personal finance. This was also introduced after the module about money. Furthermore, we are in the midst of a Social Studies unit on Economics. Students will make connections to what they have already learned, what they are learning, and their personal lives.
Thanks for sharing!
Pacing guides are helpful when they are just that: a guide and not a mandate. Hopefully you find there is enough flexibility to do what you need to do for your students. Sounds like you’ve got a great thing going !
I appreciate the time and effort you put into using the AGES model to craft your plan for an upcoming lesson!


I want to begin the year with probability because it seems to be a topic we never have time to get to. I want to get my students attention by showing them the video of the Memphis basketball player who misses the free throws at the end of the game (many of our students love basketball). For generating, I think I am going to use one of the probability lessons from MMM, but not sure which one just yet (I’ve got two months to decide). For emotional I plan on allowing students to turn and talk about the different things we do, but I also plan on allowing them to roll dice for themselves (I have some large foam dice that will work well), and hope to even incorporate them making choices or taking risks based on probability. One of these risks would be something like offering break time versus extra work based on probability, and discussing why or why not students were willing to take the risk. Not sure how I will incorporate the spacing, but hope to figure out how to return to this within other units.

This sounds awesome! I like the isometric introduction and how you will piece it with transformations later. The movement aspect will definitely be appreciated by a large group of students that sit in their desks most of the day or are in dance. You might get some super creative movements which are a great way to build relationships with your students and among themselves. Thanks for sharing!

I used the Niagara Falls Ferris Wheel Problem but I would continue the problem as ask if you started in the bottom car, where are you after 30 seconds. They would need more information like how long it takes to get around 1 time, how high off the ground is the bottom, what is the diameter of the circle, etc. I would slow reveal this as they asked for it. Ideally they would be writing a sinusoidal function for the wheel. Prior Knowledge would be they know the basic graphs and transformations of sine and cosine and now are applying it to a real world example.
Attention – Notice and Wonder about the picture and the number of cars/people. Then would follow with the challenge of the height of the car and withholding information. This would spark curiosity.
Generation – students would have freedom of how they want to solve and would be able to look around the room at what others are doing.
Emotions – possibly connect to a time in their childhood they went on a Ferris wheel and make them realize all the was involved that they probably never thought about. They would have social interaction with their peers to solve a challenging problem in a supported environment.
Spacing – Right triangle trig could come back up here along with proportions, rates, and transformations of functions. This would then blend into graphs of tangent and cofunctions.

I admit up front that I want checked out “MMM How to Teach Exponents at https://www.youtube.com/watch?v=nZJBKr3ZLfk before I completed this task. I like it and as a new classroom teacher for intervention math I need to practice and with good lessons that have been successful.
Day 1 Would you rather (see attached image) and use WYR sample student response sheet to spark curiosity (students love $$) and allow students to work in pairs on response sheet or at boards. Have students work together with a few examples that are related to their real world in terms of saving money for items desired (this will help engage emotion by giving them autonomy and relatedness. Status will also be promoted through individual positive feedback and peer association.
Day 2 Introducing Exponents through Play With Your Math – Split 25.
I really like that it starts off as a puzzle. (I need to help students build resilience)
Then going to wall space with a partner gives nice social learning opportunities.
Introduce a few math problems from text.
Day 3 Present another Would You Rather and give students more independence in finding solutions as they work in pairs. Practice exponent skills formally on paper and end with
Exponent card game (https://www.learnwithmathgames.com/exponentgame.html)

I like the idea of using Would you rather prompts. I am looking into using them more in my class because I feel these fit very easily in the AGES Learning Model.


I am planning to use the AGES model when we are learning to solve systems of equations. The fact that we can generate attention and with interesting tasks. The ability to pull in solving equations repeatedly in every aspect will help with spacing.

Awesome! Let us know how this goes. Would love to hear your ideas on this.


It’s hard sometimes to rethink our triedandtrue lessons, but I’m going to try. I tend to teach integer addition by telling a story (with visuals) about a box suspended in midair. As the story progresses, balloons get tied to the top and weights get tied to the bottom of the box. I tell students that the box goes up if there are more balloons, and the box goes down if there are more weights. The box floats in midair if there are equal numbers of balloons and weights (zero pair).
I’m ready to make over this lesson using the AGES model.
Attention: I can get students’ attention by showing them the opening page of the story, which is a typical brown box floating in midair. I will remove any explanatory text and do a Notice & Wonder. The picture will capture students’ attention because it is a new and unusual situation, and it’s silly. It gets sillier when you think about tying balloons and weights to it, and a balloon’s pull is supposed to be equal to the pull of a weight (students always argue with me about this – but I can use it to start a math fight!)
Generation: Students will be able to generate their own learning if I withhold information from the story. Instead of telling them the box will go up if I tie balloons to it, I can ask them to make predictions. The same with weights. Then I can ask them to draw conclusions about what might happen if there were equal numbers of balloons and weights. Or 5 weights and 3 balloons. I will ask students if they have found any shortcuts – they will literally generate the algorithm and rules for integer addition!
Emotion: This lesson happens very close to the beginning of the school year, and I think it can be a great lesson for building confidence in students (certainty). It can also increase their sense of status when they feel important for making a new mathematical discovery and having the opportunity to teach it to their classmates.
Spacing: Once students are familiar with the scenario, I can revisit it throughout the year to teach more concepts, such as subtracting integers, multiplying integers, and maybe dividing integers. I could even try using it for other rational numbers, like fractions and decimals, although that might be too silly (3/4 of a balloon and 5/6 of a weight). The point is that I can revisit it, especially if students get stuck on a concept.

Hi Christine,
I love the way you are adjusting this integer addition lesson. I am going to be teaching 7th grade this year and have been away from that grade for a few years. I’ve done a similar lesson with hanger diagrams and the balloon concept, but yours is way more fun! I wish you great success and hope it’s okay if I try it too.
Missy


I am really excited to teach the first lesson of the year. I will be using a lesson that I decided to skip last year because I felt I should do procedures on the first day (I’d like to pivot away from that). This lesson will have students exploring. I will catch their attention with a short video that they will notice and wonder. Students will then run a simulation to model the event they see in their video and collect data. We will then use it to calculate a simple proportion of dots. Near the end of the lesson, students will have calculated a pvalue, without knowing this is what they are doing it. I will use the graphs generated during this lesson to point out to them throughout the year, that they already know how to calculate this very important HOLY GRAIL of statistics.

I’m excited to hear how this goes! I love how you pivoted what you did last year to something you feel more valuable for the students in the long run. Something I am curious about is the whole idea of spending longer on the class culture will speed up the lessons later in the year. I am one who is always worried about getting through the curriculum but am hopeful this new way of teaching/presenting the information will be so much more beneficial!

That sounds like a great lesson! I love when students figure things out without realizing that they have. It makes the reveal or aha moment all the more satisfying for both the teacher and the student. I would love to know how they reacted when you reintroduced the graphs at the time of teaching the topic.


I went back and forth with the idea of using the Evergreen task or the Snack Time task for early in our number sense – operations with rational numbers unit. I know we are supposed to focus on connections with positive and negative numbers, but I want to shore up their number sense around fractions and decimals first, then be able to connect that to the concept of making 0 and then to positive and negatives due to opposites. In the end, I decided to start with the Snack time task as fair sharing is intuitive to most by 7th grade. It also lends itself to representations of the same amounts in a variety of partitions and connects the idea of fractions to division. I can see using Piggy Bank as a continuation.
Attention – Food! Also, without more context, it raises many questions. I think students will be surprised that they aren’t being given more information, so that will get their attention too.
Generation – Students will need to find a way to generate fair sharing of the given amount of cheese and not be sure of the number of crackers. Once they find out the number of crackers and move to breaking up the 3 pieces into 4 each, they will be able to have generated that breaking thirds into 4 pieces each is 12 small bits, or 1/3 divided by 4 gives 1/12 of the original amount. We can contemplate why it isn’t 1/3 x 4 or why 1/4 of 1/3 is 1/12.
Emotion – Not sure beyond the social connection and fun in solving a puzzle, while overcoming a reasonable level of frustration. There may be students who are masters at fractions already and can feel great as leaders, or others who were able to know they needed to break each 1/3 stick into 4 pieces, but will have a hard time internalizing that the algorithm isn’t 1/3 divided by 1/4 but 1/3 divided by 4 because of each stick being broken up into 4 pieces.
I could also bring in some food that they are able to actually consume at the conclusion.
Spacing – This task so far, allows students to mostly work at their own pace, as I can nudge or grant more time for them to explore this one concept. We can then move to fair sharing other things or looking at things in parts and find ways to describe them, including with the Piggy Bank Task.
I am looking forward to working with these tasks and more, but yet not rushing my summer. 🙂

I will be teaching in a new position next year, Math Teacher K2. I will not have my own classroom and I will be pushing into other teachers’ math classes. I am very excited about this and am looking forward to helping students grow as a second adult in the room. I am not sure how often I will be leading whole group lessons as it is a new position. I do know that I will be working with small groups often and am looking forward to using these strategies within small groups, especially as the students will not have retained a prior skill. I will use the curiosity path to help with gaining student attention, especially as these may be students who have not yet experienced many positive math learning experiences. I will use reflection and discussion and potentially data chats with students to help them take ownership of generation of new knowledge. I will work hard to create positive fun feelings with my math lessons. I am looking forward to learning more about spacing, especially as an interventionist as I want to help students retain the skills that I am addressing.

The lesson I am looking at is Ocean Plastic Pollution problem, which I would use as an introduction to exponential growth function.
1. Attention: I would show the class a video of a floating garbage island. With this I would do a notice/wonder about the video and maybe have a little discussion about what it is and what caused it, etc.
2. Generation: Next I would give some interesting data that is associated with the production of plastic and the percent of increase of plastic products. We would them connect this information the basic exponential function.
3. Emotion: I am going to look at the Autonomy part and create a problem that allows the student a choice on how to create a solution for this problem. For example, they might remove the current plastic from the oceans.
4. Spacing: Once the students have thought of ways to solve this problem, I will give them additional information that the students can then use to prove that their solution will help the problem of plastic pollution in the oceans.

I am currently attending a workshop with Sunil Singh, so I am gunna go for a lesson which uses one of his magic number challenges while adding in a historical context of Mesenne Prime. To me this is a great way to add context when it is hard to make close world connection. Being honest though the thought of adding history to my math is a little daunting. I absolutely love how Sunil is able to create curiosity with a historical context and the playfulness of numbers. However, with little background knowledge about history myself, this new goal is definitely going to be a good challenge for me. However, starting with this lesson I am going to try it out.
I have attached my tentative lesson. There may be a bit more tweaking as I continue to reflect, but I feel I already am able to fulfill the AGES model.
**Note one PDF has teacher notes and the other is just the slides.
AAttention
I feel this activity really allows students to play with Math, trying new combinationations. With the recap of exponents and prime numbers most students can continually try and test out possibilities.
GGeneration
With this lesson I have included a combination of independent work on indivdual white boards and then also in collaborative groups, allowing them to bounce ideas off of each other.
EEmotion
One of the focuses with Sunil is the idea of developing context or connections with the math. In this case adding in the story of Mersenne and his own mistakes in a historic context, add a learning story, which is an effective tool for drawing out emotion. Students can pair the joyful or as Sunil says the “Romance” of Math with prime numbers and calculations.
SSpacing
By allowing students to review the two main concepts of exponents and prime numbers, the learning or review of learning takes effective ministeps to allow all learners access to the bigger challenge.

I have not yet started the new year but I can recall a lesson I have done that I feel exemplifies some of the AGES learning model. For combining like terms, I introduced the lesson with a video from MadTV of a man placing a fast food order. He speaks very fast and is quite repetitive with his items order. The kids were very engaged and laughed at the ridiculousness of what was being ordered but also insisted that it could have been done easier. I gave them a transcribed script of the order and in groups they dove into finding the parts that were repeated and could be consolidated. Each group was trying to best simplify the order so it would not take quite so long to say. When the simplified order was all set, I asked groups to look at certain amounts of fries, cheeseburgers, and drinks while representing each item with a respective variable; f, c, d. They very quickly were able to tell each other and myself how many of each that they would have after combining them all. I’m honestly not sure if I have addressed all of the pieces of the learning model but I can attest to the fact that student engagement was high on this lesson and transfer of knowledge to more abstract variables was much easier than in the past with a traditional lesson.

This coming week we will be talking about combining like terms in 7th grade. I am going to start with a piece of the video from the SNL skit where the young man orders a large order in a random way. While I have used this clip before, I plan to shorten it this year and apply the “Notice and wonder” strategy to generate more engagement and interest and attention.
Then, to generate some memories and connections, we will create orders within our groups from a small menu, we will then use the polypad on the DESMOS site to create expressions using shapes, both the geometry shapes and then the algebra blocks before just using the variable forms of an expression.
I appreciate the reminder in this lesson about reflecting and I know that this is definitely one of my weak points. I will relook at my lesson to implement more moments of partner reflection, or ThinkPairShare type moments. A good stopping moment here might be within each stage….between the menu gathering and the shape representations. Then between the shape representations and the algebra blocks and again between the algebra blocks and the variable use.

I agree with you that the reflecting piece at the end of the class is what I usually run out of time with. Having students sharing with each other and not as a whole class is something I need to do more of.


I used the AGES learning model when I taught writing linear equations. I got the students attention by putting them in random groups of 3 and sending them directly to the whiteboards. I told them that I was not going to teach them the objective but have them “Grapple” out word problems with their peers and use their previous knowledge to figure out how to write equations from the given information. At first students were not sure what to do with the information but with a little prodding from me, I encouraged them to talk to their partners, write down information on the whiteboard and brainstorm ideas. I was pleased to see that through “Generation” they were able to logically make connections from the price of something as being the slope or mvalue and keep going with what they know about slopeintercept form. Because students were standing up and talking with their peers to figure out problems, their “Attention” and “Emotions” were at a higher positive/safe level because of the climate set in the class. They were not just sitting at a desk alone waiting for me to give the next clue. At the whiteboards, the are able to try things out, erase things that are not working and move themselves to understanding with very little input from me.

I recently put together a lesson that explored the pythagorean theorem where students had to build an access ramp to reach the top of a building. The inspiration came from the ramp that accesses our school doorway. Ultimately, while I found that this captured the attention of the students and had them generating some ideas, I don’t think I have been as successful tapping into the emotional side or spacing the learning in a way that promotes true retention.
I actually discovered quite quickly that there were some gaps in their understanding with algebraic equations, exponents and roots so while I tried to have them follow through with the lesson, we then pivoted to explore algebraic concepts. Ultimately, my goal is to circle back to reexplore pythagorus, but I’m worried about time this semester… as usual.
My general steps went something like this:
1. Image of school ramp with a character on it… notice/wonder?
2. Intro situation of ramp construction at building… how long will the ramp be?
3. Students use string to create ramp models through a series of right angle triangles.
4. Students collect measurements and try to determine how long the ramp will be.

This sounds like a great lesson. I hope you were able to get your technology to work in order to present it! Were you able to have the students break into smaller groups? (Zoom?) and were you able to get some good feedback from your students?
This lesson intrigued me and I’m curious how it went in the remote setting.

I think your lesson is great because not only are you making it fun, using the idea of a Treasure hunt, but the topic is a great way to move into Systems of Equations in the future. What type of solutions will you find with perpendicular lines?
What solutions will you find with parallel lines ? This goes along with slope and equation of the line.
There is alot your students can learn with this, keep attention, emotion positive and using the 3part framework to enable the notice/wonder….estimation…..refining the answer, etc.
FUN !

Reflection is tough! There are a few apps for school that allow students to reflect on their learning, what they had questions on and what they can do to better understand. One I have used is called Sown to Grow. It helps me to stay on top of their reflections better than paper and pencil. Also, a quick ticket out the door is another good option that takes just a few minutes of class.

I agree, this is so hard with remote learning!
One thing I tried that helped (though not quite the same) were having students post notice and wonders on padlets, and then comment on each other’s, kind of like we’re doing here. That was pretty effective. I could then take some kid responses, organize and highlight them, and then turn it into the opener for the next day. It’s definitely slower than it would be in class, because kids have a lot of time to complete them instead of doing them on the spot. If you were doing synchronous, that could work in real time.
Another that I’m wondering about is having small groups be virtual. The management freaks me out. I don’t know my district’s plan yet for fall, but am thinking if some kids are in class and others are remote, that I could have kids in Zoom breakout rooms in class, so that a couple of kids in class could be online with a couple at home, and then those smaller discussions might work.
I don’t know if that helps or not, but to me the collaboration piece is what will be the toughest. It’s SO important, and will be different this year for sure.

I agree Justin. I know that these concepts and the idea of spirally is where I need to go, however, I am not sure how to encourage this type of thinking at home. I want students to feel their ideas are valued and I don’t want parents to feel that math is being taught in a whole new way. There is too much confusion going on right now.

Hi Lyn,
Thank you for this great reminder that repetition and flexibility, especially in this great time of uncertainty, are key to assisting students with distancelearning math. I am often so hard on my self and have unrealistic expectations because I want so much for my students to learn, but really sometimes the best way to help is to allow students as many opportunities as possible to understand a concept in a way that is as accessible and as interesting as we can make it.

I like the quick ticket out the door. We use a program that allows a student to reflect on every missions. They put a sad, happy, or neutral face at the end of every mission to indicate their level of comfort/confidence of the topic.

At one of the schools I work at, the teachers are using a ticket out the door but with more information. Level 1 is the student really doesn’t understand the concept and needs a lot of help. Level 2 is a student is confused about an item but with help could quickly get it. Level 3 is where they understand the concept but could not explain it to someone. Level 4 is “I got this and I could teach anyone the concept”. Teachers use this feedback to group students on the two days of math intervention for the week.

Interesting! I have a colleague who has students make a quick mark on the top of their papers in a similar way. Green = understanding strong, Yellow = needs a bit of help, Red = needs a lot of help… many times student work does not match their own assessment of their skills and she values knowing how the students see themselves.

I know this comment is from over 2 years ago, but I know some teachers may still be teaching virtually and some may be teaching in fulltime online programs now. Zoom has the option for virtual breakout rooms (and the teacher can virtually pop in and out). Using breakout rooms in conjunction with a site like whiteboard.fi, you may be able to facilitate group work and discussion decently well (given the circumstances).