This week in MPM1D Grade 9 Academic, we explored direct and partial variation through 3 act math tasks and solving equations visually with SolveMe Mobiles!

The post Week In Review #5 – Direct/Partial Variation & Solving Equations appeared first on Tap Into Teen Minds.

]]>After three days out of the classroom, it felt great to be back working on some math with my students. This week, I wanted to explicitly discuss the difference between direct and partial variation linear relations and then start moving towards solving multi-step linear relations that involve collecting like terms, distribution and (hopefully) equations involving fractions. Let’s see how well we did meeting those goals.

Although we have been looking at linear patterning on and off since the first day of school, most have been proportional where the initial value (or y-intercept) is 0. Since the first day, I have been asking students to identify the equation in order to find the value of the dependent when the value of the independent is large (like figure number 47) or visa versa. Occasionally, I have snuck in a linear pattern that is not proportional by changing the initial value to something other than 0 (like Placing Toothpicks Part 3). This occasional “sneakery” is because I wanted to make it easy and natural for students to tackle this learning goal:

- LR2.04 – I can compare the properties of direct variation and partial variation in applications, and identify the initial value when described in words, represented as a table, a graph, or an equation.

In Ontario, we refer to a direct variation as a linear relationship with an initial value of zero and a partial variation as a linear relationship with an initial value not equal to zero. Since we have tackled many different linear relations with descriptions, tables, and graphs, it makes sense that students are ready to tackle this not so complex learning goal. Something to note is that we have not explicitly started with the graph of a linear relation and found the other representations. We will be inching towards starting with a graphical representation in the coming weeks.

In order to get kids thinking right off the bat, my *Minds On* involves jumping straight into Jon Orr’s Flaps! 3 Act Math Task. I show them the act 1 video to get them thinking:

Can’t see the video? Click here.

I ask students to talk to their groups about what questions they have about the slow-motion video. Ultimately, we are hoping to get somewhere close to this question:

How fast are the hummingbird’s wings flapping?

Usually, I have students individually make their predictions and share out. Today, I had students make their own prediction, discuss with their group, and compromise to make a “group prediction” they could share out as a team. It was interesting because now students felt like they had to better justify their own prediction in order for the group to agree on a number closer to their individual prediction. I’ll definitely try this again in the future.

After sharing out the group predictions, I showed students Act 2 of the Flaps! task and then started a Knowledgehook Custom Gameshow that I made to use for students to interact throughout the tasks for that day. Here’s a couple of the questions from the gameshow:

Keeping with the theme of spiralling the course, I always want to make sure we don’t take for granted that things like identifying independent and dependent variables are common knowledge. So, let’s keep bringing them back throughout the year:

If you’ve been reading my other Week In Review posts, you’ve probably picked up on the fact that I haven’t been delivering a traditional lesson with a lecture and note. I have been trying to introduce new concepts as tasks are being delivered rather than formally defining these new concepts, giving examples, and then trying to have students use the knowledge throughout a task. By flipping this idea on its head, I get into the task, sort of have the students prove to themselves that they can solve any problem that is put in front of them using intuition and prior knowledge, then help them define, identify and consolidate what skills they were actually using to do the work. During the Custom Gameshow, I formally introduce the concept of direct and partial variation:

Students have been encountering direct and partial variation since the beginning of the year, yet we never had a label on it. Now, I’m hoping to start using this terminology moving forward. Some other terms we are starting to use more frequently, even though I haven’t formally introduced them in the traditional sense is ** initial value** and

The task (and custom gameshow) go on to extend the concepts here by having them identify an equation that models this relation, determining the number of flaps in 5 minutes, and finding how long it would take the hummingbird to flap its wings 1 million times.

Then, I toss them another contextual task from Jon Orr called Crazy Taxi with the intention of giving students an example of partial variation. Here’s the first act:

Can’t see the video? Click here.

After travelling a few kilometres, the game fast forwards and asks the viewer to determine:

How much would it cost to travel 30 km?

Some key information include the **initial value of $5** on the meter before the taxi begins moving and a **rate of change of $0.50 per kilometre** travelled.

Even though I created math task template files in PDF form in the past for Flaps! and Crazy Taxi, I let the Knowledgehook Custom Gameshow do all of that work. I still have the urge to give a template for everything we do, but often times, that sort of “tells” the students that they must do a certain series of things in order to solve the problem. I want them to truly make the call on how they go about things. I have enough structure on my Tuesday Assessments, I figure.

With both of these tasks and the custom gameshow, this brought us to the end of class. Tomorrow, it is Assessment Day!

Here’s the learning goal lineup for Assessment #4:

- LR2.02 – I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a variety of sources.
- LR1.04 – I can describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses.
- LR2.04 – I can compare the properties of direct variation and partial variation in applications, and identify the initial value when described in words, represented as a table, a graph, or an equation.
- NA2.07 – I can solve first-degree equations, including equations with fractional coefficients, using a variety of tools and strategies.
- LR1.01 – I can interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant.
- LR3.01 – I can determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation.
- MG3.01 – I can determine, through investigation using a variety of tools and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons.

As usual, we aren’t trying to completely assess each learning goal in its entirety. Because we are spiralling the course, we are slowly digging deeper and deeper through each expectation with the hopes that student depth of knowledge will increase each time.

Overall, the overwhelming majority of the class is right on where I would hope they would be. We do have 3 students who did struggle in a couple small areas (mixing up independent/dependent variables, uncertainty with creating an equation, etc.) but those issues can now be tackled on an individual basis prior to the start of class with a little one-on-one guidance.

Feel free to snipe the assessment below:

The grade 9 academic course has three expectations related specifically to solving linear equations:

- NA2.07 – solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies);
- NA2.08 – rearrange formulas involving variables in the first degree, with and without substitution (e.g., in analytic geometry, in measurement) (Sample problem: A circular garden has a circumference of 30 m. What is the length of a straight path that goes through the centre of this garden?);
- NA2.09 – solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods (Sample problem: Solve the following problem in more than one way: Jonah is involved in a walkathon. His goal is to walk 25 km. He begins at 9:00 a.m. and walks at a steady rate of 4 km/h. How many kilometres does he still have left to walk at 1:15 p.m. if he is to achieve his goal?).

Thus far in the course, I have had students creating direct variation (or one-step equations) quite routinely and I’ve slowly been adding in partial variation (two-step equations). Almost all students can intuitively solve these two linear equations and many in that group can also do this using opposite operations, which I have not explicitly taught. Great start, for sure. You’ll note that the first expectation involves solving first-degree equations including fractional coefficients, which can be interpreted in many different ways. I’m going to stay away from the fractional coefficients equations until we get some good confidence under our belts. I plan to tackle the second expectation a little later in the course, while continuing to hit the third expectation as we do our daily contextual tasks.

In the past, I would jump straight into rules of solving equations including the concept of opposite operations. Actually, my first “day” of solving equations had a note that looked like this:

Now, along with attacking simple equations intuitively using trial and error when they come up, I try to give students different equation puzzles to work with that make them think. The puzzles I used today were SolveMe Mobiles. Students are given a puzzle consisting of different shapes that hang in balance like the items hanging from a mobile over a baby’s bed. Here’s the first one this free website serves up:

A pretty easy place to start, in my opinion. I start the kids off by having them complete the first puzzle without any guidance. As is usual when I have the students start something without any sort of detailed instructions, it seems that the strongest students are most vocal about their initial confusion with the task. I hear a lot of “what the heck are we supposed to do?” or “what is this?” and “I have no idea what I’m doing.” This is perfect, because I want my strong students to get used to the feeling of not always knowing the answer immediately. My hypothesis is that my strong students have been grouped this way because they are really good at following steps and procedures. When I don’t give them explicit steps and procedures, they start to get a bit squirmy and what I perceive to be a fixed mindset emerges. In this case, it doesn’t take long for the entire class to “get the point” of the SolveMe Mobiles. I gave them about 25 minutes to work through problems after they created a free account to track their progress.

It didn’t take long for much of the class to be up to Puzzle #30 with some students making it even farther than that.

Great classroom discussion was taking place as some students got stuck at different parts of their learning journey. I encouraged them to talk it out and try to find other ways to represent the situation (hoping for some algebra to pop up).

At this point, I stopped the class and we took one of the SolveMe Mobile puzzles and explicitly represented the puzzles as equations. First, using the shapes in the puzzle and then eventually, using variables.

So for example, this SolveMe Mobile:

…would be represented as:

hexagon + hexagon + hexagon = triangle + triangle + triangle + triangle + triangle + triangle

When a student says “do I really have to write it out like that?” I immediately ask them for an easier way. Doesn’t take long before we see stuff like this:

3 hexagons = 6 triangles

or

3h = 6t

And since we know that a triangle = 5, then:

3h = 6(5)

3h = 30and thus, h = 10.

At this point, we went to some “puzzles” that were given to them algebraically instead of visually, like the SolveMe Mobiles. We did this through gameshow and I asked students to upload their solutions so we could discuss potential strategies that might be useful for others to see. Here’s the gameshow I used:

Students made the transition fairly easily from the SolveMe Mobiles to straight algebra. I suggested that they draw it out as a SolveMe Mobile if it would help them organize their thoughts.

I had a stack of my old “Pearce Pence” currency I created on my desk and some students had asked for some. Here’s what I got in some of the Gameshow Solutions:

Pretty slick, those kiddies!

I was pleasantly surprised with how well my students took to solving equations algebraically last day. I often hear from teachers that there just “isn’t enough time” to include manipulatives and investigations that allow students to discover new math concepts and construct their own understanding. This thinking is 100% accurate if there are no plans to adjust the remainder of a lesson. For example, if I was unwilling to ditch my traditional note where students would copy the steps and then engage them in some examples – I mean, students would sit passively while I did the examples – then I would definitely run out of time. However, by approaching my lesson as an interactive experience that is student-centred rather than teacher-centred, my lesson is no longer something that my students have “done to them”. To follow up the activity from yesterday, I wanted to make sure my students didn’t believe that the SolveMe Mobile thing was just some sort of scam to sucker them into thinking equations were fun. So, today, I wanted to give them an interactive way to continue the idea of equations requiring balance.

Here’s what I showed them:

Can’t see the video? Click here.

Next, I had students download the first of three Explain Everything project files for iOS I had created to complement the sour patch kids equation analogy in the first video clip above. Here’s what the first slide in the file looks like:

The goal of the Explain Everything file is to allow students to intuitively solve the equation. What I typically expect is to see something like this take place:

Can’t see the video? Click here.

Students then move to the next three tasks in the Explain Everything file that look like the following:

**Task #2:**

Check out a sample solution:

Can’t see the video? Click here.

**Task #3:**

Check out a sample solution:

Can’t see the video? Click here.

**Task #4:**

Check out a sample solution:

Can’t see the video? Click here.

You can download the first Explain Everything Project File below:

Although the expectations of this course do not involve solving systems of linear equations algebraically, I always try to stretch the limits when possible. With the Sour Patch Kids tasks leveraging student intuition, it seems logical that students might be able to extend their thinking to a system of equations. In a second Explain Everything file, I give students the following two tasks:

I hope students can use their problem solving skills to come up with a solution. Here’s a possible approach:

Can’t see the video? Click here.

Here’s the second task:

And finally, if there is time, students can download the third Explain Everything file to create their own tasks using sour patch kids as well as other items they find on the internet:

I was pretty psyched to keep on the solving equations train and begin sneaking in distribution into the process. Not long after arriving at school in the morning I learned that half of my class would be gone on a field trip for the day. DOH! Oh well, I still went on with the lesson for the most part, as we will be spiralling back to this content later in the semester anyway.

The Minds On today was SolveMe Mobile Puzzle #71. My challenge to my students was to solve for the values of each shape in any way they wanted, but then to attempt modelling the puzzle algebraically. Students struggled to do this as I think they thought it was more complex than it really was. They could all solve it, but most were intimidated when it came to representing with algebra. Here’s a silent solution I created to share with them after students shared their solutions:

Can’t see the video? Click here.

After that, I asked students to solve the following equation:

4x + 10 = 90

After sharing out their strategies, I offered another possible way to look at solving an equation that students found helpful:

Can’t see the video? Click here.

Then, it was on to challenging the class with some tasks via the Knowledgehook Custom Gameshow below:

Can’t see the gameshow? Check it out here.

When we got to the third question, some students were stumped trying to figure out what they needed to do:

Find the root of the equation:

2(x – 2) = 4x – 2

Note: Think of “root” like getting to the “root” of the problem or the “SOLUTION”.

Interesting enough, most students were struggling with “BEDMAS” and the idea that they had to do something inside the brackets first. We had a great chat about why just remembering rules in math can be cause for more confusion than help.

Here’s the crash course on the distributive property that we looked at on the fly:

I gave students a bit more time to work out a solution and then suggested that maybe they try to draw their own SolveMe Mobile to help them organize their thoughts:

Finally, we consolidated the problem using algebra:

Overall, it was a fun class with some great learning moments. We definitely have more work to do on distribution and how it applies to solving equations, but I know it will come in time.

That’s it for this week! Looking forward to heading into a four-day week with the Canadian Thanksgiving Holiday on Monday. Enjoy the weekend!

The post Week In Review #5 – Direct/Partial Variation & Solving Equations appeared first on Tap Into Teen Minds.

]]>This week in MPM1D Grade 9 Academic, we explored some more geometry of angles as well as identifying linear and non-linear relations.

The post Week In Review #4 – Geometry & Linear/Non-Linear Relations appeared first on Tap Into Teen Minds.

]]>I can’t believe the fourth week of school has already come and gone. This week was a bit hectic as I was away on Tuesday and Wednesday engaging in professional development as a part of my role as Middle Years Collaborative Inquiry (MYCI) Lead for my district and again on Thursday delivering a keynote for the Carleton Ottawa Mathematics Association (COMA) in Ottawa, Ontario. With me out of the classroom for three days in a row, that leaves the majority of this week a “self-directed” experience for my students. Here’s the recap:

The day before I know I will be out of the classroom is always a struggle for me. I am always a bit too excited to do too much on a regular day, so knowing I’ll be gone leaves me wanting to do way too much to compensate for the lost time. Either way, I wanted to use this class to give students a bit more exposure to some of the Geometry of Angles topics we had introduced in the previous class.

The warm-up was a Knowledgehook Custom Gameshow to get students thinking as well as some spaced practice. Here’s the three questions they did:

I know, I know… the warm-up questions aren’t breathtaking. However, I do feel that my students need some practice working with the new skills we cover, so I try to make it as enjoyable and collaborative as possible via Knowledgehook Gameshow.

Next, I wanted to get my students to begin extending their thinking about patterning from direct variation linear relations to partial variation, where the y-intercept is not equal to zero. We did this by introducing the Placing Toothpicks Part 3 task.

Here’s the act 1 video:

Can’t see the video? Click here.

Students would go on to determine the number of toothpicks in the 6th figure and 11th figure. Then, I had them think of a general rule that would help them find the number of toothpicks for any figure number. I also asked them to determine the figure number that would require 162 toothpicks to see how they would go about that. Good discussion and thinking here.

Here’s some student work:

After sharing out some interesting approaches and discussing a general rule in words and using algebra, we moved on to the final challenge of the day called Railing Reproduction (will share task online soon). Students watch a short video clip of some railings on a stairway and are asked “What’s the question?”

Can’t see the video? Click here.

In this case, I make up a short story about how Paisley, the Bull-Puggle gets pretty worked up and put her tubby body through the railing. I only had one angle to work with and had to find the other missing angles prior to making my cuts with the saw.

Can’t see the video? Click here.

Students worked diligently on this problem and it was clear that they had been able to recall some of what they learned back in grade 7 math. From what I’m seeing with this group, I should be able to jump into interior and exterior angles of n-sided polygons from an inquiry standpoint without much trouble.

On the assessment for this week, students will be tackling portions of the following learning goals:

- LR1.02 – I can pose problems, identify variables, and formulate hypotheses associated with relationships between two variables.
- LR3.01 – I can determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation.
- MG2.03 – I can solve problems involving the areas and perimeters of composite two-dimensional shapes.
- NA2.02 – I can solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion.
- MG3.01 – I can determine, through investigation using a variety of tools and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons.

You’ll notice I said we will tacking “portions” of those learning goals. This is because I decided to use specific curriculum expectations for my standards based grading approach due to the huge number of learning goals that ballooned last year when I broke them all down. I think somewhere in the middle between how I’m doing it this year and how I did it last year is probably the best bet. Maybe identifying the specific expectation with learning goals as sub-categories of that. More thinking to be done with that one.

Here’s the assessment, if you want to snag it:

As mentioned earlier, I was away today and always struggle to create a meaningful learning environment that will be easy enough for a substitute teacher to lead and beneficial to the students. In a spiralled classroom, you’ll see us jumping around from strand to strand quite a bit and constantly introducing new concepts as we go. Days when the teacher is not present might not be the best way to introduce new concepts because it is hard to determine how many students are putting in their usual effort.

When I am away delivering or receiving professional development, the lesson will typically involve a few tasks students can handle independently or collaboratively with their table groups with a realistic timeline of finishing prior to the end of the period. My instructions to the supply teacher will be explaining the tasks and the protocol in which students can tackle the tasks, followed by the opportunity for students to re-address learning goals from their gamified learning log like this sample learning log and/or they can complete some practice problems from Knowledgehook Homework that I am experimenting with this year.

The first task is called Snowy Winters, where the following situation is laid out for students:

The last snow storm lasted 6 hours. Over that time, the amount of snowfall was measured hourly, except for at the 5th hour when Mr. Pearce watched the 3rd period of the Toronto Maple Leaf game.

Student are then asked to create a scatter plot, line of best fit, make some predictions using interpolation and extrapolation based on the data, and classify the relationship. I know, I know… not the most interactive or creative task you’ve ever seen. It’ll have to do while I’m away.

Then, I had attempted to make a semi-interactive task that continues the Placing Toothpicks tasks (original and part 3) that students had worked on over the past week and a half called: Placing Toothpicks Part 4 (original, eh?). I had taken the sequel task and actually saved to use it for tomorrow as a way to introduce identifying linear and non-linear relations. Maybe I should just re-name all the tasks? Ah well.

The Part 4 Task (resource page coming soon) is another partial variation linear relation pattern that is formed using a design with toothpicks.

Here’s Act 1:

Can’t see the video? Click here.

Students are going to be looking at the 6th and 11th figures as they did in previous tasks, however they will be going through this task in a self-led fashion by downloading a math task template I created for them:

How I made the task template interactive was by adding hyperlinks in the PDF that will allow students to jump straight to the Act 1 video:

After students have come to their conclusions, they can watch the Act 3 video by clicking the link embedded in the math task template:

The task template is structurally organized to ask students to do specific things like create a table, graph and answer some questions on the back. I’m not super thrilled with using this approach as of late, but these math task templates are really the only structure from my former, more traditional, teaching approach. I would be lying if I said I don’t worry about my moving to a less structured teaching style, but I feel deep inside that it is the right thing to do.

If you want to grab the template, click below:

This would be the third day in a row that I’m out of the classroom. Luckily, I’ve had the same supply teacher who is actually the long-term occasional teacher that teaches my afternoon schedule while I do Middle Years Collaborative Inquiry (MYCI) work for the district. While there is some consistency while I’m away, this is the first time he has covered the group. I asked him to keep me posted on how things were going while I was away and it sounded like most students are on pace, but there was a school-wide interruption planned to take up a portion of the period today.

With that in mind, I left a new topic (identifying linear and non-linear relations) for students to explore with the thinking that we would be spiralling back to it a number of times throughout the semester. This would give students the opportunity to construct their own understanding of what makes a relation linear or not through an investigation. This is where the Placing Toothpicks Sequel comes in as it is quadratic. I was interested to see how students reacted to it, since they have only seen linear patterns for the most part thus far.

Here’s Act 1 of the Placing Toothpicks Sequel:

Can’t see the video? Click here.

Again, I thought I would create an interactive math task template that would allow students to link directly to the videos independently:

Students were not in school today as teachers had a scheduled professional development day.

That’s it for this week! Looking forward to being back in action next week as we spiral into our next few topics. Toss me some feedback on what you’re seeing. Any ideas how I can release more of the responsibility to my students? On my mind for this coming week is how I can better “let go” of the formal structures (i.e.: procedures) that most of our learning goals tend to lead to. Until then, have an awesome week of learning.

The post Week In Review #4 – Geometry & Linear/Non-Linear Relations appeared first on Tap Into Teen Minds.

]]>Watch the first act as you see the first three figures made with toothpicks. How many toothpicks are in the 6th figure? ...11th figure? ...the general rule?

The post Placing Toothpicks Part 3 appeared first on Tap Into Teen Minds.

]]>This task is a follow up to the Placing Toothpicks and Placing Toothpicks Sequel tasks I posted recently. The first task was proportional, followed by a quadratic in the second. This task is going to extend the original task from a proportional (direct variation) linear relation to a partial variation linear relation. That means this task could be used for patterning in elementary or for linear relations in grade 9 academic and applied. Here’s the grade 9 academic expectations we can make connections to:

- LR2.02 – I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a variety of sources.
- LR2.03 – I can identify, through investigation, some properties of linear relations and apply these properties to determine whether a relation is linear or non-linear (by rate of change/initial value when described in words, by first differences in a table, straight/curved graph, degree of terms in equation).
- AG1.01 – I can determine, through investigation, the characteristics that distinguish the equation of a linear relation (straight line) from the equations of non-linear relations (curves).
- LR2.04 – I can compare the properties of direct variation and partial variation in applications, and identify the initial value when described in words, represented as a table, a graph, or an equation.

Show the students the video below:

Can’t see the video? Click here.

If you have already used the Placing Toothpicks and Placing Toothpicks Sequel, asking them what questions they have might be a bit redundant. Sure, I could change what figure number I want them to find, but this process might be more forced than it is worth.

As we did in the previous toothpick tasks, the question(s) I want students to think about are:

How many toothpicks are in the 6th term? … the 11th term?

I would likely have students figure this out on their own, using any strategy and then consolidate the task. The following math task template might be a good option to consolidate student thinking:

You can now let students see their solution in action!

Can’t see the video? Click here.

Here’s some work I captured when I tried this task for the first time the other day.

Have you tried this task? How can we make it better? Share your thoughts in the comments below!

Click on the button below to grab all the media files for use in your own classroom:

The post Placing Toothpicks Part 3 appeared first on Tap Into Teen Minds.

]]>When we talk about people who are "Good at math" are we really referring to people who are good at memorization? Let's dig into this a bit deeper...

The post Tips Moving From Math Procedures to Understanding appeared first on Tap Into Teen Minds.

]]>I opened my inbox to the following email this morning:

Hi Kyle,

Scott Miller here. We met at the DVC Math Conference in February.

In reading/watching your presentation “Two Groups of Math Students I Created in My Classroom” have you found students that are

Not Good at Memorization, but do not struggle with unfamiliar problems?Have you gotten flack from parents that their child does not learn “that way” because you are “not teaching” them? I have used the terms

Good at ProceduresandNot Good at Procedures. I have found that by creating more challenges for a student to think through has benefited more of theNot Good at Proceduresbecause they try different things. TheGood at Proceduresstudent shuts down and is unwilling to try because he or she does not recognize a memorized pattern.

What Scott is describing is very common when you start making a shift to teaching for understanding instead of teaching for procedures.

I would agree that challenging my students to think is initially more more beneficial for my *not good at memorization* or *unwilling to memorize* students. I see this group of students giving up when they are presented with an algorithm that they must follow. However, when I challenge them to solve a problem without attempting to give them a procedure, they are more willing to get creative in their thinking. The opposite appears to be true for our *good at memorization* friends likely because they are aware of their skill to replicate a given set of steps. When we don’t offer up those steps, they are concerned that they might not get the right answer on the first try and thus, they wouldn’t be considered “good” at math.

I believe this issue has a lot to do with mindset. I often find that the typical *good at procedures* group has a fixed mindset (I’m good or not good at something and I don’t have much control over it) and they have consciously or unconsciously figured out the “game” of getting good grades in math class. It is much easier for someone who can memorize easily to follow a procedure without having to understand what they are doing. Even in a classroom where a teacher is introducing topics through investigation, if the assessment routinely requires only the use of an algorithm, students naturally pick up on this. Why bother with understanding the “why” if I can just remember this handy set of steps?

If my assessments focus primarily on steps and procedures, then we are subconsciously telling our students to treat math concepts like a job on an assembly line:

- Grab two bolts from the bin.
- Fasten one (1) bolt to the threaded hole at the top left of the vehicle.
- Fasten one (1) bolt to the threaded hole at the bottom left of the vehicle.
- Apply grease with the grease applicator to the hinges on the front passenger door.
- Repeat for each vehicle on the line.

The worker may or may not understand why she is doing those steps in that particular order to complete her job successfully. Observing the worker might make one believe that she has a deep understanding due to her competence in completing the steps. However, only when you move her to another random job on the assembly line without any training will you truly observe how much she knows about building a vehicle.

This assembly line approach is what I see in my math classroom on a regular basis when we allow students to rely too heavily on an algorithm. Unless a problem looks familiar to what they have tackled previously, students lacking a deep conceptual understanding will experience difficulty. While it is difficult to pinpoint the specific cause, my hypothesis is that students in the *good at procedures* group have not been asked to think critically often enough in the math classroom.

I think there is a connection between what we are describing here and all of the posts on social media that describe “new math” as a simple question with a solution that appears more complex than necessary vs. “old math” where the same problem is tackled with a seemingly simple algorithm. Parents often get more frustrated than the student because they believe they understand math, but can only tackle addition/subtraction and multiplication/division using the standard algorithms.

When a *good at procedures* student is frustrated because I do not give them an algorithm to memorize, I make sure that I discuss why I am teaching from a task based, inquiry approach over simply giving them the steps. The frustration will not go away immediately and we shouldn’t expect it to as we have literally ripped the mathematical carpet from under them. You can imagine how a student must feel when they come into my grade 9 math class and quickly realize that they’ve been misled into believing they are “good at math”. The first instinct of the student and his/her parents is to blame the teacher because they have made it through eight years of elementary school math without a hitch. However, I find that you can get both the student and the parents on your side by being clear about why the student has been successful in the past. I try to help the student and the parents understand that knowing procedures alone is like being a “mathemagician” with a limited number of math tricks that are only useful in very specific situations. Helping students develop a deep understanding by thinking critically on a daily basis is the only way students can truly understand math and apply their knowledge to unique situations.

We can also help ease any anxiety that this change to learning math might cause by using assessment practices that promote student learning and growth. Since learning math is a process and every student is at a different place on their learning journey, offering multiple opportunities to demonstrate learning will help the student understand that they will not suffer if they struggle with a concept initially.

Have you had a similar experience in your math classroom? Have you found a way to help students understand why you don’t want them to simply memorize? Help us out by leaving a comment below!

Here is a timely YouTube video that I came across just hours after I published this post. Fits in nicely.

http://t.co/6ZMXcmHTUq

Can’t see the video? Click here.

The post Tips Moving From Math Procedures to Understanding appeared first on Tap Into Teen Minds.

]]>Get a look at what we're up to in Grade 9 Academic as I attempt spiralling my MPM1D curriculum for the first time using a task-based approach.

The post Week In Review #3 – Measurement, Linear Relations and Geometry appeared first on Tap Into Teen Minds.

]]>Today, I had intended to use a Knowledgehook Gameshow as a warm-up related to area of composite figures and then move into the Gas Guzzler 3 Act Math Task. Unfortunately, my timing was completely off as I had 7 questions and some students who were pretty eager to solve them with their complete solutions uploaded to the system (bonus!).

Here’s the gameshow that we used:

Can’t see the Gameshow on the page? Click here.

By the time we tackled each problem while sharing student solutions over the projector using the “Share Solution” feature as we went, we had 15 minutes remaining in class. Definitely not enough time to tackle what I had planned for Gas Guzzler.

Instead, I assigned an activity related to linear correlation via Knowledgehook Homework mode and students were off to the races.

Tomorrow, we will have Assessment #2 to see how we are making out thus far with our learning goals that we have covered.

Tuesday is Assessment day where I take a few questions from **any** learning goal from the year to see what point students are at in their learning. Students are not told what they will see prior to the assessment, but also know that the purpose is to promote growth, not cement marks into a grade book. If students struggle on a concept, now they know what to look at for the following week and can submit work from given “Growth Opportunities” from their online Learning Logs. Students are also permitted and *encouraged* to create their own “Growth Opportunities” to improve.

Assessment #2 will cover the following learning goals:

- I can solve problems involving the areas and perimeters of composite two-dimensional shapes.
- I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a variety of sources.
- I can describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses.

We will also introduce, for the first time, a new learning goal:

- I can determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation.

Students get a little squirmy when I introduce a new concept on an assessment, however I do give enough information for them to apply the new concept. I consider this like a diagnostic to determine where students are in relation to the new concept. I simply provide students feedback on how they handled the new concept and ensure they know that the concept will begin coming up regularly in class and on future assessments.

You can check out the assessment below:

Today, I used the Gas Guzzler 3 Act Math Task as a way to help students build their problem solving skills while connecting **proportional reasoning** to **direct variation linear relations**.

If you’ve never come across Gas Guzzler, here’s the Act 1 Video:

Can’t see the video? Click here.

Grab the whole task here.

After watching the video, we have students share out their questions. The question I want to focus on first is:

How much does it cost per litre of gas?

We then get kids making their predictions and then I give them some more information about the task in Act 2.

Students then work in their table groups to come up with a solution prior to seeing the Act 3 video to check their answer.

For the first time this year, I decided that we could really extend this task to other learning goals we’ve covered this semester and even introduce new concepts along the way by creating a Custom Gameshow. So I started with questions pretty closely tied to proportional reasoning:

Tomorrow, I’ll do a warm-up gameshow with more questions that extend to direct variation linear relations.

Here’s some student exemplars from today:

As mentioned above, I had intentions to extend the Gas Guzzler task to direct variation linear relations by introducing initial value and rate of change. Here’s the warm-up Gameshow that I created to support the extensions:

This was the first time I’ve attempted to “embed” a new concept into practice. It seemed to work well. I attempted to define the new concepts in a question to get students to think critically about what we have introduced. Here’s one of the questions, in particular:

After we finished up the warm-up, I had the Placing Toothpicks 3 Act Math Task lined up and ready to go. Students watched this video:

After hearing the questions students had about the video, I showed them this:

Click here if you can’t see the video.

The questions I want students to think about are:

How many toothpicks are in the 6th term? … the 11th term?

I would likely have students figure this out on their own, using any strategy and then consolidate the task. The following math task template might be a good option to consolidate student thinking:

You can now let students see their solution in action!

Can’t see the video? Click here.

Can’t see the video? Click here.

This week, the focus has been on area of composite figures, proportional reasoning and linear relations. Some areas I haven’t spiralled into yet are angle geometry, exponent laws, and algebra. When I used traditional units to teach this course, I typically left angle geometry until very late in the course. This year, I wanted to slowly introduce them early on in order to give students multiple opportunities to build a deep conceptual understanding.

To this point I have struggled to find a compelling reason for why we learn the properties of interior and exterior angles of a triangle. I know that we can apply triangles to many real world situations, but how can we hook students in to want to engage in a task requiring their use?

This time around, I decided to use Dan Meyer‘s Best Triangle 3 act math task as a way to get kids thinking about triangles and allow me to branch off into properties of interior and exterior angles.

Here’s how it went down:

I showed students this video:

Can’t see the video? Click here.

The question asked in the video is:

Draw three points in the shape of an equilateral triangle.

I asked students do this on their iPads in a whiteboard app like GoodNotes 4 or Explain Everything. You’ll see why this is important later.

I then asked students to rank the triangles created by Andrew, Nathan, Chris and Timon. **Who, do they believe, created the best equilateral triangle?** Do they think that their triangle is better than all four?

We then had a discussion about how they could prove or disprove a claim that one triangle was “better” than another. Students were quick to recall from elementary school that equilateral triangles have equal sides, but it took a little while longer to get someone to state that the angles are also equal.

At this point, I had intended to use a pre-made interactive Geogebra worksheet that has a screenshot of the four triangles so students could measure the angles. My thinking was that this would be a pretty pain-free way to introduce students to this free online resource and also serve a purpose to help us measure angles. Check out the sheet below:

Can’t see the Geogebra Worksheet? ” target=”_blank”>Click here.

Unfortunately, about half of the students had some pretty significant struggles using this web based tool on their iPad. I had no such struggles on my iPad Air 2, however my students are using 5 year old iPad 2 devices. Maybe these relatively old iPads didn’t have the processing power necessary? After an abundance of troubleshooting around the room, I wiped the sweat from my brow and finally pulled the plug on this portion of the activity. I went straight for this image to reveal the angle measures of each triangle:

At this point, I asked students to work in their table groups to come up with an agreed upon order from “Best Triangle” to “Worst Triangle” and we would share out in 3 minutes.

As a whole, we managed to come up with the following order:

- Timon
- Nate
- Chris
- Andrew

The discussion was rich as students tried to justify why they ordered Nate, Chris and Andrew the way they did. Students agreed that Andrew had the “greatest” angle and thus they felt he should be last. While they noticed that Chris had the “least” angle, they failed to make a comparison to determine what else might affect their decision.

Students were really surprised to see that Chris was last, but we had a good discussion as to why that made sense. While we do not explore some of the analytic geometry required to explore this task further in grade 9, I did mention to students that we could revisit this problem in grade 10 using more mathematical tools to help us come to this same conclusion.

Once we completed this task, I had students jump into the Explain Everything Angle Journey I had created for my students last year. The intention with this task was to allow students to revisit some of the concepts they have experienced in elementary school. The screencasting features of the app also allowed them to consolidate some of their learning with the interior and exterior angles of triangles while helping me determine what we need to touch upon before moving on.

If you haven’t checked out the full blog post, you can click here to jump to the post.

The post Week In Review #3 – Measurement, Linear Relations and Geometry appeared first on Tap Into Teen Minds.

]]>Placing Toothpicks Sequel is a 3 Act Math Task that shows me creating another pattern with toothpicks. How many toothpicks are there in figure 6? ... 11?

The post Placing Toothpicks Sequel appeared first on Tap Into Teen Minds.

]]>Here’s an extension to the Placing Toothpicks task I posted recently. While the previous task hit on quite a few learning goals from the Grade 9 Academic and Applied courses in Ontario, this task will focus on identifying linear and non-linear relations in those same courses. It should be noted that this task could also be used in grade 10 courses for learning goals related to Quadratics. On my radar right now would be the following grade 9 academic expectations:

- LR2.02 – I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a variety of sources.
- LR2.03 – I can identify, through investigation, some properties of linear relations and apply these properties to determine whether a relation is linear or non-linear (by rate of change/initial value when described in words, by first differences in a table, straight/curved graph, degree of terms in equation).
- AG1.01 – I can determine, through investigation, the characteristics that distinguish the equation of a linear relation (straight line) from the equations of non-linear relations (curves).

Show the students the video below:

Can’t see the video? Click here.

At this point, I’d be asking my students what questions they have. You can write these questions on the board or if the kids have devices, use something collaborative like a Google Doc or Padlet wall.

After some questions are shared out, you can show students the following video:

Can’t see the video? Click here.

As we did in the original Placing Toothpicks task, the question(s) I want students to think about are:

How many toothpicks are in the 6th term? … the 11th term?

I would likely have students figure this out on their own, using any strategy and then consolidate the task. The following math task template might be a good option to consolidate student thinking:

You can now let students see their solution in action!

Can’t see the video? Click here.

Can’t see the video? Click here.

Have you tried this task? How can we make it better? Share your thoughts in the comments below!

Click on the button below to grab all the media files for use in your own classroom:

The post Placing Toothpicks Sequel appeared first on Tap Into Teen Minds.

]]>Placing Toothpicks is a 3 Act Math Task that shows me unwrapping toothpicks and placing them to create a pattern. How many toothpicks are there in figure...

The post Placing Toothpicks appeared first on Tap Into Teen Minds.

]]>Patterning is something that comes up early in the Ontario Elementary Math Curriculum during the primary grades often connecting directly to proportional reasoning, and then evolves into direct variation linear relations in the grade 9 academic and applied courses. In both the academic and applied grade 9 courses I teach, I try to integrate proportional reasoning early and often – slowly scaffolding students towards one-step equations and the characteristics of linear relations.

Today, I’m going to share out the following **3 act math task** that Justin Levack and I filmed last year keeping the grade 9 academic curriculum in mind. In particular, this task can be connected to:

- NA2.02 – I can solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion.
- NA2.07 – I can solve first-degree equations, including equations with fractional coefficients, using a variety of tools and strategies. (minus fractional coefficients)
- LR2.03 – I can identify, through investigation, some properties of linear relations and apply these properties to determine whether a relation is linear or non-linear (by rate of change/initial value when described in words, by first differences in a table, straight/curved graph, degree of terms in equation).
- …and many more!

Let’s get started!

Show the students the video below:

Can’t see the video? Click here.

At this point, I’d be asking my students what questions they have. You can write these questions on the board or if the kids have devices, use something collaborative like a Padlet wall:

Can’t see the padlet wall? Click here.

After some questions are shared out, you can show students the following video:

Can’t see the video? Click here.

The questions I want students to think about are:

How many toothpicks are in the 6th term? … the 11th term?

You can now let students see their solution in action!

Can’t see the video? Click here.

Can’t see the video? Click here.

Have you tried this task? How can we make it better? Share your thoughts in the comments below!

Click on the button below to grab all the media files for use in your own classroom:

The post Placing Toothpicks appeared first on Tap Into Teen Minds.

]]>Get a look at what we're up to in Grade 9 Academic as I attempt spiralling my MPM1D curriculum for the first time using a task-based approach.

The post Week In Review #2 – Spiralled Tasks & Assessment #1 appeared first on Tap Into Teen Minds.

]]>Today was the first day that most of our regular apps were installed on the iPads. It was good timing, because I wanted to explore some more concepts related to two-variable relationships. Since I am spiralling the course, I intend to avoid giving formal “notes” for students to copy, but rather introduce new concepts through tasks. The Big Ideas I’d like to hit all at once are:

- Identifying the independent and dependent variables with justification,
- Creating a table of values given 2-variable data,
- Creating a scatter plot,
- Classifying a two-variable relationship as increasing/decreasing, strong/weak, positive/negative, etc., and
- Making predictions from the graph (interpolation/extrapolation)

I plan to use the Candle Burning 3 Act Math Task to get kids thinking and lead us down the pathway to the Big Ideas. Here’s the Act 1 Video:

Can’t see the video? Click here.

After students came up with some good questions, we settled on *when will the candle burn out?* Students made predictions that we recorded on the board and we were ready for Act 2.

In order to uncover some of these ideas without a formal note, I prepared a math task template as a scaffold to help us see some of these concepts through a 3 act math task:

After trying to get started by bringing the math task template into GoodNotes 4, some students realized that their iPads were still updating. Clearly, the dust is still settling as our district moves to a new MDM for this school year. We had those students having difficulty to send their PDF to Explain Everything which did the trick.

After most students had started graphing their data points, I showed the graph being created from a Keynote animation I made to go with the Candle Burning problem. This was to help students who may not have felt confident in what they were doing. Here’s the whole thing, even though I only showed a small portion of it:

Can’t see the video? Click here.

Once students completed their table and graph, I asked them to update their prediction. I was hoping to see someone come up with using a Line of Best Fit as a strategy, and one student did. Others just eye-balled it. It was interesting to hear how students updated their original guesses based on their graph. We still had quite a range of values, though; likely due to the large scale used on the scatter plot. The lowest was 240 minutes and the highest was around 380 minutes, with most coming in around the 350 minute mark. Students completed the extension questions on the math task template and then we were out of time.

Tomorrow, I intend to show Act 3 (the actual amount of time it took to burn out the candle) with some consolidation animation videos to re-cap what we did today.

Last year with my Grade 9 Applied class, I started spiralling the course and went to “Weekly Assessments” rather than unit based tests. The goal is to not only spiral content throughout the course, but also to constantly be assessing students in a cumulative fashion. It is easy to get stuck assessing only the content from a specific unit rather than going back to ensure all is not lost from those previous.

This will be my first time trying to spiral content in the Grade 9 Academic course. Here are the learning goals we have touched on thus far in the course:

- I can solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion.
- I can pose problems, identify variables, and formulate hypotheses associated with relationships between two variables.
- I can construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools for linearly related and non-linearly related data collected from a variety of sources.
- I can describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses.
- I can interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant.
- I can solve problems involving the areas and perimeters of composite two-dimensional shapes.

Note that while it might seem like a lot for only 5 days of school, but we are just scratching the surface. These learning goals are by no means done – there is still a lot to do with them. That’s why I ensure that the questions on early assessments have a very low floor. I am hoping to get everyone on the elevator in order to slowly move it up as the semester progresses without boring anyone in the process.

Here’s what Assessment #1 looked like:

You can grab the PDF file here.

*Note that I usually indicate the learning goal(s) for each question, but forgot to do that on the second page.*

Here’s some of what I got back:

Student #1:

Student #2:

Student #3:

Overall, must students were very successful. Most did think that the trend for question #3 was “linear” when a curve would be more suitable. These are little things that are easy for me to address as we spiral back throughout the semester.

So far, so good!

In order to get this digital work to me, I use a Digital Dropbox system that Alice Keeler shared on her blog.

How we create a Shared Google Folder:

Can’t see the video? Click here.

How my students submit their work to me using Google Forms:

Can’t see the video? Click here.

Thus far in the spiral, I haven’t made it to measurement yet. Today, we’re going to touch on area and lead us into an exploration of area formulas over the next day or so. Jon Orr’s R2D2 Post-It Notes 3 Act Math Challenge is a nice low floor task that works with area of a rectangle and proportional reasoning.

Here’s the Act 1 video we show the students:

Can’t see the video? Click here.

Here’s the question we eventually settle on:

Determine how many post-it notes it will take to cover the board?

My students came up with some predictions including:

- Alex – 888
- Jaden – 700
- Olivia – 688
- Cole – 756
- Grace – 900
- Lowwwwza – 950
- Stef – 800
- Vanessa V – 820
- Tristan – 600

After making some predictions, students requested information. Here’s what I gave them:

At this point, I also gave them a math task template to help organize their thoughts and consolidate their learning once we took up the task:

Then, students were off to town.

Here’s a few student exemplars I saw walking around the room:

After showing the solution, students worked on the second page of the template and we consolidated our new knowledge. Notice that I am scaffolding students to start naming the variables as independent/dependent, labelling them on the table and graph, and also adding their own scale to the graph.

We also introduce a simple one-step (proportional) linear equation that students must create and solve for the independent variable. First time we’ve done that this year.

I had originally planned to also run a Gameshow and begin an area investigation, but we didn’t have enough time. We will do those tomorrow.

Conveniently, this task and all media files are available for download to your iOS device from iTunes U in the Curious Math course. I ran this task straight from my iPad using the files in the course. The benefit is that the files download to your device so you aren’t stuck with any streaming issues if traffic on your network is high.

You can enrol in the course below:

After working with Jon’s R2D2 Post-Its 3 Act Math Task yesterday involving area of a rectangle and proportional reasoning, we started today with a warm-up question using Knowledgehook’s Embedded Gameshow feature:

Most students jumped straight to using the formula for area of a triangle, so I verbally asked groups of students to explain why the formula works. Most students were able to give me an explanation such as:

A triangle is half of a rectangle, so we take half of the area of a rectangle.

My intention for this lesson was to give students an opportunity to take what they know about area of a rectangle and area of a triangle and extend it to discover the area of a trapezoid. This sounded like a great opportunity for students to use Explain Everything for the first time this semester as a way for them to communicate their understanding. Here are the slides from the Explain Everything Project file I provided them:

The first three slides were more as a way for students to play with the app and learn the tools. I didn’t want to overwhelm them with a difficult math problem on-top of a brand new tech tool. The first time students use Explain Everything, I typically find that the fear of failure can cause the activity to take much longer than you would expect. Students are playing with the tools, trying to write neatly, and are usually very shy to record their first screencast. Some students will finish the period with little complete for this very reason. However, as we use the tool more and they see exemplars of good finished products, most students come around.

Here is a portion of a student exemplar:

Can’t see the video? Click here.

I noticed that most of the student explanations were simply restatements of formulas or steps, but didn’t provide much in terms of justification or mathematical reasoning. This is something I hope to work on as we move forward.

Once students finish the investigation and they export to their Google Drive Shared Folders, we consolidate what took place using this Keynote slide deck:

Can’t see the video? Click here.

*Note that we go much slower in class discussing each step.*

Today, we watched a couple of our student Explain Everything videos to start class. As I write this, I’m noticing that I’ve really been slacking on my minds on/warm-up portion of my lesson – something I need to think about. I’ve been basically jumping straight into a 3 act math task, probably because it usually does the trick to hook students in. I found that much of my warm-up problems I had used in the past were just the same old boring question for them to do. I’ll keep thinking about this moving forward.

After we discussed some Best Practices for creating an effective screencast tutorial video, we moved into the Mowing the Lawn 3 Act Math Task. Students watch the following video to get them hooked:

Can’t see the video? Click here.

We then used this Google Doc to jot down the questions students had. Some included:

- How many acres is there to cut? (Vanessa Q)
- How long will it take to cut the lawn? (Kale)
- How big is the lawn? (Avery)
- How many rows would it take to cut the grass? (Hannah G)
- How many columns would it take? (Jaden)
- How much gas would it take? / Cost? (Avery)

We settled with:

How long will it take to cut the lawn?

I then gave them this image:

And as usual, students made predictions. Here’s a few from today:

- Alex – 17 mins, 38 seconds
- Jaden – 21 minutes, 38 seconds
- Kale – 20 minutes
- Olivia – 23 minutes, 16 seconds
- Yousef – 12 minutes
- Briggs – 25 minutes
- Vanessa V – 30 minutes
- Avery – 14 minutes, 47 seconds
- Zach – 19 minutes, 42 seconds
- Brooke – 16 minutes
- Cole – 15 minutes

At this point, I then gave students a math task template that they were welcome to use:

Here’s a student exemplar:

Something I’ve noted is that many of the students are not showing work and thus when they get stuck, there is really nothing they (or I) can do to help troubleshoot. This will be a focus of mine moving forward.

While I had intended to have students get some practice in using a related Knowledgehook Gameshow, we ran out of time. I’ll save the custom gameshow for a warm-up on Monday. Instead, I had students complete the following ready-made activity from Knowledgehook over the weekend:

And that’s it for this week! Looking forward to a fun-filled week ahead!

The post Week In Review #2 – Spiralled Tasks & Assessment #1 appeared first on Tap Into Teen Minds.

]]>Applying Area to Proportional Reasoning Thus far in the spiral, I haven’t made it to measurement yet. Today, we’re going to touch on area and lead us into an exploration of area formulas over the next day or so. Jon Orr’s R2D2 Post-It Notes 3 Act Math Challenge is a nice low floor task that […]

The post R2D2 Post-Its by @MrOrr_geek appeared first on Tap Into Teen Minds.

]]>Thus far in the spiral, I haven’t made it to measurement yet. Today, we’re going to touch on area and lead us into an exploration of area formulas over the next day or so. Jon Orr’s R2D2 Post-It Notes 3 Act Math Challenge is a nice low floor task that works with area of a rectangle and proportional reasoning. Here’s the Act 1 video we show the students:

Can’t see the video? Click here.

Here’s the question we eventually settle on:

Determine how many post-it notes it will take to cover the board?

My students came up with some predictions including:

- Alex – 888
- Jaden – 700
- Olivia – 688
- Cole – 756
- Grace – 900
- Lowwwwza – 950
- Stef – 800
- Vanessa V – 820
- Tristan – 600

After making some predictions, students requested information. Here’s what I gave them:

At this point, I also gave them a math task template to help organize their thoughts and consolidate their learning once we took up the task:

Then, students were off to town.

Here’s a few student exemplars I saw walking around the room:

Now, students can check there answers against what really happened:

Can’t see the video? Click here.

If you don’t think these sorts of tasks can make math fun, these kids are going to prove you wrong:

Student reactions to 3 act of @MrOrr_geek 's R2D2 lesson. Thanks Mr. Orr! pic.twitter.com/3j8tlsbvtP

— J.J. Martinez (@MrMartinezRUSD) April 21, 2015

After showing the solution, students worked on the second page of the template and we consolidated our new knowledge. Notice that I am scaffolding students to start naming the variables as independent/dependent, labelling them on the table and graph, and also adding their own scale to the graph.

We also introduce a simple one-step (proportional) linear equation that students must create and solve for the independent variable. First time we’ve done that this year.

Jon also created a Gameshow related to this task, so here it is:

Note that you can embed this gameshow on your own website/LMS/blog/etc. by simply copying the embed code that Gameshow gives you inside of your teacher account.

Conveniently, this task and all media files are available for download to your iOS device from iTunes U in the Curious Math course. I ran this task straight from my iPad using the files in the course. The benefit is that the files download to your device so you aren’t stuck with any streaming issues if traffic on your network is high.

You can enrol in the course below:

Click on the button below to grab the full task for use in your own classroom:

The post R2D2 Post-Its by @MrOrr_geek appeared first on Tap Into Teen Minds.

]]>This year, I want to be more intentional about my lesson reflections. Here is the first of my WIR's summarizing math, tech, and solutions from the past week

The post Week In Review #1: Welcome to Gr 9 Academic Math appeared first on Tap Into Teen Minds.

]]>I love posting reflections after lessons in my classroom, but often struggle to find the time to do it. This year, I’m going to try to give a short summary of what we were up to during the previous week. It might not be super detailed, but I hope it has enough meat to outline what we are up to in Grade 9 Academic Math at Tecumseh Vista Academy.

While I typically have quite a bit of iPad use in my math class, the new MDM software our district is using provided some issues with getting our apps installed for the first week. We can access the web, but that is about it for now.

So here we go…

Regardless of how hard I try when planning the first day of school, I always find it flies by way too fast. Since I only teach one class and it is the first one of the day, it seems like interruptions are at a maximum. The past few years I’ve done a pretty good job at really cutting back on my “course information” rant so we can get to some fun and collaborative math.

This year, I thought I’d give the Stacking Cups task shared by Dan Meyer way back in 2008 (but since shared by many others including Andrew Stadel, Jon Orr, Fawn Nguyen, and many others). Although I had heard about the task, I had never really looked into it too closely. I’m glad I did as it was a really great way to get the kids excited on the first day.

I asked students how many cups it would take to reach my height. I asked them to jot down their best prediction. After about 20 seconds, a hand went up and the question was “how are you stacking them?” To start with a low floor, I said we would be stacking them “bottom-to-bottom” and “top-to-top”.

With that clarified, students made their predictions, we recorded some of them on the board, and then students began asking for more information. After different requests, I decided to give them my height and the height of 3 cups stacked:

Students immediately went to work and all students came back with approximately 21 cups. We tested their work and although it was difficult to do without taping the cups together, the result looked really good!

When I glanced at the clock, we were down to less than 5 minutes left in class. So I challenged them to go home that evening and determine how many cups it would take if each cup was stacked inside the next. Here’s the information I gave them to work with:

A few students looked concerned, but I reassured them that this was for me to better understand where we are at and where we should go next in the course. I was excited to see what they came up with.

On the second day, we had the grade level assembly where administration goes over some of the school procedures with students. This took up more than half of the class.

Once we were back, I was curious to see what students came up with for the Stacking Cups task from the previous day. I asked them to take out their solutions, consider improving their communication, and then compare and contrast with neighbours. If you and a neighbour agree, discuss your strategies. Is there an easier way? If you disagree, determine where in your strategy that you went your separate ways.

What I was hoping to achieve by doing this was having students intuitively use the slope formula to determine the rate of change of this linear relationship. By giving the height of 3 cups stacked and 8 cups stacked, I have given them two points. Interestingly enough, most students did use the slope formula without knowing it.

This student does a great job of intuitively using the slope formula by subtracting the heights of two stacks of cups (y2 – y1) and subtracting the number of cups (x2 – x1) and then dividing those results to get the height of the “rim” of the cup:

This next student did something similar to the previous, but originally made the error of dividing the height of the teacher by the height of the “lid” without accounting for the height of the base of the first cup:

After crowd-sourcing solutions, we settled on 137 cups stacked to reach my height.

They came pretty close…

The assembly on Wednesday didn’t leave enough time for me to get into creating an equation to help make life a little easier. So once students arrived, I posed the following question to them:

Yesterday, you folks did a great job determining how many cups it would take to reach my height. Today, I’d like you to determine how many it would take to get to the ceiling. However, I want you to devise a way that will let you “cheat” to get to the answer without doing all kinds of work. GO!

Students were discussing what I meant by cheat and eventually, we discussed as a class that I was looking for an equation.

This student was onto something:

This student used the table of values to find the rate of change/slope and then basically created an equations using words to determine how many cups:

And then, there was also this student who went straight for a linear equation and did a fantastic job of solving it algebraically:

We had a great discussion to consolidate the different strategies used and why an equation was so valuable to us.

We then introduced the Baby Beats 3 Act Math Task that begins with the following video:

After asking students to share out what questions come to mind, I guide them to the most obvious question:

Does this baby have a healthy heart rate?

After act 2 is shown, students now know that the baby’s heart beat 18 times in 7.12 seconds. Then, they’re off to work!

It appears that this first student determined how many groups of 7 seconds there are in 60 seconds. Since there is 18 beats for every 7 seconds, he can then multiply the number of 7 second groups by 18:

Another student goes the unit rate approach by determining how many beats per second we should expect:

After consolidating this task, students were given a math task template to extend their thinking to a table, graph and some learning goals related to correlation.

Today, we spent some time taking up the Baby Beats math task template that was given near the end of class yesterday. Because I have been really trying to spiral content over the past 8 months or so, I often include some concepts that students have not been explicitly taught. My intention here is to use this approach as a sort of diagnostic, without the negatives associated with a formal diagnostic “test”. Because academic students are usually very hard workers and grade conscious, I know it will take some time for them to become comfortable with the process. When you are not used to struggling or failing at anything in the classroom, it can make one very uncomfortable.

After we spent some good time discussing the math task template, I had students create their Knowledgehook accounts that we will be using on a regular basis to take advantage of their Gameshow and Homework features. Students in my grade 9 applied course last year really enjoyed this tool last year, so I’m interested to see how my academic students feel.

Once students were in and I had a chance to explain what a “Gameshow” was, I ran the Baby Beats Custom Gameshow that include extension questions I had created for them.

By using the Embed Tool, I am able to allow you to check out and participate in the very same Gameshow. Feel free to check it out below:

Something to note is that currently, Gameshows that are embedded in websites do not have the “Upload Solution” feature active. This is my favourite part about Gameshow. Students can upload a photo or screenshot of their work and we can share them out over the projector to consolidate each question. I can also access these solutions afterwards to make this formative assessment tool more than just multiple choice. Good stuff!

We spent some good time on different solutions such as these:

The Knowledgehook “Share Your Solution” feature allowed us to consolidate the concept of solving proportions without me doing a lesson with explicit instructions and steps for this learning goal over the data projector. Great!

With approximately 15 minutes remaining, I decided to wait on the Candle Burning 3 Act Math Task until Monday and opted to give students a bit more practice with equivalent fractions, proportions, graphing, and correlation with this math task template.

That’s it for this week! Looking forward to sharing with you again next week!

The post Week In Review #1: Welcome to Gr 9 Academic Math appeared first on Tap Into Teen Minds.

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