Desmos Puppy House

We don’t cover quadratic in Math 8 this year, so we really can’t do Des-man. I come up with “Puppy House” instead so my students can still create something that allows them lots of practice with writing linear equations with domain and range restrictions.

They draft the house on paper. The house needs to have a minimum of 6 slanted lines, 5 vertical lines, 5 horizontal lines, and one image of a puppy at entrance of house.




Below are the ones from my Math 8 Honors kids who learned quadratic last year. They completed these within one 55-minute period. So proud of Ashlynn for remembering how to write inequalities.




I’d love to see what amazing dog houses your students will create. (Someone create a flap door for me to play peek-a-boo with the puppy please!)

Posted in Algebra, Math 8 | Tagged , , , , , , | Leave a comment

Students Practice Scoring Short-Text SBAC Responses

A few weeks ago I attended an all-staff PD at the County Office. During the morning session we scored samples of 2-point short-text items from grades 4, 8, and high school. It was time well spent.

I wanted to duplicate that experience for my students with two goals in mind:

  1. See how well they can interpret and use a scoring rubric.
  2. For them to attend to the same thoroughness and precision in their own solution writing when it’s their turn in May.

What I had my students do:

1.  Get to know the short-text item.

They worked on the grade 4 item below. This was intentional to diminish any math anxiety and to keep our focus on the scoring of the task.

While it was good to learn of my kids’ different solutions, it was also disheartening — but not too surprising as they are the same ones who struggle mightily — to learn that 20% of my 6th graders did not get the correct solution for this grade 4 item.


2.  Go over the solution.

I collected their papers and just had a couple of kids share their strategies to the whole class. Considering 1 out of 5 kids in the room didn’t quite know how to solve the problem, this step was really for them.

3.  Get to know the item-specific rubric.

I gave the kids quiet time to read the rubric, reminding them that they would use this rubric to score 9 students’ solution responses. I told them that they could expect to return to the rubric over and over again as they scored each response.

4.  Score the responses.

I gave them quiet time to fill out Score 1 column of this handoutI reminded them that this was one of the main goals of the task — to score the sample responses fairly and accurately using the item-specific rubric.


Why are you giving this response a 1? What is it missing to not get a 2? What does it have to earn a 1 and not a 0? Keep referring to the rubric! Does spelling matter? What does your rubric say about spelling errors?

After everyone was done filling in Score 1 column, I asked them to talk to their neighbor/s and only fill in Score 2 column if they changed their mind. (They were not to erase any score in Score 1 column.) This also made it easy for me to see how many scores they’d changed their mind on.

My favorite thing in the whole wide world is to listen in on their conversations about math.

5.  Reveal the actual scores.

[The actual scores are on 2nd page of handout above.]

If the whole class agreed with the actual score for a particular student response, then we moved on. But if anyone disagreed, then I had that student tell the class why. Then I had another student who agreed with the answer to share his/her reason.

Out of 66 students, 24 students scored 9 of 9 correctly, 19 students scored 8 of 9 correctly, and 6 students scored 7 of 9 correctly.

That meant 65% of my 6th graders did this scoring-using-a-rubric better than I did. Whatever.

I also asked the kids to write a couple of sentences about what they got out of doing this. Most of their responses echoed these:

This was helpful to me because now I know I need to be much more thorough with my work and explain why I might of did something.

This was helpful to do because it let us see how these problems are graded. Even though the problem was for 4th grade, I think the grading scale of conclusion and math will be similar or the same for all problems like this.

I believe this was helpful because when I take the test, I will be more aware of the questions and what is expected of me. I will make sure to always back up my answers with evidence.

Posted in Teaching | Tagged , , , , | 6 Responses

Grade 6 Rocks Visual Patterns

I’m always happy to hear how teachers use with their students.

Michael Fenton shares how he uses the patterns with Desmos. And this.

Alex Overwijk’s students use the big whiteboards.


Bridget Dunbar removes some figures, and kids need to draw them in.


Kristin uses the patterns with 5th graders.


I do patterns with my students on Mondays as part of our warm-up routine. I’ve already shared 28 pattern talks (and 28 number talks) on, but I’d like to share a couple more here because my 6th graders have made incredible gains in seeing a pattern in different ways and in articulating an equation to go with each visual.

This is pattern #153. I’m sharing this one because I meant to only use it with my 8th graders, but my printer was acting up and failed to print a different one for my 6th graders, so I just used the same one. Fun challenge!


Student 1:

I see these 5 spokes coming out. Each one has n number of hexagons. In between these 5 are Gauss. So, the equation is… five times n, plus five Gausses.

153 marked

 Hexagons = 5n + 5(1+n)(n/2)

 Over time, my students have come to recognize Gauss addition very quickly. They have used Gauss as a verb and a noun, as in, I Gaussed it or I saw two Gausses in the pattern.

Student 2

Each step adds another ring of hexagons on the outside. Looking at the outer most ring, I see three groups of (n+2), plus a leftover. The leftovers are odd numbers. So, the outer ring alone is 3(n+2) + 2n-1.

153 marked 2

And the rings add like Gauss!

Together we write the equation carefully, talking through each step.

Gauss means adding the first and last steps together, then multiply by the pairs of steps. The last step is the outer ring, the first step is the inner ring, which is always 10. So, 10 plus the outer ring, then multiply this by the number of pairs [of rings], which n/2.

Hexagons = [10+3(n+2) + 2n-1](n/2)

We were confident we had the correct answer when both equations simplified to the same equation.

Hexagons = [(5n^2)+15n]/2


This is pattern #147. I’m sharing this one because of the many different ways kids tried to see the pattern. Normally, when I randomly call on a kid to share and someone had already shared their same way of seeing, then they just have to come up with a different way.


147 marked

Ducks = (n^2) + (2n+1) + n

147 marked 2

Ducks = (n+1) + (3+2n+1)(n/2)

147 marked 3

Ducks = n(n+2) + (n+1)

147 marked 4

Ducks = 2(1+n)(n/2) + (n+1) + n

147 marked 5

Ducks = (n+1)(n+2) – 1

147 marked 6

Ducks = (n+1)^2 + n

I very intentionally do not have kids fill in a table of values for visual patterns. I’m afraid it becomes a starting point for them every time instead of just looking at the pattern itself. For our 8th graders using the CPM curriculum, which I like a lot, there are plenty of opportunities in the textbook to tie all the different representations (table, graph, rule, sketch). These are my 6th graders who are writing quadratic equations without all the fuss right now.

Please continue to share the site. What I love most is learning that the patterns also get used in elementary and high school classrooms.

Posted in Algebra, Course 1 (6th Grade Math), Math 8 | Tagged , , , | 8 Responses

Reversing the Question

Don Steward posted this on Sunday. Like Don, I really like this task and also think it has a certain Malcolm Swan je ne sais quoi about it.

I showed only the top part to my 6th graders, and I gave them 2 minutes to write down what they notice.

In addition to noticing the given information, the students also mentioned:

It takes a lot of grams to make a sponge cake.

A kilogram must have a lot of grams in it.

The unit of measurement is changed in the cake and in the big bag.

This problem doesn’t have a question.

The sponge cake has no price.

There is frosting on the cake.

You need to change the measurements first (kg – g)

The cake weighs more.

The cake is really small and the flour is really big.

Not much information and there’s no question.

There is no question. The weight of the bag is in kg but the flour it takes for the cake is in g.

You have to convert 24 kg to grams.

It uses only very little of the flour.

I gave them another 2 minutes to write down what they wonder.

How much the sponge cake costs.

How many sponge cakes can you make.

How big is the sponge cake.

How to convert from kg to g.

If the sponge cake is good.

24 kg is <, =, or > 150 g.

What we are going to have to solve.

Is the question going to be about if there’s enough flour or is it going to make us change it from kg to g.

How much 24 kilograms is in pounds.

How many grams are in a kilogram?

How many krumkakes can you make with the bag of flour.

How long will it take for the cake to be ready.

What a sponge cake is and what the recipe is for the cake.

How much flour is left.

What flavor is the cake. (Sorry. I’m hungry!)

What you’re wondering that I’m wondering about.

What the question is, and if there are more ingredients.

If we will have to find the price for the sponge cake, or maybe we have to find out how much half as much flour is worth.

Then we moved on to next part of providing questions that would go with the calculations. This was so very tough for my kids. While 21 of 31 kids could come up with the correct question for part (a), they were lost with what to write for the other three parts.

reverse the question 2

Because we didn’t care what the numerical answers were, the kids didn’t do any calculations, instead they were supposed to focus on the operation(s) in each problem and decide on the question that would prompt a specific operation.

The most common question for part (b) was, “How much does 1 kg of flour cost?” (I’d swapped out £ for $.)

Then my next step would be for them to go ahead and use a calculator to get the numerical answers. They will see that for part (b), 24 divided by 21.50 equals approximately 1.12. And if 1.12 were the cost for 1 kg of flour, then 24 kg of flour should cost more than $24. But, wait. We already know that the bag of flour costs $21.50. Hopefully they’ll arrive at this contradiction on their own, and re-think their question.

We’ll then attach the units to the numbers accordingly and let the conversations continue. When kids tell me that they will calculate two numbers using operation w, I always follow up with, What does your answer mean? What unit or units does it carry?

Too often kids have trouble with word problems. Too often they don’t know what to do with two numbers let alone a bunch of numbers. They guess at division when one number is big and one is small. They add when they see two fractions. They multiply because that was how they solved the last word problem.

I will also do this with my 8th graders because I suspect they will have trouble too. And this is exactly the kind of trouble we need to get into. Now rather than later. This task gets them thinking about ratios — which is like the most important math thing in all of the math things.

Steward is exactly right about this task. And I’m thankful he shared.

It was used as a fine example of how reversing the question can often lead to a more challenging task.

Posted in Course 1 (6th Grade Math), Math 8 | Tagged , , , , , , | 5 Responses

New Marking Strategy

When grading a 10-point assignment, I have a hard time deciding if the work shown is worth 4, 5, 6, or 7 points. If I like the kid, then I’m giving her a 9. If I’m hungry, then the kids gets a 4. If the kid’s mother gave me a $25 Starbucks gift card, then the kid gets an 8 with a drawn smiley face.

What I end up doing is giving every less-than-complete paper a 1 — yes, ONE — and so far this marking strategy seems to be working.

I want kids to revise their work until it’s flushed with coherent mathematics. A score of only 1 at the top of their paper — along with my comments — motivates them pisses them off so they go back and revise their work. If they need help with the revision, they know where to find me. If the revised work is still not up to par, then the score stays as a 1, and the kid gets to revise it again until the zombies come home. Or when the grading period ends. And while I haven’t kept track of any hard data, nor will this ever be FDA approved, I’m willing to bet that the revision rate has at least doubled.

Grading papers sucks. But grading with a 1 or 10 has alleviated much of the stress. Like I found a cure for my crazies.

Posted in Teaching | Tagged , , | 11 Responses


Our black lab Mandy is 3.5 years old, weighs a ton, and her breath used to smell like death. Until we started giving her one Greenies a day. My husband orders them from Amazon, he also gets them for our neighbor’s small dog Bailey.


Although both boxes weigh the same 36 ounces, Bailey gets 130 treats in the Teenie size and Mandy gets only 24 in the Large size. This caught my attention which led to this task with my 8th graders who happen to be working with similar shapes. (Like I had planned this all along.)

Greenies are sold in various size packages. I’m interested in the 27-oz and 36-oz.

To launch the task, I hold up the 2 treats: 1 Large and 1 Teenie. I tell them that there are 24 Large ones in a 36-oz package, and I want them I guess how many Teenie ones are in a 36-oz package.

both treats

Then I give the students these:

  • The photo of the 2 packages (so they know only the highlighted information in the table above).
  • Each group of 3 students get two real treats: 1 Large and 1 Teenie.

In return, the students need to give me these:

  • A 2-dimensional outline (with dimensions labeled) of what a Petite, a Regular, and a Jumbo may look like. For example, these are the actual outlines of the Large and Teenie. They may write down the thickness also.

  • A completed table with the missing counts filled in.

counts chart blank

Highlights of this task:

  1. Kids use some known information to construct new information. They use modeling to figure out what the other sizes may look like and how many of them would fit in a 27-oz or 36-oz package.
  2. It’s kinda messy and weird. While the kids can measure whatever lengths of a treat, how do these numbers translate into the mass of each treat?
  3. It’s good to work with solid objects instead of just flat polygons when learning similar shapes.
  4. The reveal (Act 3) of something like this is always a lot of fun. Not only the reveal in the count per package, but also how close their outline sketches are to the actual treats when I bring in the Petite, Regular, and Jumbo.
  5. How much does a 36-oz package cost?
  6. Is the Jumbo a shot in the dark? Would kids think to ask me for the size of the dogs? How does this help, if at all?

weights of dogs


kids working 2 Greenies kids working Greenies

Posted in Math 8 | Tagged , , , , , , , , | 5 Responses

Rigid Transformations

My 8th graders are learning about rigid transformations. I want to add a bit more complexity to what our book is asking the kids to do. For example, the book is having them reflect a shape mainly across the x-axis or y-axis, or on a rare occasion, reflect it across “the horizontal line that goes through y = 3.” Well, right before this chapter, we’ve been working with writing and graphing linear equations, so I want kids to reflect a shape across any line, including one that may cut through the shape itself.


The book surprisingly has very few examples and exercises with rotations. And from what I can find, all these rotations happen about the origin or about a point coinciding with one of the vertices of the shape. Again, I want kids to be able to rotate a shape about any point, including one that’s inside the shape. (I used a playing card — number 7 works well because it’s asymmetrical — poked my pencil through it as the center of rotation, and turned the card. I think this helps them see what I keep referring to as the pivot or anchor point.)


Then I give each student this task:

  • Draw a shape that has between 5 to 8 sides with no curved edges.
  • Transform your shape through at least 3 rigid transformations of rotation, translation, and reflection — in any order.
  • On grid paper, give your teacher your complete work on this, including the written directions for the transformations.


  • On grid paper, give your teacher only the original shape and the written instructions. Your teacher will give this paper to a random classmate to follow your written directions to arrive at the intended location of the final image.


For students who want more challenge, they may ask for a copy that has just the original shape and its final image without the written directions. The task will then be to figure the appropriate transformations that connect the two images.


I really believe that it’s good practice to always give kids more than what we believe they can handle. Let kids tell us when it’s too much for them — and we find out soon enough. An ounce of struggle on something hard is worth a pound of completion on something easy.

(And I’m hoping to update this post with pictures of kids’ work when they turn them in on Friday.)

Posted in Geometry, Math 8 | Tagged , , , , , , | 7 Responses

Let’s Not

I knew I was in trouble when the principal needed to talk with me regarding a parent complaint. The parent said I used the word crap in class often. The parent also said that I told students to memorize PEMDAS as Please Excuse My Dumb Ass Sister.

I admitted to my principal that I said crap enough times. And the PEMDAS thing… Well, it was really a ha-ha joke that my high school students from the previous year taught me, and I never actually wrote out the word Ass, I just wrote down A__, so technically my clever middle schoolers deciphered that on their own.

The parent found me in my classroom after school shortly after. She brought up the aforementioned, and I apologized. Profusely. I was genuinely sorry that she found the word crap offensive. I told her that I then realized it was unprofessional and would not utter the word again in class. I promised I would apologize to all my students the next day.

But then she had more to say, Mrs. Nguyen, we’re a Christian family, and we raise our children to be… 

The rest of her words — I don’t recall exactly — were condemning. She could have just punched me in the face. The effect felt the same. I looked over to the other side of my classroom where my own three children — then ages 8, 9, and 12 — were doing their homework. Our eyes met. My kids attended the same school.

I apologized to my students the next day.

Then after school I went to my principal’s office because what the parent had said to me in front of my children continued to anger me. She had projected her Christianity on me in front of my kids as if I were amoral and indecent for saying crap. I told my principal what happened and concluded with — and I remember my words verbatim because I was really upset — “If she ever comes back and speaks to me like that again, I will tell her exactly what I think, and then you’d have to fucking fire me.”


Maybe it was the very ugly custody battle I went through that has made me crazy protective of my three kids and my role as a parent. You don’t get to judge me from a distance. You don’t get to judge me based on what 4-letter words I say. You certainly don’t get to judge me through a religious lens.

I’m pretty much this crazy protective when it comes to my students and my role as a teacher.

We talk about the bad policies crafted by people in thick-carpet land, so let’s not have those policies trickle down into our classroom and adversely affect our students’ learning or their love of learning. Let’s not follow that textbook that we hate — so what if the school had adopted it. Just because we inadvertently bought spoiled food does not mean we should consume it. We talk about spending too much time reviewing for tests, so let’s stop reviewing for the goddamn tests.

Let’s not believe for one second that we don’t have a voice.

Let’s smile and nod and gather up all the handouts in our next meaningless PD, then throw them out when we get back into our classroom and do a Math Munch or 3-Act lesson.

I go batshit crazy when I hear of teachers doing things that they know are not good for their students. Why are we doing it then?

I’m afraid I know the answer to this already: We don’t want to lose our job.

But. But. Did we not get into teaching because we love teaching and our subject matter and most of all we love our students? How can we justify implementing poor pedagogy and delivering contrived content to the young people whom we promised to give our best and be their advocates? Why are we wasting their time?

We — classroom teachers — make a direct impact on our students’ learning. This impact is not unlike that of a parent-child relationship. And for some students, we are the missing guardian in their life. They depend on us to make the right decisions when administrators and policy makers do not. They depend on us to be the voice that they don’t always have. They trust us to work toward fixing a broken system instead of being a part of it. We would do all this and more as a parent. We should do all this and more as a teacher.

I’ve always needed a job, an income. I don’t have the luxury of shooting my mouth off and doing whatever I fancy in the classroom. I shared the opening story because it happened in my first year of teaching at Mesa and I was well aware of my probationary status. But when a parent crosses the line, or when an administrator/mandate goes too far or does too little, I need to speak up. It’s not bravery or arrogance, it’s duty.

Posted in Teaching | 15 Responses

A Tale of Two Gyms

Quick post about a scenario that I was sharing with the kids just to share and how they just took off with it.

A brand spanking new 24-Hour Fitness is opening up near me. It’s a no-brainer to switch over to this facility because I’ll save gas and travel time. However, the 2-year membership [from Costco] will cost nearly twice as much at the new one.

I gave them some information:

  • 8.02 miles one-way to current gym, at mostly highway speed
  • 1.38 miles one-way to new gym, at neighborhood speed
  • Chevron gasoline currently at $3.039/gallon
  • $370/2-year membership at current gym
  • $650/2-year membership at new gym

While it didn’t take much to figure out that the new gym costs just 38 cents more per day, but there were enough variables inherent in this scenario that the kids wanted to take a closer look.

They asked me questions like:

  1. How often do you go to the gym?
  2. How much mileage does your car get?
  3. How fast do you drive — on highway and around town?
  4. How long does it take you?

I lied about going to the gym 7 days a week, gave them my car model, then told them to look up the rest.

But then we wondered about the value of my time driving. How much is my driving time worth? I went on Twitter to ask for help, and Glenn @gwaddellnvhs thought I should divide my weekly salary by the hours of weekly driving that I do. The problem is I live pretty close to school, so this rate becomes too high to apply to this situation. For no good reason, I decided to give the kids our school’s substitute rate of $115/7 hours, or $16.43/hour.

They paired up and went online to gather more information, did a bunch of calculations, and summarized everything on the whiteboard. All in one class period.





We should just do this all year: turn a scenario into a question then into a math task. I could take a nap while they chitchat and do all the work.

Posted in General, Problem Solving | Tagged , , | 1 Response

Four Square and Other Questions

One afternoon during recess I noticed that the Four Square grid at our school had been enlarged. Naturally I yelled out to the kids, “Hey kids, when did they make this larger? I wonder what percent increase this is. What do you think?”


Taking a nanosecond pause from their game, they yelled out their estimates, anywhere from 50% to 95% increase. One kid said, “I love that you’re asking us a math question at recess time.”

I went back out to the playground during my prep with a couple of yardsticks to find the answer to the question I’d posed.

When my 6th graders came into class the next period, I told them what I’d wondered about during recess and wanted each one of them to give me an estimate of this percent increase. We walked back out to the Four Square, and I allowed them five minutes to do whatever they needed to get a good estimate.

4 pics

Once back into the classroom, I asked them to write down their estimate of the percent increase on a small slip of paper.

I then asked, “What exactly was I looking for? Percent increase in what? I really didn’t say and you didn’t ask me to specify either.”

We’ve been working A LOT with perimeter and area of rectangles, so most of them said that they’d thought I’d meant the percent increase in area. So I told them I did mean area but I was intentionally vague just to see if anyone would ask — and Four Square is so much about occupying the inside space.

This question prompted me to ask them more questions about increase in perimeter versus increase in area. I had them draw squares (or rectangles) on grid paper and explore the changes in area when the perimeter is doubled, tripled, or by some x factor. We remind ourselves that area is two-dimensional and why area units are always “squared.”

I asked them how they would figure out the percent increase in area. They told me I needed to measure the length and width of the old Square (black outlines), then do the same for the new one (white outlines).

They also agreed that I could just find the area of 1 square, then multiply this by 4 to get the whole thing. This suggestion prompted me to ask them, “Well, do I need to compare the area of the whole 4-square grid of new to old, or just the area of 1-square of new to old?”

So we just drew some squares to show that comparing the areas of just one square each: large to small is 2.25 to 1.0, this is a percent increase of 125%. And comparing the areas of each entire 4-square grid: large to small is 9 to 4, which also yields a 125% increase.

2 squares

This brief noticing and wondering yielded a fruitful discussion and it was something that was part of their environment, their playground. By the way, the answer is 118% increase in area for the Four Square. The closest written estimate was 115%.

Of course this launched us into a brainstorming session of questions that they have about their surroundings. Stuff that we can apply math to answer the questions.

I reminded them not to worry about answering the question. Just ask it.

Then I couldn’t stop them from sharing. (These 6th graders are away at Outdoor School, so I have to wait for them to return next week for us to try and answer some of these questions. They will also be jotting down more questions that may come up during the week.)

How much time does my brother waste in his room for a year?

How many gallons of water do we use if we take 5-minute showers a day? How much does this cost?

How much power is needed to charge all the devices in the house for a year?

I wonder how many pencil tips I break each year, and if added end-to-end, how long would this be?

What is the average amount of money each teacher at our school spends on supplies in a school year?

How many eggs does a chicken lay in United Kingdom?

How much pollution does the average car put into the air monthly?

How much time do the students in this class spend on YouTube in a month?

How much time do we spend on homework during the school year?

How much money does our school lose when students are absent?

How long does my hair grow in a month?

I always wondered how much bigger is the big basketball hoop compared to the small one.

How many pounds of food do kids waste in the cafeteria in a month?

How much gas does my mom burn while she is driving?

I wonder how much gasoline our 3 school buses use each year.

How many “perimeters” do we do in a year in PE?

How much money does Mrs. Nguyen spend on Oregon Ducks’ games?

And this one breaks my heart.

How long would it take to end poverty?

Posted in Course 1 (6th Grade Math), Geometry | Tagged , , , , , , | 2 Responses