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This is a book that I want to read next based on what I've read on various math teachers' blogs. This book includes information about how to encourage students to become stronger, and more independent problem solvers.

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Dylan Kane is a high school math teacher in Colorado, and his blog has a nice compilation of number talks and number talks resources for high school students. Number talks are a 15 minute warm up where students engage in a problem using mental math. The goal of number talks are to promote number sense in students and encourage mathematical discourse. Number talks are more commonly implemented at the elementary level, but research also shows that it is they should be used at the high school level too.

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I first started doing number talks (also called math talks) to start class when I taught 8th grade. If you're unfamiliar with number talks, this site by Fawn Nguyen has some great stuff to get started. My first year teaching high school (Algebra II, Precalculus, and Calculus) I stopped, opting for Visual Patterns, Open Middle, Which One Doesn't Belong?, and a few other rotating warm-up routines. I thought that the skills involved in number talks, while useful for middle school students, were less relevant for upper high school.

I came back to number talks at the start of this school year, and I've been happy with the results. When I wrote a problem up on the board one day toward the end of the year, a student blurted out, "oh, I love these". That's just one student, but engagement was usually high. Efficient strategies for these problems often did not come easily to students, which suggests that there's potential for learning from them. More importantly, as they became comfortable with the routine, many students who were rarely willing to share started to speak up and take more risks.

Here's a selection of my favorite problems, many courtesy of Fawn's site.

Picking two numbers and an operation is often insufficient for a great number talk; I've found that careful selection of the numbers involved to ensure a variety of strategies is worth the effort every time.

I have one lingering question for next year. Engagement during number talks seems high, and seems to engage both high-performing and low-performing students. There is clearly a need for the skills that number talks are targeting. At the same time, I don't have any real evidence that students are learning these mental math skills. I think they are, but that's based on my intuition and a few anecdotes. One challenge is that I tend to cycle through a variety of types of number talk problems that require different strategies. One goal for next year is to reorder the number talks I use so that I expose students to one type of problem 2 or 3 times, lead a discussion that attempts to consolidate understanding of relevant strategies and when they may be useful in the future, and then revisit that problem a few weeks later. Hopefully this sequencing will provide more robust evidence as to whether or not students are actually learning.

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I first started doing number talks (also called math talks) to start class when I taught 8th grade. If you're unfamiliar with number talks, this site by Fawn Nguyen has some great stuff to get started. My first year teaching high school (Algebra II, Precalculus, and Calculus) I stopped, opting for Visual Patterns, Open Middle,...

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Per the title of the website, this resource provides visual patterns that represent linear, quadratic, exponential, etc. sequences. Students are encouraged to draw the next term, then come up with the 43rd term in the pattern, as well as a formula that you could use to find any term.

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Welcome! Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It's an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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This website provides pre made slideshows that are slow reveal graphs. The first slide shows a graph with no context given (no titles or axes scales). The idea is that students should be making observations as they go. The slides allow students to only focus on one aspect of the graph at a time, which makes analysis a little easier. Plus, they have many graphs related to social justice issues!

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Slow Reveal Graph is an instructional routine that promotes sensemaking about data. This highly engaging routine uses scaffolded visuals and discourse to help students (in K-12 and beyond) make sense of data. As more and more of the graph is revealed, students refine their interpretation and construct meaning, often in surprising ways.

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Sarah Carter is a high school math teacher in Oklahoma and her blog, Math = Love, has great free resources for teachers to use. She is incredibly creative and has resources for almost any high school math topic.

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I'm Sarah Carter, a high school math teacher who passionately believes math equals love. Through this blog, I'm on a mission to equip other teachers to create inviting and engaging classrooms where learning mathematics is fun.

I currently teach AP Calculus AB, Pre-Calculus, and Statistics at Coweta High School in Coweta, OK. Over my eleven-year teaching career, I have taught both math and science at the secondary level. If you want to know more about my career in education, check out my About Me page.

THANKSGIVING MATH ACTIVITIES

MOST POPULAR ACTIVITIES

MOST RECENT BLOG POSTS

If you're looking for a traditional blog reading experience, I recommend checking out my BLOG page. You can find it by following the previous link or by clicking on the Blog Tab at the top of the page. This page will list all of my blog posts (over 1300 of them!) in chronological order with the most recent blog post first.

This blog started as a way for me to make sense of my student teaching experiences in the middle school and high school math classroom. It's evolved over the past decade to become a way to share free resources for engaging and fun math activities with teachers around the world.

Looking for resources for a specific math teaching topic? I recommend navigating the blog using the tabs at the top of the page or by using the search box. You can easily find and read all of my posts about polynomials, puzzles, or posters this way.

FREE PRINTABLE MATH RESOURCES

PRINTABLE MATH PUZZLES

I am a passionate proponent of incorporating puzzles into the mathematics classroom. Over the past five years, I have compiled a collection of hundreds of free printable puzzles that have been used in math classrooms around the world with students ranging from elementary school to high school as well as adults! You can find out more about how to access these free puzzles on my puzzles page!

FREE PRINTABLE MATH POSTERS AND CLASSROOM DECORATIONS

My high school math classroom is my happy place, and I love decorating it to display my love of math to my students. I have created many math posters over the years that I am sharing here on my blog. I recommend checking out my entire math poster collection - ten years' worth of math posters!

FUN AND CREATIVE MATH PRACTICE ACTIVITIES

I love creating fun, interactive, and hands-on activities. Be sure to check out some of these activities while you are here!

GAMES

Looking to infuse some fun into your math classroom? Check out these free printable games! You and your students are sure to have a ton of fun!

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I'm Sarah Carter, a high school math teacher who passionately believes math equals love. Through this blog, I'm on a mission to equip other teachers to create

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This is the textbook that I started reading this summer with a few of my colleagues. We are continuing our study of this book in my PLC this year. The book focuses on how to promote critical thinking and collaboration among students. The author emphasizes the importance of moving away from routine note taking and lecture and instead focusing on meaningful, challenging problem solving.

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Open middle is a site with lots of open ended math problems. I like it because it gets students away from doing the same old rote practice from textbooks over and over again. The problems also can help gauge whether or not a student has a conceptual understanding of the material or not.

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Fawn Nguyen is a math teacher with great resources and blog posts. I recently discovered this post on teaching absolute value and will definitely use this when I teach this topic in my algebra class next week. I also really like her Noah's Ark problem.

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I know Common Core does not have absolute value in grade 8, but I'm teaching it anyway because we're still doing "algebra 1" this year. (A year ago Raymond Johnson looked into the inclusion of this topic in the different grade levels.)My 8th graders know that the absolute value of 5 is 5, and the absolute value of -5 is also 5. Some recall that it's the distance from 0 on the number line.We begin by solving a few of these: abs(x) = 4, abs(a) = 0, abs(w) = -3. A few trip up on the last one but recover quickly and move along.

Me: What is the distance between these two points? Class: Eight.M: How did you get eight?C: Subtract.M: What about this one? The points are at -3 and 9. C: The distance is twelve.M: This one? C: Thirty-two.M: Good. Distance is always positive... How did you find the distance between the points again? What operation did you use?C: Subtraction!M: Then I'm going to add an equation below each number line showing subtraction. Is that okay? M: So, the distance between 5 and 13 is 8. Then, what is the distance between 13 and 5?C: EightM: Woah! It's the same? Meaning I can write the equation either way?

Kids agree that subtraction can be commutative when it's inside the absolute value bars because we're just measuring distance. The distance from Johnny to Julie is the same distance as from Julie to Johnny. I'm not going to argue.

Me: Given two points, you can tell me the distance between them. So now I'm going to give you just one of the two points but tell you the distance between them, and you find the missing point x. C: x is ten.M: Yea, ten works. Let's try to read this open sentence. How would you say it?C: x minus six... The absolute value of x minus six is four.M: Hmmm. Oh, you say the words 'absolute value' because they're there. Let's try again without saying those words. Use the word 'distance' instead.C: The distance of x minus six equals four.M: Let me show you again the first one that I'd asked you. I remember just asking you, 'What is the distance between 5 and 13?' What did I not say even though it's there? C: Minus.M: Right. Let's not add stuff we don't need. You know naturally that finding distance implies subtraction. So, say the equation again.C: The distance between x and six is four.M: Or you could say...? Can we switch the points around?C: The distance between six and some point x is four.M: Alright. Is 10 the only answer for x? We are trying to find a point on the line that makes the equation true. So, let's use the number line to solve this. Because we know 6 is one of the points, let's locate it. We need to find the other point that would be a distance of 4 away from 6. So, it could be to the right of 6, or to the left of 6. Where does this put us at? M: Oh, why isn't the point -6? I see a 'minus six' in the equation.C: Remember, that minus is for subtracting. We need it there to find distance.M: I remember. We need it.

We do a few more of these. Enough to bore us, need something new.

M: Let's try this. C: No subtraction sign.M: And you said we needed it. Then create it. Make it happen without changing the problem of course.C: Change it to minus minus... M: What does this problem say now?C: The distance between x and negative eight equals five. We do a few more of these. Enough to bore us, need something new again.M: What about this? M: Nothing terribly exciting. The other point(s) that we find is now worth 2x, so we just need to solve for x.

Then we do a batch of these:

Hey, what about these, where there's more stuff stuck around the absolute value quantity. Oh, we just need to first isolate the absolute value, then it's business as usual.

We spend the next whole class using Desmos to explore the shifts/changes to the parent absolute value function. Students need to write down their predictions first before graphing. One student was very excited when she got the V-shape to turn upside down. We discuss some real-life scenarios that may involve absolute values: margins of error, ranges of measurements: distances, scores, speed, temperatures, pH levels, elevations, etc.Not proud to admit that I spent a lot of hours in college playing pool instead of studying, but never once did I associate the path of the ball as an absolute value function. Consider me odd if I always thought of angles instead. Solving absolute value inequalities start similarly enough. Kids know from graphing inequalities that there's "shading" involved. They also know the difference between open and closed points. So I just have the kids use their thumb and forefinger to indicate the distance between the two points, then if the inequality says less than [or equal to], then it's natural to pinch their fingers closer together, indicating that the region inside the points need to be shaded. The textbook will tell kids to set up the "two cases" to solve these inequalities (same thing with equations). Then, kids are asked to graph the solution. But if kids learned to solve using the number line itself, then there would be nothing to memorize because they learned distance way back when they started learning to crawl. And since the graphshows the solution, then writing what that solution is is easy because it matches the graph. Like below, x lives on the green line between -8 and -2, being ≥ -8 and ≤ -2. For greater than inequalities, the student would naturally spread his fingers apart to indicate shading outside of the points. I don't know why there seems to be a lot of rules when learning to solve absolute value equations - which inequality sign for when it's and or when it's or. Oy.

Me: What is the distance between these two points? Class: Eight.M: How did you get eight?C: Subtract.M: What about this one? The points are at -3 and 9. C: The distance is twelve.M: This one? C: Thirty-two.M: Good. Distance is always positive... How did you find the distance between the points again? What operation did you use?C: Subtraction!M: Then I'm going to add an equation below each number line showing subtraction. Is that okay? M: So, the distance between 5 and 13 is 8. Then, what is the distance between 13 and 5?C: EightM: Woah! It's the same? Meaning I can write the equation either way?

Me: Given two points, you can tell me the distance between them. So now I'm going to give you just one of the two points but tell you the distance between them, and you find the missing point x. C: x is ten.M: Yea, ten works. Let's try to read this open sentence. How would you say it?C: x minus six... The absolute value of x minus six is four.M: Hmmm. Oh, you say the words 'absolute value' because they're there. Let's try again without saying those words. Use the word 'distance' instead.C: The distance of x minus six equals four.M: Let me show you again the first one that I'd asked you. I remember just asking you, 'What is the distance between 5 and 13?' What did I not say even though it's there? C: Minus.M: Right. Let's not add stuff we don't need. You know naturally that finding distance implies subtraction. So, say the equation again.C: The distance between x and six is four.M: Or you could say...? Can we switch the points around?C: The distance between six and some point x is four.M: Alright. Is 10 the only answer for x? We are trying to find a point on the line that makes the equation true. So, let's use the number line to solve this. Because we know 6 is one of the points, let's locate it. We need to find the other point that would be a distance of 4 away from 6. So, it could be to the right of 6, or to the left of 6. Where does this put us at? M: Oh, why isn't the point -6? I see a 'minus six' in the equation.C: Remember, that minus is for subtracting. We need it there to find distance.M: I remember. We need it.

M: Let's try this. C: No subtraction sign.M: And you said we needed it. Then create it. Make it happen without changing the problem of course.C: Change it to minus minus... M: What does this problem say now?C: The distance between x and negative eight equals five. We do a few more of these. Enough to bore us, need something new again.M: What about this? M: Nothing terribly exciting. The other point(s) that we find is now worth 2x, so we just need to solve for x.

Then we do a batch of these:

Hey, what about these, where there's more stuff stuck around the absolute value quantity. Oh, we just need to first isolate the absolute value, then it's business as usual.

We spend the next whole class using Desmos to explore the shifts/changes to the parent absolute value function. Students need to write down their predictions first before graphing. One student was very excited when she got the V-shape to turn upside down. We discuss some real-life scenarios that may involve absolute values: margins of error, ranges of measurements: distances, scores, speed, temperatures, pH levels, elevations, etc.Not proud to admit that I spent a lot of hours in college playing pool instead of studying, but never once did I associate the path of the ball as an absolute value function. Consider me odd if I always thought of angles instead. Solving absolute value inequalities start similarly enough. Kids know from graphing inequalities that there's "shading" involved. They also know the difference between open and closed points. So I just have the kids use their thumb and forefinger to indicate the distance between the two points, then if the inequality says less than [or equal to], then it's natural to pinch their fingers closer together, indicating that the region inside the points need to be shaded. The textbook will tell kids to set up the "two cases" to solve these inequalities (same thing with equations). Then, kids are asked to graph the solution. But if kids learned to solve using the number line itself, then there would be nothing to memorize because they learned distance way back when they started learning to crawl. And since the graphshows the solution, then writing what that solution is is easy because it matches the graph. Like below, x lives on the green line between -8 and -2, being ≥ -8 and ≤ -2. For greater than inequalities, the student would naturally spread his fingers apart to indicate shading outside of the points. I don't know why there seems to be a lot of rules when learning to solve absolute value equations - which inequality sign for when it's and or when it's or. Oy.

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I know Common Core does not have absolute value in grade 8, but I'm teaching it anyway because we're still doing "algebra 1" this year.

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This website is a wonderful resource for warm up questions. Each prompt consists of 4 images/numbers/etc. and students have to pick which one doesn't belong and JUSTIFY their answer. The cool part is that students could argue that any of the 4 don't belong.

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Which One Doesn't Belong?

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

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This website provides would you rather questions that require students to justify their answer using math! Students, for the most part, will also be intrigued by these prompts and want to answer them!

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Would You Rather Math – ASKING STUDENTS TO CHOOSE A PATH AND JUSTIFY IT WITH MATH

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Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don’t go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

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Sara VanDerWerf is a former MPLS high school teacher. She has an abundance of resources to help students shift their thinking about what math is and what mathematicians actually do. I use her 100 activity and her name tent activity at the beginning of each school year!

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Sara VanDerWerf - Inspiration and resources for mathematics teachers

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Sara VanDerWerf - Inspiration and resources for mathematics teachers

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Inspiration and resources for mathematics teachers