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Take A Picture, It Will Last Longer And Be More Effective For Your Math Lesson

Real-life examples in math are super important, but it takes time to think of examples and to prepare a lesson using your examples. A quick way to make a lesson interesting and tied to a real-life situation is to take a picture then pose a question. This gets students to analyze details of a situation.

In the next few weeks, I will be talking to my Algebra students about arithmetic sequences and direct variation. I have a great blog post titled, “Examples of Real-Life Arithmetic Sequences.” Check it out if you’d like. I love all the pictures in that post, but I thought I’d take a new picture that I could pose a question to see what the students would say. Below is the question and picture. Feel free to use it yourself if you like it. 

(Yep, that’s my dishwasher in the background😂)

I’d give students a little time to think and jot their thoughts down. Next, I’d ask for feedback. Finally, my plan is to let them create a table using height of cups vs. number of cups for each situation. We will create equations and graphs and talk about the similarities and differences. Students will pay more attention to the details and take part in this activity. All the students will need is some grid paper and the picture which I will post on the board and in Canvas for them.

As a side note, I took this picture with my iPhone, then I used a free app called Layout from Instagram to create the collage. I used another free app called Typorama to add the question. Very simple and easy once you’ve done it a couple of times. I save all my photos in Google Photos which is easy to get to via phone or computer. 

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Get Your Math Students Engaged!

How is it going in your classroom? If it seems that your students are not paying attention and just not getting the concepts you are delivering, could it be that you are not engaging them? When school really gets going and you are super busy, it seems like we go into survival mode. The way we survive is lecturing because we really don’t have time to plan and be creative. I’m going to give you some ideas that turn a dull boring lesson into an engaging lesson without much prep.

Here are 5 Easy Ideas:

1) Get the dry erase boards out and dust them off! Kids love to draw on the boards, so give them equations to solve, equations to graph or shapes to draw. Maybe you had a worksheet planned. Don’t do it the traditional way, instead call out the problems and let them work them on the board then raise the board up to show you. You can make corrections and help kids that are struggling. You can have students show their partner and talk about which person may or may not be correct. Dry erase boards are a savior for me. I get them out anytime I feel like I have a boring lesson and it really spruces it up. 
2) Find a related Desmos lesson. Desmos is easy to use and can be something quick to search and find quick lessons or activities for your students. If you are teaching exponential functions soon, I have a good activity from Desmos that I created. I would say to do this with Algebra 2 rather than Algebra 1. It’s called “The Towers“. I love the Tower of Hanoi and I use it in my Exponential Functions Stations. 
3) Another quick way to gain interest in note taking is make the notes colorful or turn it into a graphic organizer. If you have 4 things the students need to know, then create a paper folding graphic where students write on the outside 4 flaps and they open to reveal answers, definitions or a diagram. 
Here’s two examples of using colored pencils or using a foldable:

4) Let the students partner up and go to a spot on the board or use poster paper. Ask them to write everything they know about a topic. I recently did this and the students did not realize how much they actually knew. I kept adding stuff and reminding them of a few things along the way. Before they knew it, they had a ton of concepts on the board. 
5) Turn the lecture into a game. One way is to make it a Bingo Game. Create a list of things you know you will be saying that day and put it on the board. The students will be given a blank bingo card and can write the words randomly into the boxes. As they hear you say the phrase or word, they cross off that box. If they bingo, you will take off a couple of problems on the homework to shorten the assignment. 

If you look up from a lecture and you have kids falling asleep or looking at their phones, you know you’ve got to do something to change the dynamics of the class. Try implementing one or two of these ideas in the next few weeks and let me know how it goes!

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Domain and Range

Why is domain and range so tough for students? I’ve really worked on slowing down and teaching domain and range in detail the past few years. The idea that students are asked to find all the x’s and y’s that belong to a graph or situation is overwhelming. I believe part of the problem is that the concept is abstract. It’s not physically possible to name all the points that exist on a line. Students are not digging deep and realizing what the line or curve is really displaying (or saying). We’ve got to get them to see the details on the graph. Where does it start? Where does it end? What is happening between? I’ve created some online items that have worked well recently, but I have some older resources that I like to use too.

It’s important that students distinguish between finite and infinite values and which type make more sense for the problem. Give students real-life situations and make them think about these situations and what the graphs would look like in detail. A great example of a continuous function is when someone is getting gas out of a gas pump. Here’s a video you can use as an opener. There are tons of questions you could ask students about what is happening.

The concept of a vending machine is a great example of input and output (which would be a finite situation). If you push a certain button, then you get a certain item.

Photo by Erik Mclean on Pexels.com

Last year, I created the lesson below. It is a Google Docs with an embedded Google Drawings. Students can click on a Google Drawings and move pieces around or type. I have found this to be very interactive and useful.

Here’s a sample:

The one on the left is before the student has clicked on the picture.

In the same activity, before I start having student plug into a table, I have them work on a function machine:

Function Machines in Google Drawings

This activity has 3 parts:

  • Relations and Functions
  • Domain and Range
  • Infinite vs. Finite Domain and Range

Below is another useful activity that I think works well for students each year. This lesson introduces reasonable Domain and Range and we practice which variable is independent and which one is dependent. The worksheet seen below is a tiny look at this activity that contains 10 graphs where the students are asked to find the domain and range. There are 5 linear graphs, 3 quadratic graphs, one circle and a graph with only points. Another worksheet asks students to create graphs with a given domain and range.

I love Boom Cards, so I’ve got a couple of Domain and Range activities that are great for extra practice. The problem below is a sample question in this activity. The students do not know what a parabola is at this point, but I still give them all types of functions. We will come back to domain and range again when we get to quadratics and exponentials. If you click on the picture, you will be taken to a 4 page preview of this activity.

Finally an escape challenge is the ultimate fun activity to end Domain and Range. If students can get through this tough challenge, then not only do they understand domain and range as well as reasonable domain and range, but they are good at following directions, reading carefully, figuring out combinations and they have that finishing spirit!

Domain and Range Challenge
Domain and Range Challenge

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Learning Loss in Math

Learning loss is evident this year. I’m sure you have noticed it too. How do you deal with it? We can either complain about it or we can do our best to address it.

When I coached basketball, we practiced fundamentals everyday. The kids could already dribble and shoot layups, but we still practiced these skills to keep them sharp. What would be wrong with doing this same thing in a math classroom? No, don’t bring a basketball into your classroom. All I’m saying is practice those math fundamentals. There will always be learning loss and students will struggle with certain concepts in math. We should plan for it every year! Here are a few ideas on how to deal with it. If you have some other ideas, please let me hear from you.

1) Plan for mini lessons on content that you have a feeling students will struggle with. 
2) Figure out which students are your star students and make them helpers. Let them tutor other students during class time. 
3) Use bell ringers for content students should have learned last year. (I have algebra bell ringers for Geometry students if you are interested.)
4) Add a problem or two to your worksheets with content from the previous year. 
5) Use dry erase boards to have students work problems, then show you quickly if they understand.
6) For fundamental work, do quick timed worksheets. Let’s say students do not know the order of operations. Give them 5 problems each day for a week. Have a set time and do not go beyond that.
7) Announce a tutoring session that covers a basic skill. You could say, “This Tuesday after school, I’m going to focus on one- and two-step equations.” 
8) Use those videos you made last year to reinforce the material this year. You may do an in-person lesson and then post a video so students can watch it if they need it. 
9) Give students flash cards to study. Let’s say some of the students are struggling with operations with integers. Give them some index cards and some problems with solutions. Put the problem on one side and the solution on the other. 
10) Sage and scribe is a great way to get students to work through some problems and see if they know what they are doing. My algebra students are struggling with combining like terms. I could have one person stand (this is the sage) beside the other person’s desk (the scribe) and talk the scribe through simplifying an expression. The scribe can only write and is not allowed to talk at first. This is great since both students are really having to concentrate on what they are doing. The two students switch roles after each problem. 

If I could add a #11, I think I would say to just make learning more fun. Get students excited about your class. Get them more involved. When I feel like I’m being boring, I pull out games. Students want to have fun. Here are a few games that I use in my classroom:

I hope you can take an idea or two and implement in the coming weeks. Let me know what worked and what did not work. This is going to be a tough year on math teachers. Don’t let anyone put too much pressure on you. You can only do so much. Try your best, but remember to take care of yourself. 

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Solving Equations in Algebra

In Algebra, teachers tend to start completely over with solving equations as if the students have never seen equations before. Students have been solving equations for a while at this point. I thought it would be nice to take a look at a few questions from the state assessments in Texas to show what the students should know before coming to Algebra. I am a stickler for understanding what students should already know before they get to me and what they will learn after my class. This helps us to know what and how to teach certain content. My advice to all new math teachers: Do not get stuck in one math subject. Move around above and below where you like to be so that you understand fully what students have learned and will learn. Take a look at the questions below to get an idea of what they are tested on in 6th and 7th grades:

2019 6th Grade Math STAAR Test – By the end of sixth grade, students should be able to set up one-step equations and solve them.
2019 7th Grade Math STAAR Test – By the end of 7th grade, students should be able to solve 2-step equations.

I don’t think there is anything wrong with reviewing the material. If you read my last post about Algebraic Expressions, you learned that I still review this every year. I do think this means that we should not spend too much time covering material that they should already know. The Pandemic has caused some issues with learning gaps, so it’s important that we recognize that we might have to review, refresh and even reteach. Continue to look at the next set of problems to see the progression:

2019 8th Grade Math STAAR Test – By the end of 8th grade, students should be able to solve equations that have variables on both sides of the equal.
2019 Algebra Math STAAR Test
2019 Algebra Math STAAR Test

It’s obvious by the time students finish Algebra, they should be able to solve multi-step equations with variables on both sides that contain the distributive property and might contain decimals or even fractions. It is very important that students understand how to check their answers. If the test is multiple choice, they will be able to get the answer correct by plugging in the answer choices. (I don’t like that, but before the STAAR test I make sure they know all the tricks and tips.)

My progression on teaching students how to solve equations goes like this:

  • Review solving one- and two-step equations. Discuss how an x is really 1x. Discuss inverse operations.
  • Practice checking solutions.
  • Use the distributive property in equations. Show students how to distribute and other alternate methods depending on the look of the problem.
  • Solve problems with variables on both sides. Use combining like terms.
  • Solve more complicated multi-step equations.
  • Solve equations with decimals and fractions. Teach students to clear decimals and fractions. (This is a skill that will come in handy on the college entrance exams.)
  • Solve equations that have no solution or infinite solutions.
  • Setting up and solving equations from word problems.

You may end up spending more time in this area than you planned, but think about how much it will help the students in other areas. If they have a good foundation of solving equations with one variable, then solving inequalities, literal equations, linear functions, quadratic functions and exponential functions will be much easier.

The progression that I discussed earlier is contained in some lessons that you will see below. I bundled this material in a comprehensive unit that contains:

  • Expressions
  • Solving Multi-step Equations
  • Special situation in Equations (no solution, infinite solutions, clearing decimals and fractions)
  • Writing and Solving Equations
  • Equation Assessments
  • Inequalities
  • Literal equations

This will be what I’ll use this year in my Algebra classes. All of these activities come with a PowerPoint for notes, a PDF packet with notes, practice and a quiz. There are also a few digital activities dispersed among the resources. Good Luck and remember how important it is to give your math students a strong foundation!

Here’s how I start with solving equations.
A look at special situations.
Students must know how to set up equations.
This is a variety of assessment options.

The Whole UNIT!!!

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Algebraic Expressions

By the time students are in algebra, they should have experience with algebraic expressions. I never feel comfortable enough with this fact, so I always start the year with a refresher. Expressions are the building blocks of algebra, so it’s better to cover this topic and make sure students have a good foundation before heading into solving equations.

As I begin the year, I like to review operations with integers and rational numbers, order of operations, expressions and terminology. Terminology is key. Students must know what you are talking about when you use words such as like terms, coefficients, variables, distribute and constants. Also, never assume students know things like a fraction is really a division problem and all numbers have exponents of 1 when no other exponent is visible. Get all of this taken care of in the beginning and you will find out really quickly who has these foundational skills and who doesn’t. I will not get the calculator out until after all of this material has been covered.

Here’s the content that I like to make sure to cover during the expression lesson:

  • Setting up expressions from phrases like: five less than twice a number
  • Evaluating expressions by plugging in a number for a variable. It’s important to review order of operations at this point.
  • Simplifying expressions using combining like terms and distributive property.
  • Using applications with expressions.

If students are able to do the 4 items above, they will be in a good position for success when moving to solving equations. I will probably take a week to practice expressions, but I feel like this is time well spent.

My lesson plan will look something like this – (I’m on a block schedule, so I see my students 80 minutes two days and 50 minutes on Friday.)

Day 1:

  • Bell Ringer – Operations with Integers
  • Math Terminology
  • Expression Opener
  • Setting Up Expressions
  • Evaluating Expressions

Day 2:

  • Bell Ringer – Operations with Rational Numbers
  • Simplifying Expressions
  • Practice Writing, Evaluating and Simplifying with a Partner
  • Application with Expressions – Digital Practice

Day 3:

  • Quizizz Activity – (I have a Quizizz Activity that practices the skills used in the application activity.)
  • Quiz – Short quiz that will let me know how well the students understand the concept.

I have a resource that covers all of this material. The expressions lesson that I created has a PowerPoint that goes through the terminology and example problems. I like students taking notes and following along, so I have note pages that follow the PowerPoint.

Expression PowerPoint
Note Page Example

The lesson comes with a practice page that contains 12 problems covering the three categories: writing expressions, evaluating expressions and simplifying expressions. The quiz has a section where students fill in terminology and the rest of the problems are multiple choice for quick grading.

The application part of this activity is a Google Slides where students show that they understand what an expression is versus equations or inequalities. Students then see some perimeter problems where the dimensions are expressions. Students solve the problems two ways. There is a video tutorial that walks students through simplifying some expressions with the distributive method.

Expressions are the foundation of Algebra. Students start learning expressions early in their math classes, but variables are an abstract concept and tend to be something difficult for them. The more we expose our students to understanding the purpose of a variable, the better they will grasp it. Give your classes lots of examples of how expressions might be used and keep checking for understanding. See if they can come up with their own examples. If they can create their own expressions and tie it to a real-life concept, then you know they have made the leap to understanding this idea.

If you’d like to look further into my Expression Lesson, I have linked it to the picture below. Thank you for going through this thought process with me and good luck with your students.

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6 Ways to Keep Your Teaching Life Under Control

You have a ton of assignments to grade, data to decipher, forms to fill out, professional development requirements, students to manage, a club you sponsor and a curriculum to cover. You are drowning and something has got to give. Let’s talk about way to keep your teaching life under control.

Teachers are multitaskers and that’s great, but are you spreading yourself to thin? Your home life does not need to be sacrificed to keep your school life organized. It’s time to get efficient and swim on top of the water! I’ve got some suggestions that will help you manage your responsibilities more easily.

Get a piece of paper and write down what you do on a daily basis at school. Circle the things that need to be done during your planning period. Are you able to complete these tasks? Probably not all of them. There just isn’t enough time. Keep this list in front of you as you continue reading.

Before we get into how to organize your time, think about things that you do that can be eliminated completely. Do you volunteer for too many things? Do you do class activities that require too much prep? What can you start saying “no” to? Don’t feel guilty. Really think about the importance of the items on your list. Is everything on your list a MUST DO task? If not, mark it off and in the future think before signing on for something that is a time-suck.

Let’s get organized! Take a closer look at your list. Are all of these things done every day? Do you need to do some on certain days? I’d like you to organize your list into a weekly plan. You do not have to be detailed. Just jot down 3 – 6 things that have to get done during the week on certain days. Here’s a Google Sheets Planner to use if you’d like.

Congratulations. You have taken the first step toward getting your teaching life in order!

Keep your list handy so that you can check things off as you complete them. During your planning period, put your phone away and forget about it for 30 minutes. You will be amazed at what you can get done. If you tend to get sidetracked, then instead of putting your phone away, set your phone’s timer for 20 minutes and tell yourself that you have to work for 20 minutes before you can get up and do anything else. This works really well when you don’t like the task you are doing. You know you can take a break after 20 minutes. After the 20 minutes is up, then set your timer for 10 minutes and go get a drink or look at your phone or stretch and meditate!

If you need more time to accomplish your tasks you may need to consider some other options:

  • Can you come to school an hour earlier or stay an hour later?
  • Can you put the kids to bed and work an hour at night or get up earlier and work at home?

How do you plan out what you need to teach? This can take a ton of time. To make things go smoother, you will need to arrange a block of time for planning your curriculum. I suggest to plan it out six to nine weeks at a time. Put this information on a calendar and don’t worry about being detailed. Just seeing what you need to teach will take that part of the task off your plate until you plan again for the next block. This might take you a couple of hours, but you only have to do it every few months.

Is grading out of control for you? Do you really need to grade everything? Can the students grade their own work on occasion? Can assignments be graded for completion? Can you grade something quickly by walking around and putting a sticker on the paper and move on? Be creative. You truly do not have to grade every assignment. If you will decide ahead of time what needs to be graded and what does not, you will love your life!

So let’s recap.

  1. Say NO to things that take you away from what you REALLY need to do.
  2. Plan out your week by using a checklist system.
  3. Set a timer when working and stay on task. (Or just put that phone away).
  4. If you need more time, look for an hour here or there that won’t steal time from your family.
  5. Plan your curriculum in 6 – 9 week increments.
  6. Don’t grade everything.

I hope this helps you. Being able to check things off a list is the greatest thing ever.

I hope your stress level decreases and you love your job more and feel great about being so organized!

Good luck! If you are a secondary math teacher and you are interested in receiving tips and freebies, feel free to join my email list.

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The Algebra STAAR Dilemma

With COVID still going strong, it’s hard to know how to prepare for the Algebra STAAR exam. Teachers are sick, students are sick, campuses are closing or going virtual. How do you deal with all of this? First, don’t put pressure on yourself. You can only do so much. You can plan and teach the students that are there. That’s it. You are an awesome teacher. Never forget that!

It’s 2022 and we are headed into the second semester of school. I’m wrapping up linear functions in a couple of weeks and I feel pretty far behind. My plan is to give myself at least three weeks before the test to review. I still need to cover exponentials and quadratics. How do I get all of this done? I like to get a calendar and put the test dates on it and mark off the three weeks of review. I look at my school calendar and make sure I know when spring break is and when the English I & II STAAR will be.

***You can get a copy of my planning calendar, so you can make it fit your needs. I’ll attach it at the bottom of this post.

Something new that I’m doing this year is focusing on the free response questions. I’ve created activities that will help students build confidence on the types of problems that they will see on the griddables or fill-in-the-blank problems. My students will take the online STAAR, so I’ve got this Boom Card Activity for them: Algebra STAAR Review Free Response Practice

If your students are taking the paper version of the test, here is the same activity in PDF form: Algebra STAAR Griddable Activity for Paper Version

Here is an outline of my plan. Remember to pick and choose what will work with your schedule!

  • End of Jan: Finish Systems
  • February: Exponent Rules, Geometric Sequences and Exponential Functions (some things in this unit you can omit).
  • Feb 28 – March 4: Algebra Task Cards (These are in the STAAR Bundle) as Bell Ringers or Opening Activity. Polynomials – Mainly multiplying binomials and refreshers on combining like terms and distributive property.
  • March 7 – 11: Continue Task Cards and Factoring
  • March 28 – April 8: Start Taking Task Card Timed Quizzes. Start quadratics using my objective 6, 7 and 8 resources from the Algebra I STAAR Bundle.
  • April 11 – 15: Continue with quadratics and do quick reviews of objectives 4 & 12 (combined these two objectives have only been 3 – 5 questions in the past)
  • April 18 – 22: Reviews of objectives 2, 3 and 9 – I’ll use my STAAR Bundle, but I will pick and choose what I want to use from these objectives. (Bell Ringers will be key features of graphs.)
  • April 25 – 29: Objectives 5, 10 and 11 – I’ll use my STAAR Bundle, but I will pick and choose what I want to use from these objectives. Bell Ringers will be Brain Dump Practice.

Here’s my calendar. Make a copy and then make it work for you!

When all is said and done, I’ll reflect and see how it went.

Please don’t stress out Algebra Teachers! Do what you can. Have a plan and work through the plan. Things will be fine. The students will do as well as they can and we will probably be pleasantly surprised at how well most of them will do. Remember that YOU ARE AWESOME!

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Real-Life Exponential Functions

Exponential functions are right around the corner for my math classes. I always look forward to this time of year. The best part about exponential functions is the real-life aspect. Students are more interested if they can make a connection. Draw your students in and they will enjoy this topic without realizing how much they are learning.

One of the first real-life examples that I can think of right now, is COVID-19. Remember when the saying was, “Flatten the curve?” What an interesting thing to talk about with students. A flatter curve means what? A steeper curve means what? What a great thing to talk about!

Here’s a great research letter I found on the CDC website. This has some wonderful references to “doubling time”. The research brings in some formulas and if you look at some of the appendices, it gets pretty technical, but it is fascinating.

The Coronavirus is a topic that I’m sure will get the attention of your students. Another topic that students may not be as familiar, but it is definitely worth mentioning is the stock market. Let your students read this article from Forbes. They may not think the stock market is very exciting, but after reading this article, it might spark some students to consider how they can one day invest in stocks.

A really fun exponential growth activities is the paper folding activity. I’m sure most math teachers have used this when teaching exponential functions. I love that Myth Busters tried to fold a giant piece of paper to see how many times they could fold it. Check out this video below:

We’ve been focused on exponential growth, but what about decay? Carbon dating is a topic that is also fascinating. This article can help students and teachers alike to understand carbon dating a little better: What is Carbon Dating? This might help students understand how scientist can estimate the age of an object. Below is a nice video that explains carbon 14 and half-life.

If you’ve read my blog before, you know how much I love exponential functions. I’m always on the lookout to learn more and find interesting things for my students to do. Below, you’ll find some of my resources that I sell on Teachers Pay Teachers. I’ve got all kinds of exponential function activities to keep your students busy and interested. Go take a look and I hope that you will want to follow my store and join my email list!

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Slope and Rate of Change

I was going through a review of slope that I made a couple of years ago. I love this resource! It was created for the 8th grade STAAR, but I feel like all Algebra teachers would love this. Students are supposed to come into Algebra with a concept of slope already! Why do students have such a hard time with it? Slope is a fun and interesting concept and of course ties to so many real-life situations. Let me tell you what this review contains:

Now remember that it is a review of slope! The first page gives the students a picture of a line with four points on the line. The students are asked to find the slope of two different segments along the same line, two different ways. The picture also has two right triangles drawn that were created from using the endpoints of the segments. Students that already have a concept of slope should be able to think of several ways to find slope. I love this so much. On top of that, shouldn’t the slopes be the same and the two triangles created are similar. Hopefully students will have that Ah-ha moment!

The next two pages have the students interpret the meaning of slope by matching a situation to a graph. The students are thinking of slope as a rate of change and having a proportional relationship. I love the different graphs. Teachers could ask the students to find the slopes of all of the graphs first before trying to match them to the situation. Students are asked to explain why the graphs they did not choose are incorrect. Having students explain their reasoning is always important in math.

The next four pages are a set of 24 matching cards. 12 of the cards have either a graph or a table. The other 12 cards display a slope, y-intercept or another way of identifying that it matches one of the graph or table cards. This activity is engaging and students have to know what they are doing!

Finally, the last page in this resource is something that I have consistently placed in every 8th grade STAAR resource. I call it Smath’s Problem. It is an activity that reviews several of the topics in the resource. It is interesting and students enjoy working through the situation. It can be used as an assessment or a group activity.

I think you’ll enjoy this resource. All of the answer keys are included. Take a look if this sounds interesting!