Graphing in all Four Quadrants--Coordinate Graphing Activities--Math Intervention

How can my students practice coordinate graphing?

Coordinate graphing is usually a topic that my students caught onto pretty quickly. It was a lesson that could be hands on and those lessons are the ones that students caught onto more quickly. 

However, in the year of COVID-- a lot of students were remote during the coordinate graphing lesson and missed that hands-on lessons. As we progressed throughout the year, I realized students were still not getting how to graph so I created this activity to help reinforce the skill. 

I pulled students into groups of 5 or 6 and had expo markers, the cards, and a poster-sized coordinate graph that was laminated. My school had a poster maker so I could make the coordinate graph poster size. If I didn't have a poster size coordinate graph-I would print several copies of the graph for students to have access to. 

First I had students work in pairs. I gave each pair a card and had them work together to find their ordered pair based on the instructions. I asked each student pair to explain how they found their ordered pair. The expo markers were helpful because I asked students to trace the path they took to find their ordered pair. I ask them to to the same thing when they are taking a test. It is a more concrete way to learn this concept. 

Overall, this was an easy activity to prepare and got students talking about finding their ordered pairs. Any activity that gets to students to talk about their thinking in math is a win. 

Get the activity here.  

If you need more activities to teach coordinate graphing, you can find them here. 

Students Talking in Math: Activity to Get Students to Talk about Math

My favorite thing about teaching is hearing students talk about math. It is what brings me joy as a math teacher. But believe it or not, math is not a student's favorite thing to talk about. 

Why should students talk in math class?

1. Students want to talk! I want to give them as many opportunities to talk as possible-and keep it on topic as much as possible. 
2. When a student says something out loud, it helps solidify it in their brain.
3. When students hear their classmate say something out loud, they remember it better. 
4. Speaking about math helps students clarify what they are thinking until they understand it. 
5. Students will be more engaged when they have opportunities to talk to each other. 

Unfortunately, most students don't come to math class knowing how to talk about math and need scaffolding to get where we want them to be. 

One of the activities I have used to scaffold conversations about math is a True/False response. Each student gets a red and green card. They could also have different colored post its. Two colors are better so you can easily see the responses from the class. 

Before starting the activity, explain to students they are going to read the statements and determine if they are true or false. BUT, they cannot tell the class. Instead, they will turn to their neighbor or group and share their response. If students disagree, they will explain to each other why their answer is correct. If they change their mind, great. If they don't change their mind, great too. They don't have to be successful at convincing each other, the most important thing is talking. 

You put up a prompt--this can be done with any topic. I have an example below. 

Students talk with their neighbor group. When you are ready--give 1-2 minutes-tell everyone to hold up their red card for false and their green card for true. (Or whatever colors you have chosen)

These are low-stakes conversations. Students don't have to talk long--but any talking about math is a good start. The more confident they feel in their skills, the more they will talk. 

Click here to access a free True/False activity about integer operation models. 

Interested in other math activities? This has warmups for several 6th grade math topics that encourage students to talk about math. It can be used for STAAR review but also works throughout the year. 

Order of Operations Error Analysis Math Activity--Free Order of Operations Activity

 How to Practice Order of Operations?

Students love finding mistakes, especially mistakes the teacher or their peers make. I always had a tally on the board of how many mistakes that I made in math class. Finding mistakes is a higher level thinking skill because students have to understand the concept enough to be able to find where something went wrong.

One of my favorite activities for order of operations was having students look for errors when it came to solving the expressions. You can do this with little prep as long as you have a few order of operations problems and some dry erase markers like in this post. 

I also put together this presentation for 5th grade math. Each slide has an order of operation problem solved with two different answers. Students have to find which one is correct and you can take it a step further by ask him to find what mistake did someone make to get the wrong answer.

Now students are quick to find mistakes of their peers and their teachers, but when it comes to finding their own mistakes it can be a struggle. But however if we continue to expose them to common misconceptions and common mistakes and point them out hopefully they will remember them when they are solving problems on their own.

Here are some other resources for order of operations that you might be able to use. 

Order of Operations Error Analysis Task Cards (6th Grade)

Order of Operations Color by Number (5th Grade)

All my order of operations resources

Fractions as Division Lesson-Introduction to Different Representations of Division

How to teach Fractions as Division?

One of the first lessons that I taught in six grade math was fractions as division. Getting students to understand that a fraction is also a division problem is a year-long struggle so introducing an early is necessary so that we can keep practicing it over and over and over again. 

I will admit that at the beginning of my career for teaching math, I was not too big on emphasizing math vocabulary. It’s one of those things that I will regret not doing well with my first class. For this lesson, emphasizing the vocabulary for division problems is super important to help students keep what number is what in a division problem. 

I start the lesson with this PowerPoint presentation. 

Remember from this post, that the best math lessons have students connect with the new learning with something that they already learned in the past. So we discuss vocabulary and look at the division representations that they already know using the division sign and the “house”. I have my students repeat over and over again which number in the problem is the dividend and which number in the problem is the divisor. Then we look at a fraction and students learn how the numerator is the dividend and the denominator is the divisor.

As we are setting up 3 representations of division, we repeat the vocabulary again. By the end of the lesson they are sick of saying the words dividend and divisor but repetition is key here.

   
This presentation is a jumping off point for a fraction as division lesson. From here I would continue to give students real world examples of division and have them write a division representations for those examples.

What are some common misconceptions with fractions as division?

One common misconception that students have is that the bigger number must always be the dividend. This is something that an elementary school teacher probably told them as an easy way to get them to remember to put the bigger number inside the house. This is a habit that middle school teachers have to help students break.

What is next with teaching fractions as division?

I have some other fractions as division resources available in my store. 

• Here is a free puzzle where students need to match a real-world situation with the 3 division representations. 

• Notebook pages with extra practice

• Fractions as Division Math Color by Answer and Riddle

FREE Classifying Rational Numbers Lesson and Activities

How to Teach Classifying Rational Numbers?

I love teaching classifying rational numbers. I don’t know why I like it so much but I think part of the reason is that the students already know pieces of this lesson and I am just helping them connect things they’ve learned in math previously to this new skill.

The best math lessons are the ones were students make connections to something they have learned before. Research shows that when students are able to make connections to things that they already know, then those new topics stick in their brain better.

This set of classifying rational number lessons has students use number lines and come up with their own definition of things like whole numbers, which they have been using since kindergarten.

This lesson plan was originally written to be used within a classroom that uses small groups. So you will see four days of lessons that should take 15 to 20 minutes each and then the teacher would pull small groups for intervention or extra practice on this topic. However, you could also condense the lesson into 2 to 3 days depending on the length of your class period. 

You can download the set of lessons here for free. The lesson plans are editable and there is also a set of activities that go with the lesson plans.

How to Practice Classifying Rational Numbers?

If you would like more ways to practice classifying rational numbers, I have tons of resources in my TPT store. I would use these additional resources for extra practice throughout the year, for homework, for substitute lesson plans, or for stations in a small group math classroom.

Introduction to Inequalities with Desmos and Real-World Situations

 I think introducing inequalities is so much more interesting and fun than equations. There are so many more real-world situations that students can relate to. 

"Your mom says she will give you no more than $20 for lunch this week. How much money could she give you?"

"You need to be at least 48 inches to ride the roller coaster. How tall could you be and still ride it?"

"The elevator can hold up to 750 pounds. How much can the elevator hold?"

You can have some fun discussions with your students and even those students who struggle with math can participate because it is something they can relate to. It is  great way to help students build confidence. Math isn't just a set of steps and algorithms--its a way to explain the world around us. 

So this year, I was in the classroom because of lack of substitute teachers and got to start the inequality unit with some 6th graders. These are the two activities I used with students. (My campus currently has enough devices for every student.)

1. Desmos Inequalities on a Number Line

Have you used Desmos? You might know it as an online graphing calculator, but it is so much more. There are lessons on there that you can walk students through, see what they are doing in real-time, and give immediate feedback. 

The assignment I have linked has students place value on the number line with prompts like "a number less than 3." This starts students thinking about how there are multiple numbers that fit that prompt. One class would only every pick whole numbers and I had to push them to see 1.5 as a value they could select. 

Eventually this assignment shows students how we use a shaded number line to show all possible solutions. 

2. Google Slides Beginning Inequalities

Next, I had students look at some real-world statements on the board and place possible solutions on the number line. I had several students come up to the board and use a marker to mark their possible answers. Again, all students were able to participate because theses were situations they experienced in their daily lives. 

Now I know that when we get into solving and writing inequalities, that students may struggle. But by starting the unit with some low floor activities, the students can build their confidence and it is something I can continue to refer back on. 

Modeling Adding Integers with Algebra Tiles Free Google Drive Resource

 Virtual. Learning. 

Remote. Learning.

Distance. Learning.

Online. Learning.

Whatever your district calls it--this isn't easy. Not that I expected it to be. But this is just so much harder than I thought. There are so many decision to be made as new circumstances come up. I worry that our online learners aren't getting what they need. I worry about our in-class learners. I worry about my math teams and the stress they are under. I am constantly worrying. 

Hopefully in a year we can all look back on this time glad that school is filled with students talking, laughing, not on the computer all day long, etc. 

We've been working on our integer operations lessons. I filmed a video today with my favorite lesson that really needs students talking to work! I was just sitting at my desk talking to myself about the excitement that is integer operations <--that is not sarcasm. 

I love algebra tiles so much. When I first learned out them 7 years ago, I loved them. Where were these when I learned algebra, where all my math problems began!

If you aren't using algebra tiles or colored counters to teach integer operations--start now. 

This assignment has students model simple addition expressions, create zero pairs, and simplify the expression. 

Click here to copy the activity into your Google Drive. 

Using Integer Vocabulary to Get Students to Talk in Math | Free Resource

I don't like just introducing new concepts in math without talking about real-world implications. When introducing integers, we start with talking about vocabulary that show positive and negative situations. 

On the day you introduce integers, display this slide to your class and ask them to pick one word with their group that means positive and one that mean negative. 

Having your students talk in math class is important. Not just to explain math, but to build skills of sharing ideas in respectful ways with their classmates. This is a low floor questions where most students will be able to find at least 1 word that they can explain as positive or negative. It is also important for ELLs to practice their academic vocabulary with their peers. 

Talking in math class doesn't always have to be about explaining how to solve a problem. This is still math talk! It will also help students be able to connect math class to outside the classroom. 

You could even extend this to a writing activity and have students write what about the words their groups talked about. 

Click here to add this resource to your Google Drive.

Fraction Decimal Percent Google Slides Digital Assignment

 Are you are trying to figure out virtual learning and face-to-face learning at the same time? Is your school doing just virtual learning? No matter what your situations, the 2020-2021 school year will be one to remember. The first few weeks of school have been exhausting and overwhelming. 

I want to do what I can to help. I wish I could do more! 

This resource has students look at models and name the fraction, decimal, and percent modeled. 

Click here to download to the Free Activity

Multiply or Divide Decimals Word Problem Sort | Google Classroom Resource

I have learned a lot about using Google Drive to create resources for math the last few months. My district does not use Google Classroom, but we do use an LMS that allows Google Drive resources to be assigned. 

When students read word problems, they may struggle with deciding on what operations to use. Throw some decimals in there, and some get really confused. 

I made this sort in Google Slides. It has 10 word problems which similar situations. Students have to sort them into columns based on whether they will use multiplication or division to solve. 

When I introduce this topic to students, I ask them to do 2 things. 

1. Replace the numbers in the word problem with whole numbers. Does that make it easier to decide the operation to use?

2. Look for the Total. Do you have the total? Or are you looking for the total? If you have the total and you are splitting it into equal groups, it is division. If you are looking for the total and you have equal groups you need to combine together to get the total--its multiplication. 

Click here to get the sort to add to your Google Drive.