Ok...so you have taught them slope, and y-intercept and ALL the different forms you can write a linear equation. They have all the information they need, but they need practice. You could always give them 15 equations straight from the textbook ....or you could give them something fun and engaging. This was why I created graphing art.

When I was full-time in the the classroom, I kept looking and looking for something like this, but I never could find what I was looking for. So I created my own...and the kids loved it. At the time, I wish I had time to create more, but they were very time-consuming to create so I couldn't. Now that I am on a break from teaching, this was one of the first things I wanted to create. Fun pictures that were made from graphing linear equations. After I created one, I realized it definitely needed color. I also realized I could incorporate one more math skill of finding composite area to apply color.

Students are given an equation written in slope-intercept form. They then graph the line segment with the given end points. As they continue through the various equations they will gradually be forming a picture. They then color the picture given the area of the composite figures.

One last thing, can we mention that grading these pictures is an absolute breeze. SO much easier than trying to grade 15 individual graphs by students from a textbook. These literally take a glance to check for accuracy.
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I am a strong advocate in teaching students conceptual mathematics. I believe the more they understand the "why" of the mathematics and can make connections across domains they will become better mathematicians and better problem solvers. However, I also believe procedural fluency is a critical component in mathematics. One way to build procedural fluency is practice.

I know, however, that middle school students do not like a boring worksheet to practice procedures, and assigning 10 basic problems out of a textbook is just as boring. Students are more willing to engage in an assignment when it is fun. That is why I created mystery pictures.

Mystery pictures include about 20 questions for students to practice procedural fluency on a specific math topic. Once they answer they question they find the answer on the coloring grid and color the square(s) according to the key in the question. Once complete, students will have revealed a fun mystery picture. If done incorrectly, their picture will not look correct. Therefore, correcting these mystery pictures is a breeze.

I have a few available to download for free if you would like to try them out in your middle school math classroom. Click here to grab yours for FREE!

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If you don't know what the discovery method is, let me give you a quick summary of the basics. With the discovery method teachers create an opportunity for students to DISCOVER mathematics (formulas, algorithms, connections, etc...). This is basically opposite of a teacher standing in front of the classroom and TELLING the students the mathematics. The discovery method leads to a greater understanding of mathematics and also builds students' confidence. Here are 4 tips to implements the discovery method in your classroom.

1. Open-Mindedness Environment: Since students are discovering what works and what doesn't work failure is bound to happen. In fact, you want failure to happen, because students will learn what does not work. However, students hate failing, because they do not want to look inferior to their classmates. This is especially true once students hit middle school, where students protect their image fiercely. If you don't set up an open-minded classroom, many students will rather not try than try and fail.

Setting up an open-minded classroom needs to start from day 1. It's a culture you need to establish and live in your classroom. Talk to your students about how mistakes are opportunities for growth. Even displaying student's mistakes (without names) and taking time to learn what mistakes were made is a great strategy, because your students will see how learning really does happen from mistakes.

2. Guided Task: You need to give your students a guided task. Guided tasks often have more than one answer, are approachable for all levels and have room for continued challenge. A simple example might be, "Create a prism with a volume of more than 230 cubic meters and less than 200 cubic meters." A challenge you could add on to this question is a condition of surface area as well. Let your students have a productive struggle.

3. Teacher Assistance: Teacher assistance is absolutely essential for successful discovery. Teacher assistance is NOT lecturing nor is it telling students what to do. Teacher assistance IS walking around the room and asking questions to the students. The questions may look like "Explain to me what you are thinking." "Explain to me this step that you did right here." If students are stuck, "Tell me what you do understand" or "Tell me what part you don't understand." Guide your students but do not spoil the discovery process.

4. Conclusion: Since the point of the discovery method is that students discover something you need to make sure to bring it all together to verify that ALL students have actually discovered what they need to discover. Also, if your guided tasks have multiple solutions or multiple ways to arrive at the solution you need to discuss this. One way that I have done this in my classroom, is when students are working and I'm walking around I make notes of the different ways students are solving the problem. I then have groups present different aspects of their process. I usually don't have time, nor is it necessary, to have groups make a huge presentation of their whole process. You just want to highlight the important points with the goal that all students make the discovery that you need them to make, such as an algorithm or formula.

Once I implemented the discovery method in my classroom, retention of the material increased because students could connect the mathematics to experiences.

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Adding and subtracting integers can be a tough concept for middle school math students to comprehend. Especially if students have been taught that subtract always means to get smaller. I wanted to share some tried and true successful ways to teach students how to successfully add and subtract integers.

1) Use number lines: Number lines are essential when introducing adding and subtracting with integers. I always found it easier to give students a paper with a bunch of number lines on them to speed up the process of teaching. Having students draw number lines for each problem can take a lot of time. Another thing that I have done was to give students one number line in a protective sheet. Then they use a draw erase marker to draw on the number line for each problem. They can just erase the arrows after each problem. Also, students love dry erase markers...so they always creates extra engagement.

2) Teach subtraction as adding the opposite, then have students rewrite subtraction problems into addition problems. For example, 5 - (-3) changes to 5 + 3, because you add the opposite of the second number. Another example, -4 - 6 changes to -4 + (-6). Having students circle the second number also helps those struggling with distinguishing between the subtraction sign and the negative sign. You might need to remind students that when there is no written sign such as in -4 - 6, then 6 is positive, but then you will flip it to a negative.

3) Lots of practice with basic numbers: Don't jump to adding and subtracting large value integers until they have a really good conceptual understanding. Do lots and lots of number lines and rewriting subtraction into addition.

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