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. 

Different Forms of Numbers

My daughter recently upgraded one of her resources for distance learning. This resource originally had a set of 24 matching cards where the students match a number to the expanded form and to the word form. This is a great activity to see if students understand expanding numbers with decimals and then to see if they know the place values. The resource is called Matching Different Forms of Numbers.

Now she has made this ready for distance learning. She has transformed it into a Google Slides where students will drag and drop to match the various forms.

I love the last question on the Google Slides which is to create the three forms on your own. We love when students have to create. After working 8 different problems, they will be able to follow the examples and create one on their own. I love that.

The matching cards were originally in her Objective 2 5th Grade Math resource. Now the matching cards are separate and can be purchased independently.

Matching cards are fun and use lots of brain power. If you teach elementary math, go check this activity out to see if it is something you would like to add to your curriculum.

Study Guides for Math Portions of College Entrance Exams and College Readiness Exams

When you think of college entrance exams, I’m sure the SAT, PSAT and ACT come to mind. More high schools are offering these tests during school. Some students will take these tests 2 or 3 times or more. Why? Because they need a certain score to gain entrance into a school or to apply for a scholarship. The PSAT is a nice warm up to help students know where they stand before they take the real thing.

Every October, schools offer the PSAT/NMSQT to their juniors. Although sophomores can also take it , only the junior scores count toward the National Merit Scholarship competition. Schools are also starting to offer the PSAT 8/9 (for 8th and 9th graders) and PSAT 10 (this is the regular PSAT, but does not qualify for the National Merit Scholarship competition).

It’s good that schools are offering these tests to their students so they can see the format of this test and the way questions are asked. The SAT is a very important test for students planning on going to college. Colleges use the SAT (and/or ACT) to make admission decisions which makes these tests very important for students that want to go to a certain school.

The ACT is another college entrance exam. Some schools are offering this test during the school year to their juniors. The ACT is different and has a science section where the SAT does not. Again, this test requires practice and there is no pre-test like the SAT.

There are a couple of more tests worth mentioning. Nowadays, colleges want students to take a college readiness test to see if students have the skills to start taking college courses. The ACCUPLACER is used by many states. Texas has their own college readiness test called the TSI. Both the ACCUPLACER and TSI are similar. Students scores will determine if they are able to start their English and Math courses on level or if they will need to take some remedial classes first. The ACCUPLACER and the TSI can be taken as early as the 9th grade and in some cases, earlier. Early College High Schools have their students take the college ready tests the summer before their 9th grade year to give them plenty of time to retake them until they pass.

I’ve been teaching high school math for 30+ years, and it was not until I became a teacher at an Early College High School that I became fully aware of all the tests students take. I realized that I needed to be the one to help them get to where they need to be. I know how important it is for high school teachers to help incorporate college entrance and college readiness practice into their curriculum, especially math teachers. I’ve spent a lot of time creating many resources to do just this.

Below, you will find links that will take you to my Teachers Pay Teachers Store where I sell these resources. There are many options, but the option that I recommend if you are planning on doing a ton of review is the Math Test Prep Bundle for College Entrance. It contains the SAT Bundle, ACT Bundle and a TSI/ACCUPLACER Bundle that you see below:

College Readiness and College Entrance Exam Bundle
ACT Math Prep

3 Reviews – 86 Questions

SAT/PSAT Math Prep

6 Reviews – Worksheets, Bellringers and a 5 Week PSAT Plan.

TSI/ACCUPLACER Math Prep

7 Reviews!

I’ve recently started a digital version of the TSI/ACCUPLACER College Readiness Bundle (this is the exact same, but for a digital classroom setting). It is incomplete, but will be finished by the start of the next school year.

It is so important that math teachers take the time to prepare students for their future. Start making a plan now on how to meet the needs of your students. We all have different situations, but I’m sure you can find a way to include study material that will increase your students’ chances of success on college entrance exams and college readiness exams. Good Luck!

Trigonometry for the Geometry Classroom

It’s finally trig time! Yay! I love trig. Students tend to enjoy it too because it is so different from everything they have been taught so far. Over the years, I’ve tried different approaches to teaching trig. I know what kids struggle on and I finally feel like I’ve got a good way of teaching it. I see my trig unit broken into these parts:

  • Intro to Trig
  • Practice Finding Opposite, Hypotenuse and Adjacent
  • Setting Up Problems and Solving Them
  • Practice
  • Review
  • Assessment
  • More Assessment

Trig can be simple but to some students it can be complicated. They actually love it once they get the hang of it and how fun is it to use the calculator this much?! (When I first learned trig, we used charts to find the answers. We did not have calculators that would do the calculations. Yes, I’m old!)

When I created this unit, I knew what the two main issues were with teaching trig: 1) Teaching them which trig function to use 2) Teaching them how to solve the different types of problems

I decided to work backwards a little. In my introduction, I just tell them (As Bill and Ted would say) we are about to embark on an excellent adventure called Trig. I introduce a right triangle and tell them to visualize that they are in a right triangular room. They are sitting in one of the corners (not the right angle). I go on to talk about where opposite is and how when you are sitting in the corner, you can touch the hypotenuse and adjacent sides at the same time, but you can’t reach the opposite side. There are some notes we take and then we play a dice game.

For the dice game, I usually get my first class to cut out and put together the dice. Now I have the dice for the rest of the day. I put students into groups of 3 or 4 and they are competing against the rest of the class. There are three dice. One with triangles, one with dots and one with the words, hypotenuse, opposite and adjacent. Click the link below to watch the dice game which practices knowing the different sides with respect to a certain angle. Dice Game Short Video.

Before going any further, I teach kids SOH CAH TOA and we do some practice on finding those ratios. That part is normal progression, but here is the part that might seem a little backwards: I teach them how to solve trig equations next! The students do not know how to set them up yet, but I have figured out that if I go ahead and teach them how to solve the equations, then once they start setting them up, solving is a breeze. I teach them how to solve these three types of problems:

  • Looking for an angle
  • Looking for a side and the x is in the numerator
  • Looking for a side and the x is in the denominator

By the way, when teaching them how to solve these problem, get them to completely solve for x before typing anything into the calculator. Don’t let them find the sin of an angle, then multiply by the side. Let them type the whole thing in: 12 sin(36). I like this method because then the students aren’t rounding answers until the end of the problem. You can see that I did that in the examples above in problems 5 & 6.

Next is the PowerPoint. In the picture to the right, you can see one of the slides in the PowerPoint. Only the triangle with the sun, and the two arrows appear and students have to name which trig function is being referenced. I don’t use degrees for a while, I’ll just use symbols. I don’t want the variables and numbers to get in the way. Toward the end of the PowerPoint, the students are asked to set up the problems and then at the end, they go back to solve them.

Now it’s time to practice. I have 3 worksheets that help students find missing sides and angles. The first one places only an x on one side, a number on a side and gives one angle. This makes it easy to determine the trig function and it is like the PowerPoint. The next worksheet gives the students two sides and asks them to find the missing angle. The last worksheet is the toughest because now the students have to find x, y and z… two sides and an angle. This is much more difficult because it will not be obvious from the start which trig function to use. Students need to see that they actually have a choice sometimes and they need to decide where to start and ignore the extra info. I also throw in some special right triangles and an right triangle altitude problem to see if they remember those rules. The PowerPoint from earlier brings up that there might be more than one way to solve a problem, so hopefully when they get to the worksheet, they will use a quick special right triangle rule instead of trig, but if they can find the answer either way, I’m happy.

I have another resource that is not in this trig unit that I do at this point. It’s the Trig Maze. The students really get into it and work at it. It’s cool to work a problem and then see your answer on the paper (they are thinking, “YAY, I did it right!”) and it’s even cooler that it leads you to the next problem you are supposed to work. The maze comes with an answer document, so you can see all of their work!

Finally, I like to do some task cards with some real-life situations. Some of the task cards contain a ladder against a building, finding a flagpole height, finding the diagonal in a rectangle etc. There are 12 of these problems.

I end the unit with what I call the “Poodle Problem”. It is a group of 5 triangles that have been put together to look like a poodle. Go back and look at the very first picture at the top of this blog. That’s the Poodle Problem! The students find all the answers, then total them for one final answer. How fast is this to grade? Super fast! It’s a great quiz and a great end to the unit.

I’m not finished yet! Now I like to test all of the right triangle content. I have a test that I call the Right Triangle Test that has 10 questions with the following problems:

  • One Pythagorean Theorem Problem where they have to find the perimeter of the triangle.
  • One Right Triangle Altitude Problem where they have to find the perimeter of the triangle.
  • One 30-60-90 Problem where they have to find the area of the triangle.
  • One 45-45-90 Problem – easy, they just find the hypotenuse
  • Six Trig Problems – Just find a missing side, except for one problem is like the task cards, but a little tougher.

I had problems with cheating one year, so I went crazy and made 5 versions of the same test. You even have a choice of an answer bank or no answer bank. One of the 5 tests is a shortened version that I’ve used as a retest or a modified test. (It gives the students a little help on setting up some of the problems too.) I don’t like to give long tests. Students get enough testing. I like tests that are short and to the point. As long as I can tell they “get it”, why does it have to be super long?

I’m very happy with this unit. The only thing that it doesn’t contain right now is angle of elevation and depression problems. I’ll try to add this to the unit this summer. These problems were a big deal at one time, but it seems like we’ve gotten away from them in Geometry. I still think it’s good for students to see them.

Trig is fun and different and essential to future math classes. Below is all of my right triangle lessons including the Trig resource I’ve been talking about. What’s next on my agenda after right triangle trig? Law of Sines and Cosines of course! Law of Sines and Cosines is sold separately in my store, but it is also a part of Unit 7 below.