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.

Preparing Your Students for Math Portions of College Entrance Exams and a Bright Future!

High School teachers and their students should be aware of the ins and outs of both the SAT and ACT admissions exams. Both of these exams are used by colleges and universities to decide if a student is eligible to be admitted into their institution. My goal as a high school math teacher is to be aware of the testing dates and keep my students practicing the skills needed to be successful on either or both of these tests. For the upcoming year, here are the testing dates for both exams during the 2020 – 2021 testing season:

SAT ACT
Aug 29
Sept 13(SAT In School), 26Sept 12, 13, 19
Oct 3, 14(PSAT/SAT In School)Oct 10, 17, 24, 25
Nov 7
Dec 5Dec 12
Feb 6
March 13March (Possible In School Dates)
April (Possible In School Dates), 17
May 8
June 5June 12
July 17
Admissions Testing for 2020-2021 Season

When a student asks me which one they should take, I always say both. Some students do much better on one of them than the other. The students should also think about which colleges they are applying and look at the requirements to help them decide which test to take. More urban high schools are paying for students to take the tests during the school day. This is an awesome opportunity and the students should take advantage. Another thing for teachers to keep in mind is that 11th grade students have an opportunity for recognition and scholarships through the National Merit Scholarship if they do well on the PSAT in October.

If you’re wondering how the SAT and ACT math portions compare, take a look at my chart below:

SATACT
2 Sections of Math:
No Calculator – 25 minutes (20 questions)
Calculator – 55 minutes (38 questions)
1 Section of Math:
60 minutes – 60 Questions
A calculator can be used on the exam.
78% Multiple Choice with 4 Choices
22% of the Questions are Grid-in
100% Multiple Choice with 5 Choices
Problems fall into 4 Categories:
1) Heart of Algebra – linear equations
and systems.
2) Problem Solving & Data Analysis
being quantitatively literate
3) Passport to Advanced Math
manipulating
complex equations
4) Additional Topics – geometry,
degrees and radians, trig or other
college and career ready topics.
Problems fall into 3 Categories:
1) Preparing for Higher Math
a) Number & Quantity
b) Algebra
c) Functions
d) Geometry
e) Statistics & Probability
2) Integrating Essential Skills
a) Synthesizing and applying
understanding to complex problems
b) Multi-step
c) Non-routine problems
d) Understanding connections
3) Modeling – This doubles with one of
the other categories. A question can be
both “Preparing for Higher Math” and
“Modeling” in other words.
Comparing the SAT and ACT Math Portions

Now that you know more about these two exams, it’s time to start thinking about how to prepare your students. Even 9th and 10th graders can take the SAT 8/9 and the SAT 10 if you school chooses to facilitate it. All levels of students need practice over these exams. These tests are not like what students are accustomed to. One of the best ways for a teacher to understand how questions are asked is to take some practice tests. Very quickly you’ll see how you need to up your game in your classes and ask questions in different ways.

In 2016, I became a teacher on an Early College High School Campus. This is when my interest in college readiness soared. I also felt bad that in my previous years I did not give much thought about these tests. In 2016, I was given a class of seniors that had never passed the TSI (comparable to the ACCUPLACER). I had no resources, so I started researching and soon found out that I was going to need to create my own. Once I got most of my students to pass the TSI, I began preparing them for the ACT and SAT. Again, I had to create my own lessons. I’m happy to say that I’ve got all of these resources in my Teachers Pay Teachers store. I’ve got them in various forms. You can purchase bundles or individual lessons. I’m still enjoying creating these resources and I’m adding things as I go. My current project is ACT bellringers. I’m also adding distance learning resources so that no matter your situation, you can find what you need.

I’m glad you made it here. This shows that you are invested in your students. They rely on us to use our knowledge to advance their knowledge! I wish you and your students success and a happy future. Please check out my resources if you are limited on what you have available!

Other Related Posts:

TSI – ACCUPLACER READY

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

GETTING READY FOR THE OCTOBER PSAT

Are Your Students College Ready? 5 Teacher Challenges!

Resources:

First 6 Weeks in Algebra 1

Algebra 1 is a fun but challenging class to teach. So many thoughts run through my head when I think about the beginning of the year in Algebra. One of the biggies is how much do the students remember from their previous math class? This is especially a big question since last year our district went to a distance learning format. I’m not sure what to expect from the incoming students, so I need a plan.

This year will be interesting. Our district has decided to have both online learning and in class learning. I’m working hard to make sure I have plenty of lessons that will work for either scenario. I’m going to start the year off with a two day review of number sense, order of operations and basic operations with integers. I’ve used this in the past because I always get a range of abilities, so I want to know where the students are. I have a print version of what I use and I’ve recently made a digital version. After I do the two day lesson, I give the students 3 quizzes (yep 3… because I want the repetition and plus it’s a challenge). All the quizzes are similar to each other but ask slightly different questions. The quizzes contain 15 questions. To move to the next quiz, students must make an 80 or better. If they don’t, they retake it. (These are timed because I don’t want the students to take too long. Either they know it or they don’t.) This can last up to 3 weeks. It’s not hard to keep up with because I take a grade on each quiz. Here’s a peek at the print version of the quiz vs. the Google Forms version:

The majority of the six weeks should (and hopefully will) be spent on solving equations. The days in the plan are block-schedule days. We have classes every other day for 80 minutes except on Fridays when the classes are only about 35 minutes. Below is plan that I will follow with the activities:

# of Days Topic
2Pre-Algebra Review – PDF Version or Digital Version
1Patterns (Boom Card Lesson)
1.5*Setting up and Solving Equations and Inequalities
1.5*Solving Equations and Inequalities
1*Literal Equations
1*Review Equations and Inequalities
My First 6 Weeks Plan

*Get all of the resources above in a bundle: Equations Bundle

I’ve linked the topics to some of my lessons and worksheets that I used in my TpT store, but as I see the need, I go find content in other places. My district uses a couple of resources that I pull from as well, but our students know how to find answers online for these assignments, so I don’t like to use them for homework.

If you’ve never used quizziz.com, you should try it. The kids really enjoy doing these. I like that the students can do them more than one time. I have the students show work in their journal. Basically it’s just a digital quiz with 4 answer choices. These are teacher-made and there are a ton to choose from on just about every topic.

One of my favorite digital resources is Boom Learning. If you like task cards, then you will love Boom Cards. Again, these cards are teacher-made. There are a variety of ways kids can answer questions. I started creating my own decks. I used two of my own creations the first six weeks. One set of Boom Cards covered patterns and how to write an expression from a pattern. The other set was for practicing solving equations and inequalities. The kids can go through them as many times as they want so they get a lot of practice and get the best grade possible. To use Boom Cards, you need a teacher account. The free account is perfectly fine, but you don’t get to see the reports. The best thing to do is to get a paid account which is only $15 – 35 dollars a year depending on which plan you choose. Make your own decks or purchase decks. There are free choices as well. Click here to go check out my store. I’m brand new at making these, but I can already tell that this will be something I work on because all of my classes love Boom Cards!

After I get used to my students and find out who has gaps in their learning, then it will be time to dive into tutoring. I will engage my students through online tutoring this year. It will be an interesting year to say the least. I know that I will need patience and I will need to be flexible. I’m ready for anything and I hope you are too. I wish you well in your new year!

Happy Teaching!

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!