Posts tagged Algebra 1

17 results

Factoring Flowchart

On the afternoon I was digging through my Evernote archives, I stumbled upon this gem of a post by Elissa Miller. She was talking about checking to make sure they knew the difference between each type of factoring. I had just given an assessment on factoring and solving quadratic equations by factoring to my Algebra 1 students and they did poorly on it. I knew that part of it was they just didn’t practice enough, but I also recognized that they didn’t know how to figure out what kind of factoring to do. After looking at Elissa’s flowchart to help her students, I decided to create one of my own for mine. I printed these 2 to a page on card stock so students could put them in the folder in their interactive notebooks easily. What I decided to do is to offer feedback on the assessment to the students to help guide them in making better decisions on what […]

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Systems of Linear Equations Scratch Offs

An activity I’ve done with my Algebra 1s for the last two years (and is reusable) is scratch off cards. I think I originally saw the idea from Kristen Fouss but after trying to search her blog, maybe it was from Sam Shah. Regardless of where I saw it, here’s how it worked for me. Step One: Create problems with a box to place the answer. Step Two: Laminate the cards. THIS IS IMPORTANT! If you don’t laminate, you will need to put clear packing tape over the answer. I found it much easier to laminate.   Step Three: Mix 1 part dish soap and 2 parts acrylic paint together. (I got those directions from here.) Step Four. Paint the mixture over the answer. This may take a couple of times depending on how heavily you paint the mixture over the answer. The first year I did it, it took me several coats because I painted too lightly. This year, it went […]

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How do you plan a unit?

No, seriously, how do you plan a unit? I know it sounds odd for a 23-year veteran teacher to ask the question, but how do you plan a unit? Backing up… we are getting ready to begin the unit with linear functions. You know the one, the one in Algebra 1 where we work on graphing lines and writing linear equations. Where slope and rate of change are formally introduced. I know my students are already aware of y = mx + b from 8th grade. I’ll be doing a pre-assessment this week to confirm what they already know how to do. But already knowing they’ve at least been exposed to y = mx + b does change some things. So, these are the Common Core State Standards that I am planning on working with in this unit: F-IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of […]

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Arithmetic Sequences Activity

As I was driving to work today, I was trying to come up with an activity to practice working with arithmetic sequences. I had 8 practice problems on a worksheet, but I knew that wouldn’t be enough practice for my Algebra 1 students. I had thought about going and creating a Polygraph at the Desmos Teacher website, but when I got to school, I saw the chromebooks were already taken for my Algebra 1 classes. (I may still go back and do this, though). The idea popped into my head to have students create their own arithmetic sequence. It would give me a chance to make sure they understood what an arithmetic sequence was and it would give them a chance to practice writing them and creating the equations, which is what I needed them to do. These are the directions I projected on to the Smart Board: I did modify them a bit after the first class. Originally, I did […]

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Given Time, Things Work

In between conferences last night, I was grading Algebra 1 papers. My students had an assessment over graphing (using a table), confirming that points on the line belonged to the equation graphed, and comparing a graph, a table, and an equation. By no means, is this the most exciting thing I teach in Algebra, but it is a necessary thing and important for some future understandings. This is my third year teaching Algebra 1 under the Common Core State Standards for Mathematics. Although I am getting more comfortable with the standards, I am, by no means, a master of teaching them. I have made some improvements, but I don’t feel I’m at the point that I absolutely have gotten there. As my 3rd Algebra 1 class walked in yesterday, they told me, “Mrs. Henry, I heard this test was hard.” My heart sank. I had not gotten far in grading the assessments, but what I had seen so far looked great. […]

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Making Connections

A couple of tweets in the last week resonated with me as we are wrapping up the year. Julie Reulbach shared The difference between memorization and understanding is that students quickly forget things they memorized. How can I help them see that? — Julie (@jreulbach) May 29, 2015 As we are preparing for final exams, I see a lot of this. Today, we were working on reviewing solving systems of linear equations and many of them had forgotten how to graph lines. And as I was walking around, helping students, it dawned on me why. You see, my students have just come off a section on solving quadratic equations. To be honest, it was a little rushed due to time constraints, but not as rushed as last year. Prior to solving quadratic equations by taking square roots, or completing the square, or the quadratic formula, we had spent quite a bit of time on graphing quadratic equations (here is a […]

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Sketching Quadratics

In this lesson, our learning target is: I can sketch a rough graph using the zeroes of a polynomial and other easily identifiable points such as the y-intercept. I’m incorporating A-APR.3 (Identify zeroes of polynomials when suitable factorizations are available, and use the zeroes to construct a rough graph of the function defined by the polynomial.) and A-SSE.3a (Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeroes of the function it defines.) from the Common Core State Standards. We have just finished solving a quadratic equation by factoring, which incorporates A-SSE.3a. This is the first of four learning targets in my unit on Quadratic Functions, which focuses on graphing. I had originally intended to also do transformations in this unit, which I hope to do in the future. I am running out of time in the school year and I […]

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It only took me 23 years to get it right…

For the first time, I am really happy with how I am teaching factoring and how my students are catching on to it. Throughout this unit, I have been talking about how factoring is un-doing the distributive process that we did when multiplying polynomials. We are looking for the factors that we multiplied to get us the answer we are given. We are not all of the way through, but this is what I have done so far: Days -2 through 2 – Introduced X-Puzzles (Julie references them) for students to work on finding two numbers that multiply and give one number and add up to another number (example – two numbers that multiply and give 48 and add up to 14: 6 and 8) Day 1 – Taught how to factor using the GCF. Day 2 – Taught how to factor four terms using 2 and 2 grouping. Day 3 – In class practice factoring using the GCF and 2 and […]

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Common Core and PARCC Combined Tables

You may have noticed a lack of posts here lately. It is for many reasons, many of which involve the busy-ness of being a mom of a 6th grader and a 3rd grader and a math teacher and other roles. But part of why involves a project I began in late October. I teach in Ohio, which is was (as of June 30, 2015) a PARCC Consortia state. When Common Core was first released in 2010, grades K through 8 had their own set of mathematics standards. There are 5 domains of standards at the high school level, but they are not arranged by course. In addition, as you read the standards, there is some overlap. An Appendix (A) was added with a suggested list of which standards should go with which course (Algebra 1, Geometry, Algebra 2 or Math 1, 2, or 3), but that’s as much guidance that has been given. So Ohio was involved with both consortia at the beginning. […]

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Trying to build more self-reliant students

My Algebra 1 class is working on Common Core State Standard N.Q.1. I have two learning targets that we will be working on in succession: I can use and interpret units when solving formulas. I can perform unit conversions. I found some resources online I was happy with for actually doing the unit conversions, however, I did not find anything I was real happy with for using and interpreting units when solving formulas. So I developed this: My intent was to introduce the idea, put the students into groups of four and have each student work through 2 problems, comparing with other students in his or her group who would have done the problems to see if they got reasonable answers. When they were satisfied they had good answers and units, they would get another half sheet. We did number 1 together on the SMART Board so they would see what I wanted to see as far as work went, […]

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