Free Discriminant Cheat Sheet for your Quadratic Formula Unit

In this post, I want to share a few resources for teaching the discriminant as part of a Quadratic Formula unit. 

This simple discriminant cheat sheet helps students make the connection between the value of the Quadratic Formula's discriminant and the number of real solutions the equation will have. It also shows examples of graphs with 1, 2, and 0 zeros and what the discriminant will look like in each case.

The discriminant's negative signs can get to feeling a bit overwhelming for some students, so I always have then count the number of negatives to figure out if they'll be adding or subtracting under the radical sign.

(-) = - subtracting

(-)(-) = + adding

(-)(-)(-) = - subtracting

This helps students reduce the number of sign errors when evaluating the Quadratic Formula. We so also discuss b^2 and how it will always be positive, so not to count its negative sign.

I recently updated this discriminant sorting activity that helps students recognize if a quadratic will have 0, 1 or 2 real solutions. Students can cut and paste the different slips into their correct columns on the answer sheet. There's a smaller answer sheet included if you'd like students to just write each letter and not cut/paste. 

A no-prep drag and drop Google Slides version of the discriminant sorting activity is also included.

For students learning about complex solutions to the Quadratic Formula, I just finished a self-checking Quadratic Formula digital math escape room activity.

The escape room also comes printable, which is probably the version we'll be using in class. The printable versions of the digital math escape rooms are easy to grade. Students write their 4-letter codes on their answer sheet.

> Browse all Quadratics

More posts:

Free Quadratic Formula Warm-up Template

Fun With Quadratics

Domain and Range Finder Tools

Do your students struggle finding domain and range of graphs? I made a couple printable domain and range tools to help our students this year.

There are directions pointing students to look at x for domain and y for range as they drag each tool across the graphs. There are also directions printed on the tool for what to record for domain and range when a graph has an arrow.

We have always used rulers to find where graphs start and stop, but I wanted something a bit more self-teaching for our students this year. The graph cards in the photo are a free download on my blog here.

You can find the domain and range finder tools here on my website.

I also made a new domain and range of graphs cheat sheet for our students that you can find here in my drive.

UPDATE: A 3rd tool for finding increasing/decreasing intervals of graphs has been added to the file linked below.

> Browse all domain and range activities

Domain & Range Finder Tools

Perfect Squares and imaginary numbers

 

This past week, we started learning about imaginary numbers in algebra 2, which will lead into solving with the Quadratic Formula. I made this simple cheat sheet for the students so they can quickly check if a number is a perfect square and be reminded of how imaginary numbers work when simplifying and multiplying. 

You can find the sheet in my Google Drive here.

Complex number operations escape room

Patterns of i poster

Solving quadratic equations escape room

2 free factoring quadratic trinomial cheat sheets

What's your favorite method for factoring quadratic trinomials? For me, it's the AC method with grouping because there's no guess and check, which frustrated me as a high school student. I remember endlessly erasing my work, and settling with "close enough" on some problems. The box, or area, method has grown on me over the years, especially how it links back to multiplying polynomials.

The structure of the AC method works for me, and is the method I have used most when teaching students to factor. I don't know when I learned it, but I remember thinking that it would have been a helpful tool for me in high school. If making the list of factors is difficult, students can divide AC with 2, 3, 4, ... with a calculator and write down any quotients without decimals, checking which factor pair adds to B.

I made a couple factoring quadratics cheat sheets and posted them on Facebook this week.

We're getting to factoring in a few weeks after imaginary number operations, Quadratic Formula and solving with square roots and we're going to teach the kids the box (area) method, which they may have seen in algebra 1. AC with grouping will be the backup plan for students who aren't clicking with the box method. Multiplication charts will also be available to students who need them.

Box method factoring

AC method with grouping

If you are teaching factoring this year, I wanted to share the two cheat sheets above in case you find them helpful. I also wanted to mention that the cheat sheets I share are never intended to be standalone teaching tools. They always go along with lessons as a way to help students through independent work. This was something that came up this week, too. 

> Browse all Quadratics activities

You can download the two factoring cheat sheets free here.

> Browse all free math cheat sheets

free math resource library

 

Function Composition Cheat Sheet

We've been working on composition of functions in algebra 2 the last couple weeks, and some students are still having a hard time with composing functions shown in graphs and equations. We're also seeing a few students looking at the y column in tables when evaluating functions shown in tables.

There are a bunch of free math cheat sheets on my blog here, and I wanted to add another one for composing functions.

How to Make Any Math Word Problem Solvable for Students

Solving math word problems is tricky for students whether they are in 3rd grade using multiplication, in middle school solving ratios, or in high school working through quadratic word problems. If you're looking to support students through solving word problems, this math bulletin board set is a guide to solving any math word problem students will see throughout school.

The bulletin board posters are written in simple language so that all students can access the information and outline five steps in the solving process. 

1: UNDERSTANDING 

This step asks students if they understand what is being asked of them to solve and if they understand all of the vocabulary in the word problem. 

2: PROCESSING 

This step asks students if they are able to restate the problem in their own words, if they can draw a picture, if they can make an easier example, and if it's possible to add their own name into the word problem. This always seems to make word problems easier! 

3: PLANNING 

In this step, students make a plan to solve their word problem. Strategies include writing an equation, using reasoning, making a list, finding a pattern, etc. 

4: SOLVING 

Students always want to jump to solving, so they'll begin to see that solving can only come after a plan has been put in place. This step asks students to go ahead with their plan, and if their plan fails to try a new plan. Most important is staying persistent. 

5: LOOKING AHEAD 

This final step asks students to think ahead to when they might see a similar problem and to consider what approach might be best then. 

You can find this math word problems bulletin board set here.

Math Word Problems Bulletin Board

> Browse word problem activities.

More posts:

Math Classroom Decoration Ideas

Math Word Walls

Consumer Math Curriculum Warm-Ups 18 Units of Financial Literacy Bell Ringers

Do you start math class with a warm-up or a bell ringer? My classes started going more smoothly once I got my warm-up routine down. 

Our classroom routine: 

Students enter our classroom and grab a warm-up out of the basket at the front of the classroom. The warm-ups were either a 1/2-sheet or 1/4-sheet of paper and would get glued into their interactive notebooks or on binder paper. Students get time to work on their warm-up independently before we go over the answers together to make sure we were all on the same page.

Sometimes if students weren't focused, I'd switch gears and collect the warm-ups for points. This kept students on their toes. I'd only ever do this when the warm-up was a spiral review of material students had recently learned. This was usually the case with our warm-ups-- they'd be a short review of previous material before moving on to learn new math concepts.

I put together an 18-unit pack of consumer math warm-ups to get students thinking about real-world math as soon as they sit down for class. There are at least 6 warm-ups included for each curriculum unit listed below, along with answer keys:

18 units of consumer math warm-ups: 

• Wants vs. needs 
• Checks and registers 
• Wages and salary 
• Bank accounts 
• Budgets 
• Electronic banking and credit cards 
• Credit score 
• Discounts and coupons 
• Sales tax and tip 
• Percent change 
• Unit price 
• Income taxes 
• Car loans 
• Mortgages 
• Student loans 
• Investing 
• Car insurance 
• Health insurance

The warm-ups are all sized to be cut and pasted into an interactive math notebook. Students answer their warm-ups on their notebook paper, discuss with each other and report out on their answers to create a classroom discussion. These are the same warm-ups included in the Scaffolded Consumer Math Curriculum.

BROWSE MORE CONSUMER MATH