Increasing and Decreasing Finder Tool for Graphs

Do your algebra students struggle with finding the increasing and decreasing intervals of graphs? This increasing and decreasing finder tool guides students where to look when finding the increasing and decreasing intervals.

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Students watch the graph move up and down the ruler on the side.

domain and range finder tools w/ increasing and decreasing

The increasing and decreasing tool was added to a similar domain and range finder tool that guides students where to look when finding domain and range. See the tools here.

How to Stop Students from Second-Guessing on Math Exams

The brain is a funny thing. We've evolved these giant frontal lobes that can plan years in advance, but throw in a bit of test anxiety and we're suddenly running from a lion at dusk. When the brain detects danger, that massive frontal cortex shuts off and is just there taking up space.

If I had to estimate, every single student I have ever had in any of my special education math classes has had some level math anxiety. I have my theories as to why this is, but in this post I want to instead focus on ways to help students overcome this anxiety when taking tests so that they don't doubt their answers.  

How to stop students second-guessing their math

I asked teachers on Facebook what they do to help students with this, and got a bunch of great advice. Their advice is below. If you'd like to read the original thread, it's here.

Compound Interest Cheat Sheet

This week, the plan is to finish learning about compound interest so that we can squeeze in projectile motion next week before starting final exam review the week after. It'll be tight, but that's the goal! Hard to believe there are only a few weeks left.

We started our exponential functions unit learning how to graph exponential functions by building tables, identifying a and b given a table, and writing the equations of exponential graphs with the y-intercept and f(1) highlighted.

We then moved on to compound interest compounding annually, then compounding more often. Today students started a compound interest escape room that covers compounding annually, quarterly, monthly, and daily. The escape room also comes as self-checking digital, but we used the printable version. It's more forgiving and keeps students offline.

Today, I made students this exponential functions cheat sheet that they can use as we finish up the escape room, exponential decay, and on their upcoming quiz as an IEP accommodation.

For decay, I may also give students this friendly percents reference depending on how things go. We may just stick with (1 - r), but I'd like them to have another perspective for finding the base of decay functions.

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2 Percent of a Number Cheat Sheets

In this post, there are two free percent of a number cheat sheets for a consumer math unit on calculating percentages of numbers and calculating discounts. Each can be added to student notebooks as a reference when learning how to calculate percentages.

Percent of a number cheat sheet

The first percent sheet reminds students of the divisor when calculating the percent of a number. For example, We can divide 125 by 5 to find that 25 is 20% of 125. This sheet prints on half a page to fit into a student notebook.

Friendly percentages cheat sheet

The second is a friendly percentages reference that's helpful for calculating discounts. If a shirt is 15% off, we can calculate the shirt's price by finding 85% of the original cost of the shirt. I always find this easier than calculating 15% then subtracting that amount from the original price.

This friendly percentages sheet can also be referenced during an exponentials unit when calculating decay. If the value of a car is depreciating by 15% per year, we can use .85 as the exponential's base.

Percent of a Number Cheat Sheets

The two sheets are found free in the same download here: Free percent of a number cheat sheets

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How to Write an Exponential Function Equation Reference Sheet

It's almost the Massachusetts version of spring break here (April vacation), term 4 just started (hard to believe!) and we just began on our exponentials unit in algebra 2. This is going to be a super short post just to share a cheat sheet to help students remember how to write an exponential function equation given two points.

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The sheet walks students through how to write exponential function equations from a table of values, including the y-intercept and one other point. Students are shown how to solve for the exponential's base b, then how to write the equation using this base and information from the table.

You can download this cheat sheet free here.

Normal Distribution Curve Reference Sheet in Algebra 2 Statistics

 

We started our statistics unit in algebra 2 and so far have reviewed box and whiskers plots, dot plots, histograms and learned about skewed data, interquartile range and experimental vs. observational studies. Last week, we started learning about normal distribution and will be on this topic for a little while. We move onto z scores tomorrow.

We gave students a simplified version of the curve with whole number percentages to make calculations easier to manage. I wanted to share this reference with you in case it would be helpful for your students, too. If you'd rather keep the decimals in the percentages, there's also a blank curve in the file.

We printed a bunch on this orange paper (the orange reminded me of that funny normal distribution ghost meme) and laminated them so that students can write on their curves while working.

You can download this normal curve reference here from my Google Drive.

Probability error analysis

If you teach probability, I recently made a "2 truths and a lie" error analysis activity that covers independent and dependent compound probability.

Data and Statistics Activity

Before we got into symmetrical data analysis, we reviewed skewed data and completed this data and statistics activity. It covers mean, median, mode, skew, histograms, dot plots and box and whiskers plots.

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Factoring Trinomials with Algebra Tiles Visual Guide

This week, I worked on a visual guide for how to factor quadratic trinomials using algebra tiles. It has 10 examples, and each example includes the number of tiles needed with any zero pairs, notes about the example and a common student misconception about arranging the tiles for that trinomial. 

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If you have never used algebra tiles to factor trinomials and want to give them a try, I wrote this guide to make it easy to get started.

The guide covers quadratic trinomials where A=1 and where A>1, including when zero pairs are needed because of negative C values. 

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There are 10 factoring examples in the guide with their common misconceptions, along with 2 additional examples for simplifying a quadratic expression in vertex form and solving a quadratic equation by completing the square.

I've been making algebra tiles factoring videos for social media and YouTube, and thought it would be nice to have a printable algebra tiles visual guide that also shows some of the misconceptions students may have about arranging the algebra tiles when factoring quadratics.

Examples in the guide include:

• x² + 5x + 4 
• x² – x – 6 
• x² + x – 6 
• x² + 5x – 6 
• x² – 4x + 3 
• x² – 9 
• 2x² + 7x + 3 
• 2x² + x – 1 
• 3x² + 4x + 1 
• 3x² + x – 2
• Simplify (x + 3)² – 4 
• Solve x² + 2x = 3 by completing the square

If you find there's an example you'd like added to the guide, please send me an email. I'm happy to add it in. You can find the guide here.

Algebra Tiles Visual Guide

Algebra tiles connect nicely to the area (box) model of factoring trinomials for when it's time to move past these concrete models. There's a free factoring quadratics cheat sheet here for the area model, along with one for the AC grouping method. 

factoring trinomials cheat sheets

I like to teach the AC grouping method to students who struggle with multiplication facts because it takes out all guessing, but the box method has been growing on me! It's like a puzzle for students to figure out.

Additional resources:

Algebra tiles blog posts

Algebra tiles YouTube playlist

Algebra tiles reels on Facebook