In this post are ideas for teaching algebraic functions, including activities, a study that I tell students to help function vs. not a function stick, a math word wall and an awesome introductory activity to introduce nonlinear functions.
After my immensely popular tweet of these pictures: I figured I should blog about what we did for function notation in my class. We made this slider for our notebooks. The files can be found here. They are 3/page and 6/page with dotted lines where you need to cut. You will need to download into word for the files to be formatted correctly. We glued the top and bottom of the pink one down, so that the brown can slide. (Side note: 9th graders might need instruction and assistance with cutting the isolated slits on the brown one.) On the right side of our notebooks we worked through each different input value and simplified as much as we could. The next day we did a quiz-quiz-trade activity. This helped students gain confidence. After doing four problems quiz-quiz-trade style I gave them one to do individually and went around checking their work. I did a quadratic to make sure they were simplifying exponents BEFORE multiplying. If students didn't have it correct I could give them some quick feedback, they would fix it, and I would check it again. There's more to what we did (and are still doing), but that's all I feel like blogging about now. Thanks for all the encouragement via my tweet. It was amazing to see the power of twitter in that another teacher (in another country) took the idea and improved it and used it THE VERY NEXT DAY! My students all think I'm a super-star now and they are impressed that I had one idea of my own. It reminded me of what a blessing it is to be part of the #MTBoS! -Kathryn
The table below shows you how to differentiate and integrate 18 of the most common functions. As you can see, integration reverses differentiation, returning th
Algebra resources for teaching and learning mathematics. Fun and visual resources for maths teachers and kids.
This bundle of Algebra Math Anchor Charts includes 50 charts! This resource was put together using high quality photos of the hand-drawn anchor charts that I use in my classroom. You will get the individual anchor charts in PDF format of each black & white outline template as well as the completed colored version. Some outline templates contain color (they were created previous to me only making them black & white). The formats are designed for you to either print on regular-sized paper, print in poster-size (original chart was 24" by 32"), or even project the charts and trace them so you can edit whatever you need! You can also send them to a print shop for blue-printing! You can hang them up as you cover the topics on a bulletin board, or you can keep them all up all year long as a word wall! Many teachers have also been printing the outline template for students to complete and put into their notebooks, or printing smaller versions of the completed version for the same reference purpose. This bundle includes: Word for Algebraic Expressions The Order of Operations The Number Properties The Distributive Property Relations Is it a Function? Evaluating Functions Interpreting Graphs of Functions Consecutive Integer Equations One-Step Equations Solving Equations Variables on Both Sides Absolute Value Equations Ratios Percents of Change, Tax, Discount Literal Equations Weighted Averages Inequality Symbols + Compound Inequalities Inequalities in One Variable Graphs Absolute Value Inequalities Graphing Linear Equations Calculating Slope Slope-Intercept Form Graphing Linear Functions Finding the Inverse Function Systems of Equations Properties of Exponents Rational Exponents Exponential Functions Exponential Formulas (Growth, Decay, Compound Interest) Geometric Sequences Recursive Formulas Polynomials Multiplying Polynomials Factoring Flow Chart Absolute Value Functions Graphing Quadratics Quadratics - Vertex Form Completing the Square / Quadratic Formula Memorize the Squares Radical Functions Simplifying Radicals Operations with Radicals Radical Equations The Pythagorean Theorem Distance and Midpoint Formulas Graphing Rational Functions Simplifying Rationals Multiplying and Dividing Rational Expressions Adding and Subtracting Rationals
File for the Post: Relations and Functions Card Sort This lesson was created for a mandatory tutorial session for Algebra 1 students. I was in charge of creating a 30 minute review lesson over "Relations and Functions." This lesson had to include a 5-10 minute review lesson and an activity. First, students went over this graphic organizer with four practice problems to review relations and functions. After students reviewed relations and functions, they independently completed the following cut and paste activity. If you read my blog, then you know all about my love for card sorts! Students had to match up the correct table, graph, map, and ordered pairs together and determine if the relation was a function. If you download the activity, then you will notice that there is a separate document that does not require cutting (if you do not have the time). Sorry for the short and sweet post, I just had several teachers ask for the cut and pasted document.
Domain and range intervention! Teaching domain and range in special education
Do you need help decorating your math classroom? Here are 18 different Algebra posters to help! Each poster was created with a 3:4 sized ratio. This means they can be printed on 9x12, 12x16, 18x24 or 36x48 inch paper or poster. Posters can be printed at local office stores or your local school! The zip folder download contains 10 JPEG images, one for each poster. The JPEG file name matches the title of the poster. Topics Covered: - Linear functions - Slope and Rate of Change - Systems of Equations - Linear Inequalities - Parallel and Perpendicular - Quadratic Functions - Exponential Functions - Multiplying Polynomials - Factoring Quadratics - Quadratic Formula - Properties of Exponents - Exponential Functions - Growth and Decay - Domain and Range - Evaluating Functions - Parent Functions - Transformations of Functions - Simplifying Radicals - Rational vs Irrational Numbers Terms of Use: This product is for the use of your classroom only. Thank you for respecting these terms and the work put into creating these resources! :)
Precalculus will be moving beyond their introduction to functions and function notation from Algebra II and into a in-depth development of transformations. We will be applying transformations (translations, reflections, dilations, etc.) to many of the parent functions included in the image above (we will save trigonometry for the Spring!). Understanding transformations is a crucial link between the algebraic form of a function and its graphical behavior. We will spend a considerable amount of time exploring this topic and working toward mastery. You all will continue to complete the lengthy linear programming problem set and for that reason I have a great deal of information to post--I will post the homework, reference materials, and a YouTube video that goes over the basics of linear programming from the previous week on linear programming as well as the upcoming information on transformations! Enjoy. Text Examplars: Homework Reference Material Wolfram Demonstration Upcoming Material for the next two weeks. Text Examplars: Homework Reference Material Videos on Transformations: Brightstorm Videos ______________________________________________________________________________ Algebra 2 will be moving into systems of equations through the lens of coordinate geometry. Below is a student work example of some of the resources I will be using and what we will be exploring. The purpose is for students to have a concrete link between their algebraic worlds and geometric worlds as well as to ground the solving of systems in the graphical world and slowly move to more abstract manipulation. Check out this 3D Lathe that will help you visualize the creation of 3D geometric figures from the two-dimensions of the coordinate plane. http://www.fi.uu.nl/toepassingen/00182/toepassing_wisweb.en.html Homework (from the University of Houston) Reference Material Reference Sheet 1 Reference Sheet 2 Brightstorm Videos: These videos are aligned to the sections from your textbook, so as you are completing homework from your textbook you can easily locate the most relevant videos for you!
This water lab is a super fun way to introduce nonlinear functions in an algebra class. The math department at my school uses this lab as a way to start the school year in Algebra 2. The students love it, and by the end of the lab every student understands what it means to be an algebraic function!
This has been my favorite project for two years now! I have reserved the computer lab for an entire week each time and let the students show...
File for the Post: Relations and Functions Card Sort This lesson was created for a mandatory tutorial session for Algebra 1 students. I was in charge of creating a 30 minute review lesson over "Relations and Functions." This lesson had to include a 5-10 minute review lesson and an activity. First, students went over this graphic organizer with four practice problems to review relations and functions. After students reviewed relations and functions, they independently completed the following cut and paste activity. If you read my blog, then you know all about my love for card sorts! Students had to match up the correct table, graph, map, and ordered pairs together and determine if the relation was a function. If you download the activity, then you will notice that there is a separate document that does not require cutting (if you do not have the time). Sorry for the short and sweet post, I just had several teachers ask for the cut and pasted document.
Properties of logarithms can be tricky for students in Algebra 2 and teachers. I love using activities to teach logs and this post explains how I teach them to my kids!
With summer here, it is a good time to reflect over the last school year – what went well, what didn’t, what I want to keep, what I want to change, etc… so for my next few posts I will be sharing s…
This function vs not a function card sort activity is the perfect way to assess whether or not students can apply the definition of a function to determine
Introducing Quadratic Factoring with Conspiracy Theory in Special Ed Algebra 2
I've finished up with my 8th grade curriculum, and so it's time to start reviewing for our state test. With two weeks left until Spring Break, I wasn't quite ready to hit the test practice yet, and I was thrilled when I stumbled across this Water Park Project. The project allowed me to review slope, midpoints, the distance formula, proportional relationships, slope-intercept form, and solving systems of linear equations in one assignment! I've even treated the project as a real job assignment by doing "foreman checks" to see if they had met their deadlines for finishing each task. I purchased a flip chart that was actually large sheets of graph paper from the office supply store, and the kids loved that they were like giant post-its. We finally finished up with the final designs and reflection assignment today, so I wanted to show off their finished projects.
Relations and functions notes and worksheets for high school algebra 1. Notes, worksheets, and all answer keys are included!
Editable dice for function operations in Algebra 2
The Forming Expressions from Function Machines Worksheet employs function machines to teach algebraic expressions, their connection to function machines, and simple formula rearrangement.
File for the Post: Relations and Functions Card Sort This lesson was created for a mandatory tutorial session for Algebra 1 students. I was in charge of creating a 30 minute review lesson over "Relations and Functions." This lesson had to include a 5-10 minute review lesson and an activity. First, students went over this graphic organizer with four practice problems to review relations and functions. After students reviewed relations and functions, they independently completed the following cut and paste activity. If you read my blog, then you know all about my love for card sorts! Students had to match up the correct table, graph, map, and ordered pairs together and determine if the relation was a function. If you download the activity, then you will notice that there is a separate document that does not require cutting (if you do not have the time). Sorry for the short and sweet post, I just had several teachers ask for the cut and pasted document.
Permutations and Combinations can be taught in many different ways. Here are some solid ideas for attention getters using card tricks!
"Miss, why are we cutting and pasting? Do you think we're babies?" Then within a few weeks, my consumer math seniors would be pretty into building their interactive notebooks. And not one student lost a notebook over the years. I believe this ownership was built along with the cutting, coloring, arranging and pasting. Their notebooks became something my students didn't want to lose because of all the work they represented. Though the cutting and pasting does take more time than typical math notes, I feel this tradeoff is well worth it. Linear equations foldables Do your students enjoy building interactive notebooks? Or maybe you haven't yet tried them and are interested in learning about the benefits. To me, that ownership is the main benefit. Kids like and deserve getting creative, and math is a good a place as any for a little creativity. In this post, I want to show you some of the interactive notebook foldables I've made over the years for students of all ages. They can all stand alone as flipbooks. Each comes together with scissors and a stapler. MATH FOLDABLES 1: Whole number place value foldable This place value foldable highlights what exactly the expanded form of a number means. Place value foldable Under each flap is a visual representation of the place value (above you can see 5 blocks of 1000 to represent 5000) and a piece of the number's expanded form. 2: Decimal place value foldable Decimals are so weird to visualize. Underneath each flap of this decimal place value foldable is a visual representation of how small these tenths, hundredths, thousandths get in relation to a unit cube. Decimal place value foldable A thousandth is really small! It really becomes concrete seeing how small 0.005 is compared to a unit cube. 3: Slope foldable This slope foldable comes in a larger set of linear equations foldables that includes the slope formula, the point-slope form of a linear equation and the slope-intercept form of a linear equation. Slope foldable In this photo you can see the scaled-down version of the foldable that students can use to take notes. There is also a version that is more scaffolded along with a digital version in Google Slides. The printable foldables can be glued into student notebooks or can stand alone as references for the equations. 4: Comparing slope foldable This one takes more than scissors and a staple to go together, but if your students are like most and struggle with slope, this comparing slope foldable lets them see and feel it. Comparing slope foldable The foldable folds in half to fit right into a notebook. 5: Quadratic word problem keywords foldable Our quadratics unit was always one of my favorites to teach. Kids would start our unit totally intimidated but end as quadratic bosses. I loved being there for that growth. Quadratic word problems foldable This quadratic word problems foldable helps students identify the important parts of a parabola as they work through projectile motion problems. 6: Quadratic functions in vertex form foldable This quadratics in vertex form foldable comes in a larger set of nonlinear functions in vertex form foldables. Included in the set is this one for quadratics, along with one for absolute value functions in vertex form and radical functions in vertex form. Quadratic functions foldable Under each flap is an explanation of the a value, that x stays as x, which way h shifts, to remember to square the parenthesis, and which way k shifts. 7: Compound interest foldable I loved teaching consumer math because of how learning to be smart with money was so empowering. This compound interest foldable is part of a larger set that includes a simple interest foldable, an annual compound interest foldable and this one where interest is compounded multiple times throughout the year. Compound interest foldable I put parenthesis around the exponent to remind students that n and t are multiplied first. This was the #1 issue I'd see when students worked with this formula. You can see all of the foldables I've made here: Math Foldables More posts: Fun activities for teaching teens financial literacy Teaching linear equations Hands-on even & odd number investigation! Math word walls Free math resource library
There are a total of 10 units that include: Unit 1 - Prerequisite for Algebra and Algebraic Expressions Unit 2 - Solving and Graphing Linear Equations and Inequalities Unit 3 - Features of a Function Unit 4 - Sequences (Arithmetic and Geometric) Unit 5 - Graphing Lines and Determining Slope Unit 6 - Expressions Containing Exponents Unit 7 - Solving and Graphing Systems of Equations and Inequalities Unit 8 - Identifying, Classifying, and Operations on Polynomials Unit 9 - Features of Quadratics Unit 10 - Defining and Simplifying Radicals There are two pages for each concept. The first page is used for direct instruction (notes) and the second page is for students to practice the concept. The first page includes a "I can..." statement and the second page includes an area where students can rate themselves on how well they understand the concept. This allows students to look back in their interactive notebook before a test and know which concept they need to study. There are some pages that have foldables. The complete break down for each unit is given below: -- Unit 1: Prerequisite for Algebra and Algebraic Expressions • Rational/Irrational Numbers • Real Number Properties (Commutative, Associative, Distributive, Additive Identity, Multiplicative, Zero Property, and Additive Inverse) • Solve One-Step Equations Involving One Variable • Solve and Graph One-Step Inequalities Involving One Variable • Use Order of Operations to Simplify Expressions • Analyze and Evaluate Expressions • Define and Apply the Absolute Value • Simplify Expressions by Combining Like Terms • Simplify Expressions by using the Distributive Property -- Unit 2: Solving and Graphing Linear Equations and Inequalities • Solve Two-Step Equations involving One Variable • Solve Multi-Step Equations involving One Variable • Solve Equations with Variables on Both Sides involving One Variable • Solve Equations involving Multi-Variables • Solve and Graph Two-Step Inequalities • Solve and Graph Multi-Step Inequalities • Solve and Graph Compound Inequalities • Solve Absolute Value Equations • Solve and Graph Absolute Value Inequalities • Properties of Equality (Addition, Subtraction, Multiplication, Division, Reflexive, Symmetric, Transitive, and Substitution) • Use Proportions to Solve for an Unknown -- Unit 3: Features of a Function • Intro to Functions • Evaluating a Function & Function Notation • Domain, Range, Minimum, and Maximum • Piecewise Functions -- Unit 4: Sequences (Arithmetic and Geometric) • Intro to Sequences • Arithmetic Sequences (Recursive and Explicit) • Geometric Sequences (Recursive and Explicit) -- Unit 5: Graphing Lines and Determining Slope • Plotting Points on the Coordinate System • Determine Slope Given a Graph • Determine Slope Given a Table or Two Points • Define, Write, and Graph Slope-Intercept Form • Determine a Linear Equations Given a Table • Standard Form to Slope Intercept Form • Determine Linear Equations Given a Graph • Determine Linear Equations Given Two Points • Determine and Graph the X and Y intercepts Given an Equation • Graph Horizontal and Vertical Lines • Write Equations of a Line Given a Slope and a Point, or Two Points • Write Parallel and Perpendicular Lines Given an Equation -- Unit 6: Expressions Containing Exponents • Intro to Exponents • Properties of Exponents • Intro to Scientific Notation • Converting Between Standard Form and Scientific Notation • Adding and Subtracting Scientific Notation • Multiplying and Dividing Scientific Notation -- Unit 7: Solving and Graphing Systems of Equations and Inequalities • The Three Types of Solutions: No Solution, Infinitely Many Solutions, and One Solution • Solving Systems of Equations by Graphing, Substitution, and Elimination • Write and Solve Word Problems involving Systems of Equations • Solve and Graph Systems of Linear Inequalities involving One Variable -- Unit 8: Identifying, Classifying, and Operations on Polynomials • Intro to Polynomials • Operations on Polynomials (Adding, Subtracting, Multiplying, and Dividing) • Multiplication of Binomials -- Unit 9: Features of Quadratics • Intro to Quadratics: What is a quadratic? • Solving Quadratics by Taking Square Roots • The Quadratic Formula to Solve for Roots • Using the Completing the Square to Solve for Roots -- Unit 10: Defining and Simplifying Radicals • What is a radical? • Basic Properties of Simplifying Radicals Total Pages: 200+ (400 pages including answer keys)Answer Key: IncludedDocument File: Zip Containing PDF Files
File for the Post: Relations and Functions Card Sort This lesson was created for a mandatory tutorial session for Algebra 1 students. I was in charge of creating a 30 minute review lesson over "Relations and Functions." This lesson had to include a 5-10 minute review lesson and an activity. First, students went over this graphic organizer with four practice problems to review relations and functions. After students reviewed relations and functions, they independently completed the following cut and paste activity. If you read my blog, then you know all about my love for card sorts! Students had to match up the correct table, graph, map, and ordered pairs together and determine if the relation was a function. If you download the activity, then you will notice that there is a separate document that does not require cutting (if you do not have the time). Sorry for the short and sweet post, I just had several teachers ask for the cut and pasted document.
Evaluating Piecewise Functions Worksheet. Evaluating Piecewise Functions Worksheet. Quiz & Worksheet Graphing Piecewise Functions
Are you looking for a fun, hands-on linear equations project? This algebra project was one of my favorite things about teaching 8th grade math and algebra. My students would run into the room and right over to the windowsill, excited to see their grass, collect the day’s date, analyze slope, write linear equations and all without even realizing they were doing algebra!
This function vs not a function card sort activity is the perfect way to assess whether or not students can apply the definition of a function to determine
"Possibly The Best Math Chart Ever Created" But really, it is pretty cool. #math #functions
interactive notebook page ideas for algebra 1
