Concord Consortium
Parameters and Clusters II
Let's give parameters a second try. Scholars take a second look at a system of linear equations that involve a parameter. Using their knowledge of solutions of systems of linear equations, learners describe the solution to the system as...
EngageNY
Vectors and the Equation of a Line
Represent linear equations in both two and three dimensions using parametric equations. Learners write parametric equations for linear equations in both two and three variables. They graph and convert the parametric equations to...
GeoGebra
Getting on the Right Wavelength
Predict an equation that waves up and down. Pupils set the height, radius, and period of a Ferris wheel. The learners write a sine equation to match the graph of the height of a point on the wheel as a function of time. Running the...
Illustrative Mathematics
Exploring Sinusoidal Functions
What effect does changing a parameter have on the graph of a trigonometric function? Pupils use a Desmos applet to explore the general sine graph. They experiment changing different parameters and record the resulting change of the...
Illustrative Mathematics
Identifying Quadratic Functions (Vertex Form)
Pupils calculate the equation of a quadratic in vertex form from a specific graph and determine an equation that would fit the description of a parabola. The final question determines the individuals' understanding of the signs of the...
Mathematics Common Core Toolbox
Golf Balls in Water
Here's a resource that models rising water levels with a linear function. The task contains three parts about the level of water in a cylinder in relationship to the number of golf balls placed in it. Class members analyze the data and...
Concord Consortium
Parameters and Clusters I
Chase the traveling solution. Pupils analyze the solutions to a system of linear equations as the parameter in one equation changes. Scholars then use graphs to illustrate their analyses.
EngageNY
Curves from Geometry
Escape to investigate hyperbolas. Pupils take a look at what happens to the elliptical orbital path of a satellite that exceeds escape velocity as the opener to the eighth lesson plan in a unit of 23. Scholars analyze basic hyperbolas...
Yummy Math
Parametric Equations and a Heart
Trigonometry, art, and Valentine's Day come together in a creative activity about parametric equations. Learners calculate several equations before graphing them either by hand, on a graphic calculator, or Excel spreadsheet to curve...
Mathematics Assessment Project
Modeling Motion: Rolling Cups
Connect the size of a rolling cup to the size of circle it makes. Pupils view videos of cups of different sizes rolling in a circle. Using the videos and additional data, they attempt to determine a relationship between cup...
PBS
Garden Grade 6 Area and Perimeter
Engage young mathematicians in applying their knowledge of area and perimeter with a fun geometry lesson. Through a series of problem solving exercises, children use their math knowledge to design different-sized garden...
Concord Consortium
Function Project
What if a coordinate plane becomes a slope-intercept plane? What does the graph of a linear function look like? Learners explore these questions by graphing the y-intercept of a linear equation as a function of its slope. The result is a...
Concord Consortium
Catching Up
Class members have some catching up to do. Given a linear equation describing the distance of a runner, young mathematicians interpret the equation in terms of the context. They consider a general equation of the same form and describe...
Mathematics Vision Project
Module 7: Modeling with Functions
The sky's the limit of what you create when combining functions! The module begins with a review of transformations of parent functions and then moves to combining different function types using addition, subtraction, and...
Curated OER
Unit 3: Scientific Writing
Write-on! Demonstrate a writing model and support learners as they write an informational essay on a water resource issue of your (or their) choosing. The lesson plan provides a well-scaffolded summative writing...
College Board
2007 AP® Calculus BC Free-Response Questions Form B
There is just a single real-world problem. Released free-response items from the 2007 AP® Calculus BC Form B contains only one real-world question. The question involves rate of change of wind chill scenario. The mathematical problems...
EngageNY
Ferris Wheels—Using Trigonometric Functions to Model Cyclical Behavior
Have class members going in circles as they model the path of a Ferris Wheel using trigonometric functions. Building on the previous lesson in this series on transformations, learners use trigonometric functions to model wheels of...
EngageNY
Modeling with Polynomials—An Introduction (part 2)
Linear, quadratic, and now cubic functions can model real-life patterns. High schoolers create cubic regression equations to model different scenarios. They then use the regression equations to make predictions.
EngageNY
Modeling from a Sequence
Building upon previous knowledge of sequences, collaborative pairs analyze sequences to determine the type and to make predictions of future terms. The exercises build through arithmetic and geometric sequences before introducing...
Teach Engineering
Discovering Relationships Between Side Length and Area
Consider the relationship between side length and area as an input-output function. Scholars create input-output tables for the area of squares to determine an equation in the first installment of a three-part unit. Ditto for the area of...
Illustrative Mathematics
Illustrative Mathematics: F Le Newton's Law of Cooling
For this problem, students use an exponential equation to investigate the cooling of a cup of coffee and how long it would take for it to cool down to different temperatures. Aligns with F-LE.B.5 and F-LE.A.4.
Illustrative Mathematics
Illustrative Mathematics: N q.a.1, a ced.a.1, and N q.a.2: Harvesting the Fields
This task is about farm-workers who are harvesting two fields. Students are presented with a scenario involving two teams of workers, two different sizes of fields, and work spread out over two days. They must calculate how many...
Khan Academy
Khan Academy: Algebra I: Linear Equations Word Problems
Solve word problems about real world relationships that are given in formulas. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Physics Aviary
Physics Aviary: Equations of Motion Lab
You will be adjusting different parameters, such as speed and time accelerating, in this lab to see how they affect the motion of your car. Record the data and then reset your system to make desired changes.