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  • CCSS.Math.Content.HSF-IF.C.7
Math Memos
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MathMemos is a teacher space where adult educators share rich math problems, samples of student work, and practical suggestions for bringing the problems to life in the classroom. All math problems are:

(1) Open-ended, meaning that it might have more than one answer or there may be multiple solution pathways to solve the problem.

(2) The prompt does not clearly direct the students towards a procedural pathway in solving the problem.

(3) Students should be able to struggle productively with the problem for an extended period of time: they are student driven.

The problems include and integrate a wide range of math content and topics such as: Algebra, Geometry, Functions, Number & Quantity, and Statistics & Probability. You can also search for specific topics (fractions, systems of equations, equality) or problem solving strategies (guess & check, charts & tables, visual strategies, manipulatives).

The resources is designed so that teachers can be thoroughly connected to a problem before taking it into the classroom, by solving it themselves and looking at samples of student work that other teachers have posted online. Then, teachers are encouraged to reflect on how the problem played out in their own classroom and post their reflections.

This collection is an ongoing project with new problems being added as teachers submit new write-ups.

A PD Module is available for Professional Developers.

MathMemos was created by Tyler Holzer with a grant from the New York State Education Department Office of Adult Career and Continuing Education Services.

Subject:
Mathematics
Material Type:
Lesson Plan
Provider:
CollectEdNY
Author:
Celia Volbrecht
Chris Giorgio
Danielle Fridstrom
Daphne Carter McKnight
Eric Appleton
Patricia Helmuth
Randy Raux
Todd Orelli
Tyler Holzer
Date Added:
09/21/2017
Push and Support Cards: A Bridge to Advanced Mathematics for the Multi-Level Adult Education Classroom Curriculum Guide
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Adult education classrooms are commonly comprised of learners who have widely disparate levels of mathematical problem-solving skills. This is true regardless of what level a student may be assessed at when entering an adult education program or what level class they are placed in. Providing students with differentiated instruction in the form of Push and Support cards is one way to level this imbalance, keeping all students engaged in one high-cognitive task that supports and encourages learners who are stuck, while at the same time, providing extensions for students who move through the initial phase of the task quickly. Thus, all
students are continually moving forward during the activity, and when the task ends, all students have made progress in their journey towards developing conceptual understanding of mathematical ideas along with a productive disposition, belief in one’s own ability to successfully engage with mathematics.

Subject:
Mathematics
Material Type:
Lesson Plan
Module
Teaching/Learning Strategy
Author:
Patricia Helmuth
Date Added:
05/24/2018
Population Growth Curves
Conditions of Use:
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Using Avida-ED freeware, students control a few factors in an environment populated with digital organisms, and then compare how changing these factors affects population growth. They experiment by altering the environment size (similar to what is called carrying capacity, the maximum population size that an environment can normally sustain), the initial organism gestation rate, and the availability of resources. How systems function often depends on many different factors. By altering these factors one at a time, and observing the results, students are able to clearly see the effect of each one.

Subject:
Engineering
Biology
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Jeff Farell
Jennifer Doherty
Wendy Johnson
Date Added:
09/18/2014
Algebra I Module 3:  Linear and Exponential Functions
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In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
09/17/2013
Graphs of Quadratic Functions
Conditions of Use:
No Strings Attached
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This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.

Subject:
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Algebra II Module 1: Polynomial, Rational, and Radical Relationships
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Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
05/14/2013
Equation Grapher
Conditions of Use:
No Strings Attached
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Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

Subject:
Algebra
Material Type:
Simulation
Provider:
University of Colorado Boulder
Provider Set:
PhET Interactive Simulations
Author:
Michael Dubson
Mindy Gratny
Trish Loeblein
Date Added:
11/16/2007
Climate Change Math Lesson Plan TACCL - Comparing and Solving Linear, Quadratic, Exponential, and Cubic Functions
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This lesson has students create, compare, and solve linear, quadratic, exponential, and cubic functions based on a primary source from Weather Underground about the melting of the polar ice caps. If the formatting is an issue, contact me at rob.leichner@gmail.com for a Google drive link to the lesson plan.

Subject:
English Language Arts
Mathematics
Material Type:
Activity/Lab
Assessment
Data Set
Homework/Assignment
Interactive
Lesson Plan
Primary Source
Reading
Author:
Rob Leichner
Date Added:
01/28/2016
Elasticity & Young's Modulus for Tissue Analysis
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As part of the engineering design process to create testable model heart valves, students learn about the forces at play in the human body to open and close aortic valves. They learn about blood flow forces, elasticity, stress, strain, valve structure and tissue properties, and Young's modulus, including laminar and oscillatory flow, stress vs. strain relationship and how to calculate Young's modulus. They complete some practice problems that use the equations learned in the lesson mathematical functions that relate to the functioning of the human heart. With this understanding, students are ready for the associated activity, during which they research and test materials and incorporate the most suitable to design, build and test their own prototype model heart valves.

Subject:
Engineering
Health, Medicine and Nursing
Material Type:
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Michael Duplessis
Date Added:
10/14/2015
Representing Polynomials
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This lesson unit is intended to help teachers assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in: recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials; and recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).

Subject:
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions
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In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
09/17/2013
Algebra II Module 3: Exponential and Logarithmic Functions
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In this module, students synthesize and generalize what they have learned about a variety of function families.  They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4).  They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions.  They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3).  Students identify appropriate types of functions to model a situation.  They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit.  The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module.  In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
09/16/2014
Does My Model Valve Stack up to the Real Thing?
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Following the steps of the iterative engineering design process, student teams use what they learned in the previous lessons and activity in this unit to research and choose materials for their model heart valves and test those materials to compare their properties to known properties of real heart valve tissues. Once testing is complete, they choose final materials and design and construct prototype valve models, then test them and evaluate their data. Based on their evaluations, students consider how they might redesign their models for improvement and then change some aspect of their models and retest aiming to design optimal heart valve models as solutions to the unit's overarching design challenge. They conclude by presenting for client review, in both verbal and written portfolio/report formats, summaries and descriptions of their final products with supporting data.

Subject:
Engineering
Health, Medicine and Nursing
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Michael Duplessis
Date Added:
10/14/2015
Forming Quadratics
Rating

This lesson unit is intended to help teachers assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help teachers identify and help students who have the following difficulties: understanding how the factored form of the function can identify a graphŐs roots; understanding how the completed square form of the function can identify a graphŐs maximum or minimum point; and understanding how the standard form of the function can identify a graphŐs intercept.

Subject:
Algebra
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Graphing the Spread of Disease
Conditions of Use:
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Students simulate disease transmission by collecting data based on their proximity to other students. One option for measuring proximity is by having Bluetooth devices "discover" each other. After data is collected, students apply graph theory to analyze it, and summarize their data and findings in lab report format. Students learn real-world engineering applications of graph theory and see how numerous instances of real-world relationships can be more thoroughly understood by applying graph theory. Also, by applying graph theory the students are able to come up with possible solutions to limit the spread of disease. The activity is intended to be part of a computer science curriculum and knowledge of the Java programming language is required. To complete the activity, a computer with Java installed and appropriate editing software is needed.

Subject:
Computer Science
Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Brian Sandall
Steve Hamersky
Date Added:
09/18/2014
Key Features of Graphs
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This is the first unit in the Algebra II curriculum and is fundamental for the rest of the year. During this course students study many different functions and their key features. Students will compare, contrast, and make generalizations about these functions using the key features and proper notation. This unit ensures that students can identify each type of key feature properly throughout the rest of the year.Objectives:  Students will express and interpret intervals using both interval and inequality notation.Students will be able to express the domain and range of graphs using both interval and inequality notation.Students will be able to find the x and y intercepts of a function from a graph or from a linear equation.Students will be able to identify extrema, increasing, decreasing and constant intervals of a graph using interval notation.Students will be able to write the end behavior for any given graph.Technology Utilized: ● Desmos - This is an online graphing tool that can be used to make basic graphs as well as premade teacher bundles with student investigations. In this unit I have taken some of the premade investigations and edited them to meet my classroom needs.● Answer Garden - This tool will be used to brainstorm key features at the beginning of the unit and to assess student’s prior knowledge.● Kahoot - This tool is used as a classroom formative assessment. Students must be all on the same question which can also elicit discussion and show misconceptions with instant feedback.● Google Forms - This tool is used for short assessments, exit tickets, and graded homework assignments. The ability for multiple types of questions and self checking quiz option make this an easy way to quickly assess students and give feedback.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
Amy Christofer
Date Added:
07/23/2017