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  • CCSS.Math.Content.HSA-REI.A.1
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
Same Solutions?
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CC BY
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The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Defining Regions Using Inequalities
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CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help teachers identify and assist students who have difficulties in: representing a constraint by shading the correct side of the inequality line; and understanding how combining inequalities affects a solution space.

Subject:
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Solar Water: Heat it Up!
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Educational Use
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Students explore energy efficiency, focusing on renewable energy, by designing and building flat-plate solar water heaters. They apply their understanding of the three forms of heat transfer (conduction, convection and radiation), as well as how they relate to energy efficiency. They calculate the efficiency of the solar water heaters during initial and final tests and compare the efficiencies to those of models currently sold on the market (requiring some additional investigation by students). After comparing efficiencies, students explain how they would further improve their devices. Students learn about the trade-offs between efficiency and cost by calculating the total cost of their devices and evaluating cost per percent efficiency and per degree change of the water.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Amanda Giuliani
Darcie Chinnis
Marissa H. Forbes
Odessa Gomez
Date Added:
09/18/2014
Algebra II Module 1: Polynomial, Rational, and Radical Relationships
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CC BY-NC-SA
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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
How does the solution change?
Unrestricted Use
CC BY
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The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level (e.g, 6.EE.5). By asking students to reason about solutions without explicily solving them, we get at the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Optimization Problems: Boomerangs
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CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the constraints and variables mathematically; select appropriate mathematical methods to use; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the optimum case, checking it for confirmation; and communicate their reasoning clearly.

Subject:
Measurement and Data
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
A-CED Products and Reciprocals
Unrestricted Use
CC BY
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the ...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
10/14/2013
A-REI Reasoning with linear inequalities
Unrestricted Use
CC BY
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This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The following is a student solution to the inequality \frac{5}{18} - \frac{x-2}{9} \leq \frac{x-4}{6}. \begin{align} \frac{5}{18} - \frac{x-2}{9} & \le...

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
09/11/2013
Magnetic Launcher
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Educational Use
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Students explore electromagnetism and engineering concepts using optimization techniques to design an efficient magnetic launcher. Groups start by algebraically solving the equations of motion for the velocity at the time when a projectile leaves a launcher. Then they test three different launchers, in which the number of coils used is different, measuring the range and comparing the three designs. Based on these observations, students record similarities and differences and hypothesize on the underling physics. They are introduced to Faraday's law and Lenz's law to explain the physics behind the launcher. Students brainstorm how these principals might be applied to real-world engineering problems.

Subject:
Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Erik Wemlinger
Date Added:
09/18/2014
Projectile Motion
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Educational Use
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Students are introduced to the concept of projectile motion, of which they are often familiar from life experiences,such as playing sports such as basketball or baseball, even though they may not understand the physics involved. Students use tabletop-sized robots to build projectile throwers and measure motion using sensors. They compute distances and velocities using simple kinematic equations and confirm their results through measurements by hand. To apply the concept, students calculate the necessary speed of an object to reach a certain distance in a hypothetical scenaro: A group of hikers stranded at the bottom of a cliff need food, but rescuers cannot deliver it themselves, so they must devise a way to get the food to the hikers.

Subject:
Engineering
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Ronald Poveda
Zachary Nishino
Date Added:
09/18/2014