This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.
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The CUNY HSE Curriculum Framework provides direction, structure and materials for teaching math, science and social studies (integrated with reading and writing) in the new era of HSE instruction. The complete framework is available for free download.
The framework was written by the CUNY Adult Literacy PD Team to respond to the challenges facing high school equivalency (HSE) teachers and their students. It is a guide for planning your instruction – including topic recommendations, model lessons, guiding questions, readings, and problems. The framework prioritizes depth over breadth. It does not address all of the content that might potentially be included on an HSE exam, but instead models a focused and coherent study of high priority topics within each content area.
As teachers in adult literacy and HSE education, our work has always been demanding. Now that our students face a new and more challenging HSE test, the demands on teachers are even greater. Teaching students to read, write and do math at the HSE level is no longer enough. Students need specific, deep and coherent content knowledge, as well as the capacity to apply this content knowledge to analysis and problem solving.
As the demands on our students and teachers are increasing, it is important that we don’t lose sight of one of our greatest strengths — our practice of starting from where students are and our serious respect for their learning processes. As a student of ours once said, “You can’t make a plant grow by pulling on it, you only make it rootless.”
The Social Studies section integrates reading and writing through a focus on U.S. history, with extensions to civics, economics and geography. This section has a curriculum map, 12 unit descriptions, six model lesson plans and additional resources.
The Science section provides an introduction to matter and basic chemistry with extensions to science/math connections. This section includes a curriculum map with 23 topic descriptions and key questions, and three complete inquiry-based model lesson plans.
The Math section focuses on problem-solving in functions and algebra. It integrates problem-solving strategies, productive struggle, perseverance and mathematical discussion into content learning. This section includes a curriculum map, model lessons, rich engaging math problems, samples of student work, powerful routines for math classrooms, classroom videos, and more.
According to the GED testing service, test takers struggle with “applying rules of exponents in numerical expressions with rational exponents to write equivalent expressions with rational exponents.” (https://www.gedtestingservice.com/uploads/files/09738c12fe4e4accd9a16bab7cb99a3c.pdf )
Students do “fairly well” with simple squares and square roots, but there is a “sharp drop-off” when things get more complicated.
These are questions included in the “no calculator” portion of the test.
These skills are Mathematics Standards Level D in the College and Career Readiness Standards for Adult Education (https://www.educateiowa.gov/sites/files/ed/documents/CCRStandardsAdultEd.pdf ) under “Expressions and Equations.”
This curriculum guide will offer opportunities to build the deeper understanding necessary to understand the rules of exponents such as (xm)n = xmn .
Write and evaluate numerical expressions involving whole-number exponents. (6.EE.1)
Know and apply the properties of integer exponents to generate equivalent numerical expressions. (8.EE.1)
This is a community contributed High School Equivalency Algebra textbook, focused on algebra material for the GED(R) math test. Use as is, or download and modify to your heart's content. Covers integers to functions.
Inequalities are mathematical statements that connect unequal expressions.
This curriculum guide will help students understand inequalities, and be able to differentiate between inequality signs. They will solve inequality problems, being able to recognize problems where the inequality signs will need to change to arrive at a solution. Students will represent inequality solutions on a number line.
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.
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.
This is an activity for students to work on in pairs practicing simple interest. It involves real online research and presents an open-ended question. This would be most effective after students have had instruction and some practice.
This is a powerful way to launch multiple types of lessons that is student-centered and spans all educational levels. It starts with two simple questions that you ask students as you show them a video, image, math situation, or just about anything you can think of that's visual. It serves as a formative assessment in that it helps teachers to understand what students already know and what they wonder about what they are seeing. This is a non-intimidating way for students to begin a lesson as there are no wrong answers: only observations and questions: that students take ownership of. This resource contains an overview of notice/wonder and a step-by-step guide for teachers. Be sure to watch the short video that's included in this resource!