Chambers, Donald L. December 9—12, , vol. Silver, Edward A. Toggle navigation. Log out. Log in. View Cart. Join Now. NCTM Store. Toggle navigation MENU. Log In Not a member? In Part I, Tom Reardon uses a phone bill to help his students deepen their understanding of linear functions and how to apply them. In Part II, Janel Green's hot dog vending scheme is a vehicle to help her students learn how to solve linear equations and inequalities using three methods: tables, graphs, and algebra. In Part I, Jenny Novak's students compare the speed at which they write with their right hands with the speed at which they write with their left hands.
This activity enables them to explore the different types of solutions possible in systems of linear equations, and the meaning of the solutions. In Part II, Patricia Valdez's students model a real-world business situation using systems of linear inequalities.
In Part I, Tom Reardon's students come to understand the process of factoring quadratic expressions by using algebra tiles, graphing, and symbolic manipulation. In Part II, Sarah Wallick's students conduct coin-tossing and die-rolling experiments and use the data to write basic recursive equations and compare them to explicit equations.
In Part I, Orlando Pajon uses a population growth simulation to introduce students to exponential growth and develop the conceptual understanding underlying the principles of exponential functions.
In Part II, a scenario from Alice in Wonderland helps Mike Melville's students develop a definition of a negative exponent and understand the reasoning behind the division property of exponents with like bases.
In Part I, Peggy Lynn's students simulate oil spills on land and investigate the relationship between the volume and the area of the spill to develop an understanding of direct variation. In Part II, they develop the concept of inverse variation by examining the relationship of the depth and surface area of a constant volume of water that is transferred to cylinders of different sizes. This workshop presents two capstone lessons that demonstrate mathematical modeling activities in Algebra 1.
In both lessons, the students first build a physical model and use it to collect data and then generate a mathematical model of the situation they've explored. In Part I, Sarah Wallick's students use a pulley system to explore the effects of one rotating object on another and develop the concept of transmission factor.
In Part II, Orlando Pajon's students conduct a series of experiments, determine the pattern by which each set of data changes over time, and model each set of data with a linear function or an exponential function. Subscribe to our monthly newsletter for announcements, education- related info, and more!
Read what Fran Curcio has to say about how Janel used her knowledge of her students to present a problem that they could successfully explore: Transcript from Fran Curcio In this particular setting, where there are students of a variety of learning abilities and levels of preparedness, Janel has provided a problem that allows for multiple entries and multiple exits.
Stimulating Students to Make Connections Students develop a framework for mathematical ideas when they model a situation in a variety of ways and then make connections between the different methods. Reflection: Describe a mathematical task that you use that helps students make connections and develop a framework for their understanding of mathematical ideas.
Promoting Communication About Mathematics Both Janel and Tom worked hard to show their students that they valued their ideas and expected their students to communicate clearly about the mathematics. Reflection: Share some tasks that you use in your classroom that promote mathematical communication by your students.
Improving Students' Disposition Toward Mathematics Selecting worthwhile mathematical tasks should also convey messages about what mathematics is, and what doing mathematics entails.
Read what she has to say: Transcript from Jenel Green This was the first time they have ever made a connection between the three methods, and I think they really appreciated the power of mathematics today.
Workshop 1 Variables and Patterns of Change In Part I, Janel Green introduces a swimming pool problem as a context to help her students understand and make connections between words and symbols as used in algebraic situations. Workshop 2 Linear Functions and Inequalities In Part I, Tom Reardon uses a phone bill to help his students deepen their understanding of linear functions and how to apply them.
Workshop 3 Systems of Equations and Inequalities In Part I, Jenny Novak's students compare the speed at which they write with their right hands with the speed at which they write with their left hands.
Workshop 4 Quadratic Functions. Workshop 5 Properties In Part I, Tom Reardon's students come to understand the process of factoring quadratic expressions by using algebra tiles, graphing, and symbolic manipulation. Workshop 6 Exponential Functions In Part I, Orlando Pajon uses a population growth simulation to introduce students to exponential growth and develop the conceptual understanding underlying the principles of exponential functions.
Workshop 7 Direct and Inverse Variation In Part I, Peggy Lynn's students simulate oil spills on land and investigate the relationship between the volume and the area of the spill to develop an understanding of direct variation. Workshop 8 Mathematical Modeling This workshop presents two capstone lessons that demonstrate mathematical modeling activities in Algebra 1.
Listen to audio clip of teacher Janel Green. Listen to audio clip of teacher Tom Reardon. Log In Not a member? Instructional programs from prekindergarten through grade 12 should enable each and every student to— Understand patterns, relations, and functions Represent and analyze mathematical situations and structures using algebraic symbols Use mathematical models to represent and understand quantitative relationships Analyze change in various contexts Understand patterns, relations, and functions Pre-K—2 Expectations : In pre-K through grade 2 each and every student should— sort, classify, and order objects by size, number, and other properties; recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another; analyze how both repeating and growing patterns are generated.
Grades 3—5 Expectations : In grades 3—5 each and every student should— describe, extend, and make generalizations about geometric and numeric patterns; represent and analyze patterns and functions, using words, tables, and graphs. Grades 6—8 Expectations : In grades 6—8 each and every student should— represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; relate and compare different forms of representation for a relationship; identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
Grades 3—5 Expectations : In grades 3—5 each and every student should— identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers; represent the idea of a variable as an unknown quantity using a letter or a symbol; express mathematical relationships using equations.
Use mathematical models to represent and understand quantitative relationships Pre-K—2 Expectations : In pre-K through grade 2 each and every student should— model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.
Grades 3—5 Expectations : In grades 3—5 each and every student should— model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions. Grades 6—8 Expectations : In grades 6—8 each and every student should— model and solve contextualized problems using various representations, such as graphs, tables, and equations.
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