Report

Meaningful Use of Symbols Two types of symbols most important to algebra, but unfortunately not well understood by many students: Equal Sign (=) and Inequality Signs (˂, ≤, ˃,≥) Variables Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 1 Meaningful Use of Symbols Border Tiles Equal Sign and Inequality Signs Conceptualizing the Equal and Inequality Signs with a Balance True/False Sentences Relational Thinking Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 2 Relational Thinking • Takes place when a student observes and uses numeric relationships between two sides of the equal sign rather than actually computing the amounts • This type of thinking is a first step toward generalizing the relationships found in arithmetic to the relationships used when variables are involved Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 3 Consider two different explanations for placing a 3 in the box for this open sentence: 2.4 ÷ = 4.8 ÷ 6 1. “Since 4.8 ÷ 6 is 0.8, then 2.4 ÷ something is also 0.8, so that must be 3.” 2. “I noticed that 2.4 is half of 4.8, so I need to divide by a number half the size of 6 in order to maintain equivalence, so the number is 3.” Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 4 Meaningful Use of Symbols Border Tiles Equal Sign Inequality Signs Equality and Inequality Signs with a Balance True/False Sentences Relational Thinking Open Sentences Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 5 Solving Equations Using a Balance Scale Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 6 The Meaning of Variables Variables Used as Unknown Values: • One-Variable Situations Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 7 • Gary ate 14 strawberries, and Jeremy at some, too. The container of 25 strawberries was empty! How many strawberries did Jeremy eat? How could we use what we learned about open sentences to write a statement representing this story problem? Can you use variables instead of ? Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 8 Two or More Variable Situations: Systems of Equations • Five Problems With Multiple Variables • What’s My Weight? Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 9 The Meaning of Variables Variables Used as Unknown Values: • One-Variable Situations • Two-or-More-Variables Situations Systems of Equations and Reflect How could you help students bridge the connection from these informal ways of solving to a more formal understanding of systems of equations? Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 10 Use relational reasoning to determine which ones of the following systems of equations can be solved for or without using algebra. Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 11 Simplifying Expressions and Solving Equations My Favorite No https://www.youtube.com/watch?v=Rulmok_9HVs Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp 12 Variables Used as Quantities That Vary • a) If you have $10 to spend on $2 granola bars and $1 fruit bars, how many ways can you spend all your money without receiving change? • Use the table below to explore ways to spend your money. Number of $2 granola bars Number of $1 fruit Total amount bars spent ($10) Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp Equation? 13 b) You bought $1.75 pencils and $1.25 erasers from the school store, and you spent exactly $35.00. What might you have purchased? What equation represents this situation? • Use the table below to explore values that work and to look for patterns. Number of $1.75 Number of $1.25 Total amount pencils erasers spent ($35) Teaching Student-Centered Mathematics by Van de Walle, Bay-Williams, Lovin and Karp Equation? 14