Friday warm-up : Simplify with only integers & Positive exponents
CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School...
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Transcript of CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School...
![Page 1: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/1.jpg)
CHAPTER 23 Developing Concepts of Exponents,
Integers, and Real Numbers
Elementary and Middle School Mathematics Teaching Developmentally
Ninth EditionVan de Walle, Karp and Bay-Williams
Developed by E. Todd Brown /Professor Emeritus University of Louisville
![Page 2: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/2.jpg)
23-2Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Big Ideas
1. Our number system includes whole numbers, fractions, decimals and integers, all of which are rational numbers.
2. Integers are the negative and positive counting numbers and 0.
3. Exponential notation is a way to express repeated products of the same number.
4. Many numbers are not rational; the irrationals can only be expressed symbolically or approximately using a close rational number.
![Page 3: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/3.jpg)
23-3Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
ExponentsExponential notation is more efficient for conveying numeric
or quantitative information.
Exponent indicated the
number of times the base is
used as a factor.
![Page 4: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/4.jpg)
23-4Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Order of operations
Order of operations is not just a convention.
Based on the meaning of the operations.
Mnemonics- PEMDAS is sometimes used to help remember the order.
![Page 5: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/5.jpg)
23-5Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Apply order of operationsTry this oneActivity 23.2 Guess My Number
![Page 6: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/6.jpg)
23-6Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Integer ExponentsExplore power of 10 changes
Negative exponent is reciprocal
of the value it would be without negative sign.
Explore negative exponents with a calculator.
Use fraction-to-decimal conversion feature.
![Page 7: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/7.jpg)
23-7Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Context for Very Large NumbersState lottery- 44 numbers from which to pick 6 (7
million possible combinations)
Estimated size of the universe of 40 billion light-years
Human body has 100 billion cells
Distance to the sun is about 150 million kilometers
Population in the world in 2011 was about 6.96 billion
Connect large numbers to meaningful points of reference.
![Page 8: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/8.jpg)
23-8Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Context for Very Small Numbers
Length of DNA strand in a cell
Human hair growth rate
Chance of winning the state lottery
Mass of one atom of hydrogen
Sound to travel the length of a football field
Finding real data that are very, very, small can build meaning.
![Page 9: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/9.jpg)
23-9Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Contexts for Exploring Positive and Negative Numbers
Quantity contexts
Golf scores
Money: Payments and Deposits
Linear Contexts
Temperature
Altitude
Timelines
Football
![Page 10: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/10.jpg)
23-10Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Models for Teaching Positive and Negative Numbers
Two color counters
Number Lines
Integers involve two concepts- magnitude (counters or length of arrows) and direction (different colors or directions)
![Page 11: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/11.jpg)
23-11Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Addition with Integers
![Page 12: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/12.jpg)
23-12Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Subtraction with Integers
![Page 13: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/13.jpg)
23-13Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Connecting Visual Representations with Equations
Notate number line illustrations
![Page 14: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/14.jpg)
23-14Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Multiplication with Integers
![Page 15: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/15.jpg)
23-15Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Division with Integers
![Page 16: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/16.jpg)
23-16Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Real Numbers
Rational numbers are all numbers that can be represented as a fraction (irrational numbers cannot be represented as a fraction)
Integers are whole numbers and their negatives or opposites
![Page 17: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/17.jpg)
23-17Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Try this oneActivity 23.14 Repeater or Terminator?
![Page 18: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/18.jpg)
23-18Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Student example:
![Page 19: CHAPTER 23 Developing Concepts of Exponents, Integers, and Real Numbers Elementary and Middle School Mathematics Teaching Developmentally Ninth Edition.](https://reader033.fdocuments.us/reader033/viewer/2022061511/56649e8e5503460f94b9149c/html5/thumbnails/19.jpg)
23-19Van de Walle, Karp, Bay-Williams, Elementary and Middle School Mathematics: Teaching Developmentally, 9/e , © 2016, 2013, 2010, 2007, 2004 by Pearson Education, Inc. All Rights Reserved.
Roots and Cubes Try this one
Activity 23.15 Edges of Squares and Cubes