Teacher Resource Guide Algebra I Nancy Foote David Kapolka Basic Functionality of the CASIO PRIZM The Common Core State standards (CCSS) Other Algebraic Topics
Casio education workbook series TEACHER RESOURCE GUIDE Algebra I AUTHORS: Nancy Foote, David Kapolka EDITORS: Nathan Austin, Amber Branch, Amy Chow This workbook is a product of the: CASIO TEACHER ADVISORY COUNCIL (CTAC) they re written By Teachers, For Teachers. CTAC represents an embodiment of this philosophy and the foundation for which we generate all CASIO support materials. For more information on CTAC, our ACE training program or how to get involved email us at calcworkshops@casio.com 2013 by Casio America, Inc. 570 Mt. Pleasant Avenue Dover, NJ 07801 The contents of this book can be used by the classroom teacher to make reproductions for student use. All rights reserved. Except as set forth in the first sentence, no part of this publication may be reproduced or utilized in any form by any means, electronic or mechanical including photocopying, recording, or by an information storage or retrieval system without written permission from CASIO America, Inc. Printed in the United States of America. 1
algebra 1 Calculator Guidebook casio education The Authors Nancy Foote Nancy Foote, M.Ed., received her B.S in chemistry from Loyola University of Chicago. After working as an industrial chemist, Nancy recognized her love of teaching. She returned to school and earned her M.Ed. from Arizona State University. She has spent years as a classroom teacher, several years as an elementary school principal and was a district math/science curriculum specialist. Nancy is the recipient of many awards, including the prestigious Presidential Award for Excellence in Mathematics and Science Teaching, (www.paemst.org). Nancy is currently a teacher of gifted children in grades 5 at Centennial Elementary School in the Higley Unified School District. She is an adjunct instructor of chemistry for Chandler Gilbert Community College. In addition, Nancy is an item writer for the state of Arizona AIMS (Arizona Instrument for Measurement of Standards) high school math assessment. She worked with the Arizona Department of Education to articulate science standards for K 12 students. Most recently Nancy received her National Board Certification and was named an Arizona Master Teacher. Nancy enjoys the use of technology. Her students make podcasts, You Tube videos and use Twitter in the classroom. David Kapolka David Kapolka taught mathematics and science for 34 years in Michigan, 9 at the middle school and 25 at the high school level. He was mathematics department chair for 13 years at Forest Hills Northern HS. He also spent 6 years as an adjunct professor of mathematics at Grand Valley State University. He holds a BA in Elem Ed majoring in math and science, an MA in Secondary Mathematics Education, and an MA in Teaching Mathematics. Before retiring from full time teaching, David spent one year working at the National Science Foundation as an Albert Einstein Distinguished Educator Fellow where his main duties were the Presidential Awards Program and evaluating grant proposals for the Teacher Professional Continuum. David currently works for Key Curriculum Press and Casio as a technology product specialist and consultant and teaches online courses for UC Berkeley. David recently completed his 4th year as an AP Reader for calculus. David is a frequent presenter at state, regional, and national math conferences. His specialty is computer and calculator technology applied to mathematics and learning. David has written many monographs on calculator and computer applications emphasizing parametric equations and recursion to model math and science applications. 2
casio education salgebra 1 Calculator Guidebook Table of Contents Basic Functionality of the CASIO Prizm...4 Fractions, Exponents, and Roots...4 Evaluating Functions in Y1: Using X-Cal and Y-Cal... 5 The Common Core State Standards (CCSS)... 7 Represent and Solve Linear Equations... 7 Represent and Solve Quadratic Equations Graphically...9 Represent and Solve Inequalities Graphically...12 Other Algebraic Topics... 14 Exploring Non-Linear Functions... 14 Modify...15 Equation Mode...18 Recursion...22 Box Plots, Pie Charts, and Histograms... 30 3
algebra 1 Calculator Guidebook casio education Basic Functionality of the CASIO Prizm: Fractions, Exponents, and Roots 1. From the Main Menu (p), enter the Run-Matrix mode (1). 2. Input the equation: ½ + ⅓ =. (1z2$+1z3l) 3. Exponents Fractions have natural display and look exactly like you expect them to look. To input 3 2 + 5 4, press: 3s+5^4l. 4. Roots (square roots, subbed roots, etc) To evaluate (25) ½ + (125) ⅓, press: (Ls25$+L^3$ 125l) 4
casio education algebra 1 Calculator Guidebook Basic Functionality Evaluating functions in Y1: Using X-Cal and Y-Cal Input the function Y 1 = x 2 + 5x = 4 To evaluate a value in a function located in Y1 from the Run Matrix mode, press (p orq1(2)l) This will generate the screen at the right. In order to use X-Cal and Y-Cal, from the graph screen press: (Lyuql) 5
Basic Functionality algebra 1 Calculator Guidebook casio education A shortcut to Y-Cal is by way of TRACE: Shift TRACE (F1), then type in a value such as 2.1 (l) 6
casio education Algebra 1 Calculator Guidebook The Common Core The Common Core State Standards CCSS: CCSS: Represent and solve linear equations. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Plotting Linear Equations 1. From the Main Menu (p), enter the Graph mode (5). 2. Input the function y = 2x + 3 (2f+3l) 3. Draw (u). If need be, change the viewing window. (e) For a standard viewing window, press: (edu) 7
The Common Core algebra 1 Calculator Guidebook casio education To see a table of values for this data: (dp7u) You can use the!$bn buttons to scroll down the list or more from one column to the other. To find the intersection of two lines; enter Y2 = -5x - 1 Draw (u) To find the intersection press: (yy) 8
casio education Algebra 1 Calculator Guidebook The Common Core CCSS: Represent and solve quadratic equations graphically. Solve quadratic equations Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Plotting Linear equations: 1. From the Main Menu (p) enter the Graph mode by pressing (5) 2. Input the function Y1 = x 2 + 5x + 4 3. Draw the Graph. Press (u) If need be, change the viewing window. Press (e). For a standard viewing window press (e). Press (d) Then press (u) again. 9
The Common Core algebra 1 Calculator Guidebook casio education To find the roots for this equation (where y = 0): Press (Ly). Press (q) to find the first root (value where y = 0) You can read directly off the screen that when y = 0, x = -4. To find the second root, press ($) The second value for x when y = 0 is x = -1. To find the minimum, press: (ye) 10
casio education Algebra 1 Calculator Guidebook The Common Core To evaluate a value in a function located in Y1 from the Run Matrix mode, press (orq1(2)l) This will generate the screen at the right. Use X-Cal and Y-Cal From the graph screen press: (Lyuq2l) Shift-GSolve $ YCal 2 l A shortcut to Y-Cal is by way of TRACE: Shift TRACE (F1), then type in a value such as 2.1 l 11
The Common Core algebra 1 Calculator Guidebook casio education CCSS: Represent and solve inequalities graphically. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Plotting Inequalities: 1. From the Main Menu (p), enter the Graph mode (5). 2. Input the function: y = x (f5) Change the function to y x by pressing Up arrow, EXIT, TYPE, CONVERT, Y X (deyr) 3. DRAW the graph (u). If need be, to change the viewing window; press (Le) Standard (e) Square (y) X-Base (w) (dd) Draw 12
casio education Algebra 1 Calculator Guidebook The Common Core Intersection of two inequalities: Enter Y2 < -X -1 Press (d) and down arrow (N)to Y2. Press TYPE (eu) to move to the next page. Press Y< (w) X (l) DRAW (u) To find the intersection, press: (yy) 13
Other Algebraic Topics Algebra 1 Calculator Guidebook casio education Other Algebraic Topics Exploring Non-Linear Functions: Press (d) to return to graph mode. Change Y1 X 2 and change Y2 < Cos X by using (e) Type. Draw the graphs (u) To find the intersections: Press (yy) to find the first intersection. Press ($) to find the next intersection. 14
casio education Algebra 1 Calculator Guidebook Other Algebraic Topics Modify Modify 1. From the Main Menu (p), enter the Graph mode (5) 2. In Y1 type (af) to insert an A, then type (f) to insert an x, then press (l). 3. Press (y) for MODIFY. 15
Other Algebraic Topics Algebra 1 Calculator Guidebook casio education 4. To adjust A and the Step press (l), type a value such as 1, and press (l). 5. Press (N.5l) to move to the Step value and change to.5. 16
casio education Algebra 1 Calculator Guidebook Other Algebraic Topics 6. Press up arrow (B) to return to the A value and press right arrow ($) to increase the A value and change the plot by the Step value. Use the arrows to continue to modify the graph, A, and Step. 17
Other Algebraic Topics Algebra 1 Calculator Guidebook casio education Equation Mode To solve equations simultaneously, put the calculator in Equation Mode Highlight Equation Mode, press (l) then (q) for Simultaneous. To solve simultaneously: 4x + 5y = 35-3x + 2y = -9 Enter Number of unknowns as 2 (q) 18
casio education Algebra 1 Calculator Guidebook Other Algebraic Topics Enter the coefficients and constants to generate the screen at the right. Press (l) to move to the next position. Press SOLVE (q) Press d 3 times to return to EQUATION solver. To run Polynomial solver, press w. 19
Other Algebraic Topics Algebra 1 Calculator Guidebook casio education To solve ax 2 + bx + c = 0 Enter degree as 2. To solve x 2 4 = 0, Enter the values 1 0-4 pressing right arrow between each value, then (l) after the last entry. Press SOLVE (q) to see the solutions. Press (d) to return to the previous screen and enter solve X 2 2X + 4 = 0 Enter -1-2 4 pressing (l) between each value, then (l) after the last entry. 20
casio education Algebra 1 Calculator Guidebook Other Algebraic Topics Press SOLVE (q) to display the solutions. Note that the first solution is displayed as an exact value. Press down arrow (N) to display the other exact value. 21
Other Algebraic Topics Algebra 1 Calculator Guidebook casio education Recursion Suppose the basement of a building is 13 feet below ground and each floor above is 10 feet apart. If we call the basement floor 0 and it s level -13, then the floors would be a sequence at heights of -13, -3, 7, 17, 27, 37, 47, etc. 1. Set the calculator in Run-Matrix Mode By pressing (p1). 2. To start the sequence, press -13 (l) This will store -13 in the ANS memory. 3. Press (+10l) this will generate the screen at the right.. 22
casio education Algebra 1 Calculator Guidebook Other Algebraic Topics 4. Continue to press l multiple times to generate more floor values. To generate an ordered pair containing floor number and height proceed as follows. 5. Press Lm0,n13LMl 6. Press + to generate List Ans +. 7. Then press (Lm1,10LMlll ) This will generate the values for several floors, increasing the floor number by one and the height by 10. 23
Other Algebraic Topics Algebra 1 Calculator Guidebook casio education Box Plots, Pie Charts and Histograms. Box and whiskers plots 1. From the Main Menu (p), enter the Statistics mode (2) 2. Construct a box and whiskers plot for this data: 43, 19, 47, 36, 24, 34, 32, 12, 45, 67, 34, 54, 32, 56 Enter the data into List 1 3. Determine statistical information (wq) Drawing a box and whiskers plot: Select graph, Set (qu), highlight Graph Type and press (uw). Make sure frequency is set to 1 and outliers are on. 24
casio education Algebra 1 Calculator Guidebook Other Algebraic Topics Press (dq). Drawing a pie chart: Select Set (u), highlight Graph Type and choose pie (r). (dq) Drawing a histogram: Select Set (u), highlight Graph Type and choose more, Hist (u,q). 25
Other Algebraic Topics Algebra 1 Calculator Guidebook casio education (dq) Use the default width and starting point or change it to meet your needs. To accept the default, (l). 26