Teaching Algebra with Manipulatives

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$Common Core MCISD Math Grade 4 12/13 Part 1 Â» Form A (Master ...$

Chapter 4 Matrices Teaching Notes and Overview Algebra Activity Matrices (pp. 229–230 of this booklet) Use With Lesson 4-1. Objective Write and interpret a matrix representation of a finite graph. Materials classroom set of Algebra Activity worksheets transparency master of Algebra Activity Display the finite graph portion of the transparency on the overhead projector. The dots (vertices) represent the rest stops and the lines (edges) represent the trails. Define a path as a route from stop to stop not passing through any other stop. Find the total number of paths for each element in the transparency chart. (Note: A path from Cook’s Corner to Cook’s Corner may be clockwise or counter-clockwise.) Write the chart in matrix form (omit names of rows and columns). 2 1 0 1 1 0 2 1 0 2 2 1 1 1 1 0 Reverse the process by drawing a graph of Matrix A on the transparency. Distribute the Algebra Activity worksheet. Ask students to assist you in completing the chart and writing the matrix for it. Work a couple of rows in the chart and show those rows in the matrix. Form groups of three students to complete the worksheet. As soon as the groups have finished, discuss and share the answers. 0 2 1 0 2 1 1 1 2 0 2 1 1 0 1 0 3. 4. 1 2 2 0 1 1 0 2 0 1 0 0 1 0 2 0 5. See students’ graphs 6. See students’ graphs Mini-Project Evaluating Determinants (p. 231 of this booklet) Use With Lesson 4-3. Objective Evaluate determinants. Materials for each group of students, two sets of two different colored 4 by 6 index cards and scissors This activity develops the process of evaluating 3 3 determinants. Have students repeat this same process by cutting another set of strips and writing different numbers on them. Ask them to show their work for evaluating the determinant. Let groups exchange their cutouts with another group and evaluate that determinant. Provide additional 3 3 determinants for students to evaluate without using the cutouts. Ask them to find out what happens when the entries in one row of a 3 3 are 0. Encourage them to investigate other properties of determinants. Answers 1. Sum of Row 2 4. There are 4 paths leading from the Dining Hall. Sum of Column 2 4. They are the same because there are 4 paths to and from the Dining Room. 2. 20. There are 10 edges, but each trial leads two ways. © Glencoe/McGraw-Hill 228 Teaching Algebra with Manipulatives
NAME ______________________________________________ DATE ____________ PERIOD ____ Algebra Activity (Use with Algebra 2, Lesson 4-1) Matrices Complete the chart. Then Cook's Corner write a matrix for the graph at the right. (Remember there is one and only one stop on each path.) Dining Hall Bridge Lake Main Lodge Nature Center PATHS TO Cook’s Corner Dining Hall Main Lodge Bridge Lake Nature Center FROM Cook’s Corner Dining Hall Main Lodge Bridge Lake Nature Center Matrix Using the matrix above, complete the following. 1. Add the elements in the second row. What does this number represent in the graph? How does your number compare to the sum of the second column? ___________________________________________________________________ 2. Add the elements in each row. Find the total of these sums. Is this total related to the number of edges in the graph? If so, how? ___________________________________________________________________ Write the matrices corresponding to the graphs. 3. A C 4. B D Y Draw the graphs corresponding to the matrices. 5. 2 1 1 0 6. 2 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 2 0 0 1 0 2 1 1 0 2 Z W X Algebra 2—Chapter 4 © Glencoe/McGraw-Hill 229 Teaching Algebra with Manipulatives
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Teaching Algebra with Manipulatives
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Contents Easy-to-Make Manipulatives
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Algebra 1 Activities Page 14-5 Alge
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Glencoe Mathematics Manipulatives G
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Centimeter Grid Paper © Glencoe/Mc
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Coordinate Planes © Glencoe/McGraw
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Coordinate Planes for Trigonometric
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Conic Graph Paper (circles and line
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Algebra Tiles (units) 1 1 1 1 1 1 1
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Integer Models Summary There are tw
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Equation Models Summary A zero pair
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Equation Mat © Glencoe/McGraw-Hill
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Rectangular Dot Paper © Glencoe/Mc
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Problem Solving Guide Problem: Expl
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Die Patterns Cut along the heavy bl
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© Glencoe/McGraw-Hill 24 Teaching
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Chapter 1 Mini-Project Evaluating E
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Chapter 1 Teaching Notes and Overvi
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Using Overhead Manipulatives (Use w
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The Distributive Property Materials
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Investigating Real-World Functions
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NAME ______________________________
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Using Overhead Manipulatives • Re
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Using Overhead Manipulatives • Ha
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Formulas NAME _____________________
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Using Overhead Manipulatives Demons
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Using Logic NAME __________________
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NAME ______________________________
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Chapter 5 Using Overhead Manipulati
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Demonstration 2 Finding Slope: Zero
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Demonstration 2 Writing an Equation
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NAME ______________________________
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Making Predictions Materials: NAME
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23 22 21 20 NAME __________________
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NAME ______________________________
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Compound Inequalities (Continued) 1
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Absolute Value NAME _______________
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NAME ______________________________
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Chapter 8 Polynomials Teaching Note
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Factoring Trinomials Materials: NAM
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Factoring Trinomials x NAME _______
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Difference of Squares Materials: NA
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Demonstration 2 Factoring 4x 2 4x
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Factoring Trinomial Squares Figure
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Chapter 10 Quadratic and Exponentia
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Chapter 10 Teaching Notes and Overv
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Page 187 and 188: Using Overhead Manipulatives • Ar
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Page 191 and 192: Chapter 11 Radical Expressions and
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Page 197 and 198: Using Overhead Manipulatives (Use w
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Page 201 and 202: Chapter 12 Rational Expressions and
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Page 207 and 208: Chapter 13 Statistics Teaching Note
Page 209 and 210: Analyze the Data 1. Cut out the gra
Page 211 and 212: Investigating Percentiles Materials
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Page 217 and 218: Simulations NAME __________________
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Page 221 and 222: Investigating Polygons and Patterns
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Page 263 and 264: Algebra Activity Draw Graph each fu
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Page 267 and 268: Chapter 8 Conic Sections Teaching N
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Page 275 and 276: Locating Foci NAME ________________
Page 277 and 278: Conic Sections NAME _______________
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Chapter 11 Sequences and Series Tea
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Algebra Activity Step 5 Step 6 Step
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Area Diagrams NAME ________________
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Simulations NAME __________________
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Chapter 13 Trigonometric Functions
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NAME ______________________________
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Investigating Regular Polygons Usin
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Chapter 14 Trigonometric Graphs and
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Teaching Algebra with Manipulatives

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