Teaching Algebra with Manipulatives

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Chapter 11 Teaching Notes and Overview Discuss the completed parts of the table in Exercise 1. Ask students questions about the table to check on their understanding. Complete the missing parts of the table as a class. Form groups of two or three to complete Exercises 2–7. You may want to have the groups complete two of the exercises, then discuss the answers as a class. Then have them complete two more and discuss the answers and so on. Encourage students to research other fractals and share their findings with the class. Answers See Teacher Wraparound Edition p. 611. Algebra Activity Recording Sheet Special Sequences (p. 285 of this booklet) Use With the activity on page 607 in Lesson 11-6 of the Student Edition. Objective Model, analyze, and make a conjecture about the Towers of Hanoi game. Materials provide each group of students with the following: penny nickel dime quarter Point out to students that the object of the Towers of Hanoi game is to move a stack of n coins from one position to another in the fewest number of a n of moves. Go over the rules with the students. Divide the class into groups. Provide a penny, nickel, dime, and quarter or a facsimile of these for each group. Ask each group to keep a record of the moves required to complete each exercise. As soon as the groups have completed the exercises, discuss the answers. Have students explain how they solved the problem. Encourage students to find other mathematical games and to share them with the rest of the class. Answers See Teacher Wraparound Edition p. 607. Algebra Activity Fractal Cut-Outs (pp. 286–287 of this booklet) Use With Lesson 11-6 as an extension. Objective Make a visual model of a self-similar structure. Materials 4 sheets of 8.5-by-11 plain paper ruler scissors colored pencils or markers Have students work in pairs. Remind students to measure and cut carefully to obtain the best results. You may want to give each pair of students extra paper in case they make an error in cutting. Make sure students realize the pattern of the placement of the cut and the length of the cut before attempting Cards 3 and 4. The cut is always one-fourth the width of the fold and the length of the cut is one-half of the height of the folded section. Students need to sharply crease their folds in order to get the desired effect, especially on Cards 3 and 4. You may want students to attach their cards to poster board to make a three-dimensional display of their work. Answers 1. 1, 3, 7, 15 2. (Card, Area): (1, 20), (2, 25), (3, 26.25), (4, 26.5625), (5, 26.640625), (6, 26.660156), (7, 26.665039), (8, 26.66626), (9, 26.666565), (10, 26.666641) 3. Sample answer: The number of boxes for Card 1 is 1. Then for each card, you add a power or 2. Card 2 1 2 1 or 3. Card 3 1 2 2 or 5, Card 4 1 2 3 or 7, and so on. Card n 1 2 n1 . Alternate answer: The number of boxes is 2 n 1, where n is the card number. 4. 1023 © Glencoe/McGraw-Hill 280 Teaching Algebra with Manipulatives
Chapter 11 Teaching Notes and Overview 5. Sample answer: It appears that the surface area of the protruding part is approaching 26.67 or 26 2 3 . 6. Card Volume (in 3 ) 1 1 2 1.25 3 1.3125 4 1.328125 5 1.3320313 6 1.3330078 7 1.333252 8 1.333313 9 1.3333283 10 1.3333321 It appears that the volume is approaching 1.33 or 1 1 3 in3 . Extension Make a different set of four fractal cards using different fractions than one fourth and one half for the cuts. Compare your table and ratios with the ones from Exercises 2 and 6. Algebra 2—Chapter 11 © Glencoe/McGraw-Hill 281 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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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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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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Making Predictions Materials: NAME
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23 22 21 20 NAME __________________
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Compound Inequalities (Continued) 1
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Absolute Value 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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Using Overhead Manipulatives • Ar
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Chapter 11 Radical Expressions and
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Chapter 12 Rational Expressions and
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Chapter 13 Statistics Teaching Note
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Analyze the Data 1. Cut out the gra
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Investigating Percentiles Materials
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Chapter 14 Teaching Notes and Overv
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Simulations NAME __________________
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Investigating Polygons and Patterns
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Chapter 2 Linear Relations and Func
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Page 309 and 310: Investigating Regular Polygons Usin
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Teaching Algebra with Manipulatives

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