VISUAL MATHEMATICS COURSE III BLACKLINE MASTERS This packet contains one copy of each display master and student activity page Math Alive! Visual Mathematics, Course III by Linda Cooper Foreman and Albert B Bennett Jr Blackline Masters Copyright ©1998 The Math Learning Center, PO Box 12929, Salem, Oregon 97309 Tel 503 370-8130 All rights reserved Produced for digital distribution November 2016 The Math Learning Center grants permission to classroom teachers to reproduce blackline masters, including those in this document, in appropriate quantities for their classroom use This project was supported, in part, by the National Science Foundation Grant ESI-9452851 Opinions expressed are those of the authors and not necessarily those of the Foundation Prepared for publication on Macintosh Desktop Publishing system Printed in the United States of America DIGITAL2016 Blackline Masters LESSON Connector Master A Connector Master B Connector Master C Connector Master D Focus Master A Focus Student Activity 1.1 Focus Student Activity 1.2 Follow-up Student Activity 1.3 LESSON Focus Master A Focus Master B Focus Master C Focus Master D Focus Master E Focus Master F Focus Master G Focus Master H Focus Master I Focus Master J Focus Student Activity 2.1 Focus Student Activity 2.2 Focus Student Activity 2.3 Follow-up Student Activity 2.4 LESSON Connector Master A Connector Master B Focus Master A Focus Master B Focus Master C Focus Master D Focus Student Activity 3.1 Focus Student Activity 3.2 Focus Student Activity 3.3 Focus Student Activity 3.4 Follow-up Student Activity 3.5 LESSON Connector Student Activity 4.1 Focus Master A Focus Master B Focus Master C Focus Student Activity 4.2 (optional) Follow-up Student Activity 4.3 LESSON Connector Master A (optional) Connector Master B Connector Master C Connector Master D Focus Master A Focus Master B Focus Master C Focus Master D Focus Student Activity 5.1 Follow-up Student Activity 5.2 Copies / Transparencies per group, transp per group, transp per group, transp per student, transp per student, transp per student, transp per student, transp per student per student, transp per student, transp per student, transp transp transp per student, transp per student, transp per student, transp transp per student, transp per student, transp per student, transp per student, transp per student per group, transp per student, transp transp per two students, transp per student per two students, transp per student, transp per student, transp per student, transp per student, transp per student per student transp transp per two students, transp per student per student per teacher per two students, transp per student, transp transp transp transp transp per student, transp per student, transp per student Math Alive! Visual Mathematics, Course III / vii Blackline Masters (continued) LESSON Connector Master A Focus Master A Focus Master B Focus Master C Focus Student Activity 6.1 Focus Student Activity 6.2 Focus Student Activity 6.3 Focus Student Activity 6.4 Focus Student Activity 6.5 Follow-up Student Activity 6.6 LESSON Connector Master A Focus Master A Focus Master B Focus Master C Focus Master D Focus Master E Focus Student Activity 7.1 Follow-up Student Activity 7.2 Copies / Transparencies per group, transp per student, transp per group, transp per group, transp per student, transp per student, transp per student, transp per student, transp per student, transp per student transp per student, transp per group, transp per group, transp transp transp per student, transp per student LESSON Connector Master A Connector Master B Connector Master C Connector Master D Connector Student Activity 8.1 Focus Master A Focus Master B Focus Master C Focus Master D Focus Student Activity 8.2 Follow-up Student Activity 8.3 per student, per group, and transp per group, transp per group, transp per group, transp per group, transp transp transp per two students, transp transp per two students, transp per student LESSON per two students, transp per two students, transp per two students, transp per student, transp per group, transp transp transp per group, transp per student, transp per student, transp per student, transp per student viii / Math Alive! Visual Mathematics, Course III Connector Master A Connector Master B Connector Master C Connector Student Activity 9.1 Focus Master A Focus Master B Focus Master C Focus Master D Focus Master E Focus Student Activity 9.2 Focus Student Activity 9.3 Follow-up Student Activity 9.4 Blackline Masters (continued) LESSON 10 Connector Master A Focus Master A Focus Master B Focus Master C Focus Master D Focus Master E Focus Student Activity 10.1 Focus Student Activity 10.2 Focus Student Activity 10.3 Focus Student Activity 10.4 Follow-up Student Activity 10.5 LESSON 11 Connector Master A Connector Student Activity 11.1 Connector Student Activity 11.2 Focus Master A Focus Master B Focus Master C Focus Master D Focus Master E Focus Master F Focus Master G Focus Student Activity 11.3 Focus Student Activity 11.4 Focus Student Activity 11.5 Focus Student Activity 11.6 Focus Student Activity 11.7 Follow-up Student Activity 11.8 LESSON 12 Connector Student Activity 12.1 Focus Master A Focus Master B Focus Master C Focus Master D Focus Master E Focus Student Activity 12.2 Focus Student Activity 12.3 Focus Student Activity 12.4 Follow-up Student Activity 12.5 LESSON 13 Connector Master A Focus Master A Focus Master B Focus Master C Focus Master D Focus Master E Focus Master F Follow-up Student Activity 13.1 Copies / Transparencies transp transp per two students, transp transp per two students, transp transp per student, transp per student, transp per student, transp per student, transp per student transp per student, transp per student, transp transp transp transp per group, transp transp transp transp per student, transp per student, transp per student, transp per student, transp per group, transp per student per two students, transp per group, transp transp per group, transp per student, transp per group, transp per student, transp per student, transp per student, transp per student transp transp per two students, transp per two students, transp transp transp per two students, transp per student Math Alive! Visual Mathematics, Course III / ix Blackline Masters (continued) LESSON 14 Focus Master A Focus Master B Focus Master C Focus Master D Focus Student Activity 14.1 Focus Student Activity 14.2 Follow-up Student Activity 14.3 LESSON 15 Connector Student Activity 15.1 Focus Master A Focus Master B Focus Master C Focus Master D Focus Student Activity 15.2 Focus Student Activity 15.3 Focus Student Activity 15.4 Focus Student Activity 15.5 Focus Student Activity 15.6 Focus Student Activity 15.7 Follow-up Student Activity 15.8 LESSON 16 Connector Master A Connector Master B Connector Master C Connector Student Activity 16.1 Focus Student Activity 16.2 Focus Student Activity 16.3 Focus Student Activity 16.4 Follow-up Student Activity 16.5 LESSON 17 Connector Master A Connector Master B Connector Student Activity 17.1 Focus Master A Focus Master B Focus Master C Focus Student Activity 17.2 Focus Student Activity 17.3 Follow-up Student Activity 17.4 x / Math Alive! Visual Mathematics, Course III Copies / Transparencies transp per group, transp per group, transp per student, transp per student, transp per student, transp per student per student, transp transp transp per student, transp per student, transp per group, transp per student, transp per student, transp per student, transp per student, transp per student, transp per student transp transp transp per two students, transp per student, transp per student, transp per student, transp per student per student, transp per student, transp per group, transp transp per student, transp transp per group, transp per group, transp per student Lesson Exploring Symmetry Connector Master A ROTATIONS/TURNS a) Complete this procedure: • Position your note card so that it fits in its frame with no gaps or overlaps • Mark a point anywhere on your card with a dot, and label this point P • Place a pencil point on your point P and hold the pencil firmly in a vertical position at P • Rotate the card about P until the card fits back into its frame with no gaps or overlaps b) How many different rotations of the card about your point P are possible so that the card fits back in its frame with no gaps or overlaps? Assume that rotations are different if they result in different placements of the card in its frame c) If only a 360° (or 0°) rotation about your point P brings the card back into its frame, find another position for P on the card so that more than one different rotation about this point is possible What are the measures of the rotations and how did you determine them? © 1998, The Math Learning Center Blackline Masters, MA! Course III Lesson Exploring Symmetry Connector Master B REFLECTIONS/FLIPS Figure below shows the frame for a rectangular card with a line l drawn across the frame In Figure 2, the card has been placed in the frame Figure shows the result of reflecting, or flipping, the card over line l Notice that after the reflection over line l, the card does not fit back in its frame A B D C l Figure l l Figure Figure Determine all the different possible placements of line l so that when you flip your card once over l, the card fits back in its frame with no gaps or overlaps HINT: As a guide for flipping the card about a line, you could tape a pencil or coffee stirrer to the card along the path of line l, as shown below Then keep the pencil or coffee stirrer aligned with line l as you flip the card Blackline Masters, MA! Course III A B D C l © 1998, The Math Learning Center Lesson Exploring Symmetry Connector Master C a) Discuss your group’s ideas and questions about the meanings of the following terms Talk about ways these terms relate to a nonsquare rectangle such as your note card Record important ideas and questions to share with the class i) reflectional symmetry ii) axis of reflection (also called line of reflection) iii) rotational symmetry iv) center of rotation v) frame test for symmetry b) If a shape is symmetrical, its order of symmetry is the number of different positions for the shape in its frame, where different means the sides of the shape and the sides of the frame match in distinctly different ways Develop a convincing argument that your rectangular note card has symmetry of order four © 1998, The Math Learning Center Blackline Masters, MA! Course III Lesson Exploring Symmetry Connector Master D a) b) c) d) e) f) g) h) i) j) © 1998, The Math Learning Center Blackline Masters, MA! Course III ➤ © The Math Learning Center ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ (cut on thin dotted lines at arrowheads) ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ Algebra Pieces—front (cut as indicated on front side) Algebra Pieces—back © The Math Learning Center Geoboard Recording Paper © The Math Learning Center Visual Mathematics Geoboard Dot Paper © The Math Learning Center Visual Mathematics ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ ➤ © The Math Learning Center ➤ ➤ oooo oooo oooo oooo oooo oooooooo oooo oooo ➤ ➤ oooo oooo oooo oooo oooo oooooooo oooo oooo oooo oooo oooo oooo oooo oooooooo oooo oooo ➤ (cut on thin dotted lines at arrowheads) ➤ ➤ oooo oooo oooo oooo oooo oooooooo oooo oooo ➤ ➤ ➤ ➤ ➤ n-Frame Pieces—front (cut as indicated on front side) n-Frame Pieces—back © The Math Learning Center Protractor © The Math Learning Center Visual Mathematics ... Alive! Visual Mathematics, Course III by Linda Cooper Foreman and Albert B Bennett Jr Blackline Masters Copyright ©1998 The Math Learning Center, PO Box 12929, Salem, Oregon 9 730 9 Tel 5 03 370-8 130 ... that are marked on the diagrams h = _ 30 0 a = _ p = _ 17 12 h = _ a = _ p = _ 20 32 14 27 13 20 12 20 h = _ a = _ p = _ 24 30 s 15 13 12 h = _ a = _ p = _ 50 h a p s =... Student Activity 3. 1 Focus Student Activity 3. 2 Focus Student Activity 3. 3 Focus Student Activity 3. 4 Follow-up Student Activity 3. 5 LESSON Connector Student Activity 4.1 Focus Master A Focus Master