Schedule for Math 107

**Good problems to do if you find spare time: p. 109: 30, p. 135: 25

**Chapter 1: 2-3 75-minute classes (1-1.5 weeks)**

· Day 1: Tuesday, August 26

o Introduction and Syllabus

o Exploration 1.1 with its variants Investigation 1.5 Sum of the first 100 numbers, Triangular numbers, etc.

o Investigation 1.1 (introduces guess-and-check and alternate problem solving strategies), 1.3 (teaches students to check that solution is really possible)

o Homework Exercises p. 27: 3, 4, 7 (make up and solve your problem), 9, 21

· Day 2: Thursday, August 28

o Investigation 1.8 (highlights the idea of mathematics having meaning beyond formulas), 1.9 (patterns and justification/reasoning), 1.13 (communication and clearly articulated arguments)

o More class problems, as time allows:

§ Investigation 1.11, 1.12, p. 28: 14, 17, 20

§
Alana, Bob, Carmela,
and Daron come to a cliff at the edge of a
canyon. There is a narrow suspension
bridge and they all need to get across the bridge in 17 minutes, because in 17
minutes and 2 seconds, a rockslide will destroy the cliff they are on. It is dark and they are sharing a single
flashlight. Alana can cross the bridge
in one minute, Bob can cross in two minutes, Carmela
in five minutes, and Daron in 10 minutes. Due to the dangerous nature of the bridge,
only two people can cross at a time, and they must use the flashlight to
cross. When two people cross a bridge
together, they must move at the rate of the slower person, and someone must
carry the flashlight back to the other people.
How can they all make it across?
(For

o Homework: Read all of chapter 1, do exercises p. 29: 28, 32, 39, 41; p. 52: 1, 2, 3.

· Day 3: Tuesday, September 2

o Collect and discuss homework

o Investigation 1.15 (the idea of unit in fractions), 2.1 (classification and need for sets and Venn diagrams)

o Exploration 2.1 Venn Diagrams

o Homework Exercises p. 52: 7, 8, 15; p. 70: 12, 13, 15

**Chapter 2: About six 75-minute classes (3 weeks)**

· Day 4: Thursday, September 4

o Exploration 2.5 Growth Patterns

o Exploration 2.6, if time, with pattern blocks

o Homework: Read all of chapter 2 and do exercises p. 70: 23; p. 91: 4, 11, 14, 20

· Day 5: Tuesday, September 9

o Collect and discuss homework

o Exploration 2.6

o Discuss

o Investigation 2.5, 2.7, 2.10

o Homework Exercises p. 91: 24; p. 107: 2, 3, 5, 6, 7

· Day 6: Thursday, September 11

o Exploration 2.7 Alphabitia Part 1 and Part 2: 1, 2 Use base 5 blocks (can be homemade, or algebra tiles will work)

o Homework: Select the system you like best and write one paragraph explaining why it is the best. Draw 4 examples with manipulatives and write the numerals that correspond to those amounts in the system you have chosen. Also do exercises p. 107: 22, 23, 24

· Day 7: Tuesday, September 16

o Collect and discuss homework

o Finish Exploration 2.7 and discuss base 5; do Exploration 2.8 Part 1, if needed

o Review for exam

o Homework Exercises: p. 108: 11ag, 12ab, 13acde, 14abjlm

· Day 8: Thursday, September 18

o Exam 1

o Homework: Read 3.1 and do exercises p. 109: 30**; p. 134: 3, 5, 6, 7.

**Chapter 3: Seven 75-minute classes (3.5 weeks)**

· Day 9: Tuesday, September 23

o Collect homework and discuss; return exams

o Exploration 3.1 Inventing and Understanding Addition in Alphabitia: Offer base 5 blocks

o Exploration 3.4 Alternative Algorithms for Addition—can divide algorithms among groups

o Journal prompts: p. 135: 22, 26

o Homework: Read 3.2 and do exercises p. 134: 4ab, 12, 14, 15, 16, 17

· Day 10: Thursday, September 25 Bring base 10 blocks from manipulatives kit

o Exploration 3.5 Alternative Algorithms for Subtraction—divide algorithms among groups

o Exploration 3.6 Multiplication—Geometric Perspective

o Journal: Write about any unresolved issues with any algorithms.

o Homework: Finish explorations. Do exercises p. 135: 20, 25**; p. 161: 1, 2, 12,14

· Day 11: Tuesday, September 30 Base 10 blocks

o Collect and discuss homework and journal

o Exploration 3.8 Standard Multiplication Algorithm

o Homework Exercises: p. 161: 10, 13, 15, 16, 17, 19

· Day 12: Thursday, October 2 Base 10 blocks

o Exploration 3.9 Alternative Algorithm for Multiplication—Give different algorithms to each group

o Homework Exercises: p. 162: 18, 24, 25, 46, 51

· Day 13: Tuesday, October 7 Base 10 blocks

o Exploration 3.11 Different Models of Division

o Exploration 3.12 Understanding the Standard Algorithm

o Homework p. 162: 26, 29, 30, 39, 43

· Day 14: Thursday, October 9

o Exploration 3.13 Alternative Algorithms for Division

o Exploration 3.14 Dealing with Remainders

o Homework: Read 3.3 and do p. 162: 52; p. 181: 1, 3.

· Day 15: Tuesday, October 14

o Collect homework

o Wrap up division explorations

o Discuss models of the four operations

o Journal p. 164: 57.

o Review for Exam

· Day 16: Thursday, October 16

o Exam 2

o Homework: Read 4.1 and do exercises p. 202: 1, 2, 9, 11

**Chapter 4:
Three 75-minute classes (1.5 weeks)**

· Day 17: Tuesday, October 21

o Collect and discuss homework; return exams

o Exploration 4.1 Taxman (I have talked to middle school teachers who use this game)

o Exploration 4.3 Finding All Factors of a Number

o In class exercises p. 203: 15, 20, 27

o Homework: Read 4.2, finish exercises 20 and 27 above, if needed, and do exercises p. 204: 21, 26abc; p. 212: 3, 5, 7

· Day 18: Thursday, October 23

o Exercise p. 205: 28, 29, 33

o Exercises p. 212: 11, 13, 14, 17

o Homework: Read 4.3, finish the exercises above, and do exercises p. 225: 1abcd, 2a, 3ab, 5.

· Day 19: Tuesday, October 28

o Collect and discuss homework

o Exercises p. 225: 6, 7, 8, 18, 19

o Journal p. 226: 20.

o Homework: Read 5.1; do exercises p. 225: 1efgh, 2b, 10, 12, 13 and p. 237: 1abcd, 2abc

**Chapter 5: Nine
75-minute classes (4.5 weeks)**

· Day 20: Thursday, October 30 Bring Two-color counters from manipulatives kit

o Exploration 5.1 Understanding Integer Addition

o Exploration 5.2 Understanding Integer Subtraction

o Complete more examples of integer addition and subtraction with counters

o Exercises p. 237: 20, 21

o Homework: Read 5.2; finish exercises above and do exercises p. 237: 1efgh, 2def, 3, 8, 10

· Day 21: Tuesday, November 4

o Collect and discuss homework

o Exploration 5.3 Understanding Integer Multiplication

o Exploration 5.4 Understanding Integer Division

o Homework exercises p. 252: 1, 3, 5, 7

· Day 22: Thursday, November 6

o Exploration 5.7 Partitioning Wholes Part I

o Exercises p. 252: 4, 9, 10, 11, 24

o Homework: finish class exercises and also do exercises p. 252: 8, 15, 19, 20.

· Day 23: Tuesday, November 11

o Collect and discuss homework

o Exploration 5.7 Parts II, III, and Looking Back

o Exercises p. 254: 25

o Homework: Finish exercise 25, read 5.3 and do exercises p. 254: 26, 27, 28, p. 274: 1, 3.

· Day 24: Thursday, November 13

o Review for exam

o Exploration 5.8 Developing Fraction Sense

o Exploration 5.9 Developing Operation Sense

· Day 25: Tuesday, November 18

o Collect homework

o Exam 3

o Homework exercises p. 274: 2, 10, 11 (read the directions for exercises 4-12), 14, 16.

· Day 26: Thursday, November 20

o Exploration 5.10 Wholes and Units

o Exploration 5.12 An Alternative Algorithm for Dividing Fractions

o Begin homework in class if time.

o Homework p. 275: 17, 18, 20, 22, 23, 24, 25.

· Day 27: Tuesday, November 25

o Exploration 5.11 Meanings of Operations with Fractions

o Exploration 5.13 Remainders

o Homework: Read 5.4 and do exercises p. 275: 26, 29, 31, 32, 33, 36, 37; p. 299: 1-5, 7, 9, 24, 35

· Day 28: Tuesday, December 2

o Exploration 5.14 Decimals and Base 10 Blocks

o Exercises p. 300: 20, 22, 25, 29

o Exploration 5.16 The Right Bucket: A Decimal Game

· Day 29: Thursday, December 4

o Review for Final

o Exploration 5.17 Operations: A Decimal Game

o Exploration 5.18 Target: A Decimal Game

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