Numbers and Operations II
Calendar
This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any unforeseen events that may occur during the semester.
1:
### Tuesday
Before class:
- For fun, watch [The Weird Number](https://www.youtube.com/watch?v=PZWvvtbA1ME) (1970)
Class: What is Math 202?
#. assign groups
#. introductions and [syllabus scavenger hunt](handouts/syllabus-game.html)
#. Q&A
After class
- (optional) Watch [A math teacher reacts to "The Weird Number"](https://www.youtube.com/watch?v=0_36k4REvvI)
### Thursday
Before class
- try "beakers" on [visualizing percents](handouts/percents.html)
Class: Percentages as a starting place
#. "sidewalks" on [visualizing percents](handouts/percents.html)
#. referent (what a fraction or percent "refers" to)
#. percent strips → fraction strips → number line
#. percent strips to solve "computations" on [visualizing percents](handouts/percents.html)
#. discuss percents → decimals → fractions
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
- (optional) Read [Pipes, tubes and beakers: A new approach to rational-number learning](https://www.nap.edu/read/10126/chapter/8#322) (pg. 322-324)
2:
### Tuesday
Before class
- take notes on Percent (Chapter 2.5)
Class: Percent tables
#. use percent tables to solve [computations](handouts/percents.html)
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 2U.1-6 (percent tables)
#. challenge: [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 2V.1-2
After class
- Class Activity 2X (75; 250%; 168; only male bugs; ~44.4%)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- take notes on Multiplying Decimals (Chapter 5.2)
- take
formative quiz
Class: Discuss quiz
Class: Decimals
#. review how bases work
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 5G, 5F (multiplying decimals)
After class
- try Class Activity 5H
(4.14; same idea except squares represent 10 instead of 1, and so on)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
3:
### Tuesday
Before class
- take notes on Equivalent Fractions (Chapter 2.3)
- print and cut out [fraction strips](https://duckduckgo.com/?q=fraction+strips&ia=web) (any version is fine as long as lengths are consistent)
- take
formative quiz
Class: Discuss quiz
Class: Decimals (continued)
#. convert percentages to decimals
#. continue [computations](handouts/percents.html)
Class: Equivalent fractions
#. "per cent" (?/100) and equivalent fractions
#. equivalent fractions to solve [computations](handouts/percents.html)
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- finish [computations](handouts/percents.html)
- take
formative quiz
Class: Discuss quiz
Class: Equivalent fractions, continued
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 2W (equivalent fractions; #7 is challenge)
#. summarize [computations](handouts/percents.html)
#. comparison using fraction strips: same denominator, same numerator, distance below one
After class
- try [Comparing and identifying fractions visually](http://www.sineofthetimes.org/comparing-and-identifying-fractions-visually/) (Sine of the Times)
- take notes on "comparing fractions using common numerators" (Chapter 2.4)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
4:
### Tuesday
Before class
- take notes on "using other reasoning to compare fractions" (Chapter 2.4)
- prepare for summative quiz
Class: Summative quiz 1
Class: Comparing fractions
#. comparing fractions: benchmarks, more of bigger
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 2Q, 2R, 2S
After class
- try [Fraction Strips](https://toytheater.com/fraction-strips/)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- take notes on Adding and Subtracting Fractions (Chapter 3.4)
- finish [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 2Q, 2R, 2S
Class: Discuss quiz
Class: Adding and subtracting fractions
#. review equivalent fractions
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 3O.1
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 3P
After class
- try [Geogebra: Fraction addition](https://www.geogebra.org/m/z2CkQ4Ef)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
5:
### Tuesday
Before class
- finish [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 3P
- take
formative quiz
Class: Discuss quiz
Class: Story problems with addition and subtraction
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 3Q, 3R
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- print and cut [Pattern blocks](https://www.raebear.net/goodies/patternblocks/printableblocks/) (4 hexagons, 8 trapezoids, 10 blue parallelograms, 12 triangles)
- take
formative quiz
Class: Discuss quiz
Class: Pattern blocks
#. [addition and subtraction](handouts/pattern-blocks1.html)
#. [multiplication](handouts/pattern-blocks1.html)
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
6:
### Tuesday
Before class
- take notes on Multiplying Fractions (Chapter 5.1)
- take
formative quiz
Class: Discuss quiz
Class: Fraction multiplication, continued
#. [multiplication](handouts/pattern-blocks1.html)
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 5B
After class
- Sine of the Times: [Understanding fraction multiplication](http://www.sineofthetimes.org/understanding-fraction-multiplication-2/)
- [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 5A.2
(1/4 of 1/3; 3/5 of 1/4; 1/4 of 2/3; 3/4 of 3/5)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- prepare for summative quiz
Class: Summative quiz 2
Class: More story problems
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 5C (challenge: 2d & 2e)
After class
- take notes on "comparing fractions by using common denominators" (Chapter 2.4)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
7:
### Tuesday
Before class
- prepare questions for review
- prepare note sheet (1-sided, handwritten)
Class: Discuss quiz, clean out folders
Class: Review
#. review common denominators
#. [review topics](handouts/review.html)
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 7Q
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 2L
After class
- extra practice on [Pattern Blocks](handouts/pattern-blocks1.html)
- Beckmann, 3.4, practice #7-8
- Beckmann, 5.1, practice #4
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044): Midterm review (0 pts)
### Thursday
Before class
- prepare note sheet (1-sided, handwritten)
Class: Midterm exam
- allowed: one page notes (1-sided, handwritten)
- allowed: fraction strips, pattern blocks
- no calculators
8:
### Tuesday
Before class
- n/a
Class: Discuss exam, new groups
Class: Partitive division
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 2J (pattern blocks for improper fractions)
#. introduce partitive division (how many in one group?)
#. bins?
After class
- takes notes on Chapter 6.5 "how many in one group?" (aka. partitive division)
- Chapter 2.2, practice exercises: 1, 2, 3, 4
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- n/a
Class: Partitive division (continued)
#. [partitive division](handouts/pattern-blocks2.html)
#. multiply by the reciprocal
After class
- read [Nix the Tricks](http://www.nixthetricks.com/NixTheTricks21.pdf): Section 3.6
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
9:
### Tuesday
Before class
- finish [partitive division](handouts/pattern-blocks2.html)
Class: Measurement division
#. introduce "measurement division" (aka. quotative)
#. [pattern block division](handouts/pattern-blocks2.html)
#. [visual division](handouts/pattern-blocks2.html)
After class
- take notes on measurement division (Chapter 6.4 "how many groups?")
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- finish D4 on [division w/o pattern blocks](handouts/pattern-blocks2.html)
- take
formative quiz
Class: Discuss quiz
Class: Division (continued)
#. [division extra practice](handouts/pattern-blocks2.html)
After class
- take notes on [What is the difference between "partitive" and measurement"?](https://medium.com/eureka-math/fractional-division-interpretation-what-is-the-difference-between-partitive-and-measurement-d253cd963bea)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
10:
### Tuesday
Before class
- take
formative quiz
Class: Discuss quiz
Class: Division story problems
#. review [division extra practice](handouts/pattern-blocks2.html)
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 6P (answers for 1-4, create "look fors", finish 5-7)
#. create partitive division problem involving fractions
#. create measurement division problem involving fractions
After class
- Beckmann, Chapter 6.4 practice exercise #2
- Beckmann, Chapter 6.5 practice exercise #2
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- take
formative quiz
Class: Discuss quiz
Class: Division of fractions (continued)
#. Computation: divide across
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 6N
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
11:
### Tuesday
Before class
- take notes on Why Division Algorithms Work (Chapter 6.3)
- take
formative quiz
Class: Discuss quiz
Class: Converting fractions to decimals
#. recall a/b = a ÷ b
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 8O.1-2
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 8P.1-2
After class
- try [Scratch: Fraction → Decimal](https://scratch.mit.edu/projects/155117456)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- take notes on Rational and Irrational Numbers (Chapter 8.6)
- prepare for summative quiz
Class: Summative quiz 3
Class: Repeating decimals
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 8P.3
#. check with algebra
After class
- [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 8Q.1-3 (all answers result in 1=0.999...)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
12:
### Tuesday
Before class
- n/a
Class: Discuss quiz
Class: Repeating decimals (continued)
#. finish [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 8P
#. (if time) fractions that terminate and fractions that repeat
Note: WeBWorK scores will be turned on in Canvas soon
After class
- watch [terminating vs. non-terminating repeating](https://www.youtube.com/watch?v=rVhU8Vyhz7c)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
#### No class for Thanksgiving break
13:
### Tuesday
Before class
- take notes on Dividing Decimals (Chapter 6.6)
Class: Reminder about webwork scores
Class: Division with decimals
#. connections between decimal division and fraction notation
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 6R: 1-3 (decimal division)
#. if time, [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 6Q (answers: multiply by 2, multiply by 4, multiply by 3, answer is between 1 and 2 so must be 1.633) (mental decimal division)
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- take notes on Motivating and Defining Ratio and Proportional Relationships (Chapter 7.1)
- take
formative quiz
Class: Discuss quiz
Class: Finish division with decimals
Class: Ratios and proportional relationships
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) 7D (ratios with strip diagrams)
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
14:
### Tuesday
Before class
- take notes on Solving Proportion Problems (Chapter 7.2)
- take
formative quiz
Class: Student evaluations & (optional) formative feedback
Class: Discuss quiz
Class: Problem solving with ratios
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) (ratio problem solving) 7G
After class
- [extra practice problems](handouts/final-practice.html)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- prepare for summative quiz
Summative quiz 4
Class: Ratio problem solving
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) (more ratio problem solving) 7E.1-2
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
15:
### Tuesday
Before class
- n/a
Class: Discuss quiz
Class: Ratio problem solving (continued)
#. [Class Activity](https://uweau.instructure.com/courses/496066/pages/class-activities-from-beckmann) (even more ratio problem solving) 7I
After class
- [extra practice problems](handouts/final-practice.html)
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Thursday
Before class
- n/a
Class: Review
#. clean out folders
#. [review topics](handouts/review.html)
#. [more division practice](handouts/division-types.html)
After class
- [WeBWorK](https://uweau.instructure.com/courses/496066/assignments/4792044)
### Final exam
- [review topics](handouts/review.html)
- note sheet (1 page, 1-sided, handwritten)
- allowed: fraction strips, pattern blocks
- no calculator