# Mathematics for Elementary Teachers 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 apocalyptic events that may occur during the semester.

### 1:

 Monday Class canceled—Labor Day Wednesday Introductions assign groups ~order by last name Syllabus scavenger hunt pretest Friday Create a percent problem Bring "stopwatch" with hundredths (e.g., iPhone app). Percents & decimals (hundredths) percents → decimals (two-place) → fractions Per-cents & two place decimals have same base: 100 Other decimals have bases that are powers of ten Fractions have any base percents: Real word applications; 100%, 50%, 1%, 99%, 25% discuss reading & handouts Turn in copy Exchange and do problem Exchange again and "grade" problem Return to owner representations start Linear measurements (first page) stopwatches - record various attempts how many small time units in a second? names? ~no decimal notation Record 3 fastest start/stop times. Record 3 attempts between 45 hundredths and 50 hundredths Record 3 attempts between 175 hundredths and 180 hundredths. Order all. Stop at a fraction. Which fractions are easier? What other questions can we ask? Given solution create problem

### 2:

 Monday Complete Linear measurements Make Conversion cards. Fractions discuss Linear measurements names ~hundreths, tenths, fifths, fourths, thirds, halves show "three fourths" different ways card games ~draw five and order; matching; war Wednesday Identify unknown vocabulary in CCSS Fractions section (optional extra practice) how much to make one? Daily quiz (self assessed) meaning of percent, two-digit decimals, common fractions conversion between percents and decimals converting common fractions and decimals addition or subtraction with percents, decimals, or fractions CCSS Grade 3 develop at least 3 activities on whiteboards e-mail pictures of whiteboards comparing fractions with same denominator & numerator (1/5 vs 1/4, 2/5 vs 2/4, 3/5 vs 3/4, 4/5 vs 4/4) Friday Create fraction strips (emphasis on "strip") Daily quiz (peer assessed) CCSS Grade 3 activities: 1, 2, 3, 4 CCSS Grade 3 discussion activity tips: 1, 2, 3, 4 equal shares ~show 1/4 with 2 good examples and 1 bad; exchange and find bad fraction equivalence using fraction strips ~whiteboard example equivalences, how to find?, patterns? fraction strip addition and subtraction ~whiteboard explanation for how to do

### 3:

 Monday Learning exercises for 6.1: 3, 9def, 12 (Sowder, 104-105) Daily quiz (group) Fraction strips CCSS Grade 4 equivalance with area models 1/4 = 2/8; 4/5 = 12/15 compare with common denominators and benchmarks decomposition to unit fractions (multiplying by whole number) addition and subtraction with same denominator addition and subtraction with different denominators misconception: 2/3 is bigger than 8/10 because distance b/w numerator and denominator is smaller possible web app, http://www.sineofthetimes.org/adding-and-subtracting-fractions-on-a-number-line/ Last day to drop full-semester courses with no record Wednesday Learning exercise 6.2: 3, 6 (Sowder, p. 111) Learning exercise 7.1: 3 (Sowder, p. 127) Daily quiz (bonus!) Today's homework CCSS Grade 5 Distance to one ~via 6.2.6d Generalize addition Generalize multiplication CA-66, 67 Friday Learning exercises for 6.1: 14, 15 (Sowder, p. 106-107) Daily quiz (die roll) CCSS Grade 5 CCSS Grade 5 multiplication with fraction strips

### 4:

 Monday Create pattern blocks: 4 hexagons, 8 trapezoids, 10 parrellograms, 12 triangles Daily quiz (die roll) multiplication with fraction strips Pattern blocks Assign Refraction game (bonus) Note: Exam one moved up. Will be in one week! Wednesday Attempt multiplication Daily quiz pattern block addition and subtraction Pattern blocks Friday Review

### 5:

 Monday Exam 1 one page of notes allowed (1-sided, handwritten) manipulatives allowed (fraction strips, pattern blocks) Wednesday Refraction game (bonus) New dice rolls for quizzes Division two types of division: quotative and partitive Friday Pattern block division: D1 and D2 Daily quiz pattern blocks Return Exam 1 Pattern blocks

### 6:

 Monday Create story problems for D1 and D2 GeoGebraTube: Division of fractions (partitive) New groups & DQ (group) Pattern blocks division story problems Wednesday D5-D8 on pattern blocks Daily quiz division of fractions with visuals story problems for division of fractions Pattern blocks division how visuals relate to "invert and multiply" Friday challenge division problem (optional) division of fractions (Davis & Pearn) Daily quiz (group?) student work Pattern blocks Abstract methods alternate division strategies (Liping Ma, available in canvas)

### 7:

 Monday use alternate algorithms to solve $$\frac{5}{6} \div \frac{1}{3}$$ (optional) more on fraction division Daily quiz ~bonus? alternate division methods Wrap-up division of fractions how visuals relate to "invert and multiply" and part-to-whole unit fraction divided by whole number whole number divided by unit fraction Practicum information Wednesday establish practicum groups Daily quiz division of fractions CCSS Grade 5 division is inverse of multiplication decimal operations and rounding Friday (optional) chapter 7.3: activity 3 (Sowder, p. 136) CCSS Grade 6 & 7 - ratios convert ratios to fractions convert fractions to ratios "work" problems Practicum lesson preference form (in Canvas) (1 per group)

### 8:

 Monday chapter 7.3: activity 4 (Sowder, p. 137) (optional practice) ratio problems Daily quiz decimals CCSS Grade 6 & 7 - ratios Practicum lesson preference form (in Canvas) (1 per group) Wednesday chapter 7.3: discussion 5 (Sowder, p. 138) Daily quiz ratios and work problems CCSS Grade 7 - comparing ratios (proportions) proportional relationships (Sowder, 9.2 activity #1abc) battery life ~what question comes to mind? cereal boxes Practicum lesson preference form (in Canvas) (1 per group) Friday Practicum lesson preference form (in Canvas) (1 per group) (optional practice) constructing proportions Daily quiz proportions CCSS Grade 6 & 7 - percentage & ratios explore Big Ideas ratios and percentages

### 9:

 Monday (optional practice) constructing proportions Review Wednesday Exam 2 one page of notes allowed (1-sided, handwritten) manipulatives allowed (fraction strips, pattern blocks) Friday Return exam Prep for dry run day

### 10:

 Monday Dry Run Day (for practicum) Feedback and time management Schedule Practicum materials request forms Wednesday Practicum material request forms New groups CCSS Grade 7 - probability Roller derby with 2d6 Sample space: Tree, Area Roller derby with d4 + d8 Theoretical vs experimental probability Collect for practicum Friday 28.1 activity #3ab (Sowder, p. 640) Daily quiz CCSS Grade 7 - probability Review models: 2d4 Free throws Collect for practicum

### 11:

 Monday 28.1 activity #3cd (Sowder, p. 640) Practicum collection reminders self-evaluations due Friday CCSS Grade 7 - probability Last day to withdraw from individual full-semester classes. Wednesday Practicum day @Lakeshore Elementary Friday Practicum self-evaluations CCSS Grade 7 discuss expected value discuss lottery math (based on WI PowerBall) Assign practicum reflections (due Monday after Thanksgiving break)

### 12:

 Monday Learning exercise 33.1 #2, 6 (p. 779-780) Daily quiz CCSS Grade 7 spinners start famous problems: 2nd child paradox, Monty Hall problem Wednesday Learning exercise 27.2 #9, 12 (Sowder, p. 623) Daily quiz Advanced probability Assign dice distribution (bonus) Friday Learning exercise 28.4 #1 (Sowder, p. 658) Daily quiz Advanced probability finish conditional probability CCSS Grade 8 start repeating decimals

### 13:

 Monday Learning exercise 6.3: 1abc, 2def (Sowder, p. 116) Daily quiz CCSS Grade 8 repeating decimals irrational numbers Wednesday Dice distribution (bonus) Applied probability Friday No classes—Thanksgiving break

### 14:

 Monday Practicum reflections: 1 group, 2 individual Student evals & "cards" for practicum CCSS Grade 8 - similarity mug wump with geoboards (or graph paper) who are the imposters? ~Wumps are same shape as Mug, including their noses definition of similar, scale factor ~"Yug" has scale factor of 4 effects on perimeter, area Wednesday Find perimeter and area of Yug's nose (scale factor of 4) Daily quiz CCSS Grade 8 - similarity finish Wumps ~mouth perimeter and area learning exercise 20.1: 2, 9 (Sowder, p. 454-455) Friday finish Learning exercise 20.1: 2, 9 (Sowder, p. 454-455) Daily quiz CCSS Grade 8 - transformations

### 15:

 Monday Daily quiz ~similarity Review CCSS create multi-step problem for each area Wednesday Daily quiz ~transformations Class review problems Friday Daily quiz (bonus) Review

### Common final exam

Tuesday, December 17 at 3pm (HHH 103)

• One page notes (1-sided, handwritten)
• NO calculators!