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## Daily Organizer, MATH 5035/7035 Spring 2019

###### Week 1: Fraction division

Thursday, January 10: Please bring the class activities from section 6.4 to class.

• Recall the two meanings for division:

• how-many-units-in-1-group

• how-many-groups

• We can extend the two meanings of division to interpret fraction division.

• Fraction division from the how-many-groups perspective

• solving this type of word problem by reasoning about quantities shown in math drawings

• developing another general method for dividing fractions other than keep, change, flip.

###### Week 2: Fraction division

Tuesday, January 15: Please bring the class activities from section 6.4 to class as well as class activity 5B from section 5.1.

• Fraction division from the how-many-groups perspective

• solving this type of word problem by reasoning about quantities shown in math drawing

• based on reasoning about math drawings, develop this general method of fraction division: give the fractions common denominators, then just divide the resulting numerators.

•  Writing multiplication equations to compare quantities

Thursday, January 17: Please bring the class activities from section 6.5 to class as well as class activity 5B from section 5.1.

• Fraction division from the how-many-units-in-1-group perspective

• solving this type of word problem by reasoning about quantities shown in math drawings

• explain why we can "keep, change, flip": by reasoning about situations shown in math drawings and by modeling those situations with equations, explain why we can divide fractions by multiplying by the reciprocal

• Given a fraction word problem, is it a division problem, a multiplication problem, or some other kind of problem? How can we tell?

###### Week 3: Fraction division; ratio and proportional relationships

Tuesday, January 22: Please bring the class activities from section 6.5 to class.

• Fraction division from the how-many-units-in-1-group perspective

• solving this type of word problem by reasoning about quantities shown in math drawings

• explain why we can "keep, change, flip": by reasoning about situations shown in math drawings and by modeling those situations with equations, explain why we can divide fractions by multiplying by the reciprocal

• Given a fraction word problem, is it a division problem, a multiplication problem, or some other kind of problem? How can we tell?

Thursday, January 24: Please bring the class activities from section 6.5 to class.

• Given a fraction word problem, is it a division problem, a multiplication problem, or some other kind of problem? How can we tell?

• Can two mixtures have the same "quality" even though they differ in size? How can we describe all the mixtures that share the same quality?

###### Week 4: Ratio and proportional relationships

Tuesday, January 29: Please bring the class activities from section 7.2 to class.

• Solving proportion problems by reasoning about quantities from a "multiple batches" perspective

• Reasoning with double number lines

• Reasoning about multiplication and division with quantities

• Why should students learn methods for solving proportions other than setting up proportion equations and cross-multiplying?

Thursday, January 31: Please bring the class activities from section 7.2 to class.

• Solving proportion problems by reasoning about quantities from a "multiple batches" perspective

• Reasoning about multiplication and division with quantities

• Reasoning with double number lines

• Solving proportion problems by reasoning about quantities from a "variable parts" perspective

###### Week 5: Solving proportion problems by reasoning about multiplication and division with quantities

Tuesday, February 5: Please bring the class activities from section 7.2 to class.

• Solving proportion problems by reasoning about quantities from a "variable parts" perspective

Thursday, February 7: Please bring the class activities from sections 7.2 and 7.3 to class.

• Solving proportion problems by reasoning about multiplication and division with quantities from both the multiple-batches and the variable-parts perspectives.

• Interpreting the values of a ratio as rates in two ways and using these rates to relate quantities that vary together in a fixed ratio (a proportional relationship).

###### Week 6: Developing equations for proportional relationships and lines

Tuesday, February 12: Please bring the class activities from sections 7.3 and 7.4 to class.

• Interpreting the values of a ratio as rates in two ways and using these rates to relate quantities that vary together in a fixed ratio (a proportional relationship).

Thursday, February 14: Please bring the class activities from sections 7.3 and 7.4 to class.

• Using the variable-parts perspective to develop equations in two variables for quantities that vary together in a fixed proportional relationship.

• Where do the familiar formulas for equations of lines come from? Developing equations for lines from the variable-parts perspective.

###### Week 7: Developing equations for lines; Inversely proportional relationships

Tuesday, February 19: Please be prepared to work with Geogebra sketches in class on a laptop or iPad or on one of the big computers in the classroom.

Thursday, February 21: Please bring the class activities from section 7.5 to class.

• When two quantities vary together in a fixed relationship, sometimes that relationship is proportional, but sometimes it is not.

• Sometimes two quantities vary together and are related by multiplication, but are not in a proportional relationship. One such case: Inversely proportional relationships.

###### Week 8: Inversely proportional relationships; Statistics

Tuesday, February 26: Please bring the class activities from section 7.5 to class.

• Distinguishing proportional relationships from inversely proportional relationships and other relationships.

• How are equations and graphs for proportional relationships different from those for inversely proportional relationships?

Thursday, February 28: Please bring the class activities from sections 7.5 and section 15.1 to class.

• Distinguishing proportional relationships from inversely proportional relationships and other relationships.

• Statistical problem solving:

• formulate a question

• collect data

• analyze data

• interpret results

• Statistical questions versus mathematical questions

• statistical questions anticipate variability

###### Week 9: Statistics

Tuesday, March 5: Please bring the class activities from section 15.3 to class.

• Measures of center of numerical data: mean, median, mode. These are single-number summaries of a numerical data set.

• The mean as "leveling out" all the data to a single number.

• Why do we calculate the mean by adding all the numbers and then dividing by how many there are? Why does that give us a reasonable single-number summary of the data?

• The mean as balance point or fulcrum.

• When a dot plot or histogram has a "tail", the tail pulls the mean toward it.

Thursday, March 7: Please bring the class activities from section 15.4 to class.

• The median and how it is different from the mean.

• The mean is more sensitive to extreme values.

• In reports about household income, statisticians usually use the median rather than the mean. Why?

• We can use measures of center to compare two numerical data sets, but sometimes we also need information on how much variation there is in the data.

• Measures of variation:

• Range and interquartile range, which we often use with the median;

• Mean absolute deviation (MAD), which we can use with the mean.

SPRING BREAK: week of March 11

Tuesday, March 19:  Work together on the group quiz. Links to the Geogebra sketches:

Thursday, March 21:  Work together on the group quiz. See above for the links to the Geogebra sketches.

###### Week 11: Statistics

Tuesday, March 26:  Please bring class activities 15C, 15D, 15F, 15R to class.

• Random samples

• Distributions of random samples have a characteristic shape and mean

• How do distributions of larger random samples compare with distributions of smaller random samples?

• Random samples tend to be representative of the full population; larger random samples are more likely to be representative

• Statistical inference: using a random sample to predict characteristics of a population.

Thursday, March 28:  Please bring class activities 15C and 15D to class. There will also be a handout.

• Random samples

• What do the means of dstributions of random samples tell us about the population?

• Random samples tend to be representative of the full population; larger random samples are more likely to be representative

• Statistical inference: using a random sample to predict characteristics of a population.

###### Week 12: Probability

Tuesday, April 2 :  Please bring Class Activity 15D and the class activities from section 16.1 to class.

• Statistical inference: using a random sample to predict a characteristic of a population.

• Probability: When all possible outcomes are equally likely, then the probability of an event is the fraction of outcomes that compose the event.

• Theoretical probability versus empirical probability: the long-run relative frequency with which an event occurs approximates the event's probability.  Online spinner:  https://www.nctm.org/adjustablespinner/

Thursday, April 4: Please bring the class activities from sections 16.1, 16.2, and 16.3 to class

• Theoretical probability versus empirical probability: the long-run relative frequency with which an event occurs approximates the event's (theoretical) probability.  Online spinner:  https://www.nctm.org/adjustablespinner/

• Counting the number of outcomes in multi-stage experiments: independence versus dependence;

• Probability of compound events.

###### Week 13: Probability; Number Theory

Tuesday, April 9: Please bring the class activities from sections 16.3 and 8.1 to class.

• Counting the number of outcomes in multi-stage experiments: independence versus dependence;

• Probability of compound events.

• Factors and multiples

• What are factors and multiples?

• How can we find all the factors of a whole number?

Thursday, April 11:  Please bring the class activities from sections 8.1 and 8.4 to class.

• Factors and multiples

• Prime numbers

• The Sieve of Eratosthenes for finding a list of prime numbers

• Trial division for determining whether a number is prime

• Factor trees for writing numbers as products of prime numbers

• The Fundamental Theorem of Arithmetic

###### Week 14: Number Theory

Tuesday, April 16:  Please bring the class activities from sections 8.4 and 8.5 to class.

• Prime numbers

• Trial division for determining whether a number is prime -- when we can stop?

• Factor trees for writing numbers as products of prime numbers

• The Fundamental Theorem of Arithmetic

• How do we know there are infinitely many prime numbers?

• Greatest common factor (GCF) and least common multiple (LCM)

• Using the definitions to find GCF and LCM

Thursday, April 18: Please bring the class activities from section 8.5 to class.

• Greatest common factor (GCF) and least common multiple (LCM)

• Using the definitions to find GCF and LCM

• Using prime factorizations to find GCF and LCM

• Using the "slide method" to find GCF and LCM

• Situations and word problems that involve the GCF and LCM

• If time we will start to review fraction division. We will start from the how-many-units-in-1-group view and use it to explain why dividing by a fraction is equivalent to multiplying by its reciprocal.

###### Week 15: Review

Tuesday, April 23: Review of fraction division.

Thursday, April 25: Review of fraction division. Review of solving proportion problems in multiple ways by reasoning about multiplication and division with quantities, including in cases of probability and statistical inference.

###### Week 16: Review and Final Exam

Tuesday, April 30: Review