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Daily Organizer, MATH 5035/7035 Spring 2019

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Week 1: Fraction division

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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.

 

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 can be answered (or addressed) by collecting data

    • 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

 

Week 10: Statistics and a return to equations

 

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 

Wednesday, May 1: Reading day

 

Thursday, May 2: FINAL EXAM, 12 - 3 pm in our usual classroom.

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