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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:

howmanyunitsin1group

howmanygroups


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

Fraction division from the howmanygroups 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 howmanygroups 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 howmanyunitsin1group 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 howmanyunitsin1group 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 crossmultiplying?
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

Reasoning about multiplication and division with quantities

Reasoning with strip diagrams. Geogebra sketch: https://www.geogebra.org/m/jcgdmydt

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

Reasoning about multiplication and division with quantities

Reasoning with strip diagrams. Geogebra sketch: https://www.geogebra.org/m/jcgdmydt

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 multiplebatches and the variableparts 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 variableparts 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 variableparts perspective.

Links to Geogebra sketches: https://ggbm.at/jcgdmydt https://ggbm.at/uqqbg3k4 https://ggbm.at/zpkktat9 https://ggbm.at/f7xTdkSG https://ggbm.at/Lz55pEO3
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.

Where do the familiar formulas for equations of lines come from? Developing equations for lines from the variableparts perspective.

Geogebra sketches for explaining equations for lines through the origin and a given point: https://ggbm.at/jcgdmydt https://ggbm.at/uqqbg3k4 https://ggbm.at/zpkktat9 https://ggbm.at/f7xTdkSG

Geogebra sketch for explaining equations for lines through the origin more generally: https://ggbm.at/fbf57dch

Geogebra sketch for explaining equations for lines that are not through the origin: https://ggbm.at/Lz55pEO3
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 singlenumber 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 singlenumber 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:

House sketch: https://ggbm.at/nnncshgp

Ramp sketch: https://ggbm.at/zpr2mh4g

Line sketch: https://ggbm.at/pnqr3nna

Right triangle in a circle sketch: https://ggbm.at/b2whmfkx
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 longrun 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 longrun 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 multistage 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 multistage 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 howmanyunitsin1group 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.