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Daily Organizer MATH 5020/7020 Fall 2018
Week 1: The baseten system; reasoning with fractions
Tuesday, August 14: Welcome to MATH 5020/7020!

How many toothpicks are in the bag? How can we organize them to see how many there are?
Thursday, August 16: If you have your book, please bring the class activities from section 2.2 to class.

Follow up on baseten structure from last time:

A digit in a number tells you how many of a specific baseten unit there are.

The value of a place’s unit is ten times the value of the place to the right.

This structure is consistent across whole numbers and decimals.


What are fractions?

What are limitations to defining the fraction A/B as "A out of B"?

The Common Core definition of fraction


Reasoning with the Common Core definition of fraction to solve problems
Week 2: Reasoning with Fractions
Tuesday, August 21: Please bring the class activities from section 2.2 to class.

Reasoning with the Common Core definition of fraction to solve problems (A/B means the amount formed by A parts, each of size 1/B of the unit amount/whole).

What are similar ideas in the Common Core defintion of fractions and base ten?

Why is it important to attend to a fraction's unit amount (whole)?

How can we think of a fractions as numbers just like whole numbers?
Thursday, August 23: Please bring the class activities from section 2.2 to class.

How can we think of a fractions as numbers just like whole numbers?

Describing quantities with numbers: a measurement sense of number

Why is it important to attend to a fraction's unit amount (whole)?
Week 3: Reasoning about and with partitioning and equivalent fractions
Tuesday, August 28: Please bring the class activities from sections 2.2 and 2.3 to class.

How can we identify unit amounts for fractions and whole numbers in situations? From a measurement perspective, numbers are the result of measurement questions of the form “How many/much of this unit amount does it take to make this quantity?” For example, if a situation involves 2/3 of a gallon, then 2/3 is the answer to “how much of 1 gallon does it take to make this amount?” so the unit amount for the number 2/3 is “1 gallon”. Another way to think about why “1 gallon” is the unit amount: the quantity is 2/3 of the 1 gallon.

Reasoning about quantities in math drawings to solve fraction problems.

Equivalent fractions

Every fraction is equal to infinitely many others

Given a fraction, how can we find other fractions that are equal to it, and why does that method work?

Equivalent fractions can be useful in problem solving!

Thursday, August 30: Please bring the class activities from section 2.3 to class.

Instead of "unit amount" we can also say "referent unit" or "referent quantity" or just "referent" so you don't confuse it with "unit fraction" (which means 1/2, 1/3, 1/4, etc). Are any of those terms better? For example, the referent for 5 in "5 kilometers" is "1 kilometer"; the referent for 3/4 in "3/4 of a cup of flour" is "1 cup of flour."

Equivalent fractions

Using math drawings to explain why a fraction A/B is equal to (A•N)/(B•N).

Equivalent fractions can be useful in problem solving!


Making common partitions

Reasoning about common multiples to make common partitions

Caution: sometimes common partitions are NOT achieved by common denominators!

Week 4: Reasoning about and with equivalent fractions
Tuesday, September 4: Please bring the class activities from section 2.3 to class.

Equivalent fractions and making common partitions

Equivalent fractions and common partitions can be useful in problem solving!

Caution: sometimes common partitions are NOT achieved by common denominators!

Thursday, September 6: Please bring the class activities from section 2.3 to class.

Solving problems by reasoning about equivalent fractions and common partitions.

Caution: sometimes common partitions are NOT achieved by common denominators!
Week 5: Reasoning to compare fractions; percent
Tuesday, September 11: Please bring the class activities from section 2.4 to class.

What are ways we can compare fractions?

Standard methods for comparing fractions that work in all cases.

Reasoning for comparing fractions that is efficient in some special cases.

Comparing fractions by relating them to benchmark numbers.
Thursday, September 13: Please bring the class activities from section 2.5 to class.

Reasoning about percentages using tables and math drawings.
Week 6: Percent; Why we add and subtract fractions the way we do; fraction addition and subtraction word problems
Tuesday, September 18: Please bring the class activities from sections 2.5 and 3.4 to class.

Solving percent problems by reasoning about tables and math drawings.

Why do we add and subtract fractions with like denominators by keeping the same denominator?

Why our (Common Core) definition of fraction is more helpful for adding and subtracting fractions than an “A out of B” view of fractions.

In addition and subtraction equations A + B = C or A – B = C, each number A, B, C in the equation must have the same referent (i.e., must refer to the same unit amount).
Thursday, September 20: Please bring the class activities from section 3.4 to class.

Fraction addition and subtraction word problems.

In addition and subtraction equations A + B = C or A – B = C, each number A, B, C in the equation must have the same referent (i.e., must refer to the same unit amount).

Distinguishing fraction addition and subtraction word problems from other word problems and why it’s so important to pay close attention to the unit amount/referent that each fraction is of.

How equations model word problems – your thoughts.

What is multiplication? Your thoughts.

Our class definition of multiplication.
Week 7: Multiplication: what is it?
Tuesday, September 25: Please bring the class activities from section 4.1 to class.

Discussion of test 1

What is multiplication? Your thoughts.

Our class definition of multiplication.
Thursday, September 27: Work on the group quiz.
Week 8: Multiplication: reasoning about and with properties
Tuesday, October 2: Please bring the class activities from sections 4.1 to class.

We will be using our class definition of multiplication page 1, page 2 to see how multiplication is a coherent concept that applies across many different kinds of quantitative situations (word problems) that involve whole numbers, fractions, or decimals.

When we are given a quantitative situation (word problem), we have to look for structure.

We can use our class definition of multiplication to explain why multiplication applies in a quantitative situation (word problem).
Thursday, October 4: Please bring the glass activities from section 4.3 and 4.4 to class.

To email me either use OR if you want to reply to an email from eLC do so INSIDE eLC otherwise it will bounce back.

Using our class definition of multiplication to explain why a word problem is a multiplication problem.

The commutative, associative, and distributive properties are fundamental properties that allow us to calculate flexibly and efficiently by reorganizing and breaking problems apart into simpler problems.

Interpreting the equal sign in equations.

Explaining where the commutative and associative properties of multiplication come from (why they are valid) by grouping items in two different ways.

Explaining where the distributive property of multiplication over addition/subtraction comes from (why it is valid) by grouping items in two different ways.
Week 9: Multiplication: how can we use properties of multiplication and where does the whole number algorithm come from?
Tuesday, October 9: Please bring the class activities from sections 4.3, 4.4, and 4.5 to class.

Explaining where the distributive property of multiplication over addition/subtraction comes from (why it is valid) by grouping items in two different ways.

Using properties of multiplication to:

make multiplication calculations easier to do mentally

facilitate learning the basic multiplication facts

Thursday, October 11: Class is cancelled due to the hurricane. Please see the assignment page for a replacement assignment due by the end of the day on Tuesday, October 16.
Week 10: Multiplication: whole number algorithm; how does multiplication extend to fractions?
Tuesday, October 16: Please bring the class activities from sections 4.2, 4.5, and 4.6 to class.

Multiplying by 10 and powers of 10why is it special in base ten?

Using properties of multiplication to make calculations easier to do by breaking them apart.

Developing and explaining the partial products written method and the standard whole number multiplication algorithm.

How the standard algorithm arises from place value and properties of multiplication.

Thursday, October 18: Please bring the class activities from sections 4.6 and 5.1 to class.

Developing and explaining the partial products written method and the standard whole number multiplication algorithm.

How the standard algorithm arises from place value and properties of multiplication.


How can we understand multiplication as a coherent concept that extends from whole numbers to fractions? Geogebra sketch: https://ggbm.at/bmz9sgpx
Week 11: Reasoning about fraction multiplication
Tuesday, October 23: Please bring the class activities from section 5.1 to class.

Interpreting what multiplication means when the multiplier is a whole number and the multiplicand is a fraction.

Interpreting what multiplication means when the multiplier is a fraction and the multiplicand is a whole number.
Geogebra sketch for ounces: https://ggbm.at/ntebhz49 Our class definition of multiplication: Page 1 and Page 2
Thursday, October 25: Please bring the class activities from section 5.1 to class.

Interpreting what multiplication means when the multiplier and the multiplicand are fractions.

Why do we multiply fractions the way we do? What is the reasoning behind the procedure?
FALL BREAK Friday, October 26
Week 12: Reasoning about fraction multiplication
Tuesday, October 30: Please bring the class activities from section 5.1 to class.

Interpreting what multiplication means when the multiplier and the multiplicand are fractions.

Why do we multiply fractions the way we do? What is the reasoning behind the procedure?
Thursday, November 1: No class due to a project you are doing with Dr. White. We will make up this class next Thursday, 8  9:15 am.
Week 13: Division: what is it? Connecting division with fractions
Tuesday, November 6: Please bring the class activities from section 5.1 to class.

Why do we multiply fractions the way we do? What is the reasoning behind the procedure?

Distinguishing fraction multiplication word problems from other word problems.
Thursday, November 8: Two class periods today: 8  9:15 am and our usual 9:30  10:45 am (to make up the missed class on 11/1). Please bring the class activities from section 6.1 to class.

What does division mean?

We can view division as multiplication with an unknown factor:

How many units in 1 group?

How many groups?

Week 14: Division: explaining the connection with fractions; interpreting quotients and remainders
Tuesday, November 13: Please bring the class activities from sections 6.1 and 6.2 to class.

Identifying division word problems as "how many units in 1 group?" or as "how many groups?" problems.

The Fundamental Theorem of Fractions: how are division and fractions related?

Division with remainder: Interpreting quotients and remainders in whole number division word problems.
Thursday, November 15: Please bring the class activities from sections 6.3 and 6.2 to class.

Explaining why the standard algorithm for whole number division works in terms of dividing baseten bundles equally among groups.

Division with remainder: Interpreting quotients and remainders in whole number division word problems.
Activity:

Organize 372 toothpicks into baseten bundles. Be sure to make each bundle of a hundred out of 10 bundles of ten.

Distribute those 372 toothpicks equally among 3 groups. Record how you did it (Step 1 ... Step 2 ... Step 3 ... etc).

If it fits, write some notation that captures or corresponds to the steps you took in part 2.

See if you can think of a different set of steps for distributing the toothpicks equally among the 3 groups.
THANKSGIVING BREAK: November 19  23
Week 15: Division: where does the whole number algorithm come from? Review
Tuesday, November 27: Please bring the class activities from section 6.2 to class.

NOTE: hang on to your textbook because we will use it again next semester!

Division with remainder: Interpreting quotients and remainders in whole number division word problems of both types:

how many units in 1 group division

how many groups division

Thursday, November 29: Review, based on your questions.

Would you like to schedule a review session for sometime next Monday, Tuesday, or Wednesday?

NOTE: hang on to your textbook because we will use it again next semester!