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Daily Organizer MATH 5020/7020 Fall 2018

Week 1: The base-ten 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 base-ten structure from last time:

    • A digit in a number tells you how many of a specific base-ten 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 1page 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 sybilla@uga.edu 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 10--why 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 base-ten bundles equally among groups. 

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

Activity:

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

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

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

  4. 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!

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