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Daily Organizer MATH 5020/7020 Fall 2018
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Week 1: The base-ten system; reasoning with fractions
Tuesday, August 14: Welcome to MATH 5020/7020!
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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.
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Follow up on base-ten structure from last time:
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A digit in a number tells you how many of a specific base-ten unit there are.
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The value of a place’s unit is ten times the value of the place to the right.
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This structure is consistent across whole numbers and decimals.
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What are fractions?
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What are limitations to defining the fraction A/B as "A out of B"?
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The Common Core definition of fraction
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Reasoning with the Common Core definition of fraction to solve problems
Week 2: Reasoning with Fractions
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Tuesday, August 21: Please bring the class activities from section 2.2 to class.
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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).
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What are similar ideas in the Common Core defintion of fractions and base ten?
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Why is it important to attend to a fraction's unit amount (whole)?
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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.
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How can we think of a fractions as numbers just like whole numbers?
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Describing quantities with numbers: a measurement sense of number
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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.
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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.
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Reasoning about quantities in math drawings to solve fraction problems.
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Equivalent fractions
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Every fraction is equal to infinitely many others
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Given a fraction, how can we find other fractions that are equal to it, and why does that method work?
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Equivalent fractions can be useful in problem solving!
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Thursday, August 30: Please bring the class activities from section 2.3 to class.
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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."
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Equivalent fractions
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Using math drawings to explain why a fraction A/B is equal to (A•N)/(B•N).
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Equivalent fractions can be useful in problem solving!
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Making common partitions
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Reasoning about common multiples to make common partitions
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Caution: sometimes common partitions are NOT achieved by common denominators!
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Week 4: Reasoning about and with equivalent fractions
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Tuesday, September 4: Please bring the class activities from section 2.3 to class.
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Equivalent fractions and making common partitions
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Equivalent fractions and common partitions can be useful in problem solving!​​
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Caution: sometimes common partitions are NOT achieved by common denominators!
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Thursday, September 6: Please bring the class activities from section 2.3 to class.
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Solving problems by reasoning about equivalent fractions and common partitions.
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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.
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What are ways we can compare fractions?
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Standard methods for comparing fractions that work in all cases.
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Reasoning for comparing fractions that is efficient in some special cases.
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Comparing fractions by relating them to benchmark numbers.
Thursday, September 13: Please bring the class activities from section 2.5 to class.
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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.
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Solving percent problems by reasoning about tables and math drawings.
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Why do we add and subtract fractions with like denominators by keeping the same denominator?
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Why our (Common Core) definition of fraction is more helpful for adding and subtracting fractions than an “A out of B” view of fractions.
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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.
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Fraction addition and subtraction word problems.
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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).
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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.
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How equations model word problems – your thoughts.
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What is multiplication? Your thoughts.
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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.
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Discussion of test 1
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What is multiplication? Your thoughts.
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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.
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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.
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When we are given a quantitative situation (word problem), we have to look for structure.
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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.
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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.
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Using our class definition of multiplication to explain why a word problem is a multiplication problem.
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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.
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Interpreting the equal sign in equations.
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Explaining where the commutative and associative properties of multiplication come from (why they are valid) by grouping items in two different ways.
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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.
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Explaining where the distributive property of multiplication over addition/subtraction comes from (why it is valid) by grouping items in two different ways.
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Using properties of multiplication to:
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make multiplication calculations easier to do mentally
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facilitate learning the basic multiplication facts
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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.
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Multiplying by 10 and powers of 10--why is it special in base ten?
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Using properties of multiplication to make calculations easier to do by breaking them apart.
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Developing and explaining the partial products written method and the standard whole number multiplication algorithm.
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How the standard algorithm arises from place value and properties of multiplication.
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Thursday, October 18: Please bring the class activities from sections 4.6 and 5.1 to class.
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Developing and explaining the partial products written method and the standard whole number multiplication algorithm.
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How the standard algorithm arises from place value and properties of multiplication.
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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.
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Interpreting what multiplication means when the multiplier is a whole number and the multiplicand is a fraction.
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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.
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Interpreting what multiplication means when the multiplier and the multiplicand are fractions.
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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.
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Interpreting what multiplication means when the multiplier and the multiplicand are fractions.
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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.
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Why do we multiply fractions the way we do? What is the reasoning behind the procedure?
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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.
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What does division mean?
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We can view division as multiplication with an unknown factor:
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How many units in 1 group?
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How many groups?
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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.
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Identifying division word problems as "how many units in 1 group?" or as "how many groups?" problems.
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The Fundamental Theorem of Fractions: how are division and fractions related?
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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.
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Explaining why the standard algorithm for whole number division works in terms of dividing base-ten bundles equally among groups.
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Division with remainder: Interpreting quotients and remainders in whole number division word problems.
Activity:
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Organize 372 toothpicks into base-ten bundles. Be sure to make each bundle of a hundred out of 10 bundles of ten.
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Distribute those 372 toothpicks equally among 3 groups. Record how you did it (Step 1 ... Step 2 ... Step 3 ... etc).
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If it fits, write some notation that captures or corresponds to the steps you took in part 2.
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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.
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NOTE: hang on to your textbook because we will use it again next semester!
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Division with remainder: Interpreting quotients and remainders in whole number division word problems of both types:
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how many units in 1 group division
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how many groups division
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Thursday, November 29: Review, based on your questions.
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Would you like to schedule a review session for sometime next Monday, Tuesday, or Wednesday?
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NOTE: hang on to your textbook because we will use it again next semester!