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###### Week 1: The base-ten system; reasoning with fractions

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Tuesday, August 14: Welcome to MATH 5020/7020!

Due Thursday, August 16: (1) Read all the course information and policies on the course webpage. (2) The fraction survey that was handed out in class on Tuesday. Unlike other homework, please do this on your own.

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###### Week 2: Reasoning with Fractions

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Due Tuesday, August 21: (1) Read sections 1.1, 1.2, and 2.2. (2) Do (but don't hand in) practice exercises 4, 5 in section 1.1 (p. 11). (3) Post on eLC: Problem 3 b, c on page 12 and: Use our Common Core definition of fractions to explain the fractions 1/10, 3/10, and 12/10 like we did in class. Be sure to start with a unit amount. Next, explain how to get the unit fraction 1/10. Then explain 3/10 and 12/10 using our specific way of talking about those fractions. (4) MATH 7020 students: Start to brainstorm a course project. Please see me to discuss ideas.

Due Thursday, August 23: (1) Do practice exercises 1 - 4 in section 2.2, p. 54, and check your answers (see p. 55, 56). (2) Post on eLC: Problems 3 and 4 on page 57 and use our Common Core definition of fraction to explain how to think about the rectangles you are given.

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Due Tuesday, August 28: (1) Do practice exercises 8 - 12 in section 2.2 and check your answers. (2) Post on eLC: Problems 5 a, b and 7 a, b on pages 57, 58.

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Due Thursday, August 30: Post on eLC: If 3/4 of a liter of juice gives you your Daily Value of Vitamin C, then what fraction of your Daily Value of Vitamin C is in 1/4 of a liter of juice? (a) Explain how to use a math drawing to solve the problem. (b) For each fraction in the problem (and the solution), state the unit amount (whole) that that fraction is of. (c) Discuss how one amount in the problem can be described with two different fractions depending on what you take the unit amount (whole) to be.

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Due Tuesday, September 4: Post on eLC: (1) Problem 1 on page 67. Be sure also to discuss how your drawing shows that the two fractions are equal to each other. (2) If 1/3 of a cup of rice is 1 serving, then how many cups of rice is 1/4 of a serving? (a) Explain how to use a math drawing to solve the problem. (b) For each fraction in the problem (and the solution), state the unit amount (whole) that that fraction is of. (c) Discuss how one amount in the problem can be described with two different fractions depending on what you take the unit amount (whole) to be.

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Due Thursday, September 6: Post on eLC: Problems 18 a, b and 19 a, b on pages 68, 69 and be sure to discuss the reasoning that explains why you partition the way you do.

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###### Week 5: Reasoning to compare fractions; percent

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Due Tuesday, September 11:  (1) Read section 2.3 (if you haven't already). (2) Do practice exercises 1, 8, 9 in section 2.3 and check your answers. (3) Post on eLC: Problems 20 and 21 on page 69.

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Due Thursday, September 13: (1) Read section 2.4 and do practice exercises 1, 2, 3 in that section. (2) Post on eLC: Problems 6 and 7 on page 77.    MATH 7020 students: Course project proposal due.

Take-home test to be handed out in class, due Tuesday.

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###### Week 6:  Why we add and subtract fractions the way we do; fraction addition and subtraction word problems

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Due Tuesday, September 18:  Take-home test due.

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Due Thursday, September 20: (1) Read section 2.5 and do practice exercises 2 - 6 in that section. (2) Read section 3.4. (3) Post on eLC: Problem 10 on page 89 and problem 1 on page 131 and be sure to use our (Common Core) definition of fraction when you explain why we add 2/7 + 3/7 the way we do.

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###### Week 7:  Multiplication: what is it?

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Due Tuesday, September 25:  (1) Do practice exercises 1, 6, 7, 8, and 9 in section 3.4 and check the answers. (2) Post on eLC: Problems 11 and 13 on page 132.

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Due Thursday, September 27: (1) Read section 4.1 and do practice exercises 1, 2 in that section and check the answers. (2) Post on eLC: Problem 1 a, b, c on page 149.

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Due Tuesday, October 2: Group quiz due.

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Due Thursday, October 4: Post on eLC: A cupcake company makes cupcakes with 5 kinds of batter (vanilla, chocolate, red velvet, mocha, or strawberry) and 4 kinds of frosting (vanilla, chocolate, strawberry, or caramel). Each kind of cupcake is made from one kind of batter and one kind of frosting. How many different kinds of cupcakes can the company make? Explain in detail why this problem is a multiplication problem. In other words, explain in detail how our definition of multiplication applies to this situation.

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###### Week 9:  Multiplication: where does the whole number algorithm come from?

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Due Tuesday, October 9: (1) Read section 4.3 and do practice exercises 1, 2, 7, 8, 9, 11 in that section and check your answers. (2) Post on eLC: Problem 6 on page 162, 163 except you only have to write and explain 2 expressions (not 3); problem 7 a, b on page 163, and problem 5 of Class Activity 4A on page CA-68.

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Due Thursday, October 11: (1) Read section 4.4 and do the practice exercises in that section and check your answers. (2) Post on eLC: Problem 6 a, b, c, on page 174 except you can make any math drawings, they do not have to be arrays.

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###### Week 10: Multiplication: whole number algorithm; how does multiplication extend to fractions?

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Due Tuesday, October 16: (The following doesn't fit exactly into the flow of what we have been discussing, but it's fairly close and I think is reasonable to do on your own outside of class. We will discuss if we want to count it as a "group quiz".) Please find a Geogebra sketch at this link: https://ggbm.at/bmz9sgpx  and do the tasks on this handout. Feel free to write your answers on your own paper if you prefer. Post on eLC by the end of the day in the Class Work folder.

Due Thursday, October 18: (1) Read section 4.2 and do the practice exercises and check your answers. (2) Read section 4.5 and do practice exercises 1 - 3 in that section and check your answers. (3) Post on eLC: (A) Problem 1 on page 152 and (B) Write equations that show how to solve the multiplication problem 7 x 83 = ? using the distributive property and the 4th grade knowledge described in #1 of Class Activity 4N on page CA-83.    Take-home test to be handed out in class, due Tuesday.   MATH 7020 students: First draft or outline of your course project is due.

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###### Week 11: Reasoning about fraction multiplication

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Due Tuesday, October 23: Take-home test due.

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Due Thursday, October 25: (Sorry! This got posted late, so it's fine if you need to turn it in late.) (1) Read the beginning of section 5.1 through page 198 and do practice exercise 1 in that section. (2) Post on eLC: (a) Explain what 5 • 3/4 = ?  means according to our definition of multiplication and write a word problem and make a math drawing for the equation. (b) Explain what 2/3 • 15 = ? means according to our definition of multiplication and write a word problem and make a math drawing for the equation.

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FALL BREAK Friday, October 26

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###### Week 12: Reasoning about fraction multiplication

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Due Tuesday, October 30: Post on eLC: Problem 2 a, b, c on page 203.

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Due Thursday, November 1:

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###### Week 13:  Division: what is it?

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Due Tuesday, November 6: (1) Read the rest of section 5.1. (2) Write a word problem for 3/4 • 5/7 = ? and make a math drawing that shows that situation. Then explain how to partition the quantities into mini-parts by reasoning about how parts are aligned in your math drawing. Finally, explain how to solve the problem by reasoning about the quantities in your math drawings. (3) Part 1 of Class Activity 5D on page CA-91.

Due Thursday, November 8: Do practice exercises 2, 3, 4 in section 5.1 and also practice part 4 of class activity 5D on page CA-92. (There is nothing to turn in.)  Remember that we meet 8 - 9:15 in addition to our regular class time. Take-home test to be handed out in class, due Tuesday. We will do group work on the test during our normal class time.

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###### Week 14: Division: explaining the connection with fractions; where does the whole number algorithm come from?

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Due Tuesday, November 13: Take-home test due.

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Due Thursday, November 15: (1) Read section 6.1 and do practice exercises 1 and 2 in that section. Read section 6.2 through page 232 and do practice exercise 1 in that section. (2) Post on eLC: Problem 1 a - f on pages 230 - 231 and problem 1 on page 237. (3) Also do (for practice) but don't hand in: problem 2 on page 231.

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THANKSGIVING BREAK: November 19 - 23

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###### Week 15: Division: interpreting quotients and remainders;  Review

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Due Tuesday, November 27: (1) Read section 6.3, focusing on the standard division algorithm which is discussed on pages 242- 244 and do practice exercises 6 and 7 in that section. (2) Practice explaining the standard algorithm for whole number division by finishing Class Activity 6J on page CA-109. Be sure to describe the amount being divided in terms of base-ten bundles and be sure to describe the divisor as how many equal groups we are making.

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Due Thursday, November 29: Bring questions and topics you would like to discuss and review. MATH 7020 students: Your course project is due. (1) Read the rest of section 6.2 and do practice exercises 2 - 5 in that section. (2) Do for practice: problem 5 a, b, c, d on page 237.

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###### Week 16:

No class Tuesday, December 4 because of the Friday schedule.