Download presentation

Presentation is loading. Please wait.

Published byDoris Owens Modified over 2 years ago

1
Division of Fractions: Balancing Conceptual and Procedural Knowledge Part 2 January 15, 2013 Common Core Leadership in Mathematics2 (CCLM) This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

2
Learning Intentions and Success Criteria We are learning to … apply and extend understandings of division to fractions that includes a focus on unit fractions in the context of real-world problems. We will be successful when we can… explain and provide examples of standard 5.NF.7 using visual models, contexts, and concept-based language to divide unit fractions by whole numbers and whole numbers divided by unit fractions. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

3
Extending Meaning of Division to Fractions Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

4
Components of Complete Understanding of Division Estimate the answer Think about related operations Draw a diagram Write an equation Use an strategy / algorithm Division Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

5
ESTIMATE Estimate Greater than 5? Equal to 5? Less than 5? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

6
Revisiting Division of Fractions Review to Popcorn Problems for last class – What were the big ideas from these problems? – What representations did we use? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

7
Juice Party Quantity: 1/2 gallon of juice How can I divide that equally among: 2 friends 5 friends Individually solve each problem using reasoning and models As a group, take turns and share your reasoning Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

8
Looking at the Standards Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

9
Standard 5NF 7c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1 c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

10
Interpretations of Division Group Size Unknown I know the total number of objects. I know the number of groups/shares. How many objects are in each group/share? Example, How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally *Partitive division, sharing model, dealing ou t. Number of Groups Unknown I know the total number of objects. I know the number of objects in each group/share. How many equal groups/shares can be made? Example: How many 1/3-cup servings are in 2 cups of raisins? * Quotative division, measurement division, grouping, subtractive model. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

11
Standard 5NF 7a and 5NF 7b Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1 a.Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

12
A Tricky Popcorn Party Serving Size: 3/4 cup of popcorn How many servings can be made from: 2 ¼ cups of popcorn 5 cups of popcorn Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

13
Now It’s Your turn In pairs, solve each problem using reasoning and models (don’t forget the tape diagram). – How many ¾ cups servings of popcorn are in 4 ¼ cups of popcorn? – A serving is ½ of a cookie. How many servings can I make from 3/8 of a cookie? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

14
Learning Intentions and Success Criteria We are learning to … apply and extend understandings of division to fractions that includes a focus on unit fractions in the context of real-world problems. We will be successful when we can… explain and provide examples of standard 5.NF.7 using visual models, contexts, and concept-based language to divide unit fractions by whole numbers and whole numbers divided by unit fractions. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

15
Computational Procedures What procedure do you use to divide fractions? Write an example of it on your slate. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

16
Two Procedures for Division of Fractions The common denominator method Invert and Multiply Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

17
The Common Denominator Method Have you ever used this? Does it always work? Make up division problems to decide when you can use this algorithm. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

18
Two Procedures for Division of Fractions The common denominator method Invert and Multiply Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

19
Invert and Multiply Method Have you ever used this? WHY does it work? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

20
Why can we “invert and multiply”? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year Discuss this question with your shoulder partner. Record your answer on your slate Share your answer with the whole table.

21
Sample student work Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

22
Examine 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Reread this standard. Do the examples and tasks make more sense to you now? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

23
Learning Intentions and Success Criteria We are learning to … apply and extend understandings of division to fractions that includes a focus on unit fractions in the context of real-world problems. We will be successful when we can… explain and provide examples of standard 6.NS.1 using visual models, contexts, and concept-based language to divide unit fractions by whole numbers and whole numbers divided by unit fractions. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012-2013 School Year

Similar presentations

OK

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Fractions: Teaching with Understanding Part 2 This.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2012 Fractions: Teaching with Understanding Part 2 This.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

What does appt only means you love Ppt on vegetarian and non vegetarian restaurant Download ppt on cell fundamental unit of life Ppt on tamper resistant outlets Download ppt on web browser Ppt on steps to effective evangelism Ppt on agriculture in indian economy Free ppt on brain machine interface application Ppt on human resources information system Ppt on mission to mars