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Making Sense Out of Fraction Word Problems

Making Sense Out of Fraction Word Problems. Western Illinois University Mathematics Teachers’ Conference March 23 , 2012. James Olsen, Ph.D. Western Illinois University JR-Olsen@wiu.edu http://faculty.wiu.edu/JR-Olsen/wiu/. Outline. Brief History – My Life with PDF

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Making Sense Out of Fraction Word Problems

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  1. Making Sense Out of Fraction Word Problems • Western Illinois University • Mathematics Teachers’ Conference • March 23, 2012 James Olsen, Ph.D. Western Illinois University JR-Olsen@wiu.edu http://faculty.wiu.edu/JR-Olsen/wiu/

  2. Outline • Brief History – My Life with PDF • The promise of the CCSS • The meanings of the operations, which can be extended to operations on fractions. • Models For Fractions. • Meanings of the operations with fraction models. • Word problems. • Quick example with a tape (length model) 6 ÷ 4 …or… ¼ of 6 …or…

  3. Brief History – My Life with PFD • Mastery Quizzes in teacher education classes (16 objectives – see handout). • PFD Boot Camp web site – started. • Project got bigger. Two students: Hayley Moore and Joseph Illichman helped me. • We wrote 216 PFD word problems. • Hayley, Joe, and I have presented in Florida and ICTM – Springfield (2011). See Navigating the Landscape of Fraction, Decimal, and Percent Problems • http://faculty.wiu.edu/JR-Olsen/wiu/BootCamp/landscape/front.html PFD = Percents Fractions & Decimals

  4. Positive Potential for the CCSS to be Successful for Improving Student Achievement • We’ve had “standards” for about 20 years. • We have pretty good research on teaching and learning. • (We are finally getting it) “Evidence shows clearly what most people know intuitively: teachers matter more to student learning than anything else inside a school.” • Focus, coherence, and understanding. • We know that understanding fractions is HUGE ! CCSS = Common Core State Standards

  5. One of the Biggest Keys to Make CCSS a Success • Teacher knowledge and understanding of mathematics.

  6. Meanings (“situations”) of the Operations + – × ÷ • See pages 88 and 89 of the Common Core Mathematic Standards (handout). • These meanings/situations should be used in early elementary to develop the four operations. • We will use the same meanings/situations with fractions, mixed numbers, and decimals – word problems. Subtraction isn’t just Take-Away !

  7. Models For Fractions • See Fraction Model Applet at NCTM • Length (“tape”) model. • Area or Region models (rectangles or pies) • Set model. • Demo the applet (next slide). • From CCSS Glossary: • Visual fraction model. A tape diagram, number line diagram, or area model.

  8. Assumptions • We believe to understand something well it should be connected in the brain to many other ideas. • Number sense, operation sense, and fraction sense should be gained continually over time. • Physical models and pictures are useful, but we need to be moving toward the symbolic/abstract. • When you read the newspaper, there’s no bag of manipulatives hanging there to help you understand the percents.

  9. How can we show ?

  10. How can we show ?

  11. How can we show 2 ½ × 3 ½with an area model?

  12. How can we show ?

  13. Word Problems (Objective XI.) Multiply fractions (and mixed numbers). (see handout)

  14. Word Problems (Objective XIII.) Divide fractions (and mixed numbers). (see handout)

  15. Thank You • Websites • faculty.wiu.edu/JR-Olsen/wiu/ • faculty.wiu.edu/JR-Olsen/wiu/BootCamp/landscape/front.html

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