CCGPS Mathematics4th Grade Update WebinarUnit 4: Operations with Fractions

November 12, 2013

Update presentations are the result of collaboration between members of 2012 and 2013 Unit Review and Revision Teams and classroom teachers

Microphone and speakers can be configured by going to:Tools – Audio – Audio setup wizard

Turtle Toms- tgunn@doe.k12.ga.us Elementary Mathematics Specialist

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Webinar Guide

• Critical areas• Content standards and related tasks• Culminating task• Formative assessment lessons• Resources

Today’s presenters

• Jenise Sexton– Henry County

Critical Areas in 4th Grade

Unit 4 Content, Strategies and Misconceptions

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MCC4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Unit 4 Content, Strategies and Misconceptions

COMMON MISCONCEPTIONS NF.3 & 4 - Students think that it does not matter which model to use when finding the sum or difference of fractions. They may represent one fraction with a rectangle and the other fraction with a circle. They need to know that the models need to represent the same whole. In addition students have a tendency to add both the numerator and denominator when using different operations with fractions as opposed to just adding numerators.

Think About This

• John ate 1/3 of a pizza while Julie ate ½ of a pizza. John said he ate more pizza than Julie. How can this be true?

Who Put the Tang in Tangrams?

Literature Books with Fraction Connection

• Breakfast at Danny’s Diner• Grandfather Tang’s Story • Ed Emberly’s Picture Pie• A Drop of Water• My Half Day• Fraction Action• Fractions = Trouble• Earthquakes

Task – Sweet Fraction Bars

Unit 4 Content, Strategies and Misconceptions

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MCC4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Unit 4 Content, Strategies and Misconceptions

Unit 4 Content, Strategies and Misconceptions

Array Models for Multiplying Whole Numbers

10 310 100 30 1306 60 18 78

160 48 208

Unit 4 Why conceptual understanding matters

• MCC5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

• MCC5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Array Models for Multiplying Fractions & Mixed Numbers

Task – How Many CCs?

• Constructing Task

Time Drainage Fluid Albumin

6:00am 100cc 100cc12 noon ¾ of the volume at 6am 75cc6:00pm 75cc 75cc12 midnight 2/3 of the volume at 6pm 50cc6:00am 4/8 of 100cc 50cc12 noon 25cc ½ of 50cc =

Task – A Chance Surgery

• Performance Task

Revised Culminating Task –

FAL – You’ve got choices!

Resource for Number Talks with Fractions

• http://numberstrings.com/strings/

Resources

• Use area models to find common denominators http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html

• Multiply fractions using an array http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html

• Use number line bars to add, subtract, multiply & divide fractions http://nlvm.usu.edu/en/nav/frames_asid_180_g_2_t_1.html

FeedbackWhat it looks like:

http://elschools.org/student-work/butterfly-drafts

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Turtle TomsProgram Specialist (K-5)tgunn@doe.k12.ga.us

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.