CCGPS MathematicsFourth Grade Update Webinar

Unit 3: Fraction EquivalentsOctober 14, 2013

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

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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.

Thank you!

• Jenise Sexton and Graham Fletcher to the rescue!

Fraction Standards Progression by Grade Level• 1.G.3. Partition circles and rectangles

into two and four equal shares…

• 2.G.3 Partition circles and rectangles into two, three or four equal shares…

• 3.NF.1Understand unit fractions as part of a whole (paraphrased)

• 3.NF.2 Understand a fraction as a number on the number line…

• 3.NF.3 Explain equivalence of fractions in special cases…

Progression Continued…

• 3.NF.3 Explain equivalence of fractions in special cases…• 4.NF.1 Explain why a fraction is equivalent to a fraction by

using visual fraction models…• 4.NF.2 Compare two fractions with different numerators and

denominators…• 5.NF.1 Add and subtract fractions with unlike denominators

by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference…

Fraction Progression By Concept

The Meaning of Unit Fractions

Equivalent Fractions

Comparing Fractions

Addition of Fractions

Unit 3 and Fractional Understanding

• Area/Region Models • Length/Measurement Models

New Tasks• Red Rectangles • Pattern Block Puzzles

Revisited

Conceptual Focus on Equivalence

How do you know 4/6 = 2/3? Try to think of at least two different explanations.

Do You Find Yourself Here?

1. They are the same because you can simplify 4/6 and get 2/3.2. If you have a set of 6 items and you take 4 of them, that would be

4/6. but you can put the 6 items into 3 groups, and the 4 items would then be 2 groups of the 3 groups. That’s means it’s 2/3.

3. If you start with 2/3, you can multiply the numerator and the denominator by 2, and that will give you 4/6, so they are equal.

4. If you had a square cut into 3 parts and you shaded 2, that’s 2/3 shaded. If you cut all 3 of these parts in half, that would be 6 parts with 4 parts shaded, or 4/6.

Students “get” simplifying when trying to identify equivalent fractions….

Bill McCallum says…“It is possible to over-emphasis the importance of reducing fractions …. There is no mathematical reason why fractions must be written in reduced form, although it may be convenient to do so in simple cases.”

What’s My Point?

• Most of us were taught procedures with fractions that were not based on fraction sense.

1. Emphasize number sense and meaning of fractions

2. Physical models and context3. Extensive use of number lines4. Allow students time to

understand equivalence5. Use benchmark fractions and

estimation

Misconceptions…

• Numerator and denominator are separate values

• Fraction such as 1/5 is smaller than a fraction such as 1/10 because 5 is less than 10.

What do you believe about learning?

With which statements do you agree?1. My intelligence is something very

basic about me which I can’t change very much.

2. I can learn new things, but I can’t really change how intelligent I am.

3. No matter how much intelligence I have, I can always change it quite a bit.

4. I can always substantially change how intelligent I am.

What do you believe about learning?

What do you believe about learning?

What do you believe about learning?

Want more?

http://mindsetonline.com/whatisit/about/

Why RTI?

Graphic from- http://www.rti4success.org/

Why RTI?

• What does it mean to be mathematically fluent?

• What prevents kids from becoming mathematically fluent?

• How can we support mathematical fluency development?

GOT RTI?

GET STRATEGIES.

The What?

• GloSSGlobal Strategy Stage• IKANIndividual Knowledge Assessment of Number

• http://schoolwires.henry.k12.ga.us/Page/33480• http://nzmaths.co.nz/mathematics-assessment• http://prezi.com/1goefix7aclq/math-assessment-gloss-ikan/

Why?

GET STRATEGIES.

GET STRATEGIES.

GET STRATEGIES.

GET STRATEGIES.

Want more?

http://prezi.com/h5xrmvdsxhyy/understanding-the-gloss-and-ikan-assessment-forsyth/

Feedbackhttp://ccgpsmathematicsk-5.wikispaces.com/

Turtle Toms- tgunn@doe.k12.ga.usElementary Mathematics Specialist

Teachers,

Thank You! Please visit http://ccgpsmathematicsk-5.wikispaces.com/ to share your feedback, ask

questions, and share your ideas and resources!Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx

to join the K-5 Mathematics email listserve.Follow on Twitter!

Follow @GaDOEMath

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.