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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
Microphone and speakers can be configured by going to:Tools – Audio – Audio setup wizard
Turtle Toms- [email protected] Elementary Mathematics Specialist
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
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
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.
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.
Why RTI?
• What does it mean to be mathematically fluent?
• What prevents kids from becoming mathematically fluent?
• How can we support mathematical fluency development?
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/
Feedbackhttp://ccgpsmathematicsk-5.wikispaces.com/
Turtle Toms- [email protected] Mathematics Specialist
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)[email protected]
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.