ge 1 www.tie.n et Building Understanding of the Fractions Through Hands-On Experiences Marcia Torgrude and Bailey Kowalski K-12 Math Specialists [email protected] and [email protected] http:// bit.ly/19fRdDr
Page 1 Building Understanding of the Fractions Through Hands-On Experiences Marcia Torgrude and Bailey Kowalski K-12 Math Specialists [email protected]@tie.net.
Jan 18, 2016
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Page 1
www.tie.net
Building Understanding of the Fractions Through
Hands-On Experiences
Marcia Torgrude and Bailey KowalskiK-12 Math Specialists
[email protected] and [email protected] http://bit.ly/19fRdDr
Page 2
• Promote a deeper understanding of the progression of fractions within the Common Core.
• Develop hands-on strategies to build understanding of operations of fractions.
• Reinforce the Lesson in 3 Acts and Instructional planning.
• Practice the use of questioning, mathematical discourse, productive struggle, and formative assessment .
Outcomes for Today
Page 3
I Have….. Who Has
• Let’s play!• What does this have to do with
learning math?• Where does it fit the common core
standards?• What about the Standards of
Mathematical Practice?
Page 4
Rich Task Reflection & Discussion
Share anecdotal notes and pictures of using a rich task in your classroom.
Group Discussion:
After using a rich task, what was different, if anything, in your classroom – prepare student work, discussions, and any other items to share.
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Standards of Mathematical Practice
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What does it mean to “do mathematics?”
The Standards of Mathematical Practice are descriptions of the fundamental skills needed to “do” mathematics. These are our new “basic skills”.
Phil Daro’s Take on the Common Core State Standards for Mathematics
Page 7
What does it mean to “do mathematics?”
• Standards of Math Practice are the “how” of mathematics
• Content Standards are the “what” of mathematics
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We must get past the idea of mathematics as a collection of algorithms, steps, or procedures. Just getting answers, although important, is not “doing mathematics.”
“Doing mathematics”
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Working with Fraction Progressions
• Equivalence• Addition• Subtraction• Multiplication• Division• Ratio/Proportion• Rate of Change
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4th Grade Fraction Progressions
Read pages 6- 8Standards – 4.NF.1, 4.NF.2, 4.NF.3
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Fraction Equivalence, Addition and Subtraction
• Using Pattern Blocks
http://illuminations.nctm.org
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Journal Reflection
• What is a fraction?
• What happens to the fraction when we increase the whole?
• Write 3 new ideas you learned about fractions today.
Page 14
Fraction Progression
• 4th Grade – refer to 6-9 to decimals
• 5th Grade – page 11 – 14• 6th Grade – page 5-7• Write the “must do’s” for each
grade level on poster• Gallery Walk
Page 15
Fraction Using Cuisenaire Rods
Using Cuisenaire rods model:
• 1 + 12 3
• 1 – 12 3
• 1 x 12 3
• 1 x 13 2
• 1 ÷ 12 3
http://www.learner.org/courses/learningmath/number/session8/part_b/index.html
Interactive and Video
Page 16
• Array Model for Fractions• http://www.learner.org/vod/vod_wi
ndow.html?pid=1853
Modeling equivalence, adding, subtracting, multiplying, and dividing
Page 17
Why do we invert and multiply to divide?
• Show your reasoning in your journals
• Discuss Large Group
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Why do we invert and multiply to divide?
3
4
5
6
Page 20
Do We Have to Invert?
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6-8th Grade Progression – Fractions, Ratios and Proportions
• NS - Grade 6 – pg. 5-7• Ratio/Proportion
– Overview – pg. 2-4– Grade 6 – pg. 5-7– Grade 7 – pg. 8-12– Grade 8 – pg. 11-13
• Create a new poster progression• Develop a definition of a ratio and a
definition of a fraction
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6-8th Grade Progression – Ratios and Proportions
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• Do a Rich Task• Analyze the student journal for student
growth• Compare data from AimsWeb• Complete reflection survey• Final thoughts
Data Collection Time
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One Student’s Journey• What did you notice at the beginning
• What was their mathematical understanding?
• What was their ability to communicate in writing?
• How confident were they? (affective journaling)
• What growth evidence do you find?
Page 28
AimsWeb Data• Compare Fall/Winter/Spring or make a
prediction for spring• What do you notice whole group?• Determine how much each of your
students grew• What does this tell you?• What will you do with the results?
Page 29
Reflection Survey
• Please look through your binder and your journals to reflect on all the learning that has taken place this year
• Refer to the handout
http://bit.ly/MathIRMC
Page 31
Virtual Fractions
http://mtorgrude.tie.wikispaces.net – Symbaloo link on navigation bar
Page 32
Your Final Thoughts
https://www.youcubed.org/week-of-inspirational-math/
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We Made It!!!
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