April 2012 MTL Meeting Using the Number Line to Make Sense of Equivalent Fractions Connie Laughlin Lee Ann Pruske Beth Schefelker

We are learning to: Represent equivalent fractions on a number line. Read and interpret the cluster of CCSS standards related to equivalent fractions Success Criteria: Clearly explain and provide examples of focus and coherence among CCSSM fraction standards 3.NF.3a, 3.NF.3b, 3.NF.3c, 4.NF.1

Homework Discussion Triads Use your notes to share your findings from your student interviews. What were the differences in 3rd and 5th grade reasoning? What are the implications of your findings?

Explain Ken’s thinking? Use this as a launch and a link between the number line reasoning from March and the work for the day. Looking at this student what does Ken understand? What misunderstandings are evident? P. 102

Explain Judy’s thinking? What do you notice about Judy’s work? p. 104

On your slate, draw a number line from 0 to 1. Use fraction reasoning to place and on the number line. Students have trouble integrating the visual (line) model and the symbols necessary to define the unit. The symbols can act as distractors. Students don’t always understand that the numbers associated with the points on a number line tell how far the points are from zero. Researchers “hypothesize” as long as partitioning and unpartitioning are difficult for children, number line representations of fractions may not be easily taught.

Matt’s Thinking . What do you notice about Matt’s thinking? Hand out Matt’s thinking on a paper.

Equivalency Place the whole fraction strip that represents 0 to 1 on a sheet of paper. Draw a line labeling 0 and 1. Lay out your fraction strips, one at a time, and make a tally mark on the line you drew. Write the fractions below the tally mark. Look for patterns to help you decide if two fractions are equivalent. Using fractions as number to fractions as units as length.

Which fractions are equivalent? How do you know?

Standards 3.NF.3a, 3.NF.3b & 3.NF.3c On your Standards Interpretation Sheet rephrase this standard and provide an example. Share with your partner. Why is 3/1 the same as 3. Use your fraction strip to talk out the language to make this make sense. 3 parts of size 1

Matt’s Thinking . If we really align our practice to the standards, how would a deep understanding of the expectations of the standards help circumvent misunderstandings similar to Matt’s thinking?

Linking reading to classroom practice Use the two resources to deepen your understanding on the CCSSM expectations for fractions. NF Progressions CMSP Curriculum Guide Highlight and note how you are making sense of the fraction concepts Focused reading - connections to our study ? - things that you still wonder ! – something you agree with

Understanding 4.NF.1 Read the standard. Use the worksheet provided to make sense of the standard. What connections can you make to 3.NF.3a, 3.NF.3b, 3.NF.3c?

Focus and Coherence in Fractions Discuss how the progression of the standards we did today exhibits focus and coherence.

Feedback and Reflection… Discuss how the fraction standards effect classroom practice. What will need to change?