Arkansas MathLINKS Day 2 Developing Meaning of Operations Handout 1

Fractions of a Rectangle The large outer rectangle represents 1 whole unit. It is partitioned into pieces that are identified with a letter. 1. Decide what fraction each piece is in relation to the whole rectangle, and write the fraction on each piece. 2. Explain how you know the fraction name for each of these pieces: B, E, F, and H. Handout 2 Bright & Joyner (2004)

Reflections on the Fraction Task

Student Work What does the student know? Where is the evidence? What do they struggle with? Handout 3

What do you think assessment means? Why do we need to assess? Small Group Discuss and Chart Your Ideas Assessment

One way to assess is to have students explain their thinking.

Learning Targets Learning targets should be clear to teachers, students, and other interested audiences. Concepts Factual information Skills and processes Mathematical reasoning and proof Problem solving and applications Confidence and competence Bright & Joyner (2004)

Learning Targets for the Fraction Task The choice of learning targets influences the ways that we present content to students and the ways that we assess what students have learned. What learning targets might the Fractions of a Rectangle task address? Bright & Joyner (2004)

Instructional Decisions Decisions are based on the inferences made from assessment data. Used to validate programs and instructional strategies May lead to changes in instruction or reallocation of resources Influence decisions that may have consequences for students Bright & Joyner (2004)

What Might Happen Next? Once we have a sense of what students understand, we need to decide what task might be posed next. What instructional task will address students’ responses, either correct or incorrect?

Connecting to Today’s Technology

Argenta Township Labsheet Handouts 4-6

Learning About Technology

Equivalent Fractions Enter a fraction that is not in simplest form. Press SIMP and ENTER. Press FAC, see the smallest prime common factor that was used to rename the fraction. Check the upper right hand corner to see if it is now in simplest form. Repeat until the fraction is in simplest form. Linda Griffith, UCA

Using SIMP and FAC to do prime factorization Press the FRAC key. Use the Right Arrow to underline the mixed number icon. Press ENTER. Enter the number you want to prime factor in both the numerator and denominator. Repeat the SIMP/FAC sequence as we did in the previous example. Record the factors. Linda Griffith, UCA

Renaming a Fraction in Simplest Form in One Step Enter your fraction. Press SIMP. Type the greatest common factor of the numerator and denominator. Press ENTER. Linda Griffith, UCA

The Dangerous Rush to Rules:  None of the rules helps students think about the operations and what they mean. If students only know the rules, students have no means of assessing their results to see if they make sense. Ma & Pa Kettle “Using Algorithms”

“In order to add or subtract fractions, you must first get a common denominator.” Van de Walle page 319 The Myth of Common Denominators

Teachers’ Knowledge Effective mathematics teachers possess a significant understanding of content and pedagogy. What mathematics is to be learned How mathematics fits into a bigger picture What mathematics students already know How students learn mathematics Interests of the students

Think about the lessons we have done today… What do you as a teacher do to plan an effective lesson? How do you know the lesson is going well? How do you know the lesson was effective?

Planning a Problem-Based Lesson 1. Describe the MATH! 2. Consider the students. 3. Decide on a task. 4. Predict what will happen. 5. Students’ responsibilities. 6. BEFORE activities. 7. DURING activities. 8. AFTER activities. 9. Write the lesson plan. Van de Walle page 41-48,82

Collaborative Circle

Connecting our Work to the Framework & Released Items

Intermediate 2003

NAEP ITEM Estimate the answer to 12/13 + 7/8 A. 1 B. 2 C. 19 D. 21 Sean Madison

Using Technology In The Classroom  Have students add 12/13 + 7/8 on their calculator. Ask them to explain why the answer is close to (2)  Give an example of how to use the calculator to drill fractions.  Give an example of how to use the calculator to teach fractions conceptually.

Summarize/Reflection Handout 7