Required text: Elementary and Middle School Mathematics: Teaching Developmentally, Enhanced Pearson eText Van de Walle, Karp & Bay-Williams 2016 10e| Pearson
Likely, the way you were taught fractions is very different than the ways presented in our readings. It is critical that students develop a conceptual understanding of fractions prior to developing algorithms.
The better we understand the models used, the better we can assess student understandings and know the best ways to accelerate our students.
Problem Solving Set Module 4 Chapter 14
- Give examples of manipulatives and contexts that fall into each of the three categories of fraction models (area, set, length). (3 pts)
- Describe and give examples of partitioning and iteration. (2 pts)
- Describe two ways to compare 5/12 and 5/8 (not using common denominator or cross-product methods). Make sure the two ways are different. (4 pts)
- Activity 14.1 (page 342) is an example of a problem you might offer your students. Please work through this problem showing sketches of the solutions. (3 points)
Problem Solving Set Module 4 Chapter 15
Why is it important to include estimation with fractions? (3 pts)
A student adds 4/(5 ) + 2/( 3) = 6/( 8)How will you help the student understand that this is incorrect? How would you redirect him or her to do it correctly? Telling a student to find a common denominator is not helpful, and this should not be your instructional redirect. (5 pts)
For the problem 3 1/(4 ) - 1 1/( 2), think of one story problem that would be a “take-away” situation and one that would be a “compare” situation. (3 pts)
Explain at least one mental method (estimation or mental computation) for each of these: (2 pts) (if you cross multiply, you must explain how you know it will work.) ¾ x ½ 1 ⅛ of 40
Activity 15.12 (p. 396) is an example of a contextual task you might offer your students. Please work through this task offering visuals and an explanation for your thought process. It is important that we work through the math that we ask our students to do as this allows us to predict where students might struggle or where extensions might be needed. (3 points)
Write a story problem for ¼ ÷ 3. (2 points) (Take care not to write a multiplication problem)
Please choose at least 2 videos from this module to write a short reflection around. You are welcome to use bullet points to highlight your thinking. Prompts to consider: What did you learn? What will you take with you to your current or future class? What ideas were confirmed for you around teaching (math or otherwise)?(5 points)Video link options: