3. Identify three different representations (not stages of the learning trajectory) for solving mathematical problems, and give at least one advantage and one limitation for each. 5. Give one way...

File attached. Review for math


3. Identify three different representations (not stages of the learning trajectory) for solving mathematical problems, and give at least one advantage and one limitation for each. 5. Give one way discussed in class to balance the need to practice learned math facts and procedures (such as basic computation) with the need to keep students engaged via high cognitive demand tasks. BEEP 4311 Sample Exam, fall 2020 – Page 1 1. In what situations is scaffolding helpful, and in what situations is it counterproductive? Benefits of Instructional Scaffolding · Challenges students through deep learning and discovery. · Engages students in meaningful and dynamic discussions in small and large classes. · Motivates learners to become better students (learning how to learn) · Increases the likelihood for students to meet instructional objectives. 7. The article by Hallman-Thrasher and Spangler contrasted the practices of focusing and funneling. Explain the difference, and how it relates to the teaching practice of preservice teachers. 8. List two different manipulative materials that could reasonably be used to model the addition 75+36. 9. What is the main difference between the 2 concrete models (name them) for subtraction? 10. Which of the two meanings of multiplication do children typically encounter less? Why is it important for learning about properties of multiplication? 11. Explain to a child why 6-3 and 3-6 are different. BEEP 4311 Sample Exam, fall 2020 – Page 2 12. Readings, videos, and class discussion noted that students' early invented strategies for multiplication do not decompose the second factor, due to context. Why not? How does the dominant meaning for multiplication bear on this tendency? 13. Write 2 short word problems involving multiplication, each one drawing on a different definition for multiplication, and identify the definition invoked in each case. 14. Draw two different models for the division 15 ÷ 5, each invoking a different definition of division. 15. We observed several examples of students who represented two-digit numbers easily but struggled when trying to represent three-digit numbers. What error did they make? That is, how did this struggle manifest? 16. What are the 3 [principal] definitions of fraction? Which one dominates? BEEP 4311 Sample Exam, fall 2020 – Page 3 17. (a) Complete the following sentences with appropriate quantitative/comparison words: Ana has 4 eggs in her basket. Maria has 6 eggs in hers. Paula also has 6 eggs in hers. Ana has ______ eggs than Maria. Paula and Maria have the same ______ of eggs. (b) Give a situation which could give a ratio representation for 2/3. 18. Draw a pictorial proof that the sum of two odd numbers is even, which is general (not limited to a single example), and identify which definition of odd/even you are using. 19. Give a formal deconstruction of the following task: At a party, you have 5 pints of ice cream. If you serve ¾ of a pint of ice cream to each guest, how many guests can you serve? 20. A student explains her solution to adding -7+2 as follows: “The 2 positives cancel out 2 of the negatives, so the answer is 5 negatives, or -5. Addition still makes numbers bigger, because -5 is bigger than 2.” What does the student understand, and what does the student not understand?