1. Week 5 Exploration 3.1 (p. 50) Part 2: 3abck, 4ac Be able to use the base 5 blocks to compute 3abc and share your responses from #4.

3. Announda Exam 1 is on Friday! See assignments page for some practice questions. Monday Office Hour Today: Rescheduled to 12:00-1:00pm in MATHE LOBBY Don’t forget to get the class notes from the bookstore. Homework Comments: Procedural Vs. Mathematical Explanations Subtraction Algorithms

4. Procedural Vs. Mathematical Explanations 3 6 5 + 2 8 7 How to add (two numbers): Procedural: Add the numbers in the far right column. If the number has more than one digit, write down the far right digit and add the number formed by the remaining digits to the next column and repeat until finished. You can learn how to add without any concept of what place value means! Should we bother with place value at all?

5. Procedural Vs. Mathematical Explanations 3 6 5 + 2 8 7 7 4 2 Mistake: Procedural: The student carried the 1 from the ones column to the hundreds instead of the tens column. Mathematical: The student added the ones place in each number and found that there were 12 ones altogether. The student knew that algorithm says to leave the 2 in the far right column and the 1 needs to be added to another column. The student has a procedural sense of the algorithm but doesn’t understand how place value works into the it and therefore does not successfully add the 1 to the correct column. If the student understood place values and that 12 represents 1 ten and 2 ones, he would know to leave the 2 ones in the ones column and regroup the ten with the others in the tens column. Instead, the student placed the 1 in the far left column [indicating that he probably memorized the process of “carrying” from 2 digit addition (which would only involve carrying to the far left column)] without understanding that the process is really about forming a larger unit (composed of smaller units) and adding it to the other groups of the same size.

6. An Idea: A student who understands place value could potentially discover how addition (and subtraction) works on his/her own! The student would see no difference between 2 or 3 or n digit addition! Or any difference between 2 summands or n!

7. Regrouping Show a diagram for 302 - 84

8. Start with…

9. Now, indicate what you are subtracting 302 - 84: Let red be the part you take away

10. Homework Review for the exam. Bring questions on Wednesday!