Math 647 Unit 2: Base 10 numbers and algorithms

Section 6: Addition and subtraction algorithms.

Goal: The goals this week are for you to

• Know some ways of mentally computing with 2 digit numbers
  
• Know some common alternate algorithms for addition and subtraction (both student invented and used in other countries)
  
• Know how to show the standard algorithms for addition and subtraction using manipulatives and make connections between manipulatives and the pencil and paper work.

Resources

Overview:

What we're going to be doing this week and next and why.

Assignments: Please scan as necessary, and put all assignments in the dropbox.

Addition

Do first:

Do: Try it yourself

Watch: What do other people do?

Assignment 25: Base 5 addition (if this doesn't download correctly, you should right click on the link and choose "Save Link As")

Alternate algorithms and mental math:

Watch:

Invented and Expanded algorithms
UK version of the addition algorithm
Lattice algorithm

Read:

Do and read: the Mental Addition investigation 3.2 of the Bassarear textbook Mathematics for Elementary School Teachers, and read the discussion that follows (pages 134-136 of the 4th edition and pages 131-133 in the 3rd edition)

Read: The discussion of Children's Strategies for Addition in the Bassarear Textbook (pg. 136-138 of the 4th edition or pg 133-136 of the 3rd edition)

Assignment 26: Alternate addition algorithms (do, scan, dropbox) 

The standard algorithm:

Watch: modeling and making connections for the standard algorithm

Read: The Bassarear textbook discussion of the standard algorithm with base 10 manipulative pictures (p. 139-143 of edition 4 or p.137-139 of edition 3)

Assignment 27: Show how to model and make connections for the standard algorithm (video assignment: do, save, put the link in a word document and dropbox it).  Guidelines for presenting explanations

*It would be great if you did this assignment right away, so I have a chance to give you feedback before you do the similar assignment for subtraction. If you send me an email when you turn it in I'll try to get you feedback right away the next day.

Error patterns

Watch: addition error patterns

Note: I highly reccommend the book "Error Patterns in Computation" by Robert B Ashlock.  I have stolen many of my ideas and examples from this book.

Assignment 28: Do the assignment addition errors and algorithms

Note 1: if this doesn't open and print properly, let me know and I'll save it in a different format to send to you

Note 2: some error patterns give you correct answers for some kinds of problems and wrong answers for other kinds of problems, so make sure you check all of the pretend student work.

Subtraction

Do first:

Do: Try it yourself

Watch: What do other people do? Ways of subtracting base 5

Assignment 29: Write about it, and do some base 5 calculations (Print, do, scan, dropbox) July 5

Alternate and student invented algorithms:

Read:

Bassarear Textbook section 3.2, with special emphasis on Mental Subtraction, Childrens Strategies for subtraction and An Alternative Algorithm

Some notes teaching and various algorithms

Watch:

Four Student invented algorithms
Standard-type algorithms

More resources (optional)

Assignment 30: Alternate subtraction algorithms(scan, dropbox)