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

SMART notebooks with manipulatives for base 10 blocks, base 5 blocks, Montessori stamp game stamps. Montessori checkerboard, and a Montessori bead frame/abacus*, and the ALAbacus*.  Here is a site where you can find printable grid paper. 

*Note that if you want to show me what you did on these abacuses, you can't just save the SMART Notebook, because the abacus is a Flash program that is embedded in the notebook, and not a graphic.  If you want to use this and show me a picture of what you did, you will need to use some sort of screen capture device.  The screen capture camera in the SMART Notebook toolbar works fine, as does the screen capture built into Jing.

Some applets you might find useful: the base 10 blocks you can glue together and break apart; the site that has the buiilding with blocks applet, and the site with the array multiplication applet (Rectangle Multiplication)

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 27: Write about it (submit to dropbox) June 27

Alternate algorithms:

Watch:

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

Read:

The discussion of Children's Strategies for Addition in the Bassarear Textbookpg. 136-138 (previous edition pg 133-136)

Assignment 28: Practice (do, scan, dropbox)  June 27

Mental math:

Do and read: the Mental Addition investigation 3.2 on page 134, and read the discussiion that follows on pages 134-136 (pages 131-133 in the previous edition)

Assignment 29: Practice: textbook pg 151 # 11 (pg 147 # 11 in the previous edition).  You should be using the mental addition strategies from the exploration and discussion on more than half of the problems. (scan or type, dropbox)  June27

The standard algorithm:

Watch: modeling and making connections for the standard algorithm

Read: The textbook discussion p. 139-143 (p.137-139 of the previous edition)

Assignment 30: 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). June 29 Guidelines for presenting explanations

Error patterns

Watch: addition error patterns

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

Assignment 31: Do the assignment "addition error patterns and algorithms" on D2L->content->assignments. (print, do, scan, dropbox) June 29

Subtraction

Do first:

Do: Try it yourself

Watch: What do other people do? Separate subtraction solutions; compare subtraction solutions take 1, take 2.

Assignment 32: Write about it, and do some base 5 calculations (Print, do, scan, dropbox) July 1

Alternate algorithms:

Watch:

Equal Additions Algorithm

Left to right algorithms: negative numbers and a variation on the standard algorithm

Read:

Textbook (Bassarear): read Childrens Strategies for Subtraction p. 157-159 (prev. edition pgs 153-155)

An Alternative Algorithm p. 161-162 (prev edition pgs 157-158)

Assignment 33: Practice (scan, dropbox) July 1

Teaching with invented algorithms, and childrens strategies for subtraction

Tip: print the assignment for this section before watching the video, so you know what to watch for.

Watch: Negative numbers and subtracting: watch this class figure out a way to use negative numbers for 2-digit subtraction.  At the site http://learner.org/resources/series32.html Watch #15: Bean Sprouts (note: this is a long video.  If you have a slow connection or a slow computer, you might want to pause it and let it download for a while before you start watching).

Read: Two articles in D2L->Content->Readings

Assignment 34: Questions about the Video and Readings (either type into the document, or hand-write your answers and scan.  If you are planning to print it out and then hand-write onto it, you should add in a lot of spaces before you print it--I have not left writing space. Dropbox) July 1

Mental math and open number lines:

Do: Try these

Watch: Some mental subtraction strategies

More number lines, open number lines and adding up.

Read the mental subtraction discussion in the textbook pg. 155-157 (prev. edition pgs 151-152)

Assignment 35: Practice  July 6