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

Alternate algorithms:

Watch:

Read:

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

Assignment 25: 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)The standard algorithm:

Assignment 26: 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

Watch: modeling and making connections for the standard algorithmError patterns

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

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). June 29 Guidelines for presenting explanations

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 28: 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 29: Write about it, and do some base 5 calculations (Print, do, scan, dropbox) July 2

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 30: Practice (scan, dropbox) July 2

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

What Nathan Teaches Us About
Transitional Thinking

Second Graders Circumvent Addition and Subtraction Difficulties

Second Graders Circumvent Addition and Subtraction Difficulties

Assignment 31: 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 2

Mental math and open number lines:

Do: Try these

Watch: Some mental subtraction strategies

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

Assignment 32: Practice July 6

The standard algorithm:

Watch: modeling and making connections
for the standard algorithm Examples with 2 exchanges: #1, #2; Examples with a 0 in the
tens place of the minuend #1,
#2; Another way of looking at the
standard algorithm.

Read: Bassarear: Understanding subtraction in base 10 and Justifying the Standard Algorithm pg. 159-161 (prev. edition pg 155-156)

Assignment 33: Show how to model and make connections for the standard algorithm (video assignment) July 6 Guidelines for presenting explanations

Read: Bassarear: Understanding subtraction in base 10 and Justifying the Standard Algorithm pg. 159-161 (prev. edition pg 155-156)

Assignment 33: Show how to model and make connections for the standard algorithm (video assignment) July 6 Guidelines for presenting explanations

Error patterns

Watch: about error patterns

Assignment 34: Do the assignment "subtraction error patterns and algorithms" on D2L->content->assignments. (print, do, scan, dropbox) July 6

Assignment 34: Do the assignment "subtraction error patterns and algorithms" on D2L->content->assignments. (print, do, scan, dropbox) July 6