**Goal:** The goals this section are for you to

- Understanding a base positional number system: base 10 and base 5

- Manipulatives for base 10 and 5 work.

- Subitizing
- Exchanging and trading

**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. If downloading the SMART Notebooks isn't working for you (the files don't open properly), first try downloading using a different web browser (I use Firefox to test my web pages--Explorer tends to lose the .notebook at the end of the file name which turns out to be a problem), and then e-mail me, and I'll send you everything as an attachment (this pretty much always works).
**

*****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)**

**Understanding a base 10 and 5 positional number system**

The base 10 positional number system

Base 5 manipulatives and numbers

Converting base 5 to 10

Converting base 10 to 5

More counting and thinking in base 5

Other bases

Readings: Read section 2.3: Numeration in the Bassarear book. The part of this you will find most immediately useful is pgs 111-118 (110-115 if you have the previous edition of the book)

Assignments due: June 22

Assn 21: Draw what base 6 blocks would look like (scan, dropbox)

Assn 22: Bassarear (4th edition) pg. 119-122 # 5, 6, 7, 8 a, 9 a, 15. a, g, h; 16. a, b, g; 17. a, c, d, e; 18. a, b, j, l; 23, 24, 30 (correction to the text of #30: 2413 means 2 flats, 4 crates,1box and 3 cartons. Show work on problems 17, 18, 23, 24, 30.(if you have the previous edition of the textbook, your assignment is pg 117 # 11a, g, h; 12a, b, g, h; 13a, b,c, d, e, f, g; 14a, b, g, h, j, l; 19; 27a; 28a; read and think about problem 29--I expect to be referring to it later. (type or scan and upload to dropbox). Show work on problems13, 14, 27, 28: I want to be able to see how you got your answers. Make sure write out the questions as well as the answers when you turn in your assignment).

**Manipulatives and games for learning about the base 10
number system
**

Videos to watch:

Base 10 manipulatives and making 10 (this game is one that, with a few variations, I have seen used in a lot of places, and there are a lot of people who have found it is very effective for helping students gain a good understanding of place value; it is used for 1-2 grade children who are working on a good place value foundation, and for higher grades children who are showing a difficulty with place value. I've played a version with my children called "race to 100" with coins as manipulatives--pennies, nickels, and dimes, up to a dollar--where the first one to 100 wins. It's good for place value understanding and it's fun)

Assignments due: June 22

Assn 23: You saw in the videos what the number cards are like for making base 10 numbers (see also pictures here and here). Write out number cards for base 5 numbers to 4 place values. (type or scan, dropbox)

Assn 24: Get a die and play a "make 5" game. You will play it just like the make 10 game from the video, except that you will do it with base 5 materials. You can make your own base 5 blocks out of grid paper, or you can use the base 5 blocks in the SMART notebook. (You can also play with coins, but you use only pennies, nickels and quarters--you'll have to come up with something to trade 5 quarters for.) Play untill you get to 1000_{5}. What you will turn in (dropbox) is a list of the numbers (written in base 5) that you had at the end of each die roll (so I will get a list of base 5 numbers starting with a small one, and ending with a number that is at least 1000_{5)}.

**Subitizing:**

Videos to watch:

subitizing

Michael solving a problem "by thinking" And another version of the same thing (in case the first doesn't play)

My ALAbacus (I own a couple I have purchased from the AL Abacus site, but the ones you see in this video are ones I made from craft sticks, dowels--I buy the thinnest diameter I can get from the hardware store, and pony beads.)

Readings:

Read the articles in the D2L Content->Readings section:

Subitizing

Using Language and Visulization to teach place value.

Resources:

ALAbacus in a SMART notebook (not as nice as holding one in your hand, but still instructive). Note that if you want to show me what you did on this abacus, 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.

Info about ten frames

Assignment:

Assn 25: Subitizing and AL Abacus (dropbox) June 24

**Place value errors and misconceptions:**

Videos to watch:

Some place value misconceptions

Place value interviews with children

Place value and non-place value ways of adding 2-digit numbers

Readings:

Read the article in the D2L Content->Readings section:

Place Value: Problem Solving and Written Assessment

Assignment:

Assn 26: Draw 3 different ways of representing the number 48 (counters, manipulatives, whatever). Explain how each way shows the place value meanings of the digits 4 and 8 in 48. In what way are your representations useful for understanding place value meaning? You should have at least one proportional and one non-proportional representation. (do, scan, dropbox) June 24

Vocabulary:

At some point, you will need to pick up
the vocabulary we use when talking about addition, subtraction,
multiplication and division. Now would be a good time.

Read: Vocabulary
for
the
4
basic
operations

Then do the quiz: Vocabulary for the 4 basic operations
(on D2L) June 24