Math 247 Unit 2: Base 10 numbers and algorithms

Section 5: Base 10 number system.

Goal: The goals this section are for you to

Virtual manipulative resources

Understanding a base 10 and 5 positional number system
(if any of these videos do not load properly, please let me know!)

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 25

Assn 13: Other base number systems 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)

Base 10 manipulatives and the banker game 

Abacus and recap

Readings: some notes on base 10 materials

Assignments due: June 26

Assn 14: Base 10 materials assignment


Videos to watch:

(apparently I pronounce this word incorrectly.)


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

Using Language and Visulization to teach place value. (Read only the first 8 pages: up to the section "Electronic ALAbacus)


Assn 15: Subitizing and AL Abacus (dropbox) June 27

Place value errors and misconceptions:

Videos to watch:

First watch the first two videos "Snapshots of Student Misundertandings by Marilyn Burns-Cena" and "Snapshots of Student Misundertandings by Marilyn Burns-Jonathan" from the Math Solutions web site here:

I'm going to compare those to the last video (of Rudy) at this web site:


Also read the article in the D2L Content->Readings section:

What Nathan Teaches Us About Transitional Thinking

My commentary video:

Learning about place value

Optional reading: Daniel T Willingham writes about flexible and inflexible knowledge


Assn 16: Write a paragraph describing how students develop place value understanding in the primary grades. June 28