Double-Column Addition, Part 1
Double-Column Addition, Part 2
Double-Column Addition, Part 3
Giving Change When Payment Is Made with a Dime:
The Difficulty of Tens and Ones
This videotape illustrates the difficulty of constructing tens solidly out of the ones that are in the child’s head. The second grader in the videotape refused to accept the dime that the “customer” offered for a 6-cent purchase. She had all the verbal knowledge necessary to accept the dime such as the fact that a dime was worth 10 cents, and that 10 cents was “too much” for a 6-cent purchase. She could give the correct change when 8 pennies were tendered for a 4-cent purchase. She could easily add a few cents to a dime but could not subtract 6 cents from a dime because, for this subtraction, it was necessary to break “one ten” down into “ten ones.” This difficulty is explained by Chandler and Kamii in an article entitled “Giving Change When Payment Is Made with a Dime: The Difficulty of Tens and Ones” in the Journal for Research in Mathematics Education, 40(2009), 97-118.
In the videotape, giving change for a dime appears toward the end of the following sequence. It begins by showing that, as long as only pennies were involved, the child had no trouble giving change.
Candy purchased Cost Payment
1 small 2 cents 2 pennies
1 large 3 cents 4 pennies
2 small 4 cents 8 pennies
2 large 6 cents 1 dime
3 large 9 cents 1 dime and 2 pennies