Developing Mathematical Ideas
Deborah Schifter
Virginia Bastable
Susan Jo Russell
Seven DMI modules
• Building a system of tens• Making meaning for operations• Examining features of shape• Measuring space in one, two, and three
dimensions• Working with data• Reasoning algebraically about operations• Patterns, functions, and change
36 + 17
a. (30 + 6) + (10 + 7) = (30 + 10) + (6 + 7) = (40 + 13).
b. (36 + 17) = (33 + 20) Move 3 from the 36 to the 17.or(36 + 17) = (40 + 13) Move 4 from the 17 to the 36.
c. Round up to (40 + 20). Then subtract the extra 4 and the extra 3
36 x 17
a. Why isn’t (30 + 6) x (10 + 7) = (30 x 10) + (6 x 7)?
b. Why isn’t (36 x 17) = (33 x 20)?
c. Why isn’t (36 x 17) = (40 x 20) - 4 - 3 ?
17 3 36 4
X 2
X
6
(x + 2) (x + 6) = x2 + 2x + 6x + 12 = x2 + 8x + 12
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
The repeating pattern of red, blue, green, red, blue, green
continues in the same way.
The repeating pattern of red, blue, green, red, blue, green
continues in the same way.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Red, blue, green repeating pattern
Number of green square
Position on the number strip
1 3
2 6
3 9
4 12
5 15
10 ?
20 ?
Red, blue, green repeating pattern
Number of red square
Position on the number strip
1 1
2 4
3 7
4 10
5 13
10 ?
20 ?
The repeating pattern of yellow, yellow, green, green, red
continues in the same way.
This building has five rooms on each floor.