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.