Representing Decimal Tousandths - Grade 5 (Page 4 of 4) in pdf

Uncomplicating Fractions to Meet Common Core Standards in Math, K–7

Using the blocks, 0.124 could be modeled with 124 small cubes, but could also

be modeled using 1 fl at (0.1) along with 2 rods (0.02) and 4 small cubes (0.004). A

number like 3.124 could be modeled with 3 large blocks, 1 fl at, 2 rods, and 4 small

cubes.

Some students, but certainly not all, can handle more abstract concepts. For

example, knowing that 1000 mm = 1 m, students could think of 0.124 as 124 mm

compared to a meter stick. Or knowing that 1 km = 1000 m, they could think of

0.124 as 124 m relative to 1 km. Many other pairs of metric measures can be used

(e.g., 1 mg = 0.001 g; 1 g = 0.001 kg; 1 mL = 0.001 L).

In a similar way, a student might think of a $10 bill as a unit, in which case a

penny would be worth 0.001 units. Although this is mathematically correct and

might help some students, it is very abstract for others.

x Th e notion of precision when using decimals. It is important for students to un-

derstand that we are likely to use thousandths only in situations where we wish to

be very precise. For example, it is unlikely that we would measure someone’s height

in thousandths of a meter since that level of precision is not needed. However, in a

very close high-level competition, like the Olympics, a competitor might win by

only a few thousandths of a meter or thousandths of a second.

Good Questions to Ask

• • Ask students why the model for 0.238 on a thousandths grid is almost but not quite

of the grid.

• • Ask students to explain why 2.314 is actually 2314 thousandths.

• • Ask students to give several reasons why it makes sense that 10 thousandths make

1 hundredth. [Th ey might refer to models, e.g., 10 small base-ten cubes is worth a

rod, or they might use the notion that the fraction

, or they might refer

1000

100

to the 10 small rectangles that make up each of the 100 squares on the thousandths

grid.]

Representing Decimal Tousandths - Grade 5 Page 4