Decimals and Fractions
Most students know that 1/2 = .5. Beyond that, base ten grids are a convenient model for exploring decimal and fraction relationships. Dividing a 10 x 10 square 'unit' into congruent parts forms the basis for making observations and generalizations.
For example, divide the unit into four equal parts...
...or divide the unit into 5 equal parts...
From our observations of these two models, we can also determine decimal equivalents for 2/4, 3/4, 2/5, 3/5, and 4/5. What are they?
What would be the decimal equivalent for the following fractions of a unit?
Use these pictures to help you:
Many students will begin, through their exploration with the 10 x 10 grid, to know these decimal-fraction equivalents as basic facts and will be able to re-create them by thinking about the 10 x 10 model.
Try to imagine how the 10 x 10 grid would show decimal equivalents for 1/20, 3/20, 13/20, or 1/25, 7/25, and 20/25. For a challenge, use the 10 x 10 grid to find decimal equivalents for 1/3, or 5/6. In class, we discuss terminating decimals and infinite repeating decimals as we explore these ideas.