Decimals+and+Percents

Decimals and Percents
The section of the student packet related to decimals and percents is primarily an assessment, rather than a teaching tool. As students work on the tasks in this section, you will discover what they understand and what they can do with fractions and percents. If you are teaching an intervention class, you can build on the types of tasks in this assessment to give further instruction and practice to students.

The key to learning to compute with decimal numbers is to estimate an answer first, then use your estimate to place the decimal point. After students have done a number of problems using the estimating method, many can figure out the pattern (procedure) of counting the total number of decimal places in the two factors and using the number in the product. Do the estimating first, then use the procedure.

For example, 1.7 x 32.54 can be estimated as 2 x 32 = 64. Doing the full multiplication without paying attention to the decimal point gives this: 17 x 3254 = 55318. Therefore the number that is close to 64 is 55.318.

The key to understanding the concept of percents is to start with hundreds graphs. A simple connection between 7/10 to 70% is shown below.



The key to learning to compute with percents is to first find "benchmark values" such as 10%, 25% or 50% (1/10, 1/4 or 1/2), then scale up or down as needed. For example, 5% of 30 can be found by taking 10% of 30 (3), then taking half of that (1.5).

A bar model is useful for percent increase and decrease problems. Consider this problem: A store buys a refrigerator for $500 and marks it up by 75% in order to make a profit. How much would they sell it for? The whole is shown by the dark outlined box. The shaded squares represent 75% or 3/4 of the whole. The whole is $500, so each shaded square is $125. The problem says that the price is marked up (increased) by 75%, so 75% is adding on to the price. This is $500 + 3($125), or $875.