Describe how a teacher should relate addition and subtraction of decimals to addition and subtraction of whole numbers and fractions

Question

What will be an ideal response?

Answer 1

Complete answers will include the following: Addition and subtraction of decimals should be related to addition and subtraction of whole numbers and fractions. As discussed in Chapters 7 and 11, solving word problems set in familiar, real-world situations helps children understand operations and judge the reasonableness of answers. An easy-to-understand interpretation of addition is the "join" interpretation, in which two quantities are combined. The "separate" and "comparison" interpretations of subtraction, in which two quantities are separated or compared, also are easy to understand. Addition and subtraction of decimals should be introduced by posing problems based on "join" and "separate" situations involving quantities measured in decimal units, such as lengths of ribbon, pounds of food, and money. Figure 12-5 contains sample word problems for addition and subtraction of decimals and compares them with similar problems involving fractions. Notice the similarities between the problem contexts.
5. Complete answers will include the following information. Children should show concrete proof of equivalency by using base-ten blocks and comparing decimals. Children will understand the meaning, not simply the rules. When modeling decimals, children will develop a sense of the size of decimal numbers. They should be able to rename one decimal fraction to an equivalent form. They will have a mental referent for the process. The generalization that adding zeros to decimal fractions produces number of equivalent value is not difficult to conceptualize.