Decimal Ops: Computing with Decimals and Percents

Topics

Addition, subtraction, multiplication and division of decimals, estimation; solutions for a% of b = c type problems.

Overview of Changes

Minor Changes: Applying operations and card sort activities to develop and refine operations.

Detailed Description of Changes

Although users of CMP 2 might find it hard to match the specific material of Bits III with the proposed Decimal Ops for CMP3, the content coverage is similar. The pieces have been rearranged and the development streamlined in places, but the basic content goals are the same.

The main structural change in the unit for this edition is the emphasis on choosing the appropriate operation to solve a problem and estimating calculations throughout the unit. Our reasoning is that students have considerable prior experience with those tasks in non-decimal contexts, and they need only become comfortable with that reasoning with decimals. Furthermore, there is more work with estimating sums, differences, products, and quotients that help strengthen student’s operation sense and understanding. In the CMP2 version, students knew when to add, subtract, multiply, or divide because problems requiring those operations came up only in Investigations or problems focused on one operation. As a result, in this CMP3 version we made a concerted effort to include problems in which students are given several problem situations and are asked to identify the correct operation to solve each problem.

Thus Problem 1.1 asks students to identify the operation on decimals required to answer various questions—with a mix of addition, subtraction, multiplication, and division opportunities. Problem 1.2 asks students to use their intuitive sense of decimals as like whole numbers to make estimates of sums, differences, products, and quotients and to check that informal number sense with a calculator. Problem 1.3 connects ratios, rates, and decimals. Investigation 2 develops understanding and fluency with addition and subtraction of decimals. Investigation 3 develops multiplication of decimals by relating them to fractions. This is done using a card sort activity that connects decimals to fractions. Investigation 4 connects decimals to percents and builds understanding and fluency with percents. Problem 4.3 again asks students to choose the appropriate operations.

To satisfy an explicit CCSSM standard, we have introduced a new Problem 1.3 that focuses on ratios, unit rates, and the decimal forms in which those rates are commonly expressed.

Throughout the unit, we have also been more explicit in developing ‘standard algorithms’ for the four decimal operations, in direct response to expectations of the CCSSM including long division of decimals.

New Investigation	Changes in CMP2 Investigation
Investigation 1 Decimal Operations and Estimation	Investigation 1 is mostly new. It focuses just on estimation and identifying the appropriate operation
Investigation 2  Adding and Subtracting Decimals	Investigation 2 contains some of Investigation 1 in CMP2’s Bits III
Investigation 3 Multiplying and Dividing Decimals	Investigation 3 is a combination of Investigations 2 and 3 in CMP2’s Bits III with
Investigation 4 Using Percents	Investigation 4 is similar to Investigations 4 and 5 in CMP2’s Bits III with an emphasis on using a bar model for finding percents.