I'll begin with the essential question: How can you add and subtract positive and negative decimals using a procedure? I'll then ask about our conclusions from the previous lesson. In a nutshell, we concluded that signed decimal sums and differences behave just like integers.
Students take this conclusion to fill in the procedures for decimals sums and differences. Again, we have already discovered/learned this procedure with integers.
There are then 4 examples. Instead of "teaching" these examples in the manner of a direct instruction lesson, I will let students use the rules above to solve the problems on their own. I will just remind students to line up the decimal point for addition and subtraction so that we are subtracting or adding from common place values.
I'll monitor the progress of students on these 4 problems. If the majority of students are easily able to solve these problems, I know that we can skip the Guided Practice section and go straight into independent practice. I'll save the guided practice for the few students who may still be struggling.
This section of the lesson may be omitted if the majority of students are successful on the previous 4 examples. These may be saved for the few students who are still struggling after the 4 examples.
The problems presented consist of the various combinations of positive and negative values that students may encounter when adding or subtracting. Five of the six problems have decimal values of different lengths, which are there to make sure students remember to add and subtract by place value.
While working on these problems I will ask students to consider the quantities before solving by asking:
1) Will the sum or difference be greater than or less than the first addend or the minuend? How do you know?
2) Will the sum be positive or negative? How do you know?
These questions come from the essential questions of the unit. Students can use these questions as a way to see if their answers make sense (MP1).
I will also look for students to distinguish between adding decimals with the same sign compared to different signs and whether students are making mistakes with the additive inverse.
Students can find it confusing that they use subtraction to add rational numbers with different signs and that they use addition to solve subtraction problems which then may result in using subtraction again. Example: -8.5 - (-5.3) equals -8.5 + 5.3. This is where it helps to recall either the number line model or related the problems to the counter model to help students make sense of the problem.
The independent practice section is mostly intended to be an exercise in fluency. Problems 12-16 have students analyze data in a bar graph. I will push to get student through the extension because I there are equations to solve. I am trying to provide as many opportunities as possible for my students to solve simple one-step equations with positive and negative numbers before we have a formal unit on expressions and equations.
I did not provide a lot of room for students to work out problems in the lesson packet, so I will ask my students to use notebook paper or I may pass out whiteboards. Whiteboards are more fun, but notebook paper may be my preference as it is easier for me to assess student errors.
The exit ticket has 4 problems that are similar to the examples in the introduction, the problems in the guided practice, and the problems from independent practice. I am assessing for students fluency. A successful exit ticket for a student will be to answer at least 3 of the questions correctly.