Multiplying Signed Decimals
Lesson 19 of 27
Objective: SWBAT multiply signed decimals using a procedure
I will open the lesson with the essential question: Do the signs of decimal products follow the same rules as integers. There is a chart at the top of the resource about the signs of products to be filled in after going through a few questions.
Question 1 is given so that students will be reminded that multiplication can be seen as repeated addition; this fact can lead to confirming that a positive times a negative decimal results in a negative product.
Question 2 uses the commutative property and the factors from the first question to show that a negative times a positive results in a negative product.
Question 3 is a check in to the essential question - do the decimal products behave like integer products - the answer so far is yes.
Question 4 includes a pattern that leads students to seeing that the product of negative decimals equals a positive product.
For each examples I use -0.5 as a factor because it is relatively easy for students to work with mentally.
This first activity is an exercise in making sense of a problem (MP1) which is in this case, answering the essential question.
By the end of this section we conclude that signed decimal products do in fact behave like integer products.
The guided practice is a chance for students to now practice fluency with multiply decimals. The third and fourth problem may cause some controversy as students may see these as being equivalent. The purpose here is to draw out that misunderstanding. The issue here is for students to understand the notation of numbers raised to a power and how parentheses are used to create a desired meaning or outcome. It may help students to say that (-0.5)^2 is -0.5 being multiplied by itself, where -0.5^2 is the opposite of 0.5^2. It may be necessary to have a student bring the problem to the whiteboard for all to see.
Some students will inevitably make mistakes with placing the decimal point correctly. I generally like students to estimate to determine the location of the decimal. Numbers less than -1 and greater than +1 can often be rounded to the nearest integer. I generally round values betwen 0 and 1 and their opposites to the nearest half or quarter.
The independent practice mirrors the work from the previous section with a few additions. Problem 8 asks for students to compare two values and problems 9-10 need to be evaluated using order of operations.
Problem 11 is a pattern problem that is designed to lead students to understand that a negative value raised to an even power evaluates as a positive; a negative value raised to an odd power evaluates to a negative value. (MP8)
The extension includes four division equations that could require multiplication to find the unknown.
The final task is for students to work with a proportional relationship. The task should be accessible to the majority of the class and will be a nice review before the upcoming unit on proportional relationships.
The exit ticket is designed to determine if students can multiply fluently and determine the sign of products. Problems 3-4, bring out the meaning of negative bases raised to powers where one base is in parentheses and the other is not.
I will remind my students to check their work carefully because I am looking for a valid product and valid sign.