Multiplying Signed Fractions
Lesson 25 of 27
Objective: SWBAT multiply signed fractions using a procedure
I will open the lesson with the essential question: Do the signs of fractional 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 fraction 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 fractional 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 fractions equals a positive product.
For each examples I use -1/4 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 fractional products do in fact behave like integer products.
The guided practice is a chance for students to now practice fluency with multiplying fractions. The third and fourth problem should by now cause less controversy as students have seen the difference in notations of negative values raised to a power. Fewer will see these as being equivalent. If not, it's a great reminder!
Students may need to be reminded to write all whole numbers and mixed numbers as improper fractions. Yes 2 is 2/1 or in the first problem 10/5. I will not insist that students write answers in simplest form. They may even leave answers as improper fractions. This is because I want students to focus in on the process of multiplying fractions. Also, I find it frustrating when a student correctly multiplies a fraction only to incorrectly simplify it. To be clear though, I do think it is important for students to be able to recognize the various forms of equivalent fractions.
The independent practice is mostly a computational fluency exercise. The first three problems, however, are just a check to see that students understand when a product will be positive or negative. I purposely chose unfriendly values to discourage students from actually multiplying.
Problem 10 and 11 involve applying the order of operations to evaluate.
Problem 12 will be tricky because students are asked to find two factors whose product equals -2/5. Some may say some equivalent value of 1 times -2/5 and that will be okay. This would be a recognition of the structure of a product (MP7). Perhaps that seems too easy but oftentimes students miss applying properties that they have known since the 2nd or third grade (in this case the identity property) to more complicated problems. (Students who do not apply the identity property may need some assistance. I may ask students to think of equivalent fractions to -2/5. This will make it easier for them to find numerator and denominator factors that work.
The extension includes four division equations that could require multiplication to find the unknown.
There is also a basic task where students must plot values on the coordinate plane. This will be a nice refresher since we will be graphing often in the next unit on proportional relationships.
The exit ticket is similar to the guided practice and the majority of the independent practice. It is an assessment of computational fluency. A successful student will answer at least 3 questions correctly. The tricky part in assessing this is that I will accept any form of a correct answer for this exit ticket. For example in problem 1, 36/30, 18/15, 6/5. 1 1/5 etc... are all acceptable answers. If I see a student with a correct product but then simplify incorrectly, I may count it as wrong, but make a note that the student understands how to multiply. He or she may just need to work on simplifying fractions.