Multiplying Decimals Algorithm
Lesson 5 of 10
Objective: SWBAT multiply decimals.
Students previously worked on multiplying decimals using fractions (see Decimals Card Sort). The Do Now exercise is similar to the activity used in this lesson. Since this lesson relies on students' understanding of this lesson, I want to review the important concepts.
A. Which expressions below are equivalent? Explain.
1) 0.04 x 3.2
2) 4/100(3 + 2/10)
3) 4/100 x 32/10
5) 0.04 x 0.32
B. Use what you know about fraction multiplication to compute the decimal answer for the product of 0.04 x 3.2
After about 5 minutes, I will lead the class in a discussion about the exercise.
- Which expressions did you group together? Why?
- What property did you use for expression 2?
Students should realize that expressions 4 and 5 cannot be grouped with the others. I will select a few students to explain their strategy for the Do Now.
Developing an Algorithm
Yesterday, in the Multiplying Decimals Card Sort lesson, my students worked on grouping equivalent expressions of fractions and decimals. We discussed how and why students grouped expressions together. In this lesson we will continue to use this activity to develop an algorithm for multiplying decimals. I will be looking for students' to apply MP8 (Look for and express regularity in repeated reasoning).
To kick things off, I will redistribute the Multiplying Decimals Cards, which will be helpful for visual learners as we discuss the activity.
What patterns do you notice that will help you multiply decimals?
Students may mention multiplying whole factors, then adjusting the decimal point to reflect a pattern they have noticed.
Once we've multiplied the numerators, how do we know where to place the decimal point?
Students should find a relationship between the placement of the decimal point and the denominator.
What if we don't change the factors in the expression to fractions? Could we still multiply whole factors? What would we do with the decimals points?
This will lead into the algorithm for multiplying decimals.
Step 1 - Multiply the factors as if they were whole numbers.
Step 2 - Move the decimal point in the product based on the number of decimal places in the factors.
Using the algorithm, I will model multiplying decimals for students using the following example:
Find the product 0.95 x 3.7
It is important to model at least one example for students so they are able to see that lining up the decimal points, before multiplying, is not important.
Would we still get the same product if we lined up the decimal points?
Students should realize that the product will be the same, however they would have to rewrite 3.7 as 3.70, resulting in an unnecessary row of zeroes when multiplying. The product would be the same, but there is an extra step involved.
Next, I will give students the opportunity to work on practice problems using the multiplication algorithm. Based on a previous assessment, I will give students a specific worksheet to differentiate the learning opportunities for students.
- Students who have shown high aptitude with decimals will receive the Advanced Multiplying Decimals Worksheet. This worksheet has multiplication problems written horizontally, so students have to correctly line up the numbers before multiplying.
- Students who have struggled with the algorithms for decimals will receive the Multiplying Decimals Worksheet. This worksheet has multiplication problems written vertically, so students can just focus on multiplying and moving the decimal point.
As students work, I will circulate throughout the classroom. If students need help, I will suggest that they ask their group members first. If students are unsure of an answer, I will suggest that they check their work using the fraction strategy or by estimation. If I observe that students are comfortable with the Multiplying Decimals Worksheet, I will have them move on to the more advanced sheet.
I will ask students who do not complete the worksheets in class to do so for homework.
When multiplying, students often forget that multiplication is commutative and multiply the numbers in the order given even if it entails more work. To encourage a connection between decimals and the properties of math, I will pose the following questions.
Does the order matter when multiplying decimals? Why or why not?
What about other operations with decimals?
In what situations do we need to be mindful of the ordering of decimals?