Adding and Subtracting Decimals Algorithm
Lesson 2 of 10
Objective: SWBAT add and subtract decimals.
In yesterday's lesson, my students developed a strategy for adding and subtracting decimals using fractions. Before we move on to another strategy today, I would like for students to practice what they worked on yesterday:
Using a fraction strategy, find the following sum:
4.7 + 0.29 + 12.032
Based on my assessment of yesterday's Exit Ticket, I will select students who need additional help with using fractions to add decimal numbers to show their work on the board. To help them, I will assign a partner who demonstrated a good grasp of the strategy yesterday.
When we discuss the answers I plan to ask students to respond to the following questions:
- How did you change 4.7 to a fraction? 0.29? 12.032?
Students should respond with how they used the last place value to determine the denominator of the fraction.
- After changing each decimal to a fraction how did you add them?
Students should have realized that the fractions had different denominators and therefore they needed to find a common denominator first.
Developing an Algorithm
To motivate my students' interest in today's lesson, I will share a story to help them understand that when adding/subtracting decimals it is important to line up the decimal point. As I share the story, I will suggest to my students that they write down the given information.
I went to 7-11 Convenience Store the other day. I picked out a bag of chips for $0.89 and a half gallon of juice for $1.97. The cash register was broken so the cashier had to do the math mentally. She told me the bill was $10.87. Do you agree? If not, explain what the cashier probably did wrong?
After sharing the story, I will give my students about five minutes to discuss the problem together. Most students will know that the cashier was wrong, but many will have a difficult time explaining what the clerk did incorrectly. After the group discussions, we will discuss the situation as a class to try to determine and explain what the clerk did wrong (MP3).
Possible Responses from Students
- She didn't know how to do math.
- She added the 89 to 1 to get 10.
- She didn't line up the decimal points.
Our goal is to come to the conclusion that the cashier lined up the numbers without paying attention to place value. Then, she added the resulting columns and came up with the wrong result. Along the way I expect we will address the following:
- What should the total have been?
- Why is it important to line up the decimal points when adding or subtracting?
These topics generally arise organically.
Next, each group will receive copies of Adding-Subtracting Decimals Word Problems to complete together. In each of these problems the students have to determine whether to add or subtract. Then, they need to model the problem with a numerical expression and perform the operations required to find the answer. Before the start to work, I encourage my students to:
- Work together to agree on a strategy for solving the problem
- Work on their own to implement the strategy
- Compare results to check for accuracy and validate the answer
I expect that it will take my students about 10 minutes to complete these problems. After they are done, I will assign each group one problem to demonstrate on a whiteboard. The group will show their work on the whiteboard and explain their strategy. Other groups will have the chance to ask questions about the strategy or the answer (MP3).
It is important not only for students to be able to find the sum and difference of decimals, but also to verify if their answer makes sense. Today's summary question asks students to identify strategies they can use to check their calculations.
- How can you check your answer when adding or subtracting decimals? How do you know your answer makes sense?
I will collect these and review my students ideas. If time allows, I will have a few student volunteers share their answers before we leave for the day.