Adding and Subtracting Decimals
Lesson 3 of 16
Objective: SWBAT: • Read and write decimals to the thousandths • Compare decimals • Add and subtract decimals
- In Unit 1 I give a pre-test that included working with decimals. I will adjust the pace/length of part of Unit 2 depending on how students do on the pre-test.
- I will also use the pre-test as data to strategically group students throughout the unit.
See my Do Now in my Strategy folder that explains my beginning of class routines.
Often, I create do nows that have problems that connect to the task that students will be working on that day. Here, I want students to connect their knowledge of fractions to decimals. Once students have had a couple minutes to complete the shading, I ask students to write a decimal to represent each picture. I have students participate in a Think Write Pair Share. I have students share out their answers. I want students to make connections between .5 and .50. I want students to be able to use their knowledge of equivalent fractions to explain why the two decimals are equal.
A common mistake for number 2 is that students shade 3/10 instead of 3/5 of the pictures. Again, I want students to understand that 3/5 is the same as 6/10 or 60/100.
Here I want students to quickly review place value and reading numbers including decimals. To make this quicker, I may fill in the names of the place values and families (billions, millions, etc.) so that students spend their time practicing rather than copying. I have students Think Write Pair Share for the four problems.
A common mistake is for students to forget to put zeros in their numbers. For example, a student may incorrectly write .9 to represent nine hundredths. Or a student may write 50,250 instead of 50,025. When I see these mistakes I read the number the student has written and ask them if it matches the problem. Students can usually quickly identify and resolve their mistake.
Some ELL students may struggle differentiating between whole number and decimal place values (ie. thousands vs. thousandths). I try to exaggerate the “ths” when I read a number that includes a decimal. If a student has made a mistake involving the place value I go back to the visual and review the difference.
Closer to 0, 0.5, or 1?
I have a student read the directions and I give students a few minutes to complete the problems independently. As students are working, I walk around to observe student progress.
A common mistake is that students mistake nine thousandths for nine tenths and say that it is closer to 1. If I see this I will ask students to tell me if they agree or disagree and why. I want students to make the connection that .09 is the same as 9/100. 0.5 is equal to 50/100, and .09 is nowhere near that much. It is closer to .10 or .1, which is closer to 0.
We go over the answers together. I have students mark and label the other tenths that fall between 0 and 1. This can help students visualize the location of the numbers. Some students will struggle with .75, since it is exactly between .5 and 1. If students doubt this, I write 2/4 under 0.5 and 4/4 under 1.
Estimation is a great strategy for students to test if an answer is reasonable or makes sense. Oftentimes, students can make careless mistakes when computing with decimals. If they make a reasonable estimate, they are more likely to realize when they’ve made a mistake.
Here I want students to quickly practice making estimates. If I wrote the problems on the paper, many students would just try to add/subtract them quickly without making an estimate. Therefore, I will only display the problem for 5 seconds and in that time they will have to make an estimate. Some students may round to nice numbers like 10, 20, 100, etc. Other students may round to the nearest whole number and add/subtract mentally. What matters is that students are able to make a reasonable estimate in a short amount of time.
I go through the example with them and have students share out efficient estimation strategies. I show students the five problems and then we share out estimates (See 2.2 Estimating Problem Ideas). I stress that estimating helps us have a rough idea of what our answer should be. That way, it will be easier for us to realize if we make a mistake finding an exact answer.
Exact Sums & Differences
I use the pre-test data to Create Homogeneous Groups for this part of the lesson. See 2.2 Exact Sums & Differences Problem Ideas. I determine which groups need which problems and create a set of index cards with problems that are written in the same color.
I have students get into groups and work on their first addition problem. I walk around to ensure that students are estimating and explaining their process. Some students may struggle here, since I have not given them a short cut. It is important that students reason together as to how they can find an exact sum. A common mistake is that students line up the digits, not taking the decimal point into account, and then add.
Once most groups have finished their first problem, we come back together as a class. I ask students to share out how their group worked to find an exact sum. Students are engaging with MP7: Look for and make use of structure.
Here, I push students to use specific and accurate language (MP6: Attend to precision). Some students will have added added zeros to serve as place holders and then added each place value. For example, a group with the problem 6.5 + 10.09 may have adjusted the problem to add 6.50 + 10.09. This is great, but I want to make sure that students understand why they do this. I will ask students why this works. How can you change the number like that? Won’t that change the problem and the answer? I want students to explain that .5 is the same as .50, so the answer will not change. I make the connection to creating common denominators when we add fractions.
Then students complete the second problem. Once most groups are finished we come back together as a class to reflect on how our strategies worked.
I will also present an example where I line up the digits, and do not pay attention to the decimal points. For instance, for 15.06 + 4.1 I line up the 4.1 directly underneath the .06. I add and declare that the answer is 15.47. I want students to correct my mistake. I stress that if I had made an estimate, I would probably have realized that something went wrong.
We move onto exact differences and repeat the same process. Students work and develop strategies, we come together to share what happened, and then students practice with another problem. The common mistakes are the same for subtraction. If I see students see a common mistake among groups, I keep it in mind and address it in the closure.
If groups successfully complete their problems, they can move onto the College Practice problems.
Closure and Ticket to Go
I begin the Closure by asking students to share out strategies for adding and subtracting decimals. I ask students why estimates are important. I bring up any common mistakes that I noticed when students were working on exact differences.