The focus of this lesson is to have students use and discuss various strategies. Estimations strategies, including compatible numbers, or rounding. I want them to make sense of the problem they are solving using reasonableness. To do this I post a problem on the board, and I probe students a bit just to see how much they know!
It took three days for my family and I to make it to Chicago. We traveled 300 miles on the first day, 294 miles on the second day, and 65 miles on the third day. How many miles did we travel total?
Alright! Let’s take a look at some questions that can assist us in solving this equation.
What do we need to know?
How many miles did we travel total?
What information does the problem give us?
We traveled 300 miles on the first day, 294 miles on the second day, and 65 miles on the third day.
Are there any key words? Explain?
Total- The word total tells us to add the given numbers together.
How can you set the problem up?
300 + 294 + 65 =
Some typical estimation strategies for this problem:
I explain how students can use rounding to estimate what the total will be. First I write 300 on the board. What number is the highest digit? 3 Yes! Since, 3 is in the hundreds place it is the highest, so we round to the nearest hundreds. Can anyone tell me the answer? 300 I write 294 on the board. What number is the highest digit? 2 Yes! Since, 2 is in the hundreds place we will need to round to nearest hundreds. So, 294 rounded to the nearest hundred is 300. I write 65 on the board. What number is the highest digit? 6 Yes! Since, 6 is in the tens place we will need to round to the nearest tens. 65 rounded to the nearest tens is 70.
300 + 300 + 70 =670
So, the answer should be about 670. This allows me to check the reasonableness of my answer. Now you guys are ready to solve the equation. Can someone tell me the answer? 659. What do you know about the estimation and the correct answer? That both the estimation and the answer are about the same.
This lesson will focus on the following Mathematical Practices:
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.
MP.4. Model with mathematics.
MP.7. Look for and make use.
MP. 8. Look for and express regularity in repeated reasoning.
Now that we have discussed some key elements of this lesson, I want you guys to practice a bit more. Don't worrying! You guys will be working in your assigned groups.
I am going to set the timer for about 20 minutes or so. I want you guys to discuss how to represent your equation with a letter standing for the unknown quantity. Be sure to discuss how to check for the reasonableness of answers using mental computation and estimation strategies including rounding.
I provide a question check list for student, so that they can strategically assess this problem. UNDERSTAND THE PROBLEM.docx As students are working, I stop by to ask a few questions to check for their level of understanding. One student says, “I first thought about adding 400 and 10. I noticed that the sum is about 410. Then I realized I had another amount to add, so I ended up talking it over with my group. Now I know I did not perform all of the steps in this equation.
I point out that it is perfectly fine to think your way through a problem, because this is a fairly new concept for us you can expect to make mistakes. If any of you feel like you need additional practice time raise your hand and let me know. Several students raised their hand. So, I allow them about 20 more minutes to think their way through this equation. I want to really know what they are thinking. As students are working, I ask them to examine their explanations to make sure it is logical. I know that some students will need fore me to scaffold them through their thinking. I can do this by illustrating their problems with models, and drawings, or I prompt questions to get them to thinking on their own such as: What information do we need to solve?, What information does the problem give us?, What do we need to know?, What operation will help us solve?.....
I tell students to take their time and practice writing down the steps you did to solve this problem, I placed paper on your table. Now! I want you to write a draft first. to make the connection, I say you guys always write first drafts in writing class. During the first draft you don't have to worry about mistakes. After your first draft is finished, turn and talk to the person sitting beside you. Ask them to read over your response to see if you can add mathematical details to it to make it more precise.
Your dance team is collecting can goods for a service project. The goal is to collect 400 can goods. On the first day, Jane brings in 5 cases with 10 can goods in each case. Tammy brings 4 cases with 5 can goods in each case. About how many can goods still need to be collected?
In this section of the lesson, I want to encourage students to really meet the objective of this lesson and demonstrate through thinking and showing. I tell them that just giving the answer is not enough. Because you guys have had a chance to discuss, work with partners, and explore on your own to help you better understand how to solve multi-step work problems using all four operations. Now, I want you all to explore a bit on your own. I ask students to quickly move back into their assigned seats. I encourage students to think about how they are using various strategies. I do not expect all of my students to explain in detail, but I can scaffold them through solving the problems by using models such as drawings, written illustrations, and asking What do we need to know?, What information does the problem give us?, Are there any key words? Explain?, How can you set the problem up? I want to move the students forward in their own thinking by not just doing the problem for them, but instead asking, discussing, and walking them through the problem together.
I give students about 15 minutes or so to create and solve their own word problem. I ask them to write a written explanation of how they problem solved. I give students a chance to share an example of their word problem they created. The student reads the problem aloud and then asks for volunteers to tell how they solved the problem. As students are busy explaining, I remind them to make sure their response makes sense. I may invite a couple of students to come up to the board and show their solutions. We take a few moments to talk about their options for solving the problem that other students may have used. I use student’s responses and discussion to determine if additional support is needed.