In this lesson I want my students to focus on discussing various strategies. I invite students to the carpet to review estimation strategies. I ask students have you ever wanted to go to the movies and buy a new pair of shoes, but you do not think you have enough money to do both. Can anyone think of how estimation can help us solve this problem? ( You can estimate how much it will coast.) How much does it cost to go to the movies? $8.75 How much does a new pair of shoes cost? It will cost about $75.00, Who can explain how to estimate? I want you to keep in mind I giving each of you a budget of $100.00.
Since $8.75 is closer to $9.00, I will say about $9.00. Since, $75.00 is closer to $80.00, I will say about $80.00. When you add $9.00 and $80.00 the movies and a new pair of shoes will cost about $89.00.
Now, that you have estimated the cost, do you have enough money to do both? Students all respond yes. Well let me see just how much you all know. If you all have $100.00 to start, how much will you have left over. I ask student volunteers to demonstrate the steps to figure out how much will be left over. $100.00 take away $89.00 is $11.00. So we will have $11.00 left over. I was curious to know what they were going to do with the $11.00. What can we do with $11.00? They all shouted, "We are going to buy some food."
I go over a couple more problems so that students can gain a bit more confidence in explaining how they got their answers.
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.
MP.4. Model with mathematics.
MP.5. Use appropriate tools strategically.
MP.6. Attend to precision.
MP.7. Look for and make use
In this portion of the lesson I place a word problem on the board for us to discuss and work our way through step-by-step. I encourage students to take notes to help them remember important steps. Cornell Notes
On yesterday, Tom drove 276 miles, today he will drive 184 miles, and tomorrow he plans on driving 56 miles. How many miles will Tom travel in all?
I call on three student volunteers to demonstrate and explain their answer on the board. Each student will get a chance to explain why and how estimation help them understand answer that are reasonable. The first student round all three numbers listed in the word problem. She rounded 276 to 300, 184 to 200, and 56 to 100. Then, she added all three numbers, which gave her a total of 600 miles. After that, she added the original numbers 276+184+56=516.
I ask the class was her final answer reasonable. They all responded yes because it is close to 600.
You see guys this is just another way for you to be sure your answers are correct. The other students explain their answers. I encourage students to ask question if they do not fully understand.
Material: word problems.jpg
I want students to join their assigned groups to explore a little bit more. But most importantly, I want them to discuss how and why it is important to check for reasonableness of their answers. As students work their way through the given word problems, I chime in a time or to reinforce their learning skills. For instance, I ask how can you use rounding to make sure your answer make sense, what steps did you use? explain? Can you use estimate to help you solve other problems? How? can you create your own problem?
I listen to students respond to each question, and I correct any misconceptions right away.