SWBAT use ballpark estimates to check the work of an imaginary student

Estimation can tell us if we are close in our answers to math problems. If we take the time to use it, we can see if our answer is in the right ballpark.

10 minutes

Today I begin with a quick review of rounding and estimating. I have taught students in the past that numbers ending in zero are smiley face numbers because they are easy to add and subtract and make us happy. We also refer the them as ball numbers because the zero is the shape of a ball and I can throw the ball and keep it in the ball park. I have used both explanations to help students get the idea that numbers ending in zero are easy to use and they help us to see if our answers are at least close to being correct.

I ask students to find the nearest ball or smiley number to each of the numbers I say. They write down the numbers in their math journals. I start with five 2-digit numbers: 11, 57, 72, 98, and 35. I write the numbers on the board and then ask students to volunteer to come up and write the ballpark numbers next to each one. I ask students to check their work.

Now I dictate five 3-digit numbers. I say 346, 108, 877, 249 and 999. I ask students to think of the nearest ballpark (smiley face) number that ends in zero (we are rounding to the tens place). Again we write and check our answers.

As a challenge, if most students have been successful so far, I give the numbers 4,592 and 13,687. I ask if they can make these numbers into a ball park or smiley face number that ends in zero. I have a volunteer come up and write the new numbers 4,590 and 13,690 on the board.

I ask students to tell me why we might use these numbers instead of the actual numbers. We discuss why estimating might help us and I reintroduce the term estimation.

20 minutes

Today I have created a mock student work sample. Some of my answers are correct and some contain mistakes that students often make such as adding instead of subtracting (or visa versa), writing the ones and tens answers next to each other instead of regrouping (e.g. 28 + 16 = 314), mixing ones and tens, or forgetting to borrow.

I ask students to use estimation to see if the answers are correct, and then to make corrections to any problems that they think are wrong. I want students to make sense of the problems based on what they know and then solve those that are incorrect (MP1). I give students about 15 minutes to work on the problems and make the corrections. Then I bring students to the rug with their papers. We first share our ballpark answers for each problem. Next we look at the problems and try to agree on whether an answer on the paper is right or wrong and how they know.

Students take turns showing their work and how they determined the correct answer for any problems that did not seem to be correct, or in the ballpark.

10 minutes

I end the lesson by asking students to write in their journals to the following prompt: How can estimating help me when I try to solve a problem in math? I am asking student to think about how they understand math here. I want them to be able to reason abstractly and quantitatively about math and how they understand it. (MP2). If they can verbalize how estimation can help them, they will be more likely to use it as a strategy in the future.