Lesson: Estimating Differences with Whole Numbers

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Lesson Objective

SWBAT estimate differences of whole numbers by choosing the most reasonable place to round to and then subtracting.

Lesson Plan

 

State Standard:

5.NSO-E.23

Standard Name:

Estimating Differences

Objective:

SWBAT estimate differences of whole numbers by choosing the most reasonable place to round to and then subtracting.

Essential Question:

When are estimating and rounding used in real life situations?

Word Wall Words:

Estimation

Difference

 

Do Now:

Estimate the sum of each problem.

 

  1. 33 + 67 + 41     __________

  2. 987 +123 + 384      __________

  3. 6,102 + 987 +  76   __________

 

Opening:

Remember yesterday we talked about estimating the answers to addition problems to make it easier. Today we are going to continue estimating, but we are going to look at subtraction problems. Remember, in rounding, you are usually given a specific place to round to, like the tenths or the ten-thousands place. However, in estimation, we get to pick where we will round to. We decide this based on what will make the number easiest for me as a mathematician. Today, we are going to estimate differences of subtraction problems.

Direct Instruction:

We started the year 137 pencils. So far we have used 49. About how many do we have left?

 

One way I could solve this is to just write out the numbers and subtract them. However, since the problem is asking us “about,” that word tells me that it is okay to estimate. So what can I do to make this problem easier? Estimate (NOT guesstimate!)

 

Just by looking at my numbers, I see that I am working with 2 different place values here. My first number goes out to the hundreds place, and my second number only goes to the tens place. So I’m going to first try rounding 49 to 50, and then I really have two possibilities for 137. I could either round it to the tens place, which would be 140, or I could round it to the hundreds place, which would be 100. Even though those are both correct estimations, which one is going to give me a more accurate estimation? 140. So, my problem is 140 – 50.

 

Remember, if I wanted to check to make sure this is reasonable, I can actually subtract 137 – 49 which gives me 88 which is very close to my estimated answer of 90.

 

What if I just have a subtraction problem: 542 – 67. I could either do 540-70 or 500-70. Which one is easier but gives me a more accurate answer? 540 – 70. Would both be an estimation? Yes. But I also want my answer to be reasonable. If we actually solve 542-67=475. When I solve both of my estimation problems, the one that gives me an answer closer to 475 is 540-70. So if your ever stuck on which place to estimate to, you can always try both problems and then when you actually solve the problem, see which one is closer. When checking it may take you more time, but it can help you get a more reasonable answer. Eventually your brains will just automatically see which place is the most reasonable to round to.

Guided Practice:

Now let’s see if you can figure out the best estimate for these problems.

 

298 – 43

 

6,798 – 721

 

3,702 – 934

 

What is my first step? (To see what place makes the MOST sense to round to and that will give me a REASONABLE answer)

What place should I round to?

What would I round each number to?

How would I set it up?

What’s the answer?

How could I check it?

 

Independent Practice:

Students will complete a worksheet with 10 subtraction and bonus addition estimation word problems ranging from 1-digit to 4-digit numbers.

Math Journal:

Describe in your journal how you pick the places to round to when your estimating. Then tell me: Why is it important to check if your answer is reasonable?

Closing:

Today we reviewed that the purpose of estimation is to make adding and subtracting bigger numbers or a bunch of numbers easier by choosing the most reasonable place to round to that will make it easier for us as mathmeticians to solve.

Center Options:

  1. Students estimate basic addition and subtraction problems.

  2. Students use front end-rounding to round numbers to designated place values.

  3. Students play “High-Number Toss.” 2 players take turns rolling 2 dice, creating a number, and then each time they get a number they round it to the nearest tens place, and keep adding the numbers together. Each player gets 10 turns, and whoever has the biggest number after 10 turns wins.

Differentiation:

Struggling students should stick with extra practice on front end rounding of whole numbers or can try estimating addition of 1-digit numbers.

 

Advanced students should be given larger digit number to subtract with and when appropriate subtract with 3 numbers instead of 2, starting with the biggest number on top.

Lesson Resources

Estimating Differences Powerpoint   Smart Board
684
Estimating Sums Diffs  
533

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