# Estimation to Determine Reasonableness

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### Estimate to Determine Reasonableness:

Estimate to Determine Reasonableness Rounding Front-end Estimation

### I Can …:

I Can … I can round numbers or use front-end estimation to estimate sums or differences and decide if the answer is reasonable.

### When are estimates used?:

When are estimates used? In table groups take 90 seconds to brainstorm and make a list of as many examples or situations that estimates are good enough.

### Checking for Reasonableness :

Checking for Reasonableness Why do you think it would be helpful to find an estimate before you solve a problem? Discuss this in your table group and write down an answer to the question.

### Precise or Just Close:

Precise or Just Close Not all estimates are as precise as others (sometimes we need to get pretty close but at other times we just need to get fairly close) In your table group, come up with an example of a situation that we might need a more precise estimate and a situation that a pretty close estimate will be good enough.

### Rounding:

Rounding Rounding uses “nice numbers”, which are easy to compute. How precise we need to be determines what place we will round to: 10, 100, 1000, etc. Empty Number Line: a number line without any numbers written on it until you decide what to put on it.

### Using the ENL to Round:

Using the ENL to Round Draw an ENL on your paper Use your ENL to round 74 to the nearest 10

### Using Rounding to Determine Reasonableness:

Using Rounding to Determine Reasonableness Let’s learn how to estimate to find the “reasonable” answer before we try to solve the problem. Eva’s Market sold 196 jars of grape jelly in September. In October, the market sold 389 jars. How many jars of grape jelly did they sell over the two months? In your table group find the estimate first by rounding the number of jars sold in September and the number of jars sold in October and adding the two together. Discuss if you think the “actual” answer will be more or less. Why?

### Comparing our Estimate to the Actual Answer:

Comparing our Estimate to the Actual Answer Now find the actual answer: 196 + 389 = j How close was the estimate? Is your actual answer reasonable (close to the estimate?

### Using Estimation for Subtraction Problems:

Using Estimation for Subtraction Problems Eva made \$786 selling her grape jelly. The materials for making jelly cost \$453. How much money did Eva have left after paying for the materials? In this problem we know how much in all she made selling her jelly and we know that the materials cost her some money so she won’t get to keep it all. We need to find how much money Eva gets to keep. We will find this by subtracting the cost of the materials from what she made selling her jelly.

### Estimate and then solve the problem:

Estimate and then solve the problem First estimate the difference 786 – 453 = p Is your estimate the same as your neighbors? Why or why not? Now let’s find the actual difference. Was your estimate close?

### Front-End Estimation:

Front-End Estimation Front-end estimation is really fun and easy too. We just look at the first digit of each number. Our estimate might not be as close as when we round

### Using Front-End Estimation:

Using Front-End Estimation 7,840 – 3,622 = n 7,000 – 3,000 = n The estimated difference is 4,000. Let’s now solve to find the actual difference. 7840 – 3622 = n