# Estimation

## What is Estimation?

Estimation is the process of making a rough guess as to the value, number, quantity, or extent of something, usually for the purposes of quick, everyday problem solving or determining if an answer is reasonable. It is a higher-level thinking skill, requiring students to both conceptualize numbers and mentally manipulate them fairly quickly.

Because most other mathematical activities require a correct answer, estimation can be a challenging concept for young children. It is helpful to explain that when we estimate we are looking for a number that is close enough to the answer and that this is most useful in situations when “good enough” is ok.

## Language

When teaching estimation, the following vocabulary will be beneficial to ensure learners are able to grasp the basic concept:

- Exact
- Guess
- Reasonable
- Rounding

Ask students to be on the lookout for places where people ask them (or they ask others) to estimate. Some hints to get them started might be:

- How much longer is the trip going to take?
- How long until we get home?
- How much homework do I have to do before I can stop?
- How much pizza does everyone want to eat?
- How much soda should we buy for the weekend?
- How much do you have left to watch?
- How much do you think the bill will be?
- What time will it be when you finish work?

## Three Methods of Teaching Estimation

Different types of problems require different types of estimation, which is another reason why this executive functioning skill can be challenging for young learners. The three most common methods are the rounding method, the front-end method, and the clustering method.

## Rounding Method

- the most commonly-used for estimating activities
- students must be able to understand place-value to utilize this method
- after choosing the digit you want to round to (for example, if working with money, one may round to the tens place), round up by one if the digit to the right of the digit being rounded to is five or larger, round down by one if the digit is four or less
- Example: $327 rounded to the nearest tens place is estimated to be $330 because the digit to the right is 7. 7 > 5 therefore we add 1 to the tens column
- This method is good for quick adding, subtracting, multiplying, and dividing

## Front-End Method

While there are different interpretations of this method, the general idea is to discard all the digits other than the left most digit. This allows for quick estimates of large numbers. It makes more sense to use when the numbers have the same amount of digits.

- Retain the first digit and insert zeros for the other place values
- Example: 1565 + 9011 can become 1000 + 9000 or 10,000

## Clustering Method

- Useful when the numbers being added or multiplied are all relatively close in value to one single number that ends in zero
- Example: 49 + 53 + 47 + 48 + 55. All the numbers cluster around 50. Substitute 50 for each number and the problem becomes 50 + 50 + 50 + 50 + 50 = 150.

## Activities

Here are some great ways to encourage your students to have fun with estimation:

- Have students “go shopping” using newspaper circulars or online. Give them a set amount of money but don’t let them use calculators or write down exact amounts.
- Provide a snack for the class that need to be divided (i.e. Goldfish crackers, M & M’s, etc.). Inform them they must be passed out, but they only have a short amount of time to do so (not enough time to count everything evenly).
- Allow them to plan an event like a party, and create a shopping list based on how many people “might” come. Discuss how they plan for what happens if too few or too many people show up.
- Create estimation jars. Fill equal sized jars with various items and ask students to guess which jar has “10,” “50,” or “100” items.
- Bring in a large container and ask children to guess how many of an item (pebbles, tennis balls, etc.) it will take to fill the container.
- Give children string. Ask them to cut a piece that is as long as they are tall without measuring.
- Have children guess how long it would take to walk, drive, or fly from your location to various points around the country (or world!) then use Google Maps to check their answers