# Front-End Estimation of Products and Quotients Worksheets

Front-end estimation is the first of two or more steps in these problems. These are common types of problems that you will tackle when you are planning to break things into groups or prepare to have enough supplies for something. When you are planning a large scale of any kind, you will most likely work with these skills to get an idea of what you are getting yourself into. It all starts with estimating the front-end dividend of the quotient or the multiplicand. From there it is a straight up product or quotient with much easier values to work with. A collection of lessons and worksheets to help students quickly gauge an appropriate answer for multiplication and division problems.

### Aligned Standard: 3.OA.D.8

- Step-by-Step Lesson- We cover both skills and tell you to load it up front.
- Guided Lesson - It's time for a barbecue and to find out how much you owe for your wonderful meal.
- Guided Lesson Explanation - It's a process: round them, count how many you need, and let the operations finish it up for you.
- Estimating Products Practice Worksheet - The focus here is on multiplication. You will find plenty of division below in the member's resource section.
- Estimating In Action Worksheet 2 - School store price list, we meet again!

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

We start with quotients, back to products, and a final skill solver.

- Homework 1 - Round the values to their nearest tens place.
- Homework 2 - Find each product. Then use rounding to check that your answers are reasonable. (Round the 3 digit number to the nearest hundred)
- Homework 3 - If Cindy wanted 5 slices of pizza or 4 hamburgers, which one would be cheaper? Estimate to find the answer.

### Practice Worksheets

Lollipop work, a little more multiplication work, and a snack bar order for you.

- Practice 1 - Here is a chart of lollipops and how many students liked each flavor and how many disliked each flavor.
- Practice 2 - Multiply the cost of the items by the multiples needed for each item.
- Practice 3 - The best way to approach these is convert the values to the same place value.

### Math Skill Quizzes

Straight division work and the classroom supply list makes another appearance.

- Quiz 1 - This quiz will help you see where you are at with this skill.
- Quiz 2 - If there are 8 children in the classroom, how many boxes of crayons does each child get? Round the crayons to the nearest tens.

### How to Get a Rough Estimate of Multiplication and Division

There are going to be many times in your life when you do not need an exact answer, just an educated guess. These quick forms of estimation allow us to make quick educated decisions in our everyday world. For example, just last night this skill helped me get my swimmers home quickly. I am a swimming coach I had to transport 120 swimmers to a swim meet and back home. Knowing that each bus could hold 35 students, I quickly realized that we needed 4 buses (120 ÷ 35 = less than 4). This is a simple example of a quick and very useful form of division estimation.

If an accurate answer is not desired; however, producing a quick answer is the key while solving more complex multiplication questions; one should try to get an estimate instead of a precise value. There are situations like a college aptitude test where you have to solve a hundred such questions in a very limited time and keeping up with the deadline is more important than producing an accurate answer. For such situations, one can always practice on getting a rough estimate for a multiplication sum.

Getting a rough estimate of the answer to a multiplication sum is a step-by-step process. For example, if you need to multiply 159 by 72 and get an estimate of the answer, round off both the numbers and multiply them. It gets easier this way. In this case, 160 x 70 can give you an estimate but a quicker answer than multiplying 159 by 72.

In the case of decimal multiplication like multiplying 25 by 3.90, break the decimal number into 3, the numeral part, and 90, the decimal part. Then multiply 25 by 3, which is relatively a lot easier, and then multiply 25 by 90 and shift the decimal two places leftwards in whatever the answer you get. The reason for shifting the decimal point is that 90 was the double-digit decimal part. Hence, we shift the decimal point two places to the left.

After getting both the answers, we add them to get the final answer. Here is a solution to the example, as mentioned above.

25 x 3.90 => 25 x 3 = 75, 25 x 90 = 2250, 2250 -> 22.50, 75 + 22.50 = 97.50