Types of Estimation

Rounding

Rounding is a common method of estimation. When we round a number, we change it to the nearest value of a given place value. For example, if we have the number 47 and round it to the nearest ten, we get 50. Rounding makes numbers easier to work with and helps us quickly estimate calculations.

Front-End Estimation

Front-end estimation involves adding or subtracting the leftmost digits of numbers and ignoring the other digits. For example, to estimate 356 + 278, we can add 300 and 200, giving us an estimate of 500.

Compatible Numbers

Compatible numbers are numbers that are easy to work with mentally. For example, when estimating 78 ÷ 6, we can use 80 ÷ 6 to get a quick estimate of 13.

Steps for Estimation

1. Identify the problem

Understand what needs to be estimated. It could be a calculation, a measurement, or a quantity.

2. Choose an estimation method

Decide which method of estimation would be most appropriate for the problem. This could be rounding, front-end estimation, or using compatible numbers.

3. Perform the estimation

Apply the chosen estimation method to make an educated guess of the answer. Remember, the goal is not to find the exact answer, but to get a close approximation quickly.

4. Check the estimate

After estimating, compare the estimated answer to the actual answer if available. This helps in evaluating the accuracy of the estimation and improves estimation skills over time.

Study Guide for Estimation

Practice Rounding

Practice rounding numbers to the nearest ten, hundred, or thousand. This will help in quickly estimating calculations involving large numbers.

Front-End Estimation Exercises

Try front-end estimation exercises to estimate the sum or difference of numbers. This will improve the ability to quickly assess the approximate value of calculations.

Compatible Numbers Practice

Work with compatible numbers to estimate calculations involving division or multiplication. This will aid in developing a sense of which numbers are easy to work with mentally.

Real-Life Estimation

Apply estimation skills in real-life situations such as estimating the cost of items when shopping, estimating distance or time when traveling, or estimating quantities in recipes. This will help reinforce the practical application of estimation in everyday life.

◂Math Worksheets and Study Guides Seventh Grade. Introduction to Percent

Study Guide

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Work flexibly with fractions, decimals, and percents to solve problems.

Develop meaning for percents greater than 100 and less than 1.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity

Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multi-step problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.

Connections to the Grade 7 Focal Points (NCTM)

Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.

Types of Estimation

Rounding

Front-End Estimation

Compatible Numbers

Steps for Estimation

1. Identify the problem

2. Choose an estimation method

3. Perform the estimation

4. Check the estimate

Study Guide for Estimation

Practice Rounding

Front-End Estimation Exercises

Compatible Numbers Practice

Real-Life Estimation

[Estimation] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Seventh Grade. Introduction to Percent

The resources above cover the following skills: