Estimate...then Calculate

Math Practice Standard #5 includes estimation as an important skill our students should be using regularly.  “Students who can estimate well for computations rely on an understanding of many mathematical topics, including a strong number sense, which facilitates understanding the mathematical operations and contextual evidence within a problem.”  Students build number sense by estimating and it provides them with a way to check their answers for reasonableness (Cochran & Dugger, 2013).

The use of estimation is mentioned directly in several of our content standards.

• 3^rd Grade - Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [3-OA8]
• 4th Grade - Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  [4-OA3]
• 5th Grade - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5-NF2]

It is important that students develop the habit of estimating before calculating.  When they progress to more complex calculations such as 11.2 + 19.75 + 3, having the estimate of 33 (10 + 20 + 3) to reference will help them to quickly determine if an error was made when lining up the numbers. When students multiply and divide fractions and decimals, checking the estimate for reasonableness can eliminate many errors.   For example, in the calculation of 8.75 x 31.3, the ability to see that the answer should be around 270 (9 x 30) can help a student who may have placed the decimal point in the wrong place.  Students should even estimate when solving problems such as 7/8 x 3; 7/8 is close to a whole and 1 whole x 3 is 3.  The answer should be close to 3. 

Please continue to remind your students to estimate before they calculate, and to use the estimate to check answers for reasonableness.  If there is anything I can do to help you with this, please let me know.

Sources:

Cochran, J., & Dugger, M. H. (2013). Taking the Guesswork out of Computational Estimation. The Mathematics Educator, 60-73.