We all know that mathematics is often about finding the precise answer to a question, or the exact calculations we use along the way. However, math also
involves approximations that can make our lives a lot easier when we are faced with real-world problems. Young math students in grade 5 are introduced to the concept of approximate value, a vital skill that will help them estimate values and work with numbers more quickly and effectively.
Let’s take a closer look at the topic of approximation, including exciting subjects such as rounding and estimating, and see how these skills can be applied to the real-world problems students will encounter both in the classroom and beyond.
What does Approximate Value mean?
In mathematics, the process of approximation is the process of finding a value that is close enough to the actual value for it to be accurate, but this approximation is not necessarily exact. We approximate by rounding off numbers to make our complex calculations easier without losing a significant level of accuracy. The approximate value is a valuable tool in various real-life situations, and approximations can be seen every day when we are shopping, cooking, budgeting, and in many other situations where calculating the exact values are not always necessary.
When approximating, one of the fundamental aspects involved is rounding numbers. Rounding simply means reducing a number to the nearest ten, hundred, or any other specific place value. In grade 5, math learners will typically work with whole numbers and decimals, and we can see some of the most common examples below.
Rounding whole numbers
Let’s imagine we have the number 437. If we want to round this number to the nearest ten, we take a closer look at the final digit in the whole number (known as the ones digit), or the final number before the decimal point, when dealing with a decimal. In our example, 437, that number is 7.
Since 7 is greater than or equal to 5, we round up the tens digit, giving us the number 440. If we want to round to the nearest hundred, the tens digit (3) remains unchanged, and the hundreds digit (4) gets followed by two zeroes, giving us the answer 400.
Now, let’s imagine the number 3.78. If we want to round it to the nearest tenth, we look at the digit in the hundredth place, which in our case is 8. Once again, because 8 is greater than 5, we round up, giving us 3.8. To round to the nearest whole number, we look at the tenth place, which is 7, and round up to get to the whole number 4.
Estimating addition and subtraction
Let’s say we want to find the sum of 238 and 495. As opposed to adding the numbers exactly, we can simply use estimation. First, we round 238 to the nearest ten, giving us 240; then, we round 495 to 500. Now, we can quickly add 240 and 500 together to get an approximate sum of 740.
When we do the detailed addition, we get 238 + 495 = 733, which is quite close to our estimated answer, 740.
Estimating multiplication and division
Just like addition and subtraction, we can estimate using multiplication and division. Let’s consider the problem 24 x 36. To estimate, we first round 24 to 20 and then 36 to 40. Now, we can perform this multiplication in our heads. 20 x 40 = 800. This is an approximate value, but it helps us get a rough idea of the actual answer.
Similarly, if we divide, we can round the numbers and perform the operation mentally for a quick and approximate of our desired answer.
Significance of Approximate Value
We’ve seen how quickly we can approximate the values of math problems. This ability is a valuable skill for 5th grade students for several reasons:
Quick Mental Arithmetic
Approximation helps math students calculate much faster in their heads. This is a key skill in everyday life, and the ability to approximate values quickly in your head will help you estimate the cost of your groceries, or the time a particular journey may take depending on the different routes available.
Approximation is an invaluable ability when you need to cross-check the accuracy of calculated answers. If an estimated value is completely different from the exact value, there has likely been a mistake. At this point, students must review their calculations and identify potential errors.
Confidence in Math Skills
Perhaps most importantly, the ability to approximate values proficiently will generate a boost in confidence for students. Confidently handings numbers and operations will push students beyond their current abilities and give them the foundation to push on and grasp even more complex concepts when they arise in the coming years.
At OMC, we offer a wide variety of math tutoring classes, highly-tailored one-to-one classes, and specific preparation classes for the Math SAT and math competitions. Our classes are individually designed according to your child’s needs, and we focus lessons on targeting specific grade lessons to plug gaps in their knowledge and help them get ahead of their peers.