Before we talk about the seven benchmark numbers, ask your child (grade 5 or above) a simple fraction operation question like what is ½ + ½ (many kids would answer 2/4) or what is ½ of ½ (many kids would answer ‘zero’). If they don’t answer correctly, then it is highly likely their foundation of fractions is shaky. Encountering a student’s problem in fraction operation, many tutors will just teach the steps to solve this operation, without realizing that actually the root of the problem is the student’s basic understanding of fractions. This is because these tutors are not equipped with a comprehensive tool to properly assess a student’s math skills and pinpoint exactly where the problem started.
The Seven Benchmark Numbers
The seven benchmark numbers are: 0, 1, ½, 1/10, 10, 12 and 100. Using this approach is useful to make students – especially beginners – understand the interrelated, basic mathematical ideas. But why these seven numbers?
At Mathnasium, this simple seven number concept is comprehensively used to teach children critical attributes (universal properties) of the number 0, 1, 10, 12, 100, ½ and 1/10 because they can be used as models of all other numbers. This concept is a powerful tool to teach students – especially in primary grades – understand basic math concepts without overburdening them.
This approach enables us to teach the required basic mathematical knowledge in a simple and make-sense way; it is a core curriculum material for primary grades, and also the foundation of a focused remedial program for junior high, and high school.
Below is an example of how we use these benchmark numbers – in this case is to teach basic understanding of fractions.
Mathnasium Teaches for Conceptual Understanding of Fractions
Let this 4th grader show you an example of how benchmark numbers can simplify a math problem. Ignacio was asked to arrange these fractions from smallest to largest: 0, 1, ½, 5/8, 9/10, 2/5.
There are several ways to compare the values of fractions. And if you search ‘how to arrange fractions with different denominators’, most likely you will find that the first step is to make the denominators the same first. This is of course not incorrect, but for younger students, using a smarter way by using benchmark numbers can help solve this problem easily.
Instead of converting all denominators into a common name, or converting it to decimals, there is a quick and simple way to solve this. He measured these fractions against the benchmark numbers of 0, 1 and ½ .. and voilá! He was able to solve it in only a matter of seconds. (Click the picture or click here to watch).
Did you know that a fifth grader’s fraction knowledge predicts their algebra performance in high-school and overall math achievement? This 4th grader is right on track for grade 5 fraction readiness.
Ignacio demonstrates that he is expanding his number sense by growing a sense of fraction as quantity and a sense of the size of a fraction.
Understanding the size and relationship of fractions is necessary before having knowledge of solving fraction operations. Not doing this in a proper sequence could create a hard time for a student when they are in middle and high school. Remember, a fifth grader’s fraction knowledge predicts their algebra performance in high-school and overall math achievement.
Oh by the way, Ignacio can beat AI. Look at the pic below – taken from Microsoft Bing’s AI. Unlike Ignacio, it incorrectly says 5/8 is less than ½!
OK – now, to check your child’s algebra readiness, ask them: is 12/13 + 7/8 closest to 1, 2, 19 or 21?
Related Articles:
