Benchmark Numbers to 100

A benchmark number is a friendly, easy-to-picture value that you use as a landmark when counting, comparing, or estimating other numbers. When you are working with numbers up to 100, the most useful benchmark numbers are \(10\), \(25\), \(50\), \(75\), and \(100\). These numbers are spaced evenly and are easy to recognize, so they give you a quick sense of "about how much" or "about how far" a number is without counting one by one.

Before learning about benchmarks, it helps to already be comfortable counting to 100 with numbers, since benchmarks are really just special stopping points along that same count.

A benchmark number line stretches from \(0\) to \(100\) with the benchmark numbers marked clearly along the way. Instead of labeling every single number, you only highlight \(0\), \(25\), \(50\), \(75\), and \(100\). These marked points break the line into four equal sections, each worth \(25\), which makes it much faster to figure out where any other number belongs.

Look at how \(63\) is placed on the line above. Since \(63\) is between the benchmarks \(50\) and \(75\), and closer to \(50\), you immediately know that \(63\) is a little more than halfway from \(50\) toward \(75\). You did not need to count every number from \(0\); the benchmark numbers on a number line did the work for you.

Benchmark numbers are especially useful for two skills: estimating and comparing.

Estimating: if you have a pile of counters and you are not sure of the exact amount, you can ask, "Is this closer to \(25\), \(50\), or \(75\)?" If it looks like a bit more than \(50\), you can estimate the total is around \(60\) without counting each piece. This works well alongside counting to 100 with visual aids, where groups of objects are often arranged in tens and fives that match up nicely with benchmark numbers.

Comparing: benchmarks also help you compare two numbers quickly. For example, to compare \(38\) and \(54\), notice that \(38\) sits just below the benchmark \(50\), while \(54\) sits just above it. Since \(54\) is past \(50\) and \(38\) is not, you know right away that \(54\) is greater than \(38\), even before lining up the digits.

Suppose you want to round \(82\) to the nearest benchmark number.

1. Find the benchmarks on either side of \(82\): they are \(75\) and \(100\).
2. Find the halfway point between them: \(\frac{75 + 100}{2} = 87.5\).
3. Since \(82\) is less than \(87.5\), it is closer to \(75\) than to \(100\).
4. So \(82\) rounds to the benchmark \(75\).

This kind of quick rounding is handy for mental math, such as estimating a total before adding or subtracting exactly.

Benchmark numbers connect naturally to skip counting by 2s, 5s, and 10s. If you skip count by \(25\) starting at \(0\), you land exactly on \(0\), \(25\), \(50\), \(75\), and \(100\), which are the benchmark numbers themselves. Skip counting by \(10\) or \(5\) lands on many more stops, but the benchmark numbers still appear along the way as extra-important checkpoints.

• Memorize the five main benchmarks to 100: \(0\), \(25\), \(50\), \(75\), and \(100\).
• When placing a new number, first decide which two benchmarks it falls between.
• Ask whether the number is closer to the lower or upper benchmark before estimating further.
• Use benchmarks to check whether an answer "makes sense" after adding or subtracting.

Related lessons

• Math 2