Benchmarks of 25, 50, and 100
Warm-up
Estimation jar: show a jar with approximately 50 objects. Is this more or less than 25? More or less than 100? About how many? Give students 10 seconds to estimate, then count by making groups of 10. Was your estimate close? What benchmark did you use?
Explore
Benchmark placement: each pair receives 6 number cards (e.g., 17, 34, 51, 68, 82, 95). They place each on a large number line marked with 0, 25, 50, 75, 100 and explain the placement. How do you know 68 is between 50 and 75? It is bigger than 50 but less than 75.
Formalize
Share and compare placements. For each number, ask: is it closer to the lower or upper benchmark? How do you know? 47 is closer to 50 than to 25 because 47 - 25 = 22 but 50 - 47 = 3. Introduce the language: 47 is 3 less than 50.
Benchmarks of 25, 50, and 100
Real-world benchmark challenge: a feast needs seats for 73 people. We have tables for 25 each. Will two tables be enough? (2 x 25 = 50, not enough.) Three tables? (3 x 25 = 75, yes, with 2 spots to spare.) This connects benchmark reasoning to multiplication preview.
Practice
Students estimate 5 quantities using benchmark jars and record which benchmark they used. Place 10 numbers on the benchmark number line. Exit ticket: is 67 closer to 50 or 75? How do you know?
Exit ticket
Students estimate 5 quantities using benchmark jars and record which benchmark they used. Place 10 numbers on the benchmark number line. Exit ticket: is 67 closer to 50 or 75? How do you know?
Step 1: Locate the benchmarks on an open number line: draw 50 and 100 at the ends, and mark the halfway point — 75.
Step 2: Place 68: count up from 50 (past 60, past 65) — it sits left of 75.
Step 3: Reason with the halfway point instead of measuring: 68 is BELOW 75, so it's on the 50-side of halfway → closer to 50.
Step 4: Verify by distance: 68 − 50 = 18 away from 50; 100 − 68 = 32 away from 100. 18 < 32 ✓.
The reusable strategy: find halfway between the benchmarks; the halfway point makes "closer" a one-glance decision.
Step 1: Don't count the jar — scoop out 25 marbles once (count that scoop exactly) and look at how much of the jar it took.
Step 2: Ask: "About how many of these scoops does the whole jar look like?" Suppose it looks like 4 scoops.
Step 3: Count by the benchmark: 25, 50, 75, 100. The jar holds ABOUT 100 marbles.
Step 4: Emphasize the language of estimation: "about," "close to," "between 75 and 100." An estimate of 100 that turns out to be 93 is a GREAT estimate, not a wrong answer.
Why 25 works so well: it's a quarter of 100, so scoops count up in the money-like pattern students already chant (25, 50, 75, 100).
What happened: the student is matching by SIZE OF NUMERAL (two digits ≈ two digits) instead of by distance on the number line.
Step 1: Put 51 on the number line between the benchmarks 0, 25, 50, 75, 100. It lands a whisker past 50.
Step 2: Measure both distances out loud: from 51 to 50 is a hop of 1; from 51 to 100 is a leap of 49. "About" means CLOSE — and 51 is glued to 50.
Step 3: Give the counter-example that breaks the digit rule: 99 and 12 both have two digits. Is 12 "about 100"? Clearly not — so digit-count can't be the test. Distance is.
Step 4: Rebuild the habit: for one week, every estimate must be said as "closer to ___ than to ___ because it's only ___ away."