Grade 4 (age 9-10)

grade 4 Estimation — Number Range

Estimation and Number Range

Estimation turns a large number into a nearby one that is easier to handle. The place you round at decides whether you round up, to the nearest, or down. At least and at most include the boundary number; greater than and less than leave it out, as on age limits and price tables. Slide along the number line and the rounded value and the range land on their marks.

Rounding to a Place Value

🔍 Round to which place?

①Round to tens: 3746 → 3750

②Round to hundreds: 3746 → 3700

③Result changes with the rounding place

④Ceiling always goes up if anything remains; flooring writes 0 in the lower digits. That is not the same as the "round up" branch inside rounding

Number3746

Round tohundreds

At Least/At Most/Greater/Less

Reference number50

💡 Inclusion is Key!

①≥, ≤: include the reference (●)

②>, <: exclude the reference (○)

③Distinguish ≥ from >, ≤ from <

Summary

At Least / At Most

x ≥ 50 = 50, 51, 52, ... (50 included)

Includes the reference and all numbers in that direction

Greater / Less Than

x > 50 = 51, 52, 53, ... (50 excluded)

Excludes the reference, all numbers in that direction

Range of Numbers

30 ≤ x < 50

30 included, 50 excluded

🎯 Key Points

①≥, ≤ → includes the reference (filled ●)

②>, < → excludes the reference (open ○)

③Result depends on rounding place

④Ranges can be drawn on a number line

⑤Tests often ask you to distinguish ≥ from >

Examples and Unit Test

Example 1

What is 3746 rounded to the tens place?

To round to tens, look at the digit just below, the ones digit, which is 6.

6 is 5 or more, so round up to 3750.

▸ 3750

If the digit just below the rounding place is 5 or more, round up; if less, round down.

Example 2

Does "x ≥ 50" (at least 50) include 50 itself?

"At least" (≥) includes the reference number.

So x ≥ 50 includes 50, as well as 51, 52, and so on.

▸ Yes (≥ 50 includes 50)

"≥, ≤" include the reference; ">, <" exclude it.

Unit Test

Which number falls in the range "30 ≤ x < 50"?

①28

②50

③45

④52

▸ ③ 45

30 ≤ x includes 30; x < 50 excludes 50. So 30 ≤ x < 50.

28 is below 30, and 50 and 52 are out of range. Only 45 fits 30 ≤ x < 50.

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Order of Operations

Angles