### Examples

*Example:*The number 6,325 is rounded to 6,300 when rounded to the nearest 100.

*Example:* The number 2,550 is rounded to 3,000 when rounded to the nearest 1,000.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**4

**Strand:**Number Sense and Operations

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Whole Number

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to use place value understanding to explain and reason about rounding. Students should have numerous experiences using a number line and a one hundred chart as tools to support their work with rounding. This benchmark continues instruction of rounding from grade 3, where students rounded numbers from 0 to 1,000 to the nearest 10 or 100 (MA.3.NSO.1.4).- In grade 4, rounding is not a new concept and students need to build on the skills of rounding to the nearest 10 or 100 (MA.3.NSO.1.4) to include larger numbers and place value. What is new for grade 4 is rounding to the nearest 1,000 and to digits other than the leading digit (e.g., round 23,960 to the nearest hundred). This requires more complex thinking than rounding to the nearest ten thousand because the digit in the hundreds place represents 900 and when rounded it becomes 1,000, not just zero. Students should also begin to develop some efficient rules for rounding fluently by building from the basic strategy of - “Is 37 closer to 30 or 40?” Number lines are effective tools for this type of thinking. Students need to generalize the rule for much larger numbers and rounding to values that are not the leading digit.
- Rounding numbers is a skill that helps students estimate reasonable solutions when using the four operations. Instruction of rounding skills should be taught within the context of estimating when using the four operations. Rounding numbers in an expression should be done before performing operations to estimate reasonable sums or differences. Rounding sums, differences, products, and quotients should not be done after students have already performed operations.
- Instruction should not focus on tricks for rounding that do not focus on place value understanding or the use of number lines.

### Common Misconceptions or Errors

- Teaching only rote procedures for rounding may lead to misconceptions about the magnitudes of numbers. Students may need to have a strong foundation of place value concepts before students may find success with rounding.

### Strategies to Support Tiered Instruction

- Instruction includes using number lines and place value understanding to round numbers to the nearest, 10, 100, or 1,000. Instruction provides opportunities to reason about the magnitude of numbers using benchmarks and place value concepts.
- For example, the teacher has students round 3,874 to the nearest thousand using a number line and place value understanding, explaining that the endpoints of the number line will be represented using thousands, because they are rounding to the nearest thousand. Next, the teacher explains that there are 3 thousands in the number 3,874 and one more thousand would be 4 thousands. The teacher then represents these endpoints on the number line as 3 thousands (3,000) and 4 thousands (4,000) with the mid-point labeled as 3 thousand and 5 hundreds (500). This midpoint is halfway between 3,000 and 4,000. Students are asked to plot 3,874 on the number line and discuss if it is closer to 3,000 or 4,000 while the teacher explains that 3,874 rounds to 4,000 because it is greater than the midpoint of 3,500 and closer to 4,000 on the number line.

- For example, students round 283 to the nearest ten using a number line and place value understanding while the teacher explains that the endpoints of the number line will be represented using tens because they are rounding to the nearest ten. The teacher then explains that there are 28 tens in the number 283 and one more ten would be 29 tens, representing these endpoints on the number line as 28 tens (280) and 29 tens (290). The midpoint on the number line can be labeled as 28 tens and 5 ones (285). This midpoint is halfway between 280 and 290. Ask students to plot 283 on the number line and discuss if it is closer to 280 or 290. Explain that 283 rounds to 280 because it is 7 units away from 290 and only 3 units away from 280. It is also less than the midpoint of 285.

### Instructional Tasks

*Instructional Task 1 *

*ten*?

What is the smallest number that rounds to 4,000 to the nearest

*hundred*?

### Instructional Items

*Instructional Item 1*

- a. 5,000
- b. 5,700
- c. 6,000
- d. 6,600

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Educational Game

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## MFAS Formative Assessments

Students are asked to round four numbers to different places and explain their reasoning.

Students are asked to round four numbers to the thousands place and explain their reasoning

## Original Student Tutorials Mathematics - Grades K-5

Learn how to round larger whole numbers to any place value while exploring endangered species in this interactive tutorial.

Note: this tutorial exceeds clarification limits and is meant as enrichment for students who met the standards to increase problem-solving skills.

## Student Resources

## Original Student Tutorial

Learn how to round larger whole numbers to any place value while exploring endangered species in this interactive tutorial.

Note: this tutorial exceeds clarification limits and is meant as enrichment for students who met the standards to increase problem-solving skills.

Type: Original Student Tutorial

## Educational Game

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game