MA.3.NSO.1.4

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.3.NSO.1.3 
• MA.3.NSO.2.1

Terms from the K-12 Glossary

• Number Line 
• Whole Number

Vertical Alignment

Previous Benchmarks

• MA.2.NSO.1.4

Next Benchmarks

• MA.4.NSO.1.4

Purpose and Instructional Strategies

• Instruction of rounding should include place value representations (e.g., base ten blocks) and number lines (both horizontal and vertical) (MTR.2.1). 
• Students should identify benchmarks based on place value to justify rounding. For example, when rounding 643 to the nearest ten, students should use place value to determine that 643 falls between the benchmark tens, 640 and 650. Between 640 and 650, a number line shows that 643 is closer to 640 than 650. When rounding 643 to the nearest hundred, students should use place value to determine that 643 is between the benchmark hundreds, 600 and 700. Between 600 and 700, 643 is closer to 600 than 700 (MTR.2.1, MTR.3.1). 
• During instruction have students practice identifying possible answers and halfway points. In addition to, understanding that, by rule, if a number is exactly at the halfway point of two possible answers, the number is rounded up. For example, students learn the convention that when the value to the right of the rounded place value is 5, they round up to the greater of the two benchmark values. For example, when rounding 765 to the nearest ten, 765 is the same distance between 760 and 770. The rounding convention tells us to round up to 770 (MTR.2.1, MTR.3.1). 
• Rounding numbers is a skill that helps students estimate reasonable solutions when adding or subtracting. Instruction of rounding skills should be taught within the context of estimating while adding or subtracting. Rounding numbers in an expression should be done before performing operations to estimate reasonable sums or differences. Rounding sums and differences 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

• Students can confuse the place value to which they are rounding. For example, students mistakenly round 923 to 900 when rounding to the nearest ten because they observe 2 tens and round to 900, instead of using the ones value of 3 to help them determine that 923 is closest to 920. The use of benchmarks numbers and number lines helps students understand rounding conceptually. 
• Students assume numbers that are already located at benchmarks cannot be rounded. For example, students think that 920 cannot be rounded to the nearest ten. 
• It is imperative for students to develop a conceptual understanding of rounding, such as what the benchmarks are, using place value understanding to round numbers without instruction of mnemonics, rhymes or songs.

Strategies to Support Tiered Instruction

• Instruction includes using number lines, benchmark numbers and place value understanding to round numbers to the nearest ten and hundred. To develop a conceptual understanding of rounding, such as what the benchmarks are, students use place value understanding to round numbers without instruction using mnemonics, rhymes or songs. 
  • For example, students round 439 to the nearest hundred using a number line and place value understanding. The teacher explains that the endpoints of our number line will be represented using hundreds, because we are rounding to the nearest hundred. The teacher then explains that there are 4 hundreds in the number 439 and one more hundred would be 5 hundreds and represents these endpoints on the number line as 4 hundreds (400) and 5 hundreds (500). Next, the teacher explains that the mid-point on the number line can be labeled as 4 hundreds and 5 tens (450). This midpoint is halfway between 400 and 500. The teachers ask students to plot 439 on the number line and discuss if it is closer to 400 or 500. Then, explains that 439 rounds to 400 because it is 61 units away from 500 and only 39 units away from 400. 

• For example, students round 76 to the nearest ten using a number line and place value understanding. The teacher explains that the endpoints of the number line will be represented using tens, because we are rounding to the nearest ten. Then, the teacher explains that there are 7 tens in the number 76 and one more ten would be 8 tens and represents these endpoints on the number line as 7 tens (70) and 8 tens (80). The mid-point on the number line can be labeled as 7 tens and 5 ones (75). This midpoint is halfway between 70 and 80. The teacher asks students to plot 76 on the number line and discuss if it is closer to 70 or 80. Then, explains that 76 rounds to 80 because it is 6 units away from 70 and only 4 units away from 80. Once students master this concept, there should be a discussion about rounding the number 75 where the choice is made to round it up to 80.

Instructional Tasks

Instructional Task 1 

• Part A. Emily is thinking of a mystery number that rounds to 350 when rounded to the nearest ten and 300 when rounded to the nearest hundred. Could Emily’s number be 344? Why or why not? 
• Part B. Give two numbers that could be Emily’s mystery number. Justify your answer using a number line.

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