# MA.4.NSO.1.3

Plot, order and compare multi-digit whole numbers up to 1,000,000.

### Examples

The numbers 75,421; 74,241 and 74,521 can be arranged in ascending order as 74,241; 74,521 and 75,421.

### Clarifications

Clarification 1: When comparing numbers, instruction includes using an appropriately scaled number line and using place values of the hundred thousands, ten thousands, thousands, hundreds, tens and ones digits.

Clarification 2: Scaled number lines must be provided and can be a representation of any range of numbers.

Clarification 3: Within this benchmark, the expectation is to use symbols (<, > or =).

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations
Status: State Board Approved

## Benchmark Instructional Guide

• Whole Number

### Vertical Alignment

Previous Benchmarks

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### Purpose and Instructional Strategies

The purpose of this benchmark extends up to 1,000,000 the work from grade 3 of plotting, ordering, and comparing numbers using place value up to 10,000.
• Place value strategies should be used to compare numbers.
• For example, in comparing 65,570 and 65,192, a student might say both numbers have the same value of 10,000s and the same value of 1000s; however, the value in the 100s place is different so that is where the comparison of the two numbers would be determined.
• Students need opportunities to compare numbers in various situations to build procedural fluency and to compare numbers with the same number of digits, numbers that have the same number in the leading digit position, and numbers that have different numbers of digits and different leading digits (e.g., compare the four numbers) (MTR.5.1).
• As stated in MA.3.NSO.1.3, it is important for teachers to define the meaning of the ≠ symbol through instruction. It is recommended that students use = and ≠ symbols first. Once students have determined that numbers are not equal, then they can determine “how” they are not equal, with the understanding now the number is either < or >. If students cannot determine if amounts are ≠ or = then they will struggle with < or >. This will build an understanding of statements of inequality and help students determine differences between inequalities and equations.

### Common Misconceptions or Errors

• Students often assume that the first digit of a multi-digit number indicates the size of a number. The assumption is made that 864 is greater than 2,001 because students are focusing on the leading digit instead of the place values of the number.

### Strategies to Support Tiered Instruction

• Instruction includes the use of a number line, models such as place value disks, place value charts, and relational symbols to compare numbers that have a different amount of digits.
• For example, when comparing 789 and 1,202 the teacher labels the endpoints of the number line 0 and 2,000 and the midpoint of 1,000. The teacher asks students to place 789 and 1,202 on the number line and discusses the placement of the numbers and distance from zero, using the number line to show that 789 is closer to zero than 1,202 so 789 < 1,202. Also, the teacher uses the number line to show that 1,202 is farther from zero so 1,202 > 789. The teacher explains that 789 and 1,202 are different points on the number line so 789 ≠ 1,202, asking students to identify numbers that are greater than... and less than.... The teacher repeats with numbers that have a different amount of digits (number line endpoints of 0 and 100,000 marked with multiples 10,000) and discusses the placement of the other numbers on the number line and if their values are greater than or less than other numbers.

• For example, when comparing 1,123 and 954, students represent 1,123 and 954 using place value disks and a place value chart. The teacher asks students to compare these numbers, beginning with the greatest place value, explaining that the number 1,123 has 1 thousands and the number 954 does not have any thousands so 954 < 1,123 and 1,123 > 954. Additionally, the teacher explains that because 954 and 1,123 do not have the same values in the thousands place that 954 ≠ 1,123.

• Students will create numbers that meet specific criteria through this performative task. Provide students with cards numbered 0 through 9. Ask students to select 4 to 6 cards, then using all the cards make the largest number possible with all cards, the smallest number possible, the closest number to 6,000, a number that is greater than 6,000, or a number that is less than 6,000, etc. Then discussions with the students about the numbers will solidify their understanding.

### Instructional Items

Instructional Item 1

Which number correctly completes this inequality?
_________ < 44,038

• a. 40,000+600+30+7
• b. 40,000+5,000+30+7
• c. Forty − four thousand, nine hundred fifty
• d. Forty − Four thousand, one hundred twelve

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

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.NSO.1.AP.3: Plot, order and compare multi-digit whole numbers up to 10,000.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Collections:

Students are asked to compare two numbers in the context of a word problem and write an inequality statement showing the relationship between the numbers.

Type: Formative Assessment

Using Word and Expanded Form:

Students compare two numbers, one given in word form and the other given in expanded form.

Type: Formative Assessment

## Lesson Plans

Population Parity Lesson 2:

Students will plot the populations of Florida counties within two congressional districts in ascending order on a number line in this civics integrated math lesson.

Type: Lesson Plan

Order in the School Zone:

Students will learn about school zones, calculate enrollment for a school that is “overcrowded”, and discuss ideas for rezoning to balance enrollments by looking at vacancies in other schools in this integrated lesson plan.

Type: Lesson Plan

Population Parity:

In this integrated lesson plan, students will engage in discussion about a representative government in Florida. They will compare the Florida county map and the Florida Congressional map to predict the fairness of representation and consider why the representation in the district map doesn't match the Congressional map. They will investigate this question by comparing the population size in the counties of each district.

Type: Lesson Plan

My Digit is Bigger than Your Digit! Comparing Multi-digit Numbers:

In this lesson, the students will explore place value using manipulatives to help them compare multi-digit numbers in the context of the book A Million Dots by Andrew Clements.

Type: Lesson Plan

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

Type: Lesson Plan

The Street Where Place Value Lives:

Students will apply their place value knowledge to connect place value to the millions by relating it to their communities. Students can discuss and write about place value, using their connections.

Type: Lesson Plan

Oh Where, Oh Where, Should I Put You?:

This highly engaging game is played after the unit on place value has been taught. It is designed to allow the student to think about the placement of a number before writing it down, in order to write the largest and/or smallest number.

Type: Lesson Plan

## Original Student Tutorial

Who's Top Dog, Now? Comparing Numbers:

Learn how to compare numbers using the greater than and less than symbols in this interactive tutorial that compares some pretty cool things!

Type: Original Student Tutorial

## STEM Lessons - Model Eliciting Activity

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

## MFAS Formative Assessments

Collections:

Students are asked to compare two numbers in the context of a word problem and write an inequality statement showing the relationship between the numbers.

Using Word and Expanded Form:

Students compare two numbers, one given in word form and the other given in expanded form.

## Original Student Tutorials Mathematics - Grades K-5

Who's Top Dog, Now? Comparing Numbers:

Learn how to compare numbers using the greater than and less than symbols in this interactive tutorial that compares some pretty cool things!

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Who's Top Dog, Now? Comparing Numbers:

Learn how to compare numbers using the greater than and less than symbols in this interactive tutorial that compares some pretty cool things!

Type: Original Student Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.