# MA.4.NSO.1.1

Express how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left or right.
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

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### Purpose and Instructional Strategies

The purpose of this benchmark is to extend students’ understanding of place value to build a foundation for multiplying and dividing by 10. Students should work with the idea that the tens place is ten times as much as the ones place, and the ones place is $\frac{\text{1}}{\text{10}}$ the size of the tens place. Work in this benchmark builds from student understanding of what happens when they multiply by a multiple of 10 (MA.3.NSO.2.3). Students use these patterns as they generalize place value relationships with decimals in grade 5 (MTR.5.1).
• Throughout instruction, students should practice this concept using place value charts, base-ten blocks and/or digit cards to manipulate and investigate place value relationships.

### Common Misconceptions or Errors

• Students do not understand that when the digit moves to the left that it has increased a place value which is the same thing as multiplying by 10 and when the digit moves to the right that is has decreased a place value, which is the same thing as dividing by 10. It is important to have math discourse throughout instruction about why this is happening.

### Strategies to Support Tiered Instruction

• Instruction includes opportunities to use a place value chart and manipulatives such as base-ten blocks to demonstrate how the value of a digit changes if the digit moves one place to the left or right. Have math discourse throughout instruction about why this is happening.
• For example, the 5 in 543 is 10 times greater than the 5 in 156. Students write 543 and 156 in a place value chart like the one shown below and compare the value of the 5’s (500 and 50) using the place value charts and equations. The teacher explains that the 5 in the hundreds place represents the value 500, which is 10 times greater than the value 50 represented by the 5 in the tens place. Use a place value chart to show this relationship while writing the equation 10 × 50 = 500 to reinforce this relationship. The teacher explains that the 5 in the tens place represents the value 50, which is 10 times less than the value 500 represented by the 5 in the hundreds place. Use a place value chart to show this relationship while writing the equation 500 ÷ 10 = 50 to reinforce this relationship and repeat with other sets of numbers that have one digit in common such as 3,904 and 5,321.

• For example, 10 × 1 = 10 and 10 × 10 = 100. The teacher begins with a ones cube and explains to students that “we are going to model 10 × 1 = 10 using our base-ten blocks.” Students count out 10 ones cubes and exchange them for a ten rod. The teacher explains that the tens rod represents the value 10, which is 10 times greater than the value 1 represented by the ones cube. Write the equation 10 × 1 = 10 to reinforce this relationship and repeat this process to model 10 × 10 = 100. Then, students exchange a hundreds flat for 10 ten rods to model 100 ÷ 10 = 10.The teacher explains that the value represented by a tens rod is 10 times less than the value represented by the hundreds flat and use a place value chart to show this relations hip while writing the equation 100 ÷ 10 = 10. To reinforce this relationship repeat this process to model 10 ÷ 10 = 1.

Paul and his family traveled 528 miles for their summer vacation. Wayne and his family traveled 387 miles for their summer vacation. How much greater is the digit eight in 387 than the digit eight in 528? Have students explain their answer and discuss what role, if any, the other digits play.

### Instructional Items

Instructional Item 1

The clues below describe the 4 digits of a mystery number that contains the digits 3,4,7,8.
• The value of the 8 is 10 times the value of the 8 in 3,518.
• The value of the 7 is 100 times the value of the 7 in 1,273.
• The value of the 4 is 100 times the value of the 4 in 7,284.
• The missing place value is the 3.

What is the number?
• a. 7,483
• b. 8,743
• c. 7,834
• d. 4,738

*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))
5012065: Grade 4 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.1: Explore how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left.

## Related Resources

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

## Formative Assessments

Comparing Amounts of Baseball Cards:

Students are asked to compare the value of the digit three in 35 baseball cards to the value of the digit three in 350 baseball cards.

Type: Formative Assessment

Base Ten Place Value:

Students are given opportunities to explain the relationship between place value and the power of ten in multiplying and dividing.

Type: Formative Assessment

Dylan’s Baseball Card Collection:

Students are asked to find  of 500 and are assessed on the use of their knowledge of the base-ten number system.

Type: Formative Assessment

Seven Hundred Seventy Seven:

Students are asked to consider the number 777 and how each of the digits in the number are related.

Type: Formative Assessment

Family Vacations:

Students are given three-digit numbers in the context of a word problem and are asked to tell how much greater the digit in the tens place is than the digit in the ones place.

Type: Formative Assessment

## Lesson Plans

10X Bigger!:

In this lesson students will move from constructing concrete models of what happens to a number when you multiply the number by 10 into drawing their own pictorial representations of the same process with numbers up to 1,000. They will develop an understanding of the rule 'a digit in one place represents ten times what it represents in the place to its right' and apply this rule to a variety of situations.

Type: Lesson Plan

What's My Value?:

This lesson will allow students to deepen their knowledge in place value. The teacher will use modeling, guided math groups, and independent practice to help students understand that the digit in one place represents ten times what it represents in the place to its right. Students will use base 10 blocks to build numbers and make general observations about the values of numbers. Students will also draw and label models, to make understanding concrete. In groups of 4-5, students will work together and discuss (using discussion questions) to deepen their knowledge on the topic.

Type: Lesson Plan

Terrific Tim’s Ten Tiny Toes:

Students will learn how a digit in one place represents ten times what it represents in the place to its right. Students will model and solve real-world problems on their own and with their friends using word problems, snacks, and their friends' toes!

Type: Lesson Plan

## Original Student Tutorial

The Treasure of Aryabhata: Place Value Comparison:

Help solve mysteries built on patterns of ten to discover the treasure of our number system in this interactive student tutorial.

Type: Original Student Tutorial

## Perspectives Video: Teaching Idea

Estimating Decimal Multiplication:

Unlock an effective teaching strategy for teaching decimal multiplication in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

## Tutorial

How to use an abacus (to represent multi-digit numbers):

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.

Type: Tutorial

## MFAS Formative Assessments

Base Ten Place Value:

Students are given opportunities to explain the relationship between place value and the power of ten in multiplying and dividing.

Comparing Amounts of Baseball Cards:

Students are asked to compare the value of the digit three in 35 baseball cards to the value of the digit three in 350 baseball cards.

Dylan’s Baseball Card Collection:

Students are asked to find  of 500 and are assessed on the use of their knowledge of the base-ten number system.

Family Vacations:

Students are given three-digit numbers in the context of a word problem and are asked to tell how much greater the digit in the tens place is than the digit in the ones place.

Seven Hundred Seventy Seven:

Students are asked to consider the number 777 and how each of the digits in the number are related.

## Original Student Tutorials Mathematics - Grades K-5

The Treasure of Aryabhata: Place Value Comparison:

Help solve mysteries built on patterns of ten to discover the treasure of our number system in this interactive student tutorial.

## Student Resources

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

## Original Student Tutorial

The Treasure of Aryabhata: Place Value Comparison:

Help solve mysteries built on patterns of ten to discover the treasure of our number system in this interactive student tutorial.

Type: Original Student Tutorial

## Tutorial

How to use an abacus (to represent multi-digit numbers):

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.

Type: Tutorial

## Parent Resources

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

## Tutorial

How to use an abacus (to represent multi-digit numbers):

In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.

Type: Tutorial