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The number 241 can be expressed as 2 hundreds + 4 tens + 1 one or as 24 tens + 1 one or as 241 ones.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Equal sign
- Expression
- Equation
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to extend the understanding of place value from grade 1 to include three-digit numbers and help students to identify ways numbers can be renamed flexibly using composition and decomposition (MTR.2.1).- Instruction includes the use of base ten manipulatives and place value disks.
- Instruction includes the understanding that 100 can be thought of as a bundle of ten tens – called a “hundred.”
- Instruction includes the idea that the equal sign means “same as” and is used to balance equations.
Common Misconceptions or Errors
- Students may think that because the grouping of the digits changes the value also changes.
- For example, 879 is the same as 87 tens + 9 ones or 8 hundreds+ 79 ones.
- Students may think that numbers that contain a zero in a place means that the number cannot be decomposed using that place.
- For example, 205 has 0 tens but can also be decomposed into 20 tens and 5 ones.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to use base ten blocks and a place value chart with a 3-digit number. Teacher provides opportunities to allow students to exchange or decompose blocks to other place values.
- For example, teacher asks students to represent the value using a drawing. Students are asked to explain what they now have and how it is similar and different from the original representation of the number. Repeat this process with exchanging hundreds and tens. Teacher has students share the different representations with the group and again compare the similarities and differences. Students are asked to name/identify the different ways to name the values (grouping the hundreds into tens and the tens into the ones, e.g., 32 tens and 6 ones or 3 hundreds and 26 ones, etc.)
- For example, teacher asks students to represent the number 326 using base ten blocks or a drawing in their place value chart. Teacher asks students to exchange one ten into ones. Students are asked to explain what they now have and how it is similar and different from the original representation of the number. Repeat this process with exchanging hundreds and tens. Teacher has students share the different representations with the group and again compare the similarities and differences. Students are asked to name/identify the different ways to name the values (grouping the hundreds into tens and the tens into the ones, e.g., 32 tens and 6 ones or 3 hundreds and 26 ones, etc.) Utilize sentence stems for students to complete with each decomposition using: ___ hundreds + ___ tens + ___ ones.
- Instruction includes opportunities to use base ten blocks to practice exchanging tens for ones and hundreds for tens. With each exchange, teacher has students represent using both the original representation and the new representation in a drawing on a place value chart. At every opportunity teacher asks students to name/identify the values they are using in the numbers.
- Example:
Instructional Tasks
Instructional Task 1 (MTR.2.1)
The number 317 can be expressed as 3 hundreds + 1 ten + 7 ones or as 31 tens + 7 ones. Explain using objects or drawings how both expressions equal 317.
Instructional Task 2 (MTR.3.1)
Use a place value model to show how the number 134 can be represented as 13 tens and 4 ones.
Instructional Items
Instructional Item 1
Express the number 783 using only hundreds and ones.
Instructional Item 2
Express the number 783 in multiple ways using only tens and ones.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
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Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Worksheet
MFAS Formative Assessments
Students are asked to write numbers given descriptions of the number of hundreds, tens, and ones each contains.
Students are asked to describe the number of hundreds, tens, and ones in four different three-digit numbers.
Students use base ten blocks to model each of four numbers and then describe the number of hundreds, tens, and ones in each number.
Students are asked to compare ten tens to one hundred and justify their comparisons.
Original Student Tutorials Mathematics - Grades K-5
Explore the Base 10 place value system with 3-digit numbers in Bianca's Bubble Gum Factory with this interactive tutorial.
Student Resources
Original Student Tutorial
Explore the Base 10 place value system with 3-digit numbers in Bianca's Bubble Gum Factory with this interactive tutorial.
Type: Original Student Tutorial
Problem-Solving Tasks
The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.
Type: Problem-Solving Task
The purpose of this task is for students to use currency to help better understand place value.
Type: Problem-Solving Task
This tasks uses school supplies in a problem to help students gain a better understanding of place value.
Type: Problem-Solving Task
This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.
Type: Problem-Solving Task
The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred. Second graders should have been given opportunities to work with objects and pictures that represent the grouping structure of the base-ten number system, which would help prepare them for doing this task.
Type: Problem-Solving Task
Students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Student must, in some cases, decompose hundreds to tens and tens to ones. The order of the summands does not always correspond to the place value, making these problems less routine than they might seem at first glance.
Type: Problem-Solving Task
This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers. Some students might need to write the equivalent numeral as an intermediate step to solving the problem.
Type: Problem-Solving Task
This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps. If students do not recall this fact readily, one way to review it is to have them draw a strip of ten stamps on graph paper (so they don't have to draw all the individual stamps) and then draw ten strips that are side-by-side to represent a sheet and ask how many stamps there are in one sheet.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Tasks
The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.
Type: Problem-Solving Task
The purpose of this task is for students to use currency to help better understand place value.
Type: Problem-Solving Task
This tasks uses school supplies in a problem to help students gain a better understanding of place value.
Type: Problem-Solving Task
This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.
Type: Problem-Solving Task
The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred. Second graders should have been given opportunities to work with objects and pictures that represent the grouping structure of the base-ten number system, which would help prepare them for doing this task.
Type: Problem-Solving Task
Students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Student must, in some cases, decompose hundreds to tens and tens to ones. The order of the summands does not always correspond to the place value, making these problems less routine than they might seem at first glance.
Type: Problem-Solving Task
This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers. Some students might need to write the equivalent numeral as an intermediate step to solving the problem.
Type: Problem-Solving Task
This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps. If students do not recall this fact readily, one way to review it is to have them draw a strip of ten stamps on graph paper (so they don't have to draw all the individual stamps) and then draw ten strips that are side-by-side to represent a sheet and ask how many stamps there are in one sheet.
Type: Problem-Solving Task
