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Examples
The number 37 can be expressed as 3 tens + 7 ones, 2 tens+17 ones or as 37 ones.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Expression
- Equation
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to identify ways that numbers can be written flexibly using decomposition. In Kindergarten, students decomposed numbers from 0 to 10 into two numbers and decomposed numbers from 10 to 20 into a ten and the corresponding ones (MTR.2.1).- Instruction includes the use of base ten manipulatives and place value disks for students to develop a conceptual understanding that 3 tens + 7 ones is the same as 2 tens + 17 ones (MTR.5.1).
- Instruction includes the idea that the equal sign means “same as” and is used to balance equations.
Common Misconceptions or Errors
- Students may not recognize that larger sets of ones can also be seen as tens and ones.
- For example, 15 ones is the same amount as 1 ten + 5 ones. The use of base ten manipulatives can help model for students that 15 ones units is the same as amount at 1 ten + 5 ones though it is arranged differently (MTR.2.1).
Strategies to Support Tiered Instruction
- Instruction provides opportunities to use base ten blocks and a place value chart. Teacher
provides a 2-digit number, like 56, and ask students to exchange one ten for ones. Next,
the teacher asks students to represent the value using a drawing. Then, students are asked
to explain what their new model shows and how it is similar and different from the
original representation of the number. Students share the different representations with
the group and again compare the similarities and differences. Finally, students
name/identify the different ways to name the values (e.g. grouping the tens into the ones,
5 tens and 6 ones, 4 tens and 16 ones, or 3 tens and 26 ones, etc.)
- Example:
- Teacher models using connecting cubes or break-apart base ten blocks. Students practice exchanging tens for ones and a hundred for tens. Students connect ten ones to create a rod, therefore showing that the ten ones are equivalent to one ten. With each exchange, the students represent using both the original representation and the new representation in a drawing on a place value chart. At every opportunity, ask the students to name/identify the values they are using in the numbers.
Instructional Tasks
Instructional Task 1 (MTR.2.1)
- Part A. Look at each equation in the table below. Circle true or false for each expression.
- Part B. Choose one true statement from above and explain how you know it is true. Choose one false statement from above and explain how you know it is false.
Instructional Items
Instructional Item 1
Which of the following are ways to make 43?- 40 tens + 3 ones
- 4 tens + 3 ones
- 30 ones + 13 ones
- 3 tens + 13 ones
- 3 tens + 3 ones
Instructional Item 2
- Using base ten manipulatives or drawings show at least two different ways to make the number 62.
*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
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Ideas
Problem-Solving Task
Tutorial
STEM Lessons - Model Eliciting Activity
Teams of students will use math to solve an open-ended, real-world problem to help their parent or caregiver choose the best babysitter. Students will apply mathematical skills of place value (two-digit number tens and ones) and counting to perform math calculations while analyzing data sets. This MEA will facilitate students demonstrating higher level critical thinking and problem solving during class discussions and in writing.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are asked to decompose two-digit numbers in three different ways.
Students are asked to determine how many tens and ones there are in three different two-digit numbers.
Students examine two different two-digit numbers and describe the number of tens and ones in each number.
Students are asked to use base ten blocks to model numbers and are then asked to identify a number that has been modeled for them.
Students circle objects in bundles of 10, determine how many groups of 10 objects there are, and report the total number of objects.
Students are asked to identify numbers that have been modeled by base ten blocks and model numbers using base ten blocks.
Original Student Tutorials Mathematics - Grades K-5
Help Amari and Sonia build base-ten block towers using their knowledge of 2-digit place value in this interactive tutorial.
This is part 1 of 3. Click below to view the other tutorials in this series.
Explore ways to break apart 2-digit numbers into tens and ones to help Amari and Sonia build base ten block towers in this interactive tutorial.
This is part 2 of 3. Click below to view the other tutorials in this series.
Help Amari, Sonia, and their friends compose and decompose 2-digit numbers in equivalent ways to compete in a base ten block building contest with this interactive tutorial.
This is part 3 of 3. Click below to view the other tutorials in this series.
Help Astronaut Archimedes teach the alien students to show numbers using place value and equations in this interactive tutorial.
Astronaut Archimedes launches into space to teach the outside world all about place value and expanded form in this interactive tutorial.
STEM Civics Tutorials and Videos - Grades K-12
Explore the history of some counting systems and learn why rules are needed, even in math, with this video.
Student Resources
Original Student Tutorials
Help Astronaut Archimedes teach the alien students to show numbers using place value and equations in this interactive tutorial.
Type: Original Student Tutorial
Help Amari, Sonia, and their friends compose and decompose 2-digit numbers in equivalent ways to compete in a base ten block building contest with this interactive tutorial.
This is part 3 of 3. Click below to view the other tutorials in this series.
Type: Original Student Tutorial
Explore ways to break apart 2-digit numbers into tens and ones to help Amari and Sonia build base ten block towers in this interactive tutorial.
This is part 2 of 3. Click below to view the other tutorials in this series.
Type: Original Student Tutorial
Help Amari and Sonia build base-ten block towers using their knowledge of 2-digit place value in this interactive tutorial.
This is part 1 of 3. Click below to view the other tutorials in this series.
Type: Original Student Tutorial
Explore the history of some counting systems and learn why rules are needed, even in math, with this video.
Type: Original Student Tutorial
Astronaut Archimedes launches into space to teach the outside world all about place value and expanded form in this interactive tutorial.
Type: Original Student Tutorial
Tutorial
In this tutorial, you will learn to see 25 as 2 tens and 5 ones.
Type: Tutorial
Parent Resources
Problem-Solving Task
This activity provides a connection between the counting sequence and an experience from students' daily lives. It helps to give the students a sense of how "many" each number is. This task also reinforces many skills related to understanding and representing numbers, such as using tally marks, the word form, expanded form, and place value.
Type: Problem-Solving Task
