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Examples
Example: The sum 41+23 can be found by using a number line and “jumping up” by two tens and then by three ones to “land” at 64.Example: The difference 87-25 can be found by subtracting 20 from 80 to get 60 and then 5 from 7 to get 2. Then add 60 and 2 to obtain 62.
Clarifications
Clarification 1: Instruction focuses on helping a student choose a method they can use reliably.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Equation
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to develop and use reliable methods to add or subtract within 100. Students in grade 1 worked in the exploration stage which heavily relied on the use of manipulatives and drawings.- Instruction includes the understanding that when adding it is sometimes necessary to combine ones and compose a new ten from those ones.
- Instruction includes the understanding that when subtracting it is sometimes necessary to decompose tens and regroup ones.
- Instruction includes using the relationship between addition and subtraction to find differences.
- Instruction includes strategies that support decomposing and composing numbers in multiple ways (MTR.2.1).
- It is not the expectation for students to use a standard algorithm, but students should be supported if they do choose to use a standards algorithm at this stage. Students will formally learn a standard algorithm in grade 3 for addition or subtraction of multi-digit whole numbers.
Common Misconceptions or Errors
- Students may regroup ones incorrectly or forget to regroup the ones.
- Students may always think it is necessary to subtract the lesser digit from the greater digit.
- Students who use a vertical method may record the total sum of the digits in a place value instead of regrouping.
Strategies to Support Tiered Instruction
- Instruction includes the opportunities where regrouping may need to take place with addition and subtraction. Teacher provides students with addition and subtraction problems that may or may not require regrouping. Teacher asks, “Which problems require regrouping and how do you know?”
- For example, teacher may provide a few expressions like 36+27, 23+14, 87−2 and 64−28. Students sorts the problems as regrouping or no regrouping. Teacher asks how do you know that you need to regroup? Students solve a couple of the expressions and teacher checks for understanding.
- Using a number line to represent an addition problem may assist in understanding when an answer is not reasonable because the ones were not regrouped into tens and instead were wrongly recorded as two-digit number.
- For example, teacher provides the problem 54 + 39. Students use a place value chart and don’t regroup the ones into tens writing down the answer as 813. Teacher models using a number line to add 54 + 39 and show the jumps on the number line and prove that the answer is 93 and not 813.
- Instruction includes the use of base ten blocks and place value chart. Teacher provides a subtraction problem where the digit in the ones places of the subtrahend is greater than the digit in the ones place of the minuend. Students begin with the base ten blocks for the minuend, then subtract the subtrahend from the minuend where they may need to regroup a ten into ten ones. Teacher asks students to write the subtraction equation that matches the base ten model.
- For example, teacher asks students to use the base ten blocks to model the subtraction problem 73 − 48. Students use the place value chart to help organize the subtraction problem. They can exchange a ten rod for 10 ones. Students then “take away” 4 tens and 8 ones from the 6 tens and 13 ones. They may need to be reminded or revisit when regrouping/exchanging tens and ones is needed. Teacher asks students to write the equation to match.
Instructional Tasks
Instructional Task 1 (MTR.4.1)
Determine the difference between 62 and 39 in as many different ways as possible.
Instructional Items
Instructional Item 1
Tina was determining the sum of 3 tens and 8 ones + 4 tens and 5 ones. She records the sum as 7 tens and 13 ones. Her friend Brene also determined the sum, but says the sum is 83. Who is correct? Explain.*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 Tutorial
Perspectives Video: Expert
Problem-Solving Tasks
Tutorials
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, the students will work in teams to use data to determine which classroom pet teachers should get for their classrooms based on several characteristics.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
Students will determine which pizza place should be used to cater parties at the Birthday Parties 'R' Us facility given a set of data. They will create a procedure for determining the best pizza place, write an explanation about their procedure, and present their recommendations to the class.
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.
In this Model Eliciting Activity, MEA, a client is searching for the best cell phone carrier. Students will determine a procedure for ranking the companies based on votes for the favorite company and fees. The data is given in a scaled bar graph and a table. In a “twist,” the client provides more data, presented in a scaled pictograph, for the students to consider.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will devise a plan for ranking, and justify it, in order to choose the best class pet. Students will use problem-solving skills, interpret data presented in tables, add two-digit numbers, compare two and three-digit numbers, and create bar graphs.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students are asked to decide which factors are important in choosing the best cookie in a cookie contest. Students will take on the role of cookie critics to provide feedback to a teacher whose grade level is deciding which cookie to use for a fundraiser. They will rank order their choices from the best to worst cookie. Students will provide a detailed written explanation for how they decided to rank factors and their solution. They will show their work while adding up to 4 two-digit numbers to calculate the total number of votes.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
This Model-Eliciting Activity (MEA) is designed for a second grade level. Students will be working in small groups to figure out what companies to hire for the art gallery to have a successful charity event. The students will be evaluating criteria such as bands for the event, caterers, and artists. Students will need to add money to stay within a budget. They will write their procedure for making their selections.
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.
In this Model Eliciting Activity, MEA, students must decide the best way to spend the money earned in a fundraiser to buy new playground equipment.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will devise a procedure, and justify it, in order to determine the best features of a water park. Students will use problem-solving skills and data sets presented in a bar graph and table. In a “twist,” students will be given new information and asked to determine whether their procedure still works. Students will create a bar graph representing the new data.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
MFAS Formative Assessments
Students add a multiple of 10 to a two-digit number and are asked to relate the strategy used to a written method.
Students are asked to solve two addition problems and are observed for the use of place value strategies.
The student is asked to solve an addition and a subtraction problem in which a decade (i.e., a multiple of ten) must be crossed.
Students use a number line to find to the difference between 17 and 42.
Students are asked to solve three subtraction within 100 problems and are observed for the use of place value strategies.
Students use a number line to add 23 and 19 and to find a segment whose length is the sum of 23 and 19.
Students are asked to solve a two-digit addition problem using a place value strategy and then are asked to explain why this strategy works.
Students are asked to complete addition and subtraction problems that can be done efficiently by using properties of operations.
Original Student Tutorials Mathematics - Grades K-5
Learn to use place value to solve subtraction problems within 100 in this interactive, basketball-themed tutorial.
Student Resources
Original Student Tutorial
Learn to use place value to solve subtraction problems within 100 in this interactive, basketball-themed tutorial.
Type: Original Student Tutorial
Problem-Solving Tasks
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This task is an instructional task that brings many aspects of the mathematical work that second graders will be doing together with an opportunity to learn about financial literacy concepts.
Type: Problem-Solving Task
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This task has students adding two 2-digit numbers that require regrouping and the solution shows a concrete approach to the solution. This problem can be adjusted based on where students are in their understanding of addition involving two-digit numbers.
Type: Problem-Solving Task
Tutorials
In this tutorial video from Khan Academy, a subtraction problem is solved which contains two numbers each with two-digits. The video demonstrates subtraction with regrouping using the standard algorithm, as well as a method using expanded form.
Type: Tutorial
In this video tutorial from Khan Academy, explore subtracting two-digit numbers by using the standard algorithm. This video does not include regrouping.
Type: Tutorial
In this tutorial video from Khan Academy, explore adding two-digits numbers with base ten blocks and connect this to the standard algorithm. The examples do not include regrouping.
Type: Tutorial
In this video tutorial from Khan Academy, explore the connection between place value and subtraction. This video explains how to solve a subtraction problem with numbers less than one hundred using base ten blocks.
Type: Tutorial
Learn how to add 23 + 30 by thinking about place value.
Type: Tutorial
Parent Resources
Problem-Solving Tasks
The purpose of this task is to help students articulate their addition strategies and would be most appropriately used once students have a solid understanding of coin values. This task would be best used in an instructional setting especially since the language is somewhat complex and the teacher might need to help students decode the task statement.
Type: Problem-Solving Task
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This task is an instructional task that brings many aspects of the mathematical work that second graders will be doing together with an opportunity to learn about financial literacy concepts.
Type: Problem-Solving Task
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This task has students adding two 2-digit numbers that require regrouping and the solution shows a concrete approach to the solution. This problem can be adjusted based on where students are in their understanding of addition involving two-digit numbers.
Type: Problem-Solving Task
Tutorials
In this tutorial video from Khan Academy, a subtraction problem is solved which contains two numbers each with two-digits. The video demonstrates subtraction with regrouping using the standard algorithm, as well as a method using expanded form.
Type: Tutorial
In this video tutorial from Khan Academy, explore subtracting two-digit numbers by using the standard algorithm. This video does not include regrouping.
Type: Tutorial
In this tutorial video from Khan Academy, explore adding two-digits numbers with base ten blocks and connect this to the standard algorithm. The examples do not include regrouping.
Type: Tutorial
In this video tutorial from Khan Academy, explore the connection between place value and subtraction. This video explains how to solve a subtraction problem with numbers less than one hundred using base ten blocks.
Type: Tutorial
Learn how to add 23 + 30 by thinking about place value.
Type: Tutorial
