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Clarifications
Clarification 1: Instruction focuses on developing an understanding of cardinality and one-to-one correspondence.Clarification 2: Instruction includes counting objects and pictures presented in a line, rectangular array, circle or scattered arrangement. Objects presented in a scattered arrangement are limited to 10.
Clarification 3: Within this benchmark, the expectation is not to write the number in word form.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Cardinality Principle
- Natural Number
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to help students develop an understanding of cardinality: the principle that the last number when counted in a set represents the total number within the set, and that the number of objects in a set remains the same regardless of the arrangement of the set. Additionally, this benchmark allows students to begin recognizing and writing numerals.- Instruction includes the use of manipulatives, pictorial representations and real-world contexts to provide a purpose for counting (MTR.2.1, MTR.7.1).
- Instruction includes symbolic representation of numbers 0 – 20 (MTR.7.1).
- Instruction includes the opportunity to demonstrate a consistent one-to-one correspondence when counting a row of objects. The teacher provides an opportunity to observe counters from the same set to be rearranged into a circle (and later, a rectangular array) and asks to determine how many there are (MTR.3.1).
Common Misconceptions or Errors
- Students may inaccurately report the number of objects in a set that has been rearranged even though the number was accurately counted before the set was rearranged (i.e., conservation of cardinality).
- Students may recount the number of objects in a set that has been rearranged even though the number was accurately counted before the set was rearranged.
- Students may recount a group of objects when asked “how many,” rather than reporting the last number counted.
- Students may not be systematic in their counting.
- For example, a student may double count or skip numbers.
Strategies to Support Tiered Instruction
- Instruction includes modeling how to count objects in a set using identical counters presented in a horizontal row. Students must demonstrate how to count all the objects in the sequence and understand that the last number they state tells how many there are in the group.
- For example, questions and think-aloud statements can include the following:
- “How many counters are there? What do we have to do to find out how many?”
- “I will have to count to find out how many there are. Each time I touch a counter, I will say a number. I know that I can only touch each counter one time. The last number I say will tell me how many counters there are.”
- “Will you count with me to find out how many there are?” Students may represent counting the set by drawing and labeling with numbers.
- Students may represent counting the set by drawing counters and labeling with numbers. Have students count aloud to ensure no numbers were skipped or duplicated. After students finish, they can mark the last number stated and complete the sentence frame: “There are ____ counters.”
- For example, questions and think-aloud statements can include the following:
- Student: “There are 8 counters.”
- Teacher provides students with a labeled number path/ten frame to allow students to place counters on top of numbers as they count aloud. Emphasize that the number where the last counter is laid indicates how many counters are in the whole set.
- Instruction includes removing the verbal counting sequence to isolate the concept of one- to-one correspondence. The teacher provides a model with a set of red and yellow counters, red side up, arranged in a horizontal row and then students place a yellow counter below each red counter. Students must demonstrate the understanding that each red counter is matched with only one yellow counter if there are the same number. Students can also represent their model using drawings.
- Example:
Instructional Tasks
Instructional Task 1 (MTR.2.1, MTR.3.1)
Teacher gives students a number of objects to count (between 0 and 20).- Part A. Observe as students count, mapping each number to one object. Ask the student,
How many in all? Students should report the last number counted without having
to recount the set.
- Part B. Once the student has reported the numbers of objects, rearrange the orientation of the objects and ask the student again. Students should report the number without recounting. Ask the student why they needed or did not need to count the set again after the set was rearranged.
Instructional Items
Instructional Item 1
Instructional Item 2
The stars have been rearranged. How many stars are there now?
Instructional Item 3(image of a calendar provided)
- How many days are in a week?
- How many Mondays are in this month?
- How many Saturdays and Sundays are in the month?
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Ideas
Presentation/Slideshow
Student Center Activity
Teaching Idea
Worksheet
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will work in teams to determine the best unique pizza topping to add to a restaurant menu.
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 work in collaborative groups to choose the best ice cream bar that an ice cream truck may sell. Students will analyze the data provided and come up with a solution. They will also be asked to reevaluate their written procedures once a second data set is presented.
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
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In this Model Eliciting Activity, MEA, students, in teams, will make decisions about how to select a new bicycle for a mountain bicycle company to start selling.
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 MEA, students will help pick a flower that will be the focus of the Spring Festival. They will practice counting pictures and representing the number of pictures with a written numeral.
In teams, students will make decisions about how to select the best bakery based on various cupcake characteristics (e.g., taste, smell).
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 will work in teams to determine the best pet toys to buy for a pet daycare.
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 are asked to count eight books and decide how many bookmarks they would need if they gave each book a bookmark.
Students are asked to count a set of cubes, rearrange the cubes, and then determine the number of cubes in the rearranged set.
Students count the objects in a set and write the number of objects they counted.
Students are asked to count sets of cubes and determine how many cubes are in each set. Next, students are given a set of cubes and asked to count out a given number of cubes.
Students are asked to count a set of seven cubes, rearrange the cubes, and then determine the number of cubes in the rearranged set.
Students are asked to match four ten frames representing different numbers to the correct numerals.
Students are read the book, You Can Do It, Sam, by Amy Hest and are asked to count the number of cakes and houses in the illustrations.
Original Student Tutorials Mathematics - Grades K-5
Help Polly Parrot count to 7, recognize the numeral 7, and count 7 objects in a line with this interactive tutorial.
Help Brent earn supplies to adopt a cat by counting to 8, recognizing the number 8, and counting 8 objects in a line in this interactive tutorial.
Help Brent and his new cat count 8 objects in an array, recognize groups of 8 objects, and count out 8 objects to earn supplies for adopting a dog in this interactive tutorial.
Help Buddy count to six, recognize the number 6, and count six objects in a line with this interactive tutorial,
Help Buddy count 6 objects in an array, group with 6 objects, and count out 6 objects as he builds his treehouse in this interactive tutorial.
This is part 2 in a two-part series. Click HERE to open part 1.
Help Lucy the dog recognize and write number 4. She will also learn to count up to 4 objects using a ten frame and number line in this interactive tutorial.
Help Tyler count seven objects in a scattered arrangement, group seven objects, and count out seven objects one by one with this interactive tutorial.
Come along with Scout as he prepares supplies for a camping adventure. You will learn to count to 10, recognize the number 10, and count 10 objects in this interactive tutorial.
Get ready to set up camp with Scout as you explore the number 10. You will count 10 objects in a circle, count a group of 10 objects, and count out 10 objects in this interactive tutorial.
Learn to how to recognize and write the number 5 and count up to 5 objects using 10 frames and number lines as you help Lucy the dog plan a party in this interactive tutorial.
In Part 1 of Summer's Pool Party, students assist Summer in preparing for a pool party with her friends. They will help Summer count to 9, recognize the number 9, and count 9 objects in a line.
Help Summer count 9 objects in an array, recognize groups of 9 objects, and count out 9 objects for her pool party with friends in this interactive tutorial.
This is part two in a two-part series. Open Part One.
Help Lucy and Izzy learn to recognize and write the number 2. In this interactive tutorial, you'll also count two objects and use a 10 frame and a number line.
This is part 2 in a multi-part series. Click below to open the other tutorials.
Help Lucy and Izzy explore the numbers 0 and 1 using writing, ten frames and number lines in this interactive tutorial.
STEM Civics Tutorials and Videos - Grades K-12
Learn about the American flag by identifying colors and shapes and sorting parts of flag designs into groups in this interactive S.T.E.M. and civics integrated tutorial.
This is part 1 of 2-part series, click HERE to view part 2.
Learn about the American flag by sorting flag designs and features into groups and counting the objects in a group in this interactive S.T.E.M. and civics integrated tutorial.
This is part 2 of 2-part series, click HERE to view part 1.
Student Resources
Original Student Tutorials
Help Summer count 9 objects in an array, recognize groups of 9 objects, and count out 9 objects for her pool party with friends in this interactive tutorial.
This is part two in a two-part series. Open Part One.
Type: Original Student Tutorial
Help Brent and his new cat count 8 objects in an array, recognize groups of 8 objects, and count out 8 objects to earn supplies for adopting a dog in this interactive tutorial.
Type: Original Student Tutorial
Help Brent earn supplies to adopt a cat by counting to 8, recognizing the number 8, and counting 8 objects in a line in this interactive tutorial.
Type: Original Student Tutorial
Come along with Scout as he prepares supplies for a camping adventure. You will learn to count to 10, recognize the number 10, and count 10 objects in this interactive tutorial.
Type: Original Student Tutorial
Get ready to set up camp with Scout as you explore the number 10. You will count 10 objects in a circle, count a group of 10 objects, and count out 10 objects in this interactive tutorial.
Type: Original Student Tutorial
In Part 1 of Summer's Pool Party, students assist Summer in preparing for a pool party with her friends. They will help Summer count to 9, recognize the number 9, and count 9 objects in a line.
Type: Original Student Tutorial
Help Tyler count seven objects in a scattered arrangement, group seven objects, and count out seven objects one by one with this interactive tutorial.
Type: Original Student Tutorial
Help Polly Parrot count to 7, recognize the numeral 7, and count 7 objects in a line with this interactive tutorial.
Type: Original Student Tutorial
Help Buddy count 6 objects in an array, group with 6 objects, and count out 6 objects as he builds his treehouse in this interactive tutorial.
This is part 2 in a two-part series. Click HERE to open part 1.
Type: Original Student Tutorial
Help Buddy count to six, recognize the number 6, and count six objects in a line with this interactive tutorial,
Type: Original Student Tutorial
Learn about the American flag by identifying colors and shapes and sorting parts of flag designs into groups in this interactive S.T.E.M. and civics integrated tutorial.
This is part 1 of 2-part series, click HERE to view part 2.
Type: Original Student Tutorial
Learn about the American flag by sorting flag designs and features into groups and counting the objects in a group in this interactive S.T.E.M. and civics integrated tutorial.
This is part 2 of 2-part series, click HERE to view part 1.
Type: Original Student Tutorial
Learn to how to recognize and write the number 5 and count up to 5 objects using 10 frames and number lines as you help Lucy the dog plan a party in this interactive tutorial.
Type: Original Student Tutorial
Help Lucy the dog recognize and write number 4. She will also learn to count up to 4 objects using a ten frame and number line in this interactive tutorial.
Type: Original Student Tutorial
Help Lucy and Izzy learn to recognize and write the number 2. In this interactive tutorial, you'll also count two objects and use a 10 frame and a number line.
This is part 2 in a multi-part series. Click below to open the other tutorials.
Type: Original Student Tutorial
Help Lucy and Izzy explore the numbers 0 and 1 using writing, ten frames and number lines in this interactive tutorial.
Type: Original Student Tutorial
Parent Resources
Student Center Activity
In this game, students develop fluency with counting sequences and number patterns and strengthen number sense through movement, rhythm, and voice modulation while also practicing active participation and listening skills.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
