KCCA3 About the Math, Learning Targets, and Opportunities for Enrichment
Kindergarten Mathematics Counting and Cardinality
K.CC.A.3
Full Standard
Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects.
Measurement Topic
This standard is reported on the report card in these quarters as follows:
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Report Card Measurement Topic: Demonstrates understanding of counting principles.
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About the Math
Skills and concepts below are learning goals for this standard.
- Write numbers 0-10.
- Write numbers 11-20.
- Represent a group of objects, in any arrangement, with a written numeral 0-20.
- Explain how 0 represents no objects.
One way students can learn the left to right orientation of numbers is to use a finger to write numbers in air (sky writing), on their knee or hands, or on a partner’s back. Children will see mathematics as something that is alive and that they are involved.
Students should study and write numbers 0 to 20 in this order: numbers 1 to 9, the number 0, then numbers 10 to 20. They need to know that 0 is the number of items left after all items in a set are taken away. Do not accept “none” as the answer to “How many items are left?” for this situation.
Common Misconceptions
When writing numerals, it is not uncommon for students to write reversals. Students often write an E for a 3. Confusing a 6 and 9 is also a common error. Asking students to write the numbers in the air, may reinforce the correct direction.
Progression of Standard within Kindergarten
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Progression of this Standard Across Grades
This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.
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TASKS
These tasks can be used with small group or whole group instruction.
- Cut note cards in half. Give students ten (or twenty) cards and ask them to write out one number on each card. Students can use markers, colored pencils or crayons. Have students mix up the cards and put them in order from least to greatest. Have students draw a representation of the number on the other side. Discuss what types of representations would work on the cards with limited space, such as dots, lines, hearts, etc.
- Prepare strips of adding machine tape or cut paper strips (about two inches wide). Strips can be one and a half to two feet long. Students can use markers or colored pencils to write numbers from least to greatest vertically down the strip. Variations include writing numbers up to 10, up to 20, writing up to 100. If writing larger numbers, students can change colors when they begin a new ten/decade.
- Represent numbers greater than 20 with written numerals. Move from decade to decade through 50 and beyond.
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
Module 3 • Counting to 20
Write Numerals 0-20, Count Objects and Write the Corresponding Numeral 0-20:
Additional Tasks
These links provide instructional ideas connected to this standard.
- Race to the Top Links to an external site. (Illustrative Mathematics)
- Rainbow Number Line Links to an external site. (Illustrative Mathematics)
- Number TIC TAC TOE Links to an external site. (Illustrative Mathematics)
- Bags of Stuff Links to an external site. (Illustrative Mathematics)
- MSDE Lesson Seeds
Tasks From Print Resources
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Book Thumbnail | Title | Reference |
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Teaching Student-Centered Mathematics by: John A. Van de Walle and Lou Ann H. Lovin |
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Hands-On Standard published by: Learning Resources |
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Math Intervention K-2 by: Jennifer Taylor-Cox |
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Developing Number Concepts Book 1 by: Kathy Richardson |
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Centers
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
- What's Missing Download What's Missing (HCPSS-adapted resource)
- Number Race Download Number Race (HCPSS-adapted resource)
- Number Writing Download Number Writing (HCPSS-adapted resource)
- Numbers Three Ways Download Numbers Three Ways (HCPSS-adapted resource)
PRACTICE/ASSESSMENT
These materials can be used for independent practice and/or for assessment purposes. These tasks align with the learning goals for the standard.
Assessment and Instructional Tasks
- Task 5a: K.CC.A.3, K.CC.B.4, K.CC.B.5 Links to an external site.
- K.CC.A.3, K.CC.B.4, K.CC.B.5 Show 7 Links to an external site.
- K.CC.A.3, K.CC.B.4, K.CC.B.5 Show 11 Links to an external site.
- K.CC.A.3, K.CC.B.4, K.CC.B.5 Show 16 Links to an external site.
- K.CC.A.3, K.CC.B.4, K.CC.B.5 Write and Show 9 Links to an external site.
- K.CC.A.3, K.CC.B.4, K.CC.B.5 Write and Show 13 Links to an external site.
- K.CC.A.3 Write Numbers Links to an external site.
- K.CC.A.3 Count and Write A Links to an external site.
- K.CC.A.3 Count and Write B Links to an external site.
- K.CC.A.3 Writes Numbers Recording Sheet Links to an external site.
Full Standard
Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects.
Measurement Topic
The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.
Kindergarten Students Learning Kindergarten Standards by Measurement Topic
Demonstrates understanding of counting principles
Quarter 1
- Accurately write numbers 0-20.
- Represent a group of objects, within 20 (including zero), with the corresponding written numeral.
KCC3 Anecdotal Data Collection Tool Links to an external site.
Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification.
Rubric (for thinking and reasoning evidence)
Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).
Rubric for Tasks (pdf) Links to an external site.
Exemplars for this standard (if available)
These samples are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.
TASK | MEETS EXPECTATIONS | MAKING PROGRESS | MAKING LIMITED/NO PROGRESS |
Show students 5 counters and ask students to count and write the numeral that represents the set. Observe. Repeat with 13 and 9. | Student write the correct numeral to match the sets. Student may need one prompt to recount a set. | Student writes the correct numeral for 1-2 sets correctly, but needs prompting to recount the other sets. Student makes errors in counting even after prompting. | Student may identify the correct count but is unable to write the numerals. |
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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.