KCCA1 About the Math, Learning Targets, and Opportunities for Enrichment

Kindergarten Mathematics Counting and Cardinality

K.CC.A.1

About the Math

Full Standard

Count to 100 by ones and tens.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

Kindergarten Students Learning Kindergarten Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of counting principles.   Report Card Measurement Topic: Demonstrates understanding of counting principles.

 

About the Math

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  Skills and concepts below are learning goals for this standard.

  • Count to 10 by ones.
  • Count to 50 by ones.
  • Count to 100 by ones.
  • Count to 100 by tens.

Students view counting as a mechanism used to land on a number. Young students mimic counting often with initial lack of purpose or meaning. Coordinating the number words, touching or moving objects in a one-to-one correspondence may be little more than a matching activity. However, saying number words as a chant or a rote procedure plays a part in students constructing meaning for the conceptual idea of counting. They will learn how to count before they understand cardinality, i.e. that the last count word is the amount of the set.

  

Common Misconceptions

Some students might not see zero as a number. Ask students to write 0 and use zero to represent the number of items left when all items have been taken away. Avoid using the word none to represent this situation. When counting over decades, students may say, "Twenty-eight, twenty-nine, twenty-ten". They are following the sequence from 1 to 10. Use a fifty or hundreds chart so students can see the progression of the numbers.

 

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.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Count to 10 by ones.
  • Count to 20 by ones.
  • Count to 50 by ones.
  • Count to 100 by ones.
  • Count to 100 by tens.

 

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.

Progression Across Grades
Grade 1

 

 

 

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction. 

  • Count backwards from 100 by 10s and 1s.
  • Create a chart with the title “How many students are here today?” Ask the class how we could figure out how many students are here today. Choose one of the suggested ways to count the class. Discuss how you could show on the chart how many students are here today (write out names, draw dots, draw stick figures). Select one way to record and add it to the chart. On other days you can use different representations. Display Unifix cubes. How could we use cubes to show how many students are here today? Extend the counting to tens by asking students to figure out how many fingers or toes everyone has. How could you show this on the chart?
  • Count to ten or twenty pairing an action with each count. Actions could include clapping, stomping, jumping, etc.
  • Count up to nine. What are three numbers that we counted before we got to nine? If we keep counting to twenty what are three numbers we will count after nine?
  • Have students stand in a circle. Choose a number to count to (within 10 or 20). Count around the circle, when you land on the chosen number, everyone claps. The person where the count stopped moves into the center of the circle. Continue counting around the circle until only one or two people are left. Debrief when you are finished. How could you tell if the count was going to stop with you? How could you tell if you were going to stay standing up? If you were in the center of the circle, could you tell where the count was going to stop before we got there?
  • Count forwards and backwards from any given number to 100.
  • Give students a blank fifty chart have them fill the chart in starting at 28 and ending at 46. 
  • Give students a blank hundred chart with the number 54 filled in. Ask students to work backwards from 54, completing the chart until they reach 12 and stop.
  • Give students a completed hundred chart that is cut up into six, seven or eight sections. Have them put it back together and justify the puzzle placements.
  • Draw a number line with the endpoints of 0 and 100. Place a dot on the number line. What number on the number line does the dot represent? How do you know?

 

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 7 • Counting to 50

Module 13 • Count to 100

Count to 100 starting at 1 (includes using objects, number charts, etc.):

  • Extend ideas from Hide the Numbers 1-50 to 100

Count to 100 by tens:

  • Connect to 100 chart and filled ten frames

 

 

Additional Tasks

These links provide instructional ideas connected to this standard. 

 

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. 

All kindergarten teams have been provided with the resources listed below.

Print Resources
Book Thumbnail Title Reference
Teaching Student-Centered Mathematics by John A. Van de Walle and Lou Ann H. Lovin
  • Up and Back Counting, p. 40
  • Patterns on the Hundreds Chart, p. 57
Math Intervention K-2
by Jennifer Taylor-Cox
  • Stomp Your Feet, p. 22
  • Clover Patch, p. 90-92
  • Number Line Fill Up, p. 109-110
Developing Number Concepts Book 1 by Kathy Richardson
  • Creating a Number Chart, p. 122

 

 

Tasks Connected to Literature 

Suggested titles to support the standard can be found in the table below. Check your school library or Howard County Library System for availability, or purchase using Materials of Instruction (MOI) funds. When available, select links to view activities aligned to each title.

 

100 School Days

by Anne Rockwell 

 

Reese's Pieces

by Jerry Pallotta

Anno's Counting Book

by Mitsumasa Anno

Counting Follow

by John Burstein

One Hundred Hungry Ants

by Elinor J. Pinczes

 

 

 

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Centers and Practice

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

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

 

 

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Assessment

Full Standard

Count to 100 by ones and tens.

 

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 2

  • Fluently count to 50 by ones.

Quarter 4

  • Fluently count to 100 by ones.
  • Fluently count to 100 by tens.

 

KCC1 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.

Ask the student to count from 1 to as high as they can (stopping at 100)

Expectations by quarter:

  • Q1: Count to 20
  • Q2: Count to 50
  • Q4: Count to 100
Student fluently counts to or beyond the target number. 1 prompt from the teacher is still acceptable Student needs prompting and support to cross decades when counting. Student needs to be prompted 2 - 4 times.  Student is unable to count accurately with adult support, prompts, and use of math tools to help (i.e. 100 chart).

Ask the student to start at 0 and count to 100 by tens. (Q4 only)

 

Student fluently counts up to 100 by tens. 1 prompt from the teacher is still acceptable. Student needs prompting and support to count to 100 by tens. Student needs 2 - 3 prompts. Student is unable to count accurately with adult support, prompts, and use of math tools to help (i.e, 100 chart).

 

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