KCCC6 About the Math, Learning Targets, and Opportunities for Enrichment

Kindergarten Mathematics Counting and Cardinality

K.CC.C.6

About the Math

Full Standard

Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (Include groups with up to ten objects).

 

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 number concepts and relationships.  

 

About the Math

Skills and concepts below are learning goals for this standard.

As children develop meaning for numerals, they also compare these numerals to the quantities represented and their number words. The modeling numbers with manipulatives such as dot cards and five- and ten-frames become tools for such comparisons. Children can look for similarities and differences in these different representations of numbers. They begin to “see” the relationship of one more, one less, two more and two less, thus landing on the concept that successive numbers name quantities where one is larger. In order to encourage this idea, children need discussion and reflection of pairs of numbers from 1 to 10. Activities that utilize anchors of 5 and 10 are helpful in securing understanding of the relationships between numbers. This flexibility with numbers will greatly impact children’s ability to break numbers into parts.

Children demonstrate their understanding of the meaning of numbers when they can justify why their answer represents a quantity just counted. This justification could merely be the expression that the number said is the total because it was just counted, or a “proof” by demonstrating a one- to-one match, by counting again or other similar means (concretely or pictorially) that makes sense. An ultimate level of understanding is reached when children can compare two numbers from 1 to 10 represented as written numerals without counting.

Students need to explain their reasoning when they determine whether a number is greater than, less than, or equal to another number. Teachers need to ask probing questions such as “how do you know?” to elicit their thinking. For students, these comparisons increase in difficulty, from greater than to less than to equal. It is easier for students to identify differences than to find similarities.

  • Tell which has more by matching or counting the number of objects in both groups.
  • Tell which has less by matching or counting the number of objects in both groups.

See more information above. Counting individual objects is the extent of the expectation for this standard. However, it is not the required limit. As students demonstrate understanding we should move them to more efficient comparisons. For example, it is desirable for a student to compare 5 and 8 using ten frames noting that 8 has (5 and some more) therefore it is more. 

  • Tell when groups are equal by matching or counting.
  • Create equal groups in different arrangements.

It essential that students can compare and determine equivalence when groups are arranged in a variety of ways. Students should also be able to create a new group that is equal to or greater/less than a given group.

 

Common Misconceptions

Students may need to line up the objects and compare them to see which set has more. This is a prerequisite to being able to look at the numerals and know which set is greater. Students are more comfortable when working with more as opposed to less. Using a number line or hundreds chart may help them see numbers that are more or less than another number.

 

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
  • I can say which group has more by matching or counting the number of objects in both groups.
  • I can say which group has less by matching or counting the number of objects in both groups.
  • I can say when groups are equal by matching or counting.

 

 

 

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
  • Compare two two-digit numbers based on meanings of the tens and ones digits  (1.NBT.B.3) 

 

 

 

 

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Instructional Tasks

TASKS

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

  • Show students a basket of supplies that include pencils, erasers and crayons. Explain that each person in the group will need to have one of each item. Explain that you are going to give each group (four to six students) some supplies, and they will need to figure out if they have enough, need more or have too much. Give groups one type of supply at a time, purposefully giving different amounts. Discuss with groups how they could tell if they have the right number of supplies. Do they have too many? How could they fix that? Do they not have enough? What would they need to do to have enough? Encourage students to use language comparing the number of students in the group to the number of supplies they have.
  • Start with five to ten animal (bear) counters. Use a small container or box with a cutout to act as a cave. This can be done with a small group or in partners. Students count how many animals there are total. One student hides some of the animals in the cave while everyone else covers their eyes. When the animals are hidden students uncover their eyes and discuss how many are outside the cave/burrow and make an estimate of how many they think are inside. Students do not need to figure out exactly how many animals are in the cave at this time. After a brief discussion, uncover the hidden animals. Are there more animals outside the cave or more inside the cave? Are there the same inside and outside the cave? How do we know? Students can take turns hiding the animals.
  • Place some (start with up to ten and move to within twenty) two-color counters in a cup. Have students shake the cup and then pour out the counters and decide which color has more, less or if both colors have the same amount.

 

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 6 • Comparison

Compare objects and groups up to 10:

Compare objects and groups up to 20:

 

 

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. 

Print Resources
Book Thumbnail Title Reference
Teaching Student-Centered Mathematics by: John A. Van de Walle and Lou Ann H. Lovin
  • Make Sets of More/Less/Same, p 38
  • At a workstation or table, provide about 8 dot cards with sets of 4-12 objects, sets of small counters or blocks, and some word cards labeled More/Less/Same. Next to each card have students make three collections of counters: a set that is more, one that is less, and one that is the same. The appropriate labels are placed on the sets.
  • Blackline Masters Links to an external site.
Hands-On Standards published by: Learning Resources
  • Number Shapes, p. 22
  • Estimate and Count, p. 24
  • Comparing Groups, p. 26
  • Equal Groups, p. 28
  • More and Fewer, p. 30
  • More Than, Less Than, Same As, p. 56
Developing Number Concepts Book 1 by: Kathy Richardson
  • Is It More/Less?, p. 146
  • Spin and Peek, p. 150
  • Two-Color Grab-Bags, p. 163

 

 

 

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.

Just Enough Carrots

by Stuart J Murphy

 

More More More Said the Baby

by Vera B. Williams

Who Has More? Who Has Fewer?

by Caroline Arnold

More, Fewer, Less by Tana Hoban

More or Less

by Stuart J. Murphy

 

 

 

 

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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. If used for independent practice, teachers should introduce the resources through modeling and guided practice.

 

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

Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (Include groups with up to ten 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 number concepts and relationships

Quarter 2

  • Identify which set of objects (up to 10 in each) has more or less.
  • Identify when two sets of objects (up to 10 in each) are equal.
  • Create a set of objects (up to 10) that is greater than, less than, or equal to a shown set.

 

KCC6 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 the student a set of 5 counters and prompt the student to make a set that is greater than the set you are showing. Observe. Show the student a set of 9 and ask the student to make a set equal to your set. Observe. Finally, make a set of 7 and ask the student to show a set that is less than your set. Observe. Student is able to make all 3 sets. Student may need a prompt to make an adjustment, but student is able to correct their work. Student is able to make 1-2 sets correctly, but not all three. Student may show an understanding of 2 types of comparisons, but not all three. Student may need prompting to understand vocabulary (more vs. greater, same vs. equal). Student guesses when creating sets to compare to the original set. Student confuses the vocabulary terms greater, less and equal. Even with prompting and use of different vocabulary, student is unable to make at least 2 sets.

Materials: Teddy bear counters;  7 green bears, 9 red bears, 4 blue bears, 4 yellow bears (Teddy bears should be of like sizes)

 

Detailed description of task:  

  • Show students two sets/groups of bears at a time as described. (bears can be presented in piles by color)
  • Tasks:
    • Comparison task #1- Show students 7 green bears and 9 red bears.
      • Say:  “I have some green bears and some red bears.”
      • Ask:  Which set is more, or are they equal?  How do you know?
    • Comparison task #2- Show students 7 green bears and 4 blue bears.
      • Say:  “I have some green bears and some blue bears.”
      • Ask:  Which set is less, or are they equal?  How do you know?
  • Comparison task #3- Show students a set of 4 yellow bears and 4 blue bears.   
      • “I have some yellow bears and some blue bears”
      • Ask:  Which set is more, or are they equal?  How do you know?

If a student responds without counting, prompt to count.  Could you count them to check?

MEETS EXPECTATIONS

MAKING PROGRESS

MAKING LIMITED/NO PROGRESS

The student correctly identifies the set that is more, less, or equal.

The student may use a counting or matching strategy to support his/her thinking.

The student correctly identifies two of the three sets as more, less, or equal.

Attempts to use a counting or matching strategy to compare the set but incorrectly answers.

The student is unable to or only identifies one of the three sets.

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