Sample problems for kindergarten students to practice counting, one-to-one correspondence, cardinality, quantity, and comparison

1. Sample problems for Math
Common Core State Standard:
K.CC
Designed by Priyanka R. Reddy

2. Goals
• The sample problems aim to provide sufficient practice for a
kindergarten student to master the concepts listed below. These
concepts are consistent with the Common Core State Standards.
1) Counting
2) One-to-One Correspondence
3) Cardinality
4) Quantity
5) Comparison

3. Knowledge That Builds
• Math is a subject that builds. Mastering fundamental concepts will
make learning more advanced concepts easier. The flow chart
illustrated below depicts the progression of topics to achieve the
requirements listed under K.C.C.
Counting
Correspondence
One to One Cardinality Quantity Comparison

4. Building Blocks
• The following design principles were incorporated into the sample
questions in order to enhance student learning and experience.
1) Repetition – enforces concepts and strengthens fundamentals.
2) Prompts – ask student to answer questions that test overall concepts
3) Audio features – incorporates cues such as inflection to guide students through the
learning process
4) Interactive – facilitates one-to-one correspondence with counting

5. Program Structure
Sample question categories are created for each of the 5 goals. Each category tests
a distinct concept. Within one category, a fixed number of questions are asked.
However, the numbers used in the question are variable.
C = questions answered correctly in category A
if C > 70%
student moves on to next section automatically
else
student is tested in category A with different questions
a “pass” button is enabled, in case a student wants to move ahead
end

6. Sample Questions

7. Goal #1: Counting

8. Category A: Let’s count together in ones!
Example Question:
• Audio feature: “Let’s count! 1…2…3…4…” Which number comes after 4?
• Visual display: As numbers are counted, the numeric value flashes on the
screen as each number is said.
• System input – student enters or selects the answer 5
• System response:
if input = 5
audio(“That’s right!”)
else audio(“The number that comes after 4 is 5! 1..2..3..4..5!”)
Visual display – highlights the numbers in succession on the number chart

9. Category B: Let’s count together by tens!
Example Question:
• Audio feature: “Let’s count by tens! 10..20..30..40..” Which number comes after
40?
• Visual display: As numbers are counted, the numeric value is highlighted on a
number chart
• System input – student enters or selects the answer 50
• System response:
if input = 50
audio(“That’s right!”)
else audio(“When we count by tens, the number after 40 is 50. If we take 10 hops
from 40, we land at 50! 10..20..30..40…50!”)
visual display – animation illustrating ten hops from 40

10. Category C: Let’s count together!
• In this category, we start from a randomly generated number and
repeat the prompt from Category A.

11. Goal #2 & #3:
One-to-One Correspondence
&
Cardinality

12. Category A: Let’s count the number of objects!
• Display a randomly generated set of objects (i.e. a ball) from 1– 10 in
a randomly selected formation (circle, triangle, rectangle, etc.)
• Ask the student to use their mouse and click on the objects while
counting
• As the student clicks on an object, the object is highlighted.
• Once the student counts (or highlights) all objects, ask the student:
How many objects are there?
• Student enters or selects their response

13. Category B: What if we add one more?
• Format from Category A is repeated; however, this time an extra
question is added at the end.
• After answering how many objects, another object is added to the
existing set of objects.
• The student must now answer the question: If we add one more
object, how many objects do we have?

14. Goal #4: Quantity

15. Category A: Let’s take a peek!
• An image of a set of objects appears on the screen for approximately
2-3 seconds
• Objects are uniform in the image
• The cardinality of the set of objects is randomly generated except the
maximum number of objects that can be displayed at one time is
constrained to 5
• Students must answer the question: How many objects did you see?
• A student may choose to see the image one more time for 2-3
seconds. After that an answer must be entered or selected.

16. Goal #5: Comparison

17. Category A: Which group has more (less)?

18. Category B: Which number is bigger (smaller)?

19. Resources
• Consulted Early Childhood Education Videos from Eastern
Connecticut State University
(https://www.youtube.com/user/EarlyChildhoodVideos/about?disabl
e_polymer=1)