You count some apples on a plate: 1, 2, 3, 4, 5, 6, 7. Someone asks you 'How many apples are on the plate?' What is the answer?
AYou have to start counting over to find out
B7 — the last number you said is the answer
C1 — because you started counting at 1
DIt could be any number
There are 7 apples. When you finish counting and the last number you say is 7, that means there are 7 objects in the group. You do not need to count again — the last number already tells you the total. Understanding that the last number is the answer is an important part of knowing how to count.
Question 2 Multiple Choice
A child counts 5 blocks but accidentally touches the first block twice, counting it as both '1' and '2.' She announces there are 6 blocks. Which counting principle did she violate?
AStable order — she said the number names in the wrong sequence
BCardinality — she misidentified the total
COne-to-one correspondence — each object must be counted exactly once
DNo principle was violated; her answer is correct
One-to-one correspondence requires pairing exactly one number word with each distinct object — no object gets counted twice and none gets skipped. By touching the first block twice, she broke this pairing, which caused her final count to be wrong. Cardinality (option B) wasn't the root problem; she applied the cardinality principle correctly by reporting her last number — the underlying error was the double-count.
Question 3 True / False
A child who can perfectly recite 'one, two, three, four, five' already knows how to count objects correctly.
TTrue
FFalse
Answer: False
Reciting the counting sequence and using it to count real objects are two separate skills. A child who has memorized the sequence might still rush ahead, skip an object, or count the same object twice — all violations of one-to-one correspondence. Counting objects correctly also requires cardinality: understanding that the final number gives the total, not just that it comes last in the sequence.
Question 4 True / False
The cardinality principle states that the last number word you say when counting a group tells you how many objects are in the entire group.
TTrue
FFalse
Answer: True
This is the cardinality principle. When you count five blocks and land on 'five,' that word doesn't just mean 'the fifth thing I touched' — it means the whole group has five members. Children who understand cardinality can answer 'how many?' without recounting. Children who haven't internalized it tend to recount every time, because they haven't grasped that the final count *is* the answer.
Question 5 Short Answer
What are the three counting principles that children must learn when learning to count objects, and why is knowing the sequence alone not enough?
Think about your answer, then reveal below.
Model answer: The three principles are: (1) stable order — always say the number names in the same fixed sequence; (2) one-to-one correspondence — match exactly one number word to each object, no skips or doubles; (3) cardinality — the last number said tells you the total quantity in the group. Knowing the sequence alone is not enough because a child could recite 'one, two, three' perfectly but still count the same block twice or not understand that 'three' means the group has three members.
Counting involves weaving together three distinct ideas. Each is learnable separately and children often master them in sequence. A child may have stable order before one-to-one correspondence, and one-to-one correspondence before cardinality. Only when all three work together does counting function as a reliable tool for determining quantity.