Number Theory

Question 1

What does one-to-one correspondence mean?

Answer 1

Pair each object with one number word when counting.

Question 2

Give an example of rote counting.

Answer 2

Saying “1, 2, 3, 4…” from memory.

Question 3

How does skip counting by 5s sound?

Answer 3

5, 10, 15, 20, 25…

Question 4

In a part-part-whole model, what do the “parts” do?

Answer 4

They combine to make the “whole” or split from it.

Question 5

Define a rational number.

Answer 5

Any number expressible as a fraction a/b with b ≠ 0.

Question 6

Why is π irrational?

Answer 6

It cannot be written exactly as a fraction of two integers and its decimal never ends or repeats.

Question 7

Explain the hungry-alligator analogy.

Answer 7

The open mouth (< or >) always points to the larger number.

Question 8

If –123 and –122 are compared, which is greater?

Answer 8

–122 (smaller absolute value is greater on the number line).

Question 9

What benchmark helps compare ⅘ and 0.7?

Answer 9

Convert ⅘ to 0.8; since 0.8 > 0.7, ⅘ is greater.

Question 10

How does a number line support learning operations?

Answer 10

Hops to the right show addition; hops to the left show subtraction; equal-size hops model multiplication/division.