Recognize, show, and explain the relationship between whole numbers and their factors using concrete or pictorial representations (e.g., using a set number of tiles, create rectangular regions and record the dimensions of those regions, and describe how those dimensions relate to the factors of the number).

Infer and verify relationships between the factors of a perfect square and the principle square root of a perfect square.

Determine if specific numbers are perfect squares through the use of different types of representations and reasoning, and explain the reasoning.

Describe and apply the relationship between the principle square roots of numbers and benchmarks using a number line.

Explain why the square root of a number shown on a calculator may be an approximation.

Apply estimation strategies to determine approximate values for principle square roots.

Determine the value or an approximate value of a principle square root with or without the use of technology.

Identify a number with a principle square root between two given numbers and explain the reasoning.

Share the story, in writing, orally, drama, dance, art, music, or other media, of the role and significance of square roots in a personally selected historical or modern application situation (e.g., Archimedes and the square root of 3, Pythagoras and the existence of square roots, role of square roots in Pythagoras’ theorem, use of square roots in determining dimensions of a square region from the area, use of square roots to determine measurements in First Nations beading patterns, use of square roots to determine dimensions of nets).