Curricular objectives
Strand: Numbers
1. Demonstrate an understanding of perfect squares and square roots, concretely, pictorially and symbolically (limited to whole numbers).
a. Represent a given perfect square as a square region, using materials such as grid paper or square shapes.
b. Determine the factors of a given perfect square, and explain why one of the factors is the square root and the others are not.
c. Determine whether or not a given number is a perfect square, using materials and strategies such as square shapes, grid paper or prime factorization, and explain the reasoning.
d. Determine the square root of a given perfect square, and record it symbolically.
e. Determine the square of a given number.
2. Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).
a. Estimate the square root of a given number that is not a perfect square, using the roots of perfect squares as benchmarks.
b. Approximate the square root of a given number that is not a perfect square, using technology; e.g., a calculator, a computer.
c. Explain why the square root of a number shown on a calculator may be an approximation.
d. Identify a number with a square root that is between two given numbers.
Strand: Shape and Space (Measurement)
3. Develop and apply the Pythagorean theorem to solve problems.
a. Model and explain the Pythagorean theorem concretely, pictorially or using technology.
b. Explain, using examples, that the Pythagorean theorem applies only to right triangles.
c.Determine whether or not a given triangle is a right triangle by applying the Pythagorean
theorem.
d. Determine the measure of the third side of a right triangle, given the measures of the other two
sides, to solve a given problem.
e.Solve a given problem that involves Pythagorean triples; e.g., 3, 4, 5 or 5, 12, 13.