This week your student will be working with the relationship between the side length and area of squares. We know two main ways to find the area of a square:
But what is the side length of this tilted square? It cannot be 3 units since
Here is a task to try with your student:
If each grid square represents 1 square unit, what is the side length of this titled square? Explain your reasoning.
Solution:
The side length is
This week your student will work with the Pythagorean Theorem, which describes the relationship between the sides of any right triangle. A right triangle is any triangle with a right angle. The side opposite the right angle is called the hypotenuse, and the two other sides are called the legs. Here we have a triangle with hypotenuse
We can use the Pythagorean Theorem to tell if a triangle is a right triangle or not, to find the value of one side length of a right triangle if we know the other two, and to answer questions about situations that can be modeled with right triangles. For example, let’s say we wanted to find the length of this line segment:
We can first draw a right triangle and determine the lengths of the two legs:
Next, since this is a right triangle, we know that
Here is a task to try with your student:
Solution:
This week your student will learn about cube roots. We previously learned that a square root is the side length of a square with a certain area. For example, if a square has an area of 16 square units then its edge length is 4 units because
Even without the useful grid, we can calculate that the edge length is 4 from the volume since
Cube roots that are not integers are still numbers that we can plot on a number line. If we have the three numbers
Here is a task to try with your student:
Plot the given numbers on the number line:
Solution:
Since
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.