Illustrative Math Alignment: Grade 7 Unit 2

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

This is part of a collection of math examples that focus on ratios, proportions, and percents.

Topic

Equations

Description

This example demonstrates solving equations using angle properties, specifically focusing on supplementary angles. Supplementary angles are two angles that add up to 180 degrees. In this case, we have one known angle of 135° and an unknown angle x. 

To solve such equations, we use the fundamental property of supplementary angles: their sum equals 180°. 

Topic

Equations

Description

This example illustrates solving equations using angle properties, focusing on parallel lines cut by a transversal and supplementary angles. When parallel lines are cut by a transversal, pairs of supplementary angles are formed, meaning they sum to 180°. 

In this scenario, we have one known angle of 118° and an unknown angle x. However, angle y and the 118° angle are alternate exterior angles, which are congruent. This means we can set up this equation using the property of supplementary angles:

118 + x = 180

Topic

Equations

Description

This example illustrates solving equations using angle properties, focusing on supplementary angles. Supplementary angles are two angles that sum to 180 degrees. In this scenario, we have one known angle of 75° and an unknown angle x. The equation for supplementary angles is always in the form: angle1 + angle2 = 180°. 

Here, we can write 75 + x = 180. To solve for x, we subtract 75 from both sides: x = 180 - 75, giving us x = 105°. 

Topic

Equations

Description

This example demonstrates solving equations using angle properties, specifically focusing on straight angles and vertical angles. A straight angle measures 180°, and vertical angles are always congruent. In this scenario, we have two known angles (36° and 72°) and an unknown angle x. This unknown angle x is vertical (and therefore congruent) to angle z. 

The angles 36, 72, and z form a straight, but since z is congruent to x, we can write the sum of this straight angle:

x + 36 + 72 = 180

x = 72°

Topic

Equations

Description

This example illustrates solving equations using angle properties, focusing on straight angles and vertical angles. A straight angle measures 180°, and vertical angles are always congruent. In this scenario, we have two known angles (42° and 55°) and an unknown angle x. However, angle x is vertical (and therefore congruent) to angle y.

The equation can be set up based on the fact that the sum of angles on a straight line is 180°. Thus, we have: 

42 + 55 + x = 180

Topic

Equations

Description

This example demonstrates solving equations using angle properties, specifically focusing on complementary angles and the exterior angle theorem. Complementary angles are two angles that sum to 90°, while the exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. In this scenario, we have a right angle (90°), an exterior angle (125°), and an unknown angle x. Using the exterior angle theorem, we can set up the equation: x + 90 = 125. To solve for x, we subtract 90 from both sides: x = 35°.