Module 4: Linear Equations
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Standard for Lessons 6-7: 8.EE.7 Solve real-world and mathematical problems by writing and solving equations and inequalities in one variable. ▪ Recognize linear equations in one variable as having one solution, infinitely many solutions, or no solutions. Standard for Lessons 1-9, A1-M1-L14: 8.EE.7 Solve real-world and mathematical problems by writing and solving equations and inequalities in one variable. ▪ Solve linear equations and inequalities including multi-step equations and inequalities with the same variable on both sides. Previous Grade Standards: 7.EE.1, 7.EE.4a |
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Tips for Parents, Topics D & E | |
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Standard for Lessons 24-30: 8.EE.8 Analyze and solve a system of two linear equations in two variables in slope-intercept form.
▪ Understand that solutions to a system of two linear equations correspond to the points of intersection of their graphs
because the point of intersection satisfies both equations simultaneously. ▪ Solve real-world and mathematical problems leading to systems of linear equations by graphing the equations. Solve simple cases by inspection. Previous Grade Standards: 6.EE.5, 7.EE.4a |
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Pythagorean Triples: legs a and b, and hypotenuse c are all natural numbers.
Here are 16 Pythagorean triples with c<100:
(3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61),
(16, 63, 65), (33, 56, 65), (48, 55, 73), (13, 84, 85), (36, 77, 85), (39, 80, 89), and (65, 72, 97)
Note: (6, 8, 10) is not included, as it is the same ratio as (3, 4, 5).
Standard for Lesson 31: 8.G.7 Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.