Standards in Unit:
Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities
NC.7.EE.3 Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions.
NC.7.EE.4 Use variables to represent quantities to solve real-world or mathematical problems.
A. Construct equations to solve problems by reasoning about the quantities.
NC.8.EE.7 Solve real-world and mathematical problems by writing and solving equations and inequalities in one variable.
Draw, construct, and describe geometrical figures and describe the relationships between them
• NC.7.G.2 Understand the characteristics of angles and side lengths that create a unique triangle, more than one triangle or no triangle. Build triangles from three measures of angles and/or sides.
Solve real-world and mathematical problems involving triangle properties and angle measures
NC.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
NC.8.G.5 Use informal arguments to analyze angle relationships.
Summary of Unpacking for Each Standard:
7.EE.3: Students solve contextual problems and mathematical problems using expressions with all forms of rational numbers, including negatives, decimals, fractions, and percents. Students convert between fractions, decimals, and percents as needed to solve the problem, and problems can include multiple steps for students to interpret. Students use estimation to justify the reasonableness of answers.
7.EE.4: Students write multi-step equations and inequalities with all forms of rational numbers to model situations in a real-world or mathematical context, including those where they need to combine like terms and/or use the distributive property to solve. (For this standard, all variables are on one side of the equal sign.) For inequalities, students will need to graph their solutions on a number line. Students explain how they determined whether to write an equation or inequality and the properties of the real number system that you used to find a solution. In contextual problems, students define the variable and use appropriate units.
8.EE.7: Students build on their work with one-variable equations and inequalities to solve those with variables on both sides of the equals sign in a real-world or mathematical context. Students recognize that the solution to the equation is the value(s) of the variable, which make a true equality when substituted back into the equation. They will also discover and recognize properties of equations and inequalities and how they relate to the number of solutions.
7.G.2: Students begin to discover and work with properties of triangles, including the Triangle Inequality relating side lengths, Angle Sum Theorem in which the 3 angles add to 180 degrees, and relationships between side lengths and angle measures. They will construct triangles from given characteristics, including isosceles and equilateral, and use the properties to determine the uniqueness of certain triangles based on their characteristics.
7.G.5: Students will discover and apply angle relationships formed by two intersecting lines, including vertical angles, linear pairs, adjacent angles, supplementary angles, and complementary angles. Modeling and informal proof are appropriate to ensure students discover these relationships, and they should be able to explain their reasoning as they determine angle measures using the relationships.
8.G.5: Students will build on the angle relationships learned in 7th grade (vertical, adjacent, supplementary, and complementary) to learn properties of interior and exterior angles or triangles and relationships when two parallel lines are cut by a transversal. They will also explore the relationships between corresponding angles in similar figures.
Prerequisite Skills:
Future Skills:
Key Vocabulary:
Cornerstone Task
1. What's Your Angle: Extension Activity: http://www.cpalms.org/Public/PreviewResourceLesson/Preview/48732 (Links to an external site.)Links to an external site.
2. Writing and Solving Equations for Ages: http://map.mathshell.org/download.php?fileid=1094 (Links to an external site.)Links to an external site.
MTSS/Remediation Resources
Math Topic/DPI Bucket: Equations/Algebraic Expressions and Equations
Engage NY F2F Intervention: Grade 7, Module 3 (Links to an external site.)Links to an external site., Topic B
Edgenuity Online Intervention: Grade 7, Equations Unit
Math Topic/DPI Bucket: Angle Relationships/Geometry
Engage NY F2F Intervention: Grade 7, Module 6 (Links to an external site.)Links to an external site., Topic A
Edgenuity Online Intervention: Grade 7, Two-Dimensional Geometry Unit, Lessons 1-2