# 1. Carnival combos: Find solutions to a system (C)

teaches Common Core State Standards CCSS.Math.Content.8.EE.C.8a http://corestandards.org/Math/Content/8/EE/C/8/a
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1

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Lesson objective: Understand that a solution for a system of two equations (conditions) is an ordered pair of values that makes both equations true.

Students bring prior knowledge of solutions of linear equations from 8.EE.C.7. This prior knowledge is extended to solutions of systems of equations as students determine an ordered pair of values that makes two conditions true. A conceptual challenge students may encounter is a solution having two numbers rather than just one number.

The concept is developed through work with equations and tables, which show how equations are true and two conditions can share an ordered pair of values.

This work helps students deepen their understanding of number because an ordered pair represents a two-dimensional number as a solution to an equation or relationship with two quantities.

Students engage in Mathematical Practice 1 (Make sense of problems and perservere in solving them) as they use lists, tables, diagrams, pictures, or other representations to show solutions to two different conditions with two variables and consider the overlap.

Key vocabulary:

• condition
• solution
• system

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