Core Skills Analysis
Mathematics: Algebra
Ella used the elimination method to solve five systems of linear equations, multiplying an equation when needed so that one variable’s terms canceled when the equations were added. She found the ordered-pair solutions (3, 2), (2, 3), (1, 2), (2, 1), and (4, 2), and used substitution to determine the second variable after solving for the first. Through these examples, Ella practiced preserving equivalent equations when multiplying by a constant and combining like terms accurately. She also connected each algebraic solution to the idea of a point that satisfies both equations in a system.
Tips
Tips To deepen Ella’s understanding, have her graph one of the systems and compare the intersection with her algebraic solution. Invite her to create a real-life scenario—such as comparing two pricing plans—that can be modeled by a pair of linear equations, then explain what the solution means in context. For a visual challenge, use color-coded cards to show how multiplying equations creates matching opposite coefficients before elimination. Finish with a short “error detective” activity in which Ella checks a sample solution by substituting its ordered pair into both original equations.
Book Recommendations
- The Cartoon Guide to Algebra by Larry Gonick: A visual, humorous guide to algebra that explains core ideas through cartoons and examples.
Learning Standards
- Florida B.E.S.T. Mathematics — MA.912.AR.3.4: Ella solved systems of linear equations in two variables algebraically by eliminating a variable, solving the resulting equation, and substituting to find the ordered pair.
Try This Next
- Make a color-coded elimination worksheet: highlight opposite variable terms, show the addition step, then box the resulting one-variable equation.
- Create a five-question check-your-solution quiz: substitute each ordered pair into both original equations and mark whether both statements are true.
- Graph one of the solved systems and label its intersection with the ordered pair Ella found algebraically.
- Write a short real-world pricing-plan problem that can be represented by two linear equations, and explain what the solution represents.