Tacos For Sale- by Manuel Castillo
This activity allows students to make connections through multiple representations, which is a key concept for Algebra students. In this activity, students are given a situation where they must find combinations of breakfast and lunch tacos that will use up all their money. In essence, these are Diophantine equations.
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Timeline: 1 – 2 days
Instructional Focus: Multiple Representations from Problem Situations, Linear Equations in Standard Form (Algebra 1)
Driving Question: How many ways can I combine two unknowns with a set total? How can I use this information to write an equation in Standard Form?
Challenge Brief: Jose and Saul have $$$10 to spend on lunch tacos that cost $$$2 and breakfast tacos that cost $$$1 dollar, how many ways can you spend all your money without receiving change? All tacos, no change. Can you think of an equation in standard form that fits this data? (AX + BY = C).
- Begin by asking students in groups to find possible solutions if Breakfast Tacos (B) cost $$$1 and Lunch Tacos (L) cost $$$2 with $$$10 to spend.
- Ask students to make a table of values, keep a Total (T) on the table by the values.
- Ask students to graph and guide them to find the pattern through both table and graph.
- Students should come up with an equation.
- Repeat with more difficult problems, ie change total or cost per tacos
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(3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:
(A) compare and contrast proportional and non-proportional linear relationships
(1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to:
(B) gather and record data and use data sets to determine functional relationships between quantities;
(C) describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;
(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and
(5) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to:
(C) use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.
(6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to:
(A) develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;
(D) graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y‑intercept;