Unit 7, Lesson 4
Grafiquemos desigualdades lineales en dos variables (parte 1)
Matemáticas integradas 1
4.2
Activity
Soluciones y no soluciones
Instructional Routines
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NoneEstas son cuatro desigualdades. Con su grupo, para cada desigualdad que se les asignó:
- Encuentren algunos pares de coordenadas que sean soluciones de la desigualdad y algunos pares de coordenadas que no sean soluciones.
- Marquen los puntos de ambos conjuntos (las soluciones y las no soluciones) en el plano de coordenadas. Usen dos colores diferentes o dos símbolos diferentes, como X y O.
- Marquen suficientes puntos para empezar a ver la región que contiene las soluciones y la región que contiene las no soluciones. Busquen una regla que describa la región en la que están las soluciones.
4.3
Activity
Dibujemos soluciones de desigualdades
Instructional Routines
NoneMaterials
NoneActivity Narrative
In the preceding activity, students looked at the regions that represent solutions and non-solutions to inequalities. They recognized that the boundary between the two regions is the graph of an equation that is related to the inequality. Students did not, however, look closely at whether the boundary line itself is a part of the solution. That investigation is the focus of this activity.
Students reason with algebraic and graphical representations of inequalities in two directions. They first graph the solutions to given inequalities, and later write inequalities whose solutions could be represented by given graphs.
If many students get stuck on graphing or writing inequalities, consider moving fairly quickly through the activity and using the discussion questions in the Lesson Synthesis to help students gain clarity and focus.
Launch
Display the inequalities
Make sure that students understand why all three coordinate pairs are solutions to
Ask students to predict which graph represents which inequality. Consider polling the class on their predictions.
Explain that the solid line is a way to say that all the points on that line (
Because the solutions to
Tell students that they will now sketch the solutions of some other inequalities and think about whether or not the boundary line is included in the solutions.
Representation: Develop Language and Symbols. Create a display of the four inequality symbols
Supports accessibility for: Conceptual Processing; Language
Supports accessibility for: Conceptual Processing; Language
Student Lesson Summary
La ecuación
Podemos representar todas las soluciones de
La gráfica es una recta. Todos los puntos en la recta son soluciones de
La desigualdad
Esto significa que las soluciones de
En un plano de coordenadas, la solución de
Podemos sombrear la región a un lado de la recta que contiene las soluciones para indicar que todos sus puntos son soluciones.
Inequality graphed on a coordinate plane, origin O. Each axis from negative 8 to 10, by 2’s. Solid line goes through 0 comma 7 and 5 comma 2. The region below the solid line is shaded. The points negative 6 comma 0 and 4 comma negative 7 are labeled.
¿Y qué ocurre con la desigualdad
Las soluciones son las parejas de
En un plano de coordenadas, la solución de la desigualdad no incluye los puntos que están en la recta que representa
Para excluir los puntos de esa recta frontera, podemos usar una recta punteada.
Todos los puntos que están abajo de esta recta son parejas
Inequality graphed on a coordinate plane, origin O. Each axis from negative 8 to 10, by 2’s. Dashed line goes through 0 comma 7 and 7 comma 0. The region below the dashed line is shaded.
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