Thinking ProportionallyIn this module, students build on their experiences with
ratios and proportional relationships from grade 6. They will investigate special ratios to develop and connect formulas for the circumference and area of circles. Students will identify and describe proportional and non-proportional mathematical and real-world situations to understand the characteristics of proportional relationships. They will then use formal strategies to solve proportion and percent problems. Topic 1: Circles & RatioTopic 2: Fractional RatesTopic 3: ProportionalityTopic 4: Proportional RelationshipsIn this topic, students use their knowledge of proportionality to solve real-world problems about money and scale drawings. They solve a wide variety of multistep ratio and percent problems, including problems about tips, commissions, gratuities, simple interest, taxes, markups and markdowns, and scale factors and drawings. 1. Markups and Markdowns: Introducing Proportions to Solve Percent Problems 2. Perks of Work: Calculating Tips,
Commission, and Simple Interest 3. No Taxation Without Calculation: Sales Tax, Income Tax, and Fees 4. More Ups and Downs: Percent Increase and Percent
Decrease 5. Pound for Pound, Inch for Inch: Scale and Scale Drawings Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software WorkspacesOperating with Signed NumbersIn this module, students build on their experiences with signed numbers and absolute value in grade 6.
They will use physical motion, number line models, and two-color counters to develop an understanding of the rules for operating with positive and negative numbers. Students will then solve real-world and mathematical problems involving positive and negative rational numbers. Topic 1: Adding and Subtracting Rational NumbersIn this topic, students use number lines and two-color counters to model addition and subtraction of integers before developing
rules for the sum and difference of signed numbers. 1. Math Football: Using Models to Understand Integer Addition 2. Walk the Line: Adding Integers, Part I 3. Two-Color Counters: Adding Integers, Part II 4. What's the Difference?: Subtracting Integers 5. All Mixed Up: Adding and Subtracting Rational Numbers Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software WorkspacesTopic 2: Multiplying and Dividing Rational NumbersIn this topic, students again use number lines and two-color counters to model the multiplication of integers before developing rules for the product of signed numbers. 1. Equal Groups: Multiplying and Dividing Integers 2. Be Rational!: Quotients of Integers 3. Building a Wright Brothers' Flyer: Simplifying Expressions to Solve Problems 4. Properties Schmoperties: Using Number Properties to Interpret Expressions with Signed Numbers Assessments
Student MaterialsStudent Lessons and Assignments
Reasoning AlgebraicallyIn this module, students build on their experiences with algebraic expressions and one-step equations in grade 6. The
expressions, equations, and inequalities they encounter will involve a wide range of rational numbers and require two steps rather than one. Students will write equations and inequalities for problem situations, interpret the meanings of quantities in the problems, create tables of values, graph problem situations, and make connections across the representations. Topic 1: Algebraic ExpressionsTopic 2: Two-Step Equations & InequalitiesTopic 3: Multiple Representations of EquationsAnalyzing Populations and ProbabilitiesIn this module, students will learn the basics of probability and use the theoretical and experimental probability of simple and compound events to make predictions. They will use models and simulations to determine probabilities. Students will build on their experiences with measures of center, the five-number summary, plots
of numerical data, and proportional reasoning to draw comparative inferences between two populations. Topic 1: Introduction to ProbabilityTopic 2: Compound ProbabilityTopic 3: Drawing InferencesIn this topic, students continue developing their understanding of the statistical process by exploring the second component of the process: data collection. They learn about samples,
populations, censuses, parameters, and statistics. Students then discuss the importance of representative samples, including random samples, for the purpose of making generalizations about the populations represented by the samples. 1. We Want to Hear From You!: Collecting Random Samples 2. Tiles, Gumballs, and Pumpkins: Using Random Samples to Draw Inferences 3. Spicy or Dark?: Comparing Two Populations 4.
Finding Your Spot to Live: Using Random Samples from Two Populations to Draw Conclusions Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software WorkspacesConstructing and MeasuringIn this module, students build on their experiences with angles and triangles and introduce the construction of familiar geometric objects. They will construct basic geometric objects with a compass and straightedge and later use these techniques to construct triangles. Students will use patty paper to investigate special types of angle
relationships and then use those relationships to write and solve equations to determine unknown values in a figure. They will use their knowledge of polygons and polyhedra to create and describe cross-sections of right rectangular prisms and pyramids. Finally, students will extend their knowledge of volume and surface area to solve problems involving a variety of three-dimensional solids. Topic 1: Angles & TrianglesTopic 2: Three-Dimensional Figures
Piensa Proporcionalmente
Tema 3: Proporcionalidad1. ¿Cómo crece tu
huerto?: Relaciones proporcionales 2. Cumplir con el Título IX: Constante de proporcionalidad 3. Peces-pulgadas: Identificar la
constante de proporcionalidad en gráficas 4. Presta atención: Constante de proporcionalidad en múltiples representaciones . Tema 4: Relaciones proporcionales1. Márgenes de ganancia y descuento: Introducir proporciones para resolver problemas de porcentajes 2. Ventajas del trabajo: Calcular propinas, comisiones e interés simple 3. Cálculos e impuestos: Impuesto sobre la venta, impuesto sobre la renta y
aranceles 4. Más incrementos y reducciones: Porcentaje de aumento y porcentaje de disminución 5. Libra por libra, pulgada por pulgada:
Escala y dibujos a escala Operaciones de números con signo
Tema 1: Sumar y restar números racionales1.
Fútbol americano matemático: Utilizar modelos para comprender la suma de números enteros 2. Caminar por la línea: Sumar números enteros, Parte I 3. Fichas de dos colores: Sumar números enteros, Parte II 4. ¿Cuál es la diferencia?: Restar números enteros 5. Una mezcla
de todo: Sumar y restar números racionales Tema 2: Multiplicar y dividir números racionales1. Grupos iguales: Multiplicar y dividir números enteros 2. ¡Ser racional!: Cociente de números enteros 3. Construir un avión como el de los hermanos Wright: Simplificar expresiones para resolver problemas 4. Conocer las propiedades: Utilizar las
propiedades para interpretar expresiones con números con signo Razonamiento algebraico
Tema 2: Ecuaciones y desigualdades de dos pasos1. Álgebra con dibujos: Representar ecuaciones como expresiones iguales 2. Expresiones que juegan juntas…: Resolver ecuaciones sobre una recta numérica doble 3. Formalmente tuyo: Utilizar operaciones inversas para la resolución de ecuaciones 4. Ser mayor que: Resolver desigualdades con operaciones inversas Tema 3: Varias representaciones1. Poner en el plano: Representar ecuaciones con tablas y gráficas 2. Tramos, pilas y estructura: Estructurar ecuaciones lineales 3. Deep Flight I: Construir desigualdades y ecuaciones para resolver problemas 4. Té de Texas y temperatura: Utilizar varias representaciones para resolver problemas Analizar poblaciones y probabilidades
Tema 1: La probabilidad1. Lanzar, lanzar,
lanzar...: Definir y representar la probabilidad 2. Dar a los modelos una oportunidad: Modelos de probabilidad 3. Lanzar el vaso:
Determinar la probabilidad experimental de eventos simples 4. Simular una conversación: Experimentos simples simulados Tema 2: Probabilidad compuesta1. ¿Pares o impares?: Utilizar matrices para organizar resultados 2. ¿Tres niñas y ningún niño?: Utilizar diagramas de árbol 3. Probabilidad en la tienda de mascotas: Determinar la probabilidad compuesta 4. Con buena racha: Simular la probabilidad de eventos compuestos Tema 3: Dibujar inferencias
1. ¡Queremos saber de ti!: Recopilar muestras aleatorias 2. Azulejos, bolas de goma de mascar y calabazas: Utilizar muestras aleatorias para dibujar inferencias 3. ¿Condimentado o amargo?: Comparar dos poblaciones 4. Encontrar tu lugar para vivir: Utilizar muestras aleatorias de dos poblaciones para sacar conclusiones Construir y medir
Tema 1: Ángulos y triángulos1. Conocer a
Euclides: Construcciones de formas geométricas 2. Entrega especial: Relaciones especiales de ángulos 3. Considerar todos los lados:
Construir triángulos con lados dados 4. ¿Único o no?: Construir triángulos con ángulos dados Tema 2: Figuras tridimensionales1. Fragmentación: Secciones transversales de prismas rectangulares 2. Dividir una pirámide: Secciones transversales de pirámides rectangulares 3. Oiga, señor, ¿tiene comida para pájaros?: Volumen de las pirámides 4. El sonido del área de la superficie: Área de la superficie de pirámides 5. Más de cuatro lados de la historia: Volumen y área de la
superficie de prismas y pirámides
Transforming Geometric ObjectsIn this module, students build on their experience
with rational numbers, proportionality, scale drawings, triangles, and angle pairs formed when two lines intersect. They will use patty paper to investigate transformations of geometric objects to develop an understanding of congruence and similarity. Students will then use this new knowledge about transformations to establish facts about triangles and relationships between special angle pairs. Topic 1: Rigid Motion TransformationsIn this topic, students use patty paper and the coordinate plane to investigate congruent figures. Throughout the topic, students are expected to make conjectures, investigate conjectures, and justify true results about transformations. 1. Patty Paper, Patty Paper: Introduction to Congruent Figures 2. Slides, Flips, and Spins: Introduction to Rigid Motion 3. Lateral Moves:
Translations of Figures on the Coordinate Plane 4. Mirror, Mirror: Reflections of Figures on the Coordinate Plane 5. Half Turns and Quarter Turns: Rotations of Figures
on the Coordinate Plane 6. Every Which Way: Combining Rigid Motions Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software WorkspacesTopic 2: SimilarityTopic 3: Line and Angle RelationshipsDeveloping Function FoundationsIn this
module, students build on their experience with proportional relationships and the work they did in Transforming Geometric Objects. Students will analyze and represent linear relationships using tables, equations, graphs, and scenarios. They will develop an understanding of functions. Once they know how to describe functional relationships and construct linear models, they will apply these skills to analyze bivariate data. The concepts in this module will provide the basis for the majority of
their high school algebra and statistics studies. Topic 2: Linear RelationshipsIn this topic, students develop fluency with analyzing linear relationships, writing equations of lines, and graphing lines. Using prior knowledge, students learn to calculate the slope for linear relationships represented in tables and from contexts, connecting the geometric representaions used in the previous topic with the algebraic processes used to calculate slope. 1. U.S. Shirts: Using Tables, Graphs, and Equations 2. At the Arcade: Linear Relationships in Tables 3. Dining, Dancing, Driving: Linear Relationships in Contexts 4. Derby Day: Slope-Intercept Form of a Line 5. What's the Point?: Point-Slope Form of a Line 6. The Arts Are Alive: Using Linear Equations Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software WorkspacesTopic 3: Introduction to FunctionsIn this topic, students begin to formalize the concept of function, which is a concept they may intuitively understand. They explore functions in terms of sequences, mappings, sets of ordered pairs, graphs, tables, verbal descriptions, and equations. 1. Patterns, Sequences, Rules...: Analyzing Sequences as Rules 2. Once Upon a Graph: Analyzing the Characteristics of Graphs of Relationships 3. One or More Xs to One Y: Defining Functional Relationships
4. Over the River and Through the Woods: Describing Functions
5. Comparing Apples to Oranges: Comparing Functions Using Different Representations
Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software WorkspacesTopic 4: Patterns in Bivariate DataIn this topic, students review the statistical process and investigate associations in bivariate data, both quantitative and categorical. Students use their experience plotting points to create graphical representations of data to identify and explain patterns they notice. 1. Pass the Squeeze: Analyzing Patterns in Scatter Plots 2. Where Do You Buy Your Books?: Drawing Lines of Best Fit 3. Mia Is Growing Like a Weed: Analyzing Lines of Best Fit 4.
The Stroop Test: Comparing Slopes and Intercepts of Data from Experiments 5. Would You Rather...?: Patterns of Association in Two-Way Tables Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software WorkspacesModeling with Linear EquationsIn this module, students build on their experiences of solving two-step equations
and graphing linear equations. They will apply number properties as strategies to write equations in equivalent forms and explore strategies for solving equations with variables on both sides of the equals sign. Students will write and solve equations to answer questions about real-world situations. They will also use systems of linear equations to solve real-world problems. Topic 1: Solving Linear EquationsTopic 2: Systems of Linear EquationsExpanding Number SystemsIn this module, students connect number, equations, and geometry. They will explore the properties that define the number systems that they are familiar with and then learn about a new system. Students will develop an understanding of the Pythagorean Theorem and its converse and then apply those theorems to
solve real-world problems. Topic 1: The Real Number SystemTopic 2: Pythagorean TheoremApplying PowersIn this module, students build on their knowledge of exponents to develop new rules for operating with integer exponents. They will learn how to write, recognize, compare, and operate with numbers expressed in scientific notation. Students will build on their prior experiences with the volume of prisms
and pyramids to develop formulas for the volume of cylinders, cones, and spheres. Topic 1: Exponents and Scientific NotationTopic 2: Volume of Curved FiguresIn this topic, students solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Students explore each figure in turn and determine the formula for the volume of each. They practice applying each formula, and then they solve problems requiring the use of multiple volume formulas. 1. Drum Roll, Please!: Volume of a Cylinder 2. Cone of Silence: Volume of a Cone 3. Pulled in All Directions: Volume of a Sphere 4. Silos, Frozen Yogurt, and Popcorn: Volume Problems with Cylinders, Cones, and Spheres Assessments
Student MaterialsStudent Lessons and Assignments
MATHia Software Workspaces
Transformar objetos geométricos
Tema 1: Transformaciones de movimientos rígidos
1. Practiquemos con papel parafinado: Introducción a figuras congruentes 2. Deslizar, voltear y girar: Introducción a los movimientos rígidos 3. Movimientos laterales: Traslaciones de figuras en el plano de coordenadas 4. Espejito, espejito: Reflexiones de figuras en el plano de coordenadas 5. Medias vueltas y cuartos de vuelta: Rotaciones de figuras en el plano de
coordenadas 6. En todas direcciones: Combinar movimientos rígidos Tema 2: Semejanza
1. Geometría de alejar-acercar: Dilataciones de figuras 2. Subir, correr, pisar, escalar: Dilatar figuras en el plano de coordenadas 3. De aquí para allá: Mapear figuras semejantes utilizando transformaciones Desarrollar los fundamentos de las funciones
Tema 1: De proporciones a relaciones lineales1. Proporciones postsecundarias: Representaciones de relaciones proporcionales 2. Jack y Jill subieron la colina: Utilizar triángulos semejantes para describir la inclinación de una recta 3. Pendientes resbalosas: Explorar pendientes utilizando triángulos semejantes 4. Arriba, abajo y por todos lados: Transformaciones de rectas Tema 2: Relaciones lineales1. U.S. Shirts: Utilizar tablas, gráficas y ecuaciones 2. En el salón de juegos: Relaciones lineales en tablas 3. Comer, bailar y conducir: Relaciones lineales en contextos 4. Día del
derbi: Forma pendiente-intercepto de una recta 5. ¿Cuál es el punto?: Forma punto-pendiente de una recta 6. Las artes tienen vida:
Utilizar ecuaciones lineales Tema 3: Introducción a las funciones1. Patrones, secuencias, reglas...: Analizar secuencias como reglas 2. Había una vez una gráfica: Analizar las características de las gráficas de las relaciones 3. Una o más X para una Y: Definir las relaciones funcionales 4. Por el río y a través del bosque: Describir las funciones 5. Comparar manzanas con naranjas: Comparar funciones utilizando diferentes representaciones Tema 4: Patrones en datos bivariados1. Pasa el apretón: Analizar patrones en diagramas de dispersión 2. ¿Dónde compras tus libros?: Dibujar rectas que mejor se ajustan 3. Mia crece como la maleza: Analizar rectas que mejor se ajustan 4. Prueba de Stroop: Comparar pendientes e interceptos de datos de experimentos 5. ¿Qué prefieres?: Patrones de asociación en tablas de doble
entrada Representar ecuaciones lineales
Tema 2: Sistemas de ecuaciones lineales1.
Caminos cruzados: Punto de intersección de gráficas lineales 2. El camino menos transitado: Sistemas de ecuaciones lineales 3. La feria
del condado: Utilización de la sustitución para resolver sistemas lineales 4. Pistas de patinaje: Elección de un método para resolver un sistema lineal Expandir los sistemas numéricos
Tema 2: Teorema de Pitágoras1. La conexión del triángulo rectángulo: El Teorema de Pitágoras 2. ¿Puede ser eso correcto?: El inverso del Teorema de Pitágoras 3. Pitágoras conoce a Descartes: Distancias en un sistema de coordenadas 4. Catty Corner: La longitud de los lados en dos y tres dimensiones Aplicar potencias
Tema 1: Exponentes y notación científica1. Es algo generacional: Propiedades de las potencias con exponentes de número entero 2. Muestra lo que sabes: Análisis de propiedades de las potencias 3. Lo grande y lo pequeño: Notación científica 4. ¿Cuánto más grande?: Operaciones con notación científica Tema 2: Volumen de figuras curvas
1. ¡Redoble de tambores, por favor!: Volumen de un cilindro 2. El cono del silencio: Volumen de un cono 3. Operar en todas direcciones: Volumen de una esfera 4. Silos, yogur congelado y palomitas de maíz: Problemas de volumen con cilindros, conos y
esferas
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