Content Area Mathematics Grade/Course 06 (Accelerated Track) School Year 2017-18 Framework Number: Name 04: Geometry Calendar Dates; Pacing 01/08/18 – 02/09/18; 4.5 weeks (23 days)
ULTIMATE CURRICULUM FRAMEWORK GOALS Ultimate Performance Task The Ultimate Performance Task for this Framework is: Designing 3D Products: Candy Cartons The goal (within the scenario) is to design a new candy carton for a company based on certain requirement. Students will work with two- and three-dimensional shapes in order to solve a real-world problem involving capacity and surface area.
The Mathalicious Lessons for this Framework are: Cartogra-fail What does earth really look like? Students approximate the areas of different landmasses by decomposing them into triangles and rectangles. They do this for two different maps, and debate whether or not the map you use affects how you see — both literally and figuratively — the world. Tricks of the Tray’d What's the best way to design a food tray? Students calculate the volumes of rectangular prisms and use that information to design a cafeteria tray that looks good and holds a balanced meal.
The most important performance we want learners to be able to do with the acquired content knowledge and skills of this framework is: ● agility and adaptability. ● critical thinking and problem solving. Transfer Goal(s) Students will be able to independently use their learning to … ● think critically and solve geometric problems through the use of all math operations in real-world context. ● be agile and adaptable while using appropriate formulas or using various strategies in order to solve a complex problem with a geometric focus. Meaning Goals BIG IDEAS / UNDERSTANDINGS ESSENTIAL QUESTIONS Student will understand that … Students will keep considering: ● two figures can have the same volume but have different ● What is the relationship between a formula and the other shapes and therefore different surface areas. strategies used to find geometric measurements? ● any geometric figure can be described using a variety of ● How are formulas used in real-world situations? measurements that give different information about the figure. ● knowledge of how to find geometric measurements of different shapes helps us do projects in the home and community. IDEAS IMPORTANTES / CONOCIMIENTOS PREGUNTAS ESENCIALES Los estudiantes comprenderán que … Los estudiantes seguirán teniendo en cuenta: ● dos figuras pueden tener el mismo volumen pero pueden tener ● ¿Cuál es la relación entre una fórmula y las otras estrategias diferente figura y por lo tanto diferentes superficies de área. usadas para encontrar medidas geométricas? ● cualquier figura geométrica puede ser descrita usando una ● ¿Cómo se usan las fórmulas en situaciones en la vida real? variedad de medidas que te dan diferente información sobre la figura. ● el conocimiento en cómo encontrar medidas geométricas de diferentes figuras nos ayuda a hacer proyectos en la casa y comunidad. Acquisition Goals In order to reach the ULTIMATE GOALS, students must have acquired the following knowledge, skills, and vocabulary. However, depending on the student, it MAY NOT be necessary to teach everything listed. Students will be skilled at … And in order to demonstrate the skill, students will need to know … ● applying all four operations of whole number, fractions, and ● how to substitute given values into a formula to solve the decimals with accuracy and efficiency to geometric formulas. (3) equation for the unknown variable. ● solving geometric problems by graphing points in all four ● irregular polygons can be decomposed into triangles and quadrants of the coordinate plane. (3) quadrilaterals. ● calculating the area of triangles and quadrilaterals. (3) ● the relationship between the formulas V = l w h and V = B h. ● decomposing complex figures into triangles and quadrilaterals ● measurements of two-dimensional geometric figures can be to calculate geometric measurements. represented by horizontal and vertical distances on a coordinate ● applying various strategies, including the use of formulas, to find plane. the volume and surface area of regular prisms. (3) ● a three-dimensional figure can be represented using a net. ● determining the measurement required to solve a real-world problem. (4) ● determining missing dimensions of a figure given its area (or surface area or volume) and some of the dimensions. (4) Vocabulary / Vocabulario Tier 1 / Nivel 1 Tier 2 / Nivel 2 Tier 3 / Nivel 3 (everyday words) (general academic words) (domain specific words) ● length / longitud ● parallel / paralelo ● width / ancho ● perpendicular / perpendicular ● height / altura ● triangle / triángulo ● perimeter / perimetro ● angle / ángulo ● quadrilateral / cuadrilátero ● polygons / polígonos ● volume / volumen ● rectangular prism / prisma rectangular ● coordinate plane / plano de coordenadas ● coordinate / coordenada ● surface area / superficie de área ● face / cara ● area / área ● edge / borde ● vertex (vertices) / vértice (vértices) ● segment / segmento ● base / base
Optional Learning Plan Other Evidence of Understanding Module 05: Area, Surface Area, and Volume Problems may help you ● Illustrative Mathematics: with choosing lessons and designing your progression of learning for o Morning Walk – Equations in one variable. this framework. Within this module you may want to reference these o Distances Between Points – Coordinate plane graphing. topics: o Rectangle Perimeter 1 – Writing expressions. ● Topic A: Area of Triangles, Quadrilaterals, and Polygons o Wallpaper Decomposition – Compose and decompose ● Topic B: Polygons on the Coordinate Plane Polygons. ● Topic C: Volume of Right Rectangle Prisms o Computing Volume Progression 1 – Volume of cubes. ● Topic D: Nets and Surface Area o Nets for Pyramids and Prisms – Surface area. ● Mid and End-Assessments o Sand Under the Swing Set – Surface area. ● Nrich.maths.org: To help support families on content within this framework please see ○ Cuboid Challenge – Volume. Tips for Parents (Grade 6). ● PARCC: ○ 2015 Released Items Video Libraries: ■ Answer Key ● EngageNY (engageny.org) ● Common Core Inc. (greatminds.net) Optional Mathalicious Lessons (for remediation on a topic not listed, email [email protected] for a lesson recommendation): ● 1600 Pennsylvania – How big is the White House? Students build scale models to determine the surface area and volume of America's most famous home. ● Advertising Aged – How much of what you see is advertising? Students use decomposition to calculate the areas of irregularly shaped billboards from Times Square in 1938 and 2015 and describe how much of the visual field is occupied by advertisements. The ULTIMATE GOALS were developed from these Common Core State Standards (CCSS):
The Number System Apply and extend previous understandings of numbers to the system of rational numbers. (6.NS.C) 6.NS.C.8: SOLVE real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.NS.C.6.b: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 6.NS.C.6.c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Geometry – Solve real-world and mathematical problems involving area, surface area, and volume. (6.G.A) 6.G.A.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. (6.EE.A) 6.EE.A.2: WRITE, READ, and EVALUATE expressions in which letters stand for numbers. Reason about and solve one-variable equations and inequalities. (6.EE.B) 6.EE.B.7: SOLVE real-world and mathematical problems by WRITING and SOLVING equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Geometry Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. (7.G.B) 7.G.B.6: SOLVE real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Solve real-world and mathematical problems involving area, surface area, and volume. (6.G.A) 6.G.A.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.G.A.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.A.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Teacher Notes The key additions to this framework of study are the inclusion of more than just one-step equations. These students will go further by solving two-step and three-step equations, solving and graphing one-step and two-step inequalities, and constructing simple equations and inequalities to model real-life situations.
This framework builds upon students’ learning in earlier grades with finding the areas of rectangles. In grade 06, students will use what they know about area of rectangles to investigate triangles, special quadrilaterals, and polygons. Additionally, they will have the opportunity to develop their understanding and use of equations in geometric contexts.
In addition to working with two-dimensional figures, students will build on their knowledge of finding volume from earlier grades. In this framework, students learn how to calculate the volume of rectangular prisms with fractional side lengths. Students also model three-dimensional figures with nets and use the nets to find surface area. Students apply the skills of evaluating expressions to calculating area, surface area, and volume using appropriate formulas. Standards for Mathematical Practice Through a variety of activities and lessons, students will... ● Make sense of problems and persevere in solving them. (MP.1) Make sense of real-world problems that involve area, volume, and surface area. ● Construct viable arguments and critique the reasoning of others. (MP.3) Develop different arguments as to why area formulas work for different polygons. Through this development, students may discuss and critique their peers’ thinking process. ● Model with mathematics (MP.4) Use models to demonstrate why the area formulas for different quadrilaterals are accurate. Students will use unit cubes to build right rectangular prisms and use these to calculate volume. ● Attend to precision. (MP.6) Attend to precision while they understand and use labels correctly throughout the module. For example, when calculating the area of a triangle, the answer will be labeled units2 because the area is the product of two dimensions. Partnership for Assessment of Readiness for College and Careers (PARCC) ● CCSS.6.NS.C.6, CCSS.6.NS.C.8, CCSS.6.EE.A.2, and CCSS.6.EE.B.7 are categorized under Sub-Claim A –Major Content for this grade/course and will be assessed on the the End-of-Year Assessment. Problems should connect to the Math Practice Standards, especially MP.3 and MP.4. ● CCSS.6.G.A.1-4 are categorized under Sub-Claim B – Supporting Content for this grade/course and will be assessed on the End-of-Year Assessment.
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