Geometry Unit: 8 Geometric Measurements and Dimensions

Approximate Time Frame: 3-4 weeks

Connections to Previous Learning:
7.G.4 – Area and circumference of circles.
7.G.6 – Apply formulas for area, volume and surface area of triangles, quadrilaterals, polygons, cubes and right prisms.
8.G.9 – Apply formulas for volume, cone, cylinder and spheres to real world applications.
Focus of the Unit:
  • Discover the formulas for the circumference and area of circle, volume of cylinder, pyramid and cone.
  • Apply volume and surface area formulas to real life problems. Focus on cylinder, cone, pyramid and sphere.
  • Discover the relationship between 2-D cross sections and 3-D objects (both ways).
  • Use area and volume for density problems.
  • Apply geometric properties to solve design problems.

Connections to Subsequent Learning:
Application project with marketing, construction/architecture and/or population density.
Calculus uses cross sections and rotational 2-D objects.
Desired Outcomes
Standard(s):
G-MD.1, 2, 4 G-MD.4 G-MD.2
G-MG.1, 3 G-MG.2
Priority Standards Supporting Standards Additional Standards
Transfer: Students will apply…
Understandings: Students will understand that…
Essential Questions:
Highlighted Mathematical Practices: (Practices to be explicitly emphasized are indicated with an *.)
  1. Make sense of problems and persevere in solving them. Students demonstrate their ability to persevere by selecting a modality to begin representing their understanding (i.emanipulatives, pictures). They can work collaboratively to represent their measurements or quantities and discuss their representations.
  1. Reason abstractly and quantitatively. Students will demonstrate their abstract and quantitative reasoning by estimating lengths
and then refining their estimates based upon new information. They also demonstrate reasoning by explaining indirect
measurements. They need to use measurement units correctly – understanding that the smaller the unit, the more units you need to
measure a given object.
  1. Construct viable arguments and critique the reasoning of others. Students will explain why they chose to represent a quantity or measurement in a particular way. They will also listen to each other and explain what their peers have said.
  1. Model with mathematics. In this unit, students are asked to transfer between manipulative, number line, drawings and other visual representations. They are asked to explain in words how their visuals are representing measurements or quantities.
  1. Use appropriate tools strategically. Students demonstrate their ability to use non-standard measurement units to measure lengths of objects. Hey need to select the correct tools and know when a number line is an appropriate representation.
  1. Attend to precision. Students demonstrate precision by using comparison language appropriately to describe their measurements and quantities. They count precisely to measure accurately.
  1. Look for and make use of structure. Students demonstrate the ability to use structure in their graphs, ten frames and on the 120 chart. Students can use these structures to explain the patterns and answer questions about measurements and quantities.
  1. Look for express regularity in repeated reasoning. When students note patterns on, and can use the 10 frames, 120 chart and graphs to solve problems or create new representations, they are using their repeated reasoning.

Prerequisite Skills/Concepts:
Students should already be able to… / Advanced Skills/Concepts:
Some students may be ready to…
Knowledge:
Students will know… / Skills:
Students will be able to…
WIDA Standard: English Language Learners
English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.
English language learners would benefit from:
Academic Vocabulary:
Critical Terms: Supplemental Terms:
Assessment
Pre-Assessments / Formative Assessments / Summative Assessments / Self-Assessments
Sample Lesson Sequence

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