This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.
CK-12's Geometry - Second Edition is a clear presentation of the essentials …
CK-12's Geometry - Second Edition is a clear presentation of the essentials of geometry for the high school student. Topics include: Proofs, Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations.
CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of …
CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of exercises intended to enrich a student's understanding of basic geometric principles.
CK-12's Texas Instruments Geometry Teachers Edition Flexbook is a useful collection of …
CK-12's Texas Instruments Geometry Teachers Edition Flexbook is a useful collection of exercises intended to enrich a student's understanding of basic geometric principles.
Measurement in Grade 7 sees us move from simply finding the perimeter …
Measurement in Grade 7 sees us move from simply finding the perimeter and area of a common object, such as a rectangle or triangle, and move into complex shapes that may involve a combination of different shapes or circles. This unit reviews the basics of finding the area of rectangles, triangles, and parallelograms. It concludes with some real-life problems to which these concepts can be applied.This unit is designed for the Alberta Grade 7 Curriculum.
This lesson unit is intended to help you assess how students reason …
This lesson unit is intended to help you assess how students reason about geometry and, in particular, how well they are able to: use facts about the angle sum and exterior angles of triangles to calculate missing angles; apply angle theorems to parallel lines cut by a transversal; interpret geometrical diagrams using mathematical properties to identify similarity of triangles.
This task shows how to inscribe a circle in a triangle using …
This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.
This problem introduces the circumcenter of a triangle and shows how it …
This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.
This task focuses on a remarkable fact which comes out of the …
This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.
Brigitte Tennis uses the visual aid of spraying water from one point …
Brigitte Tennis uses the visual aid of spraying water from one point of a triangle to illustrate to her students opposite and adjacent sides. She then beats out a rhythm on drums to teach her students the mnemonic device SOH-CAH-TOA for finding sine, cosine, and tangent.
This task is intended for instruction, providing the students with a chance …
This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections.
This is a three-credit course which covers topics that enhance the students’ …
This is a three-credit course which covers topics that enhance the students’ problem solving abilities, knowledge of the basic principles of probability/statistics, and guides students to master critical thinking/logic skills, geometric principles, personal finance skills. This course requires that students apply their knowledge to real-world problems. A TI-84 or comparable calculator is required. The course has four main units: Thinking Algebraically, Thinking Logically and Geometrically, Thinking Statistically, and Making Connections. This course is paired with a course in MyOpenMath which contains the instructor materials (including answer keys) and online homework system with immediate feedback. All course materials are licensed by CC-BY-SA unless otherwise noted.
Topics List for this Lesson: Points, Lines, Planes, and AnglesTriangles Plus Similarity and …
Topics List for this Lesson: Points, Lines, Planes, and AnglesTriangles Plus Similarity and ProportionsPerimeter, Area, and CircumferenceVolume and Surface Area
Surface Area and Volume Type of Unit: Conceptual Prior Knowledge Students should …
Surface Area and Volume
Type of Unit: Conceptual
Prior Knowledge
Students should be able to:
Identify rectangles, parallelograms, trapezoids, and triangles and their bases and heights. Identify cubes, rectangular prisms, and pyramids and their faces, edges, and vertices. Understand that area of a 2-D figure is a measure of the figure's surface and that it is measured in square units. Understand volume of a 3-D figure is a measure of the space the figure occupies and is measured in cubic units.
Lesson Flow
The unit begins with an exploratory lesson about the volumes of containers. Then in Lessons 2–5, students investigate areas of 2-D figures. To find the area of a parallelogram, students consider how it can be rearranged to form a rectangle. To find the area of a trapezoid, students think about how two copies of the trapezoid can be put together to form a parallelogram. To find the area of a triangle, students consider how two copies of the triangle can be put together to form a parallelogram. By sketching and analyzing several parallelograms, trapezoids, and triangles, students develop area formulas for these figures. Students then find areas of composite figures by decomposing them into familiar figures. In the last lesson on area, students estimate the area of an irregular figure by overlaying it with a grid. In Lesson 6, the focus shifts to 3-D figures. Students build rectangular prisms from unit cubes and develop a formula for finding the volume of any rectangular prism. In Lesson 7, students analyze and create nets for prisms. In Lesson 8, students compare a cube to a square pyramid with the same base and height as the cube. They consider the number of faces, edges, and vertices, as well as the surface area and volume. In Lesson 9, students use their knowledge of volume, area, and linear measurements to solve a packing problem.
Lesson OverviewStudents find the area of a triangle by putting together a …
Lesson OverviewStudents find the area of a triangle by putting together a triangle and a copy of the triangle to form a parallelogram with the same base and height as the triangle. Students also create several examples of triangles and look for relationships among the base, height, and area measures. These activities lead students to develop and understand a formula for the area of a triangle.Key ConceptsTo find the area of a triangle, you must know the length of a base and the corresponding height. The base of a triangle can be any of the three sides. The height is the perpendicular distance from the vertex opposite the base to the line containing the base. The height can be found inside or outside the triangle, or it can be the length of one of the sides.You can put together a triangle and a copy of the triangle to form a parallelogram with the same base and height as the triangle. The area of the original triangle is half of the area of the parallelogram. Because the area formula for a parallelogram is A = bh, the area formula for a triangle is A = 12bh.Goals and Learning ObjectivesDevelop and explore the formula for the area of a triangle.
Four full-year digital course, built from the ground up and fully-aligned to …
Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.
Algebraic Reasoning Type of Unit: Concept Prior Knowledge Students should be able …
Algebraic Reasoning
Type of Unit: Concept
Prior Knowledge
Students should be able to:
Add, subtract, multiply, and divide rational numbers. Evaluate expressions for a value of a variable. Use the distributive property to generate equivalent expressions including combining like terms. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers. Understand and graph solutions to inequalities x<c or x>c. Use equations, tables, and graphs to represent the relationship between two variables. Relate fractions, decimals, and percents. Solve percent problems included those involving percent of increase or percent of decrease.
Lesson Flow
This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.
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