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Math, Grade 6, Ratios, Student Presentations
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Student groups make their presentations, provide feedback for other students’ presentations, and get evaluated on their listening skills.Key ConceptsIn this culminating event, students must present their project plan and solution to the class. The presentation allows students to explain their problem-solving plan, to communicate their reasoning, and to construct a viable argument about a mathematical problem. Students also listen to other project presentations and provide feedback to the presenters. Listeners have the opportunity to critique the mathematical reasoning of others.Goals and Learning ObjectivesPresent project to the class.Give feedback on other project presentations.Exhibit good listening skills.

Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Ratios, Student Project
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Students choose a project idea and a partner or group. They write a proposal for the project.Key ConceptsProjects engage students in the applications of mathematics. It is important for students to apply mathematical ways of thinking to solve rich problems. Students are more motivated to understand mathematical concepts if they are engaged in solving a problem of their own choosing. In this lesson, students are challenged to identify an interesting mathematical problem and to choose a partner or a group to work with collaboratively in order to solve that problem. Students gain valuable skills in problem solving, reasoning, and communicating mathematical ideas with others.Goals and Learning ObjectivesIdentify a project ideaIdentify a partner or group to work with collaboratively on a math project

Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Ratios, Student Self Check
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Students begin the lesson with a critique of their own work on the Self Check using questions and comments from you to reflect on their work. They then critique three examples of student work on the task, each with its own tools for modeling the given relationship between quantities. Finally, they apply what they learned to a closely related problem.Key ConceptsStudents reflect on their work and connect different ways of representing ratio relationships: tape diagrams, double number lines, and ratio tables.Goals and Learning ObjectivesUse teacher comments to refine solution strategies for ratio problems.Deepen understanding of ratio relationships.Synthesize and connect strategies for representing and investigating ratio relationships.Critique given student models created to solve ratio problems.Apply deepened understanding of ratio relationships to a new ratio problem.

Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Ratios, Tape Diagrams
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Students use tape diagrams to model relationships and solve problems about types of DVDs.Key ConceptsTape diagrams are useful for visualizing ratio relationships between two (or more) quantities that have the same units. They can be used to highlight the multiplicative relationship between the quantities.Goals and Learning ObjectivesUnderstand tape diagrams as a way to visually compare two or more quantities.Use tape diagrams to solve ratio problems.

Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Ratios, Using Ratio Tables to Solve Problems
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Students focus on interpreting, creating, and using ratio tables to solve problems.Key ConceptsA ratio table shows pairs of corresponding values, with an equivalent ratio between each pair. Ratio tables have both an additive and a multiplicative structure:Goals and Learning ObjectivesComplete ratio tables.Use ratio tables to solve problems.

Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume
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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.

Subject:
Geometry
Mathematics
Provider:
Pearson
Math, Grade 6, Surface Area and Volume, Analyzing The Formula of A Parallelogram & Trapezoid
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Lesson OverviewStudents find the area of a parallelogram by rearranging it to form a rectangle. They find the area of a trapezoid by putting together two copies of it to form a parallelogram. By doing these activities and by analyzing the dimensions and areas of several examples of each figure, students develop and understand area formulas for parallelograms and trapezoids.Key ConceptsA parallelogram is a quadrilateral with two pairs of parallel sides. The base of a parallelogram can be any of the four sides. The height is the perpendicular distance from the base to the opposite side.A trapezoid is a quadrilateral with exactly one pair of parallel sides. The bases of a trapezoid are the parallel sides. The height is the perpendicular distance between the bases.You can cut a parallelogram into two pieces and reassemble them to form a rectangle. Because the area does not change, the area of the rectangle is the same as the area of the parallelogram. This gives the parallelogram area formula A = bh.You can put two identical trapezoids together to form a parallelogram with the same height as the trapezoid and a base length equal to the sum of the base lengths of the trapezoid. The area of the parallelogram is (b1 + b2)h, so the area of the trapezoid is one-half of this area. Thus, the trapezoid area formula is A = 12(b1 + b2)h.Goals and Learning ObjectivesDevelop and explore the formula for the area of a parallelogram.Develop and explore the formula for the area of a trapezoid.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Analyzing The Formula of A Triangle
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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.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Basic & Composite Figures
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Lesson OverviewStudents use what they know about finding the areas of basic figures to find areas of composite figures.Key ConceptsA composite figure is a figure that can be divided into two or more basic figures.The area of a composite figure can be found by dividing it into basic figures whose areas can be calculated easily.For some figures, the area can also be found by surrounding the figure with a basic figure, creating other basic figures “between” the original figure and the surrounding figure. The area of the original figure can then be found by subtracting the basic figure.Goals and Learning ObjectivesFind the area of composite figures by decomposing and composing them into more basic figures. 

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Comparing Surface Area & Volume
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Lesson OverviewStudents make two different rectangular prisms by folding two 812 in. by 11 in. sheets of paper in different ways. Then students use reasoning to compare the total areas of the faces of the two prisms (i.e., their surface areas). Students also predict how the amounts of space inside the prisms (i.e., their volumes) compare. They will check their predictions in Lesson 6.Key ConceptsStudents compare the total area of the faces (i.e., surface area) of one rectangular prism to the total area of the faces of another prism. Students make predictions about which prism has the greater amount of space inside (i.e., the greater volume). Students do not compute actual surface areas or volumes. This exploration helps pave the way for a more formal study of volume in Lesson 6 and a more formal study of surface area in Lesson 7.Goals and Learning ObjectivesExplore how the surface areas and volumes of two different prisms made from the same-sized sheet of paper compare.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Diagrams & Problem Solving Strategies
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Lesson OverviewStudents revise their packing plans based on teacher feedback and then take a quiz.Students will use their knowledge of volume, area, and linear measurements to solve problems. They will draw diagrams to help them solve a problem and track and review their choice of problem-solving strategies.Key ConceptsConcepts from previous lessons are integrated into this assessment task: finding the volume of rectangular prisms. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply your knowledge of the volume of rectangular prisms.Track and review your choice of strategy when problem-solving.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Gallery Problems Exercise (Groups)
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Gallery OverviewStudents who are caught up can spend this time working on gallery problems while you work with other students in study groups. Students have a choice of problems, and they can work on however many problems time permits.Gallery DescriptionsFinding the Missing BaseStudents will find the length of one of the bases of a trapezoid given the length of the other base, the height, and the area.Utah UnitsStudents will estimate the area of Utah and then estimate the area of the United States in “Utah” units.Growing RectanglesStudents know how to find the lengths of the sides of polygons on the coordinate plane. They will use this knowledge to find the area of each rectangle in a series of growing rectangles.The Volumes of SolidsStudents will find the volume of solids that are built out of cubes. They will also build their own solid out of cubes and have their partner find its volume.From 3-D to 2-D and BackStudents will investigate the net of a milk carton.Geometry of GardeningStudents will use their knowledge of perimeter and area to design a garden on grid paper.Net of a Number CubeStudents will draw a net of a number cube.Dividing ParallelogramsStudents will prove or disprove Emma's statement about dividing parallelograms into four triangles, all with the same area.Area of TrianglesStudents will find the areas of two different triangles on the coordinate plane.Placing a RugStudents will place a square rug exactly in the middle of a floor and find the number of square feet not covered by the rug.

Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Identifying Nets For Cubes
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Lesson OverviewStudents explore nets—2-D patterns that can be folded to form 3-D figures. They start by examining several patterns and determining which nets form a cube. Then, they sketch nets for rectangular prisms. They also find the surface area of the rectangular prisms.ELL: Remind students of the units used to measure area and volume. Use this opportunity to reinforce why square units are used for area (2-D) and cubed units are used for volume (3-D).MathematicsA net is a 2-D pattern that can be folded to form a 3-D figure. In this lesson, the focus is on nets for rectangular prisms. There are many possible nets for any given prism. For example, there are 11 different nets for a cube, as shown below.The surface area of a prism is the area of its net.Goals and Learning ObjectivesIdentify nets for cubes.Sketch the net of a rectangular prism.Find the surface area of a rectangular prism.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Transforming The Net of A Cube Into The Net of A Pyramid
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Lesson OverviewStudents use scissors to transform a net for a unit cube into a net for a square pyramid. They then investigate how changing a figure from a cube to a square pyramid affects the number of faces, edges, and vertices and how it changes the surface area and volume.Key ConceptsA square pyramid is a 3-D figure with a square base and four triangular faces.In this lesson, the net for a cube is transformed into a net for a square pyramid. This requires cutting off one square completely and changing four others into isosceles triangles.It is easy to see that the surface area of the pyramid is less than the surface area of the cube, because part of the cube's surface is cut off to create the pyramid. Specifically, the surface area of the pyramid is 3 square units, and the surface area of the cube is 6 square units. Students will be able to see visually that the volume of the pyramid is less than that of the cube.Students consider the number of faces, vertices, and edges of the two figures. A face is a flat side of a figure. An edge is a segment where 2 faces meet. A vertex is the point where three or more faces meet. A cube has 6 faces, 8 vertices, and 12 edges. A square pyramid has 5 faces, 5 vertices, and 8 edges.Goals and Learning ObjectivesChange the net of a cube into the net of a pyramid.Find the surface area of the pyramid. 

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Using A Grid To Calculate The Area Of An Irregular Figure
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Lesson OverviewStudents estimate the area of Lake Chad by overlaying a grid on the map of the lake.Key ConceptThe area of an irregular figure can be found by overlaying a grid on the figure. By estimating the number of grid squares the figure covers and multiplying by the area of each square, you can find the approximate area of the figure. The accuracy of the estimate depends on the size of the grid squares. Using a smaller grid leads to a more accurate estimate because more whole grid squares are completely filled. However, using a smaller grid also requires more counting and more combining of partially-filled squares and is, therefore, more time-consuming. Using a larger grid gives a quicker, but rougher, estimate of the area.Goals and Learning ObjectivesUse a grid to find the area of an irregular figure.MaterialsMap of Lake Chad handout (one for each pair of students)Rulers, optional (one for each pair of students)

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 6, Surface Area and Volume, Volume Formula For Rectangular Prisms
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Lesson OverviewStudents build prisms with fractional side lengths by using unit-fraction cubes (i.e., cubes with side lengths that are unit fractions, such as 13 unit or 14 unit). Students verify that the volume formula for rectangular prisms, V = lwh or V = bh, applies to prisms with side lengths that are not whole numbers.Key ConceptsIn fifth grade, students found volumes of prisms with whole-number dimensions by finding the number of unit cubes that fit inside the prisms. They found that the total number of unit cubes required is the number of unit cubes in one layer (which is the same as the area of the base) times the number of layers (which is the same as the height). This idea was generalized as V = lwh, where l, w, and h are the length, width, and height of the prism, or as V = Bh, where B is the area of the base of the prism and h is the height.Unit cubes in each layer = 3 × 4Number of layers = 5Total number of unit cubes = 3 × 4 × 5 = 60Volume = 60 cubic unitsIn this lesson, students extend this idea to prisms with fractional side lengths. They build prisms using unit-fraction cubes. The volume is the number of unit-fraction cubes in the prism times the volume of each unit-fraction cube. Students show that this result is the same as the volume found by using the formula.For example, you can build a 45-unit by 35-unit by 25-unit prism using 15-unit cubes. This requires 4 × 3  × 2, or 24, 15-unit cubes. Each 15-unit cube has a volume of 1125 cubic unit, so the total volume is 24125 cubic units. This is the same volume obtained by using the formula V = lwh:V=lwh=45×35×25=24125.15-unit cubes in each layer = 3 × 4Number of layers = 2Total number of 15-unit cubes = 3 × 4 × 2 =  24Volume = 24 × 1125 = 24125 cubic units Goals and Learning ObjectivesVerify that the volume formula for rectangular prisms, V = lwh or V = Bh, applies to prisms with side lengths that are not whole numbers.

Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 7
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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.

Subject:
Mathematics
Material Type:
Full Course
Provider:
Pearson
Date Added:
11/02/2020
Math, Grade 7, Algebraic Reasoning
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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.

Subject:
Algebra
Mathematics
Provider:
Pearson
Math, Grade 7, Algebraic Reasoning, Algebraic Expressions & Equations
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Students use algebraic expressions and equations to represent rules of thumb involving measurement. They use properties of operations and the relationships between fractions, decimals, and percents to write equivalent expressions.Key ConceptsExpressions and equations are different. An expression is a number, a variable, or a combination of numbers and variables. Some examples of expressions are:74x5a + b3(2m + 1)In Grade 7, the focus is on linear expressions. A linear expression is a sum of terms that are either rational numbers or a rational number times a variable (with an exponent of either 0 or 1). If an expression contains a variable, it is called an algebraic expression. To evaluate an expression, each variable is replaced with a given value.Equivalent expressions are expressions for which a given value can be substituted for each variable and the value of the expressions are the same.An equation is a statement that two expressions are equal. An equation can be true or false. To solve an equation, students find the value of the variable that makes the equation true.Students solve an equation that involves finding 10% of a number. They see that finding 10% of the number is the same as finding 0.1 of the number, or finding 110 of the number.Goals and Learning ObjectivesWrite expressions and equations to represent real-world situations.Evaluate expressions for given values of a variable.Use properties of operations to write equivalent expressions.Solve one-step equations.Check the solution to an equation.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020
Math, Grade 7, Algebraic Reasoning, Algebraic Reasoning
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Students explore the effects of wind on a plane's time and distance and represent these situations using algebraic expressions and equations. They use terms with positive, negative, and zero coefficients.Key ConceptsIn this lesson, students show what they remember from Grade 6 about writing expressions and solving one-step equations. They use what they learned earlier in Grade 7 about adding and subtracting integers. They extend these concepts to write and interpret an expression with a negative coefficient.Goals and Learning ObjectivesReview addition and subtraction of integers.Review the relationship between distance, time, and speed.Write an algebraic expression for distance in terms of time, t.Write a term with a negative coefficient.Review solving a one-step equation using the multiplication property of equality.

Subject:
Algebra
Material Type:
Lesson Plan
Author:
Pearson
Date Added:
11/02/2020