ALEX Lesson Plans
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Title: Lay It on the Line
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This lesson allows students to explore their surroundings to locate and prove the presence of perpendicular lines. Students will use the corner of a ruler as a tester to determine right angles contained in classroom items. It can be included in a unit on geometry and measurement.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2]
Subject: Mathematics (4)
Title: Lay It on the Line
Description: This lesson allows students to explore their surroundings to locate and prove the presence of perpendicular lines. Students will use the corner of a ruler as a tester to determine right angles contained in classroom items. It can be included in a unit on geometry and measurement.
This is a College and CareerReady Standards showcase lesson plan.
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Title: Look Around, What do You See? Origamis!
Description:
Students will make origamis using Japanese paper folding techniques. This lesson will enhance the students ability to understand geometry concepts.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [MA2013] (1) 20: Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as "right rectangular prism.") [1G2] [MA2013] (2) 24: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2G1] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3]
Subject: Mathematics (1  4)
Title: Look Around, What do You See? Origamis!
Description: Students will make origamis using Japanese paper folding techniques. This lesson will enhance the students ability to understand geometry concepts.
This is a College and CareerReady Standards showcase lesson plan.
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Title: Wanted: Angles of all Sizes!
Description:
In this lesson, students will explore straight, right, acute and obtuse angles. Students will go to the playground to search for angles. The students will use digital cameras to record their findings. They will use their findings to create a Power Point to present to the class.
Standard(s): [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [TC2] (35) 10: Use digital environments to collaborate and communicate. [TC2] (35) 12: Create a product using digital tools.
Subject: Mathematics (4), or Technology Education (3  5)
Title: Wanted: Angles of all Sizes!
Description: In this lesson, students will explore straight, right, acute and obtuse angles. Students will go to the playground to search for angles. The students will use digital cameras to record their findings. They will use their findings to create a Power Point to present to the class.
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Title: A Triangle to Remember
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This lesson will introduce students to different types of triangles by using a clip from the movie A Walk to Remember. They will take part in interactive tutorials to strengthen the concepts of classifying triangles. The students will then use features on Microsoft Word to create an interactive triangle poster and show what they know.
Standard(s): [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Subject: Mathematics (4)
Title: A Triangle to Remember
Description: This lesson will introduce students to different types of triangles by using a clip from the movie A Walk to Remember. They will take part in interactive tutorials to strengthen the concepts of classifying triangles. The students will then use features on Microsoft Word to create an interactive triangle poster and show what they know.
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Title: Geometric Man
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The students will explore angles, rays, line segments, perpendicular lines, parallel lines, and twodimensional figures through the use of the book "Shape Up! Fun With Triangles and Other Polygons" by David A. Adler. They will also classify quadrilaterals through an interactive website.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2]
Subject: Mathematics (3  4)
Title: Geometric Man
Description: The students will explore angles, rays, line segments, perpendicular lines, parallel lines, and twodimensional figures through the use of the book "Shape Up! Fun With Triangles and Other Polygons" by David A. Adler. They will also classify quadrilaterals through an interactive website.
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Title: Angle Scavenger Hunt
Description:
In this lesson, students will explore straight, right, acute, and obtuse angles. Students will go on a scavenger hunt throughout the school to search for examples of these types of angles. The students will use digital cameras to record and communicate their findings.
Standard(s): [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [TC2] (35) 10: Use digital environments to collaborate and communicate. [TC2] (35) 12: Create a product using digital tools.
Subject: Mathematics (4), or Technology Education (3  5)
Title: Angle Scavenger Hunt
Description: In this lesson, students will explore straight, right, acute, and obtuse angles. Students will go on a scavenger hunt throughout the school to search for examples of these types of angles. The students will use digital cameras to record and communicate their findings.
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Title: A What? A What? A Quadrilateral
Description:
In this lesson, students will identify the characteristics of a quadrilateral. Students will have a chance categorize quadrilaterals into subgroups such as squares, rhombuses, rectangles, and nonregular quadrilaterals. This lesson using geometric shapes for a handson activity and includes a quadrilateral quest via the internet at the end.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [TC2] (35) 2: Use various technology applications, including word processing and multimedia software. [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [TC2] (35) 2: Use various technology applications, including word processing and multimedia software.
Subject: Mathematics (3  5), or Technology Education (3  5)
Title: A What? A What? A Quadrilateral
Description: In this lesson, students will identify the characteristics of a quadrilateral. Students will have a chance categorize quadrilaterals into subgroups such as squares, rhombuses, rectangles, and nonregular quadrilaterals. This lesson using geometric shapes for a handson activity and includes a quadrilateral quest via the internet at the end.
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Title: Weight vs. Capacity
Description:
This lesson will introduce students to measuring weight, mass, volume, and capacity using metric and cutomary units.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [ELA2013] (3) 36: Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See Grade 3 Language standards 37 and 39 for specific expectations.) [SL.3.6] [ELA2013] (3) 34: Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace. [SL.3.4] [TC2] (35) 1: Use input and output devices of technology systems. [TC2] (35) 2: Use various technology applications, including word processing and multimedia software. [TC2] (35) 5: Practice safe use of technology systems and applications. [TC2] (35) 6: Describe social and ethical behaviors related to technology use. [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2]
Subject: English Language Arts (3), or Mathematics (3  5), or Technology Education (3  5)
Title: Weight vs. Capacity
Description: This lesson will introduce students to measuring weight, mass, volume, and capacity using metric and cutomary units.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: $100 Picture
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This is a lesson where collaborative learning groups are used to explore perimeter and area of an irregular figure using pattern blocks. This lesson should be used after students have already had some experience with finding the perimeter and area of a figure.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [TC2] (35) 1: Use input and output devices of technology systems. [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4]
Subject: Mathematics (3  5), or Technology Education (3  5)
Title: $100 Picture
Description: This is a lesson where collaborative learning groups are used to explore perimeter and area of an irregular figure using pattern blocks. This lesson should be used after students have already had some experience with finding the perimeter and area of a figure.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: The Class Quilt
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Students will design a 12 inch quilt square consisting of geometrical shapes.They must use their knowledge of fractions and polygons in order to create an exact 12" by 12" square.Students will use knowledge of area of a figure in order to create a quilt using their squares.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 14: Understand a fraction ^{a}/_{b} with a > 1 as a sum of fractions ^{1}/_{b}. [4NF3] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4]
Subject: Mathematics (3  5)
Title: The Class Quilt
Description: Students will design a 12 inch quilt square consisting of geometrical shapes.They must use their knowledge of fractions and polygons in order to create an exact 12" by 12" square.Students will use knowledge of area of a figure in order to create a quilt using their squares.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Geometric Shadows
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Students will identify objects as translucent, transparent, or opaque. Upon seeing the shadow of the opaque object, students will identify the geometric figure created by the shadow.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [S1] (4) 3: Recognize how light interacts with transparent, translucent, and opaque materials. [MA2013] (0) 19: Identify shapes as twodimensional (lying in a plane, "flat") or threedimensional ("solid"). [KG3] [MA2013] (0) 20: Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices or "corners"), and other attributes (e.g., having sides of equal length). [KG4] [MA2013] (1) 19: Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. [1G1] [MA2013] (1) 20: Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as "right rectangular prism.") [1G2] [MA2013] (2) 24: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (0) 17: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. [KG1] [MA2013] (0) 18: Correctly name shapes regardless of their orientations or overall size. [KG2] [MA2013] (0) 19: Identify shapes as twodimensional (lying in a plane, "flat") or threedimensional ("solid"). [KG3] [MA2013] (1) 20: Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as "right rectangular prism.") [1G2] [MA2013] (2) 15: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. [2MD2] [MA2013] (2) 16: Estimate lengths using units of inches, feet, centimeters, and meters. [2MD3] [MA2013] (2) 26: Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape. [2G3]
Subject: Mathematics (K  4), or Science (4)
Title: Geometric Shadows
Description: Students will identify objects as translucent, transparent, or opaque. Upon seeing the shadow of the opaque object, students will identify the geometric figure created by the shadow.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Twisted Tangrams
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In this lesson students will use a handson approach to problem solving. They will construct and manipulate tangrams to recreate animals from a story. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [ELA2013] (0) 16: With prompting and support, describe the relationship between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts). [RI.K.7] [ELA2013] (0) 10: With prompting and support, ask and answer questions about key details in a text. [RI.K.1] [ELA2013] (0) 7: With prompting and support, describe the relationship between illustrations and the story in which they appear (e.g., what moment in a story an illustration depicts). [RL.K.7] [CE] (012) 8: Cooperation [CE] (012) 10: Selfcontrol [CE] (012) 6: Respect for others [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (0) 17: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. [KG1] [MA2013] (0) 18: Correctly name shapes regardless of their orientations or overall size. [KG2] [MA2013] (0) 19: Identify shapes as twodimensional (lying in a plane, "flat") or threedimensional ("solid"). [KG3] [MA2013] (0) 20: Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices or "corners"), and other attributes (e.g., having sides of equal length). [KG4] [MA2013] (0) 21: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. [KG5] [MA2013] (0) 22: Compose simple shapes to form larger shapes. [KG6] [MA2013] (1) 19: Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. [1G1] [MA2013] (1) 20: Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as "right rectangular prism.") [1G2] [MA2013] (1) 21: Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. [1G3] [MA2013] (2) 24: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2G1] [MA2013] (2) 25: Partition a rectangle into rows and columns of samesize squares, and count to find the total number of them. [2G2] [MA2013] (2) 26: Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape. [2G3]
Subject: Character Education (K  12), or English Language Arts (K), or Mathematics (K  4)
Title: Twisted Tangrams
Description: In this lesson students will use a handson approach to problem solving. They will construct and manipulate tangrams to recreate animals from a story. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Thinkfinity Lesson Plans
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Title: Getting to Know the Shapes
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In this lesson, one of a multipart unit from Illuminations, students discover the uses of geometry and measurement in the world of architecture as they are introduced to a project in which they design a clubhouse.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Subject: Arts,Mathematics Title: Getting to Know the Shapes
Description: In this lesson, one of a multipart unit from Illuminations, students discover the uses of geometry and measurement in the world of architecture as they are introduced to a project in which they design a clubhouse. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Describing Designs
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In this lesson, one of a multipart unit from Illuminations, students create designs and describe them to classmates, using fractional and geometric terms. The lesson provides a context for using the vocabulary terms horizontal, vertical, square, rectangle, triangle, diagonal, onehalf, and onefourth. Several pieces of literature appropriate for use with this lesson are suggested.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1]
Subject: Arts,Language Arts,Mathematics Title: Describing Designs
Description: In this lesson, one of a multipart unit from Illuminations, students create designs and describe them to classmates, using fractional and geometric terms. The lesson provides a context for using the vocabulary terms horizontal, vertical, square, rectangle, triangle, diagonal, onehalf, and onefourth. Several pieces of literature appropriate for use with this lesson are suggested. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: More Work with Shapes
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In this lesson, one of a multipart unit from Illuminations, students explore geometric concepts by modeling on the geoboard. They investigate parallel, perpendicular, and intersecting lines.
Standard(s): [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Subject: Mathematics Title: More Work with Shapes
Description: In this lesson, one of a multipart unit from Illuminations, students explore geometric concepts by modeling on the geoboard. They investigate parallel, perpendicular, and intersecting lines. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Geography of Pizza
Description:
In this lesson, from Xpeditions, students analyze Earth's surface according to the spatial elements of points, lines, and areas, and use a simple map to identify features in terms of spatial elements. This lesson uses a pizza restaurant to introduce these components to students, e.g., the location of a restaurant (point), roads and sidewalks (lines), and the city blocks or the region served by a restaurant (area).
Standard(s): [MA2013] (3) 20: Recognize area as an attribute of plane figures, and understand concepts of area measurement. [3MD5] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2] [SS2010] GHS (3) 1: Locate the prime meridian, equator, Tropic of Capricorn, Tropic of Cancer, International Date Line, and lines of latitude and longitude on maps and globes. [SS2010] GHS (3) 2: Locate the continents on a map or globe [SS2010] GHS (3) 3: Describe ways the environment is affected by humans in Alabama and the world. (Alabama) [SS2010] GHS (3) 4: Relate population dispersion to geographic, economic, and historic changes in Alabama and the world. (Alabama) [SS2010] GHS (3) 5: Compare trading patterns between countries and regions. [SS2010] GHS (3) 6: Identify conflicts within and between geographic areas involving use of land, economic competition for scarce resources, opposing political views, boundary disputes, and cultural differences. [SS2010] GHS (3) 7: Describe the relationship between locations of resources and patterns of population distribution. [SS2010] GHS (3) 8: Identify geographic links of land regions, river systems, and interstate highways between Alabama and other states. (Alabama)
Subject: Mathematics  Applied Mathematics  Social Studies  Geography Title: Geography of Pizza
Description: In this lesson, from Xpeditions, students analyze Earth's surface according to the spatial elements of points, lines, and areas, and use a simple map to identify features in terms of spatial elements. This lesson uses a pizza restaurant to introduce these components to students, e.g., the location of a restaurant (point), roads and sidewalks (lines), and the city blocks or the region served by a restaurant (area). Thinkfinity Partner: National Geographic Education Grade Span: 3,4,5
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Title: Constructing a ThreeDimensional Model
Description:
In this lesson, one of a multipart unit from Illuminations, students build a three dimensional model of a clubhouse from two dimensional blueprints designed in an earlier lesson. In addition, they solve problems related to constructing and decorating their clubhouse.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Subject: Arts,Mathematics Title: Constructing a ThreeDimensional Model
Description: In this lesson, one of a multipart unit from Illuminations, students build a three dimensional model of a clubhouse from two dimensional blueprints designed in an earlier lesson. In addition, they solve problems related to constructing and decorating their clubhouse. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Shapes Art
Description:
In this lesson, one of a multipart unit from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. They listen to the poem Shapes from Shel Silverstein s A Light in the Attic and then recognize, draw, and describe geometric figures.
Standard(s): [MA2013] (0) 18: Correctly name shapes regardless of their orientations or overall size. [KG2] [MA2013] (1) 20: Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as "right rectangular prism.") [1G2] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [ELA2013] (3) 1: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. [RL.3.1] [ELA2013] (3) 3: Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. [RL.3.3] [ELA2013] (3) 13: Determine the meaning of general academic and domainspecific words and phrases in a text relevant to a Grade 3 topic or subject area. [RI.3.4] [ELA2013] (3) 21: Read with sufficient accuracy and fluency to support comprehension. [RF.3.4]
Subject: Language Arts,Mathematics Title: Shapes Art
Description: In this lesson, one of a multipart unit from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. They listen to the poem Shapes from Shel Silverstein s A Light in the Attic and then recognize, draw, and describe geometric figures. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5
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Title: Who Was Wassily Kandinsky?
Description:
In this lesson, one of a multipart unit from Illuminations, students explore the geometric figures Wassily Kandinsky used in his art. Students participate in a scavenger hunt to become familiar with Kandinsky s works and the geometric figures used in his paintings.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Subject: Arts,Mathematics Title: Who Was Wassily Kandinsky?
Description: In this lesson, one of a multipart unit from Illuminations, students explore the geometric figures Wassily Kandinsky used in his art. Students participate in a scavenger hunt to become familiar with Kandinsky s works and the geometric figures used in his paintings. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Mirroring Kandinsky
Description:
In this lesson, one of a multipart unit from Illuminations, students explore the geometric figures Wassily Kandinsky used in his art. Students apply what they have learned in previous lessons by designing their own art, and they use Kandinsky s style of art and their own creativity to make paintings that reflect their understanding of geometry.
Standard(s): [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Subject: Arts,Mathematics Title: Mirroring Kandinsky
Description: In this lesson, one of a multipart unit from Illuminations, students explore the geometric figures Wassily Kandinsky used in his art. Students apply what they have learned in previous lessons by designing their own art, and they use Kandinsky s style of art and their own creativity to make paintings that reflect their understanding of geometry. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Rectangles and Parallelograms
Description:
In this lesson, from Illuminations, students use dynamic software to examine the properties of rectangles and parallelograms and then identify what distinguishes a rectangle from a more general parallelogram. Using spatial relationships, they examine the properties of two and threedimensional shapes. The lesson links to a virtual manipulative that allows students to compare rectangles and parallelograms.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Subject: Mathematics Title: Rectangles and Parallelograms
Description: In this lesson, from Illuminations, students use dynamic software to examine the properties of rectangles and parallelograms and then identify what distinguishes a rectangle from a more general parallelogram. Using spatial relationships, they examine the properties of two and threedimensional shapes. The lesson links to a virtual manipulative that allows students to compare rectangles and parallelograms. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Study the Shapes
Description:
In this lesson, one of a multipart unit from Illuminations, students use an online, interactive activity to analyze characteristics and properties of threedimensional geometric shapes; develop mathematical arguments about geometric relationships; and use visualization, spatial reasoning, and geometric modeling to solve problems. Students investigate geometric shapes in the classroom and complete a chart describing the characteristics of several geometric solids.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1]
Subject: Mathematics Title: Study the Shapes
Description: In this lesson, one of a multipart unit from Illuminations, students use an online, interactive activity to analyze characteristics and properties of threedimensional geometric shapes; develop mathematical arguments about geometric relationships; and use visualization, spatial reasoning, and geometric modeling to solve problems. Students investigate geometric shapes in the classroom and complete a chart describing the characteristics of several geometric solids. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
ALEX Podcasts
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Title: Classifying Lines
Overview:
Watch as two sixth grade boys explore different kinds of lines found on their school campus. Throughout the podcast, they give the definition for a variety of line types. Then you are asked to identify the lines represented in pictures they took. Watch carefully, because after you have the opportunity to identify the lines, they illustrate the correct response. This interactive podcast is sure to help anyone who is learning how to identify various types of lines. Standard(s):
[MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Classifying Lines Overview: Watch as two sixth grade boys explore different kinds of lines found on their school campus. Throughout the podcast, they give the definition for a variety of line types. Then you are asked to identify the lines represented in pictures they took. Watch carefully, because after you have the opportunity to identify the lines, they illustrate the correct response. This interactive podcast is sure to help anyone who is learning how to identify various types of lines.
Web Resources
Assessments
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Title: Go Bananas over Angles!
Description:
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
Standard(s): [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Go Bananas over Angles!
http://www.oswego.or...
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
Interactives/Games
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Title: Go Bananas over Angles!
Description:
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
Standard(s): [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Go Bananas over Angles!
http://www.oswego.or...
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
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Title: Geoboard
Description:
This FREE Geoboard app is a tool for exploring a variety of mathematical topics introduced in the elementary and middle grades. Learners stretch bands around pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more.
Standard(s): [MA2013] (2) 24: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2G1] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (6) 21: 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 realworld and mathematical problems. [6G1]
Geoboard
https://itunes.apple...
This FREE Geoboard app is a tool for exploring a variety of mathematical topics introduced in the elementary and middle grades. Learners stretch bands around pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more.
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Title: Geoboard App by The Math Learning Center
Description:
Free iPad app for exploring geometry. Learners stretch bands around pegs to discover geometric concepts.
Standard(s): [MA2013] (2) 24: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2G1] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Geoboard App by The Math Learning Center
https://itunes.apple...
Free iPad app for exploring geometry. Learners stretch bands around pegs to discover geometric concepts.
Learning Activities
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Title: Go Bananas over Angles!
Description:
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
Standard(s): [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Go Bananas over Angles!
http://www.oswego.or...
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
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Title: Geoboard
Description:
This FREE Geoboard app is a tool for exploring a variety of mathematical topics introduced in the elementary and middle grades. Learners stretch bands around pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more.
Standard(s): [MA2013] (2) 24: Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2G1] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (6) 21: 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 realworld and mathematical problems. [6G1]
Geoboard
https://itunes.apple...
This FREE Geoboard app is a tool for exploring a variety of mathematical topics introduced in the elementary and middle grades. Learners stretch bands around pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more.
Teacher Tools
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Title: Go Bananas over Angles!
Description:
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
Standard(s): [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1]
Go Bananas over Angles!
http://www.oswego.or...
Banana Hunt is an online interactive activity that can be used in a wholeclass setting, cooperative groups, small groups, or with individuals. This fun website will have your students going "bananas" over recognizing angles. The interactive game ask, "How many bananas can you find in 10 searches?". The game has a large circle with an angle with a monkey on the end of one of the rays. Students will drag the monkey(ray) to the location of the banana by creating the correct angle. Students will press "search". If the students find the right location(angle) on the circle of the banana they will receive 10 bananas.
Thinkfinity Informational Materials
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Title: Number and Operations Web Links
Description:
This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.
Standard(s): [MA2013] (0) 1: Count to 100 by ones and by tens. [KCC1] [MA2013] (0) 2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). [KCC2] [MA2013] (0) 3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). [KCC3] [MA2013] (0) 4: Understand the relationship between numbers and quantities; connect counting to cardinality. [KCC4] [MA2013] (0) 5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects. [KCC5] [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3OA3] [MA2013] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 6: Understand division as an unknownfactor problem. [3OA6] [MA2013] (3) 7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. [3OA7] [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (3) 10: Use place value understanding to round whole numbers to the nearest 10 or 100. [3NBT1] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (3) 12: Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 14: Understand a fraction as a number on the number line; represent fractions on a number line diagram. [3NF2] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (3) 16: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. [3MD1] [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (3) 20: Recognize area as an attribute of plane figures, and understand concepts of area measurement. [3MD5] [MA2013] (3) 21: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (4) 1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. [4OA1] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. [4OA4] [MA2013] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4OA5] [MA2013] (4) 6: Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. [4NBT1] [MA2013] (4) 7: Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4NBT2] [MA2013] (4) 8: Use place value understanding to round multidigit whole numbers to any place. [4NBT3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT5] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 14: Understand a fraction ^{a}/_{b} with a > 1 as a sum of fractions ^{1}/_{b}. [4NF3] [MA2013] (4) 15: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4NF4] [MA2013] (4) 16: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) [4NF5] [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (4) 18: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. [4NF7] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [MA2013] (5) 1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5OA1] [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5OA3] [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 9: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5NBT6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 15: Interpret multiplication as scaling (resizing), by: [5NF5] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 18: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. [5MD1] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4]
Subject: Mathematics Title: Number and Operations Web Links
Description: This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites. Thinkfinity Partner: Illuminations Grade Span: K,1,2,3,4,5,6,7,8,9,10,11,12
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Title: Communicating about Mathematics Using Games: Playing Fraction Tracks
Description:
Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This eexample from Illuminations contains an interactive version of a game that can be used in the grades 35 classroom to support students' learning about fractions. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations.
Standard(s): [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3OA3] [MA2013] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 6: Understand division as an unknownfactor problem. [3OA6] [MA2013] (3) 7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. [3OA7] [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (3) 10: Use place value understanding to round whole numbers to the nearest 10 or 100. [3NBT1] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (3) 12: Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 14: Understand a fraction as a number on the number line; represent fractions on a number line diagram. [3NF2] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (3) 16: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. [3MD1] [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (3) 21: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (4) 1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. [4OA1] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. [4OA4] [MA2013] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4OA5] [MA2013] (4) 6: Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. [4NBT1] [MA2013] (4) 7: Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4NBT2] [MA2013] (4) 8: Use place value understanding to round multidigit whole numbers to any place. [4NBT3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT5] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 14: Understand a fraction ^{a}/_{b} with a > 1 as a sum of fractions ^{1}/_{b}. [4NF3] [MA2013] (4) 15: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4NF4] [MA2013] (4) 16: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) [4NF5] [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (4) 18: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. [4NF7] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [MA2013] (5) 1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5OA1] [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5OA3] [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 9: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5NBT6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 15: Interpret multiplication as scaling (resizing), by: [5NF5] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 18: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. [5MD1] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4]
Subject: Mathematics Title: Communicating about Mathematics Using Games: Playing Fraction Tracks
Description: Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This eexample from Illuminations contains an interactive version of a game that can be used in the grades 35 classroom to support students' learning about fractions. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Isometric Drawing Tool
Description:
Create dynamic drawings on isometric dot paper with this interactive tool. Draw 2D and 3D figures using edges, faces, or cubes that you can shift, rotate, color, or decompose.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4] [MA2013] (6) 22: 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 = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4] [MA2013] GEO (912) 2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [GCO2] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4]
Subject: Mathematics Title: Isometric Drawing Tool
Description: Create dynamic drawings on isometric dot paper with this interactive tool. Draw 2D and 3D figures using edges, faces, or cubes that you can shift, rotate, color, or decompose. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12

