Element Cards Geometry
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| style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | | style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | ||
− | * Teach using example, non-example varying the shape size and orientation (one shape at a time). | + | * Teach using example, non-example varying the shape size and orientation (one shape at a time). |
− | * Teach using time delay (multiple shapes). | + | * Teach using time delay (multiple shapes). |
* Teach rules for identifying shapes/properties of shapes (e.g., circles have no straight lines). | * Teach rules for identifying shapes/properties of shapes (e.g., circles have no straight lines). | ||
* Teach using sorting and classifying. | * Teach using sorting and classifying. | ||
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− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
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* Students label varying sized real-world objects around the classroom by shape (e.g., put a cutout of a rectangle on the white board). | * Students label varying sized real-world objects around the classroom by shape (e.g., put a cutout of a rectangle on the white board). | ||
* Teacher models and encourages students to use size and shape vocabulary during lessons (e.g., I see/feel a ''big'' rectangle). | * Teacher models and encourages students to use size and shape vocabulary during lessons (e.g., I see/feel a ''big'' rectangle). | ||
− | * Use multiple exemplar strategy (various sized/textured/colored shapes) to have students search for and identify various shapes in a sensory table (sand, rice, water). | + | * Use multiple exemplar strategy (various sized/textured/colored shapes) to have students search for and identify various shapes in a sensory table (sand, rice, water). |
− | * Use multiple exemplar strategy (various sized/textured shapes) while having students find specific shapes by touch (students feel for shapes placed in a bag). | + | * Use multiple exemplar strategy (various sized/textured shapes) while having students find specific shapes by touch (students feel for shapes placed in a bag). |
* Graphic Organizers can be used to sort varying sized shapes (4-column chart with shapes taped/glued on, labeled buckets with shapes placed inside). | * Graphic Organizers can be used to sort varying sized shapes (4-column chart with shapes taped/glued on, labeled buckets with shapes placed inside). | ||
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− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
|width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' K.G.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as ''above, below, beside, in front of, behind, and next to.'' | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' K.G.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as ''above, below, beside, in front of, behind, and next to.'' | ||
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* Shape movement games (e.g., The Shape Hokey Pokey, put the circle in, put the circle out, put the circle above (above your head), and shake it all about...) | * Shape movement games (e.g., The Shape Hokey Pokey, put the circle in, put the circle out, put the circle above (above your head), and shake it all about...) | ||
* Teacher models the use of positional and shape vocabulary during lessons (e.g., I see/feel a triangle ''under'' the table.) | * Teacher models the use of positional and shape vocabulary during lessons (e.g., I see/feel a triangle ''under'' the table.) | ||
− | * Model-Lead-Test (teacher models a math problem: the square is above my head, leads students in positioning shapes correctly, and then tests students' ability to position shapes with minimal needed supports) | + | * Model-Lead-Test (teacher models a math problem: the square is above my head, leads students in positioning shapes correctly, and then tests students' ability to position shapes with minimal needed supports) |
* Students explore and manipulate shape blocks and are encouraged to identify the position of the shapes | * Students explore and manipulate shape blocks and are encouraged to identify the position of the shapes | ||
* Give each child a shape (can make shape hats, put shapes on Popsicle sticks, make a shape necklace, etc.) and instruct shapes (circles stand up, squares crawl under the table, triangles put your hands above your head, etc.) | * Give each child a shape (can make shape hats, put shapes on Popsicle sticks, make a shape necklace, etc.) and instruct shapes (circles stand up, squares crawl under the table, triangles put your hands above your head, etc.) | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
===Additional Resources=== | ===Additional Resources=== | ||
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| style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | | style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | ||
* Teach explicit rules for discriminating 2-D from 3-D shapes (e.g., 2-D is flat). | * Teach explicit rules for discriminating 2-D from 3-D shapes (e.g., 2-D is flat). | ||
− | * Teach using example, non-example. | + | * Teach using example, non-example. |
* Sort and classify 2-D and 3-D shapes. | * Sort and classify 2-D and 3-D shapes. | ||
* Have students create their own shape (cut, decorate, mold, etc.) and then have the class join their shapes together to make a larger shapes. | * Have students create their own shape (cut, decorate, mold, etc.) and then have the class join their shapes together to make a larger shapes. | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
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* Model naming shapes in the environment then ask students to identify or locate shapes within their own learning environment. | * Model naming shapes in the environment then ask students to identify or locate shapes within their own learning environment. | ||
* Model naming shapes shown in pictures of the environment then ask students to identify shapes found in pictures of their environment. Generalize to novel pictures such as illustrations in books. | * Model naming shapes shown in pictures of the environment then ask students to identify shapes found in pictures of their environment. Generalize to novel pictures such as illustrations in books. | ||
− | * Time delay to teach shapes. | + | * Time delay to teach shapes. |
* Teach using example, non-example. | * Teach using example, non-example. | ||
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|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
|width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | ||
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| style="background-color:#FFFFFF;"|2.GM.1b3 | | style="background-color:#FFFFFF;"|2.GM.1b3 | ||
− | | style="background-color:#FFFFFF;"|Distinguish two- or three- dimensional shapes based upon their attributes (i.e., | + | | style="background-color:#FFFFFF;"|Distinguish two- or three- dimensional shapes based upon their attributes (i.e., #of sides, equal or different lengths of sides, # of faces, # of corners). |
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| style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | | style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | ||
− | * Model-Lead-Test: Partition objects that have a real-world application (e.g., graham crackers, fruit, paper for art projects). | + | * Model-Lead-Test: Partition objects that have a real-world application (e.g., graham crackers, fruit, paper for art projects). |
* Demonstrate for students, using fraction bars, interactive whiteboard manipulatives, or iPad manipulates as they are available. | * Demonstrate for students, using fraction bars, interactive whiteboard manipulatives, or iPad manipulates as they are available. | ||
− | * Use a System of Least prompt. | + | * Use a System of Least prompt. |
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|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
|width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 2.G.3 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, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | |width = "33%" style="background-color:#FFFFFF;" colspan=3|'''CCSS:''' 2.G.3 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, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | ||
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* Tiling | * Tiling | ||
* Task analysis (measure length, divide by number of parts, mark each equal part) | * Task analysis (measure length, divide by number of parts, mark each equal part) | ||
− | * Multiple exemplars for equal and not equal | + | * Multiple exemplars for equal and not equal |
− | * Model-Lead-Test | + | * Model-Lead-Test |
* Use physical models and a trial and error approach (e.g., give student the "whole" rectangle, then give student various fractional pieces; students use trial and error with fractional pieces to determine the equal pieces that fit on the "whole"). | * Use physical models and a trial and error approach (e.g., give student the "whole" rectangle, then give student various fractional pieces; students use trial and error with fractional pieces to determine the equal pieces that fit on the "whole"). | ||
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|- | |- | ||
|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
{|border=1 | {|border=1 | ||
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| style="background-color:#FFFFFF;"|4GM.1h2 | | style="background-color:#FFFFFF;"|4GM.1h2 | ||
− | | style="background-color:#FFFFFF;"|Classify two-dimensional shapes based on attributes ( | + | | style="background-color:#FFFFFF;"|Classify two-dimensional shapes based on attributes (# of angles). |
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* Explicit instruction on attributes | * Explicit instruction on attributes | ||
* Model at least one example of thinking through the attributes. | * Model at least one example of thinking through the attributes. | ||
− | * Multiple exemplar (e.g., shapes, angles, polygons) | + | * Multiple exemplar (e.g., shapes, angles, polygons) |
* Think, pair, share | * Think, pair, share | ||
* Match the same to classify shape | * Match the same to classify shape | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | |
===Additional Resource=== | ===Additional Resource=== | ||
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* Review right triangles (need a right angle). Have students draw a right triangle on the graph paper. Using a highlighter, have them cut the triangle in half, and color one half of the triangle. Is this still a right triangle? (No, not a right angle.) This is a smaller angle than the right triangle, so I think it is very cute. Angles that are smaller than right angles are called acute angles. Have the students cut the remaining angle in half again, and color. Is this angle acute? (Yes, it is still smaller than the right angle). Have the students make a guess with a partner as to how far they could go before the angle was not acute anymore. Show some of the attempts and talk about which ones are correct, which ones are incorrect. You can also simply do this on the overhead as a group (keep dividing and discussing). | * Review right triangles (need a right angle). Have students draw a right triangle on the graph paper. Using a highlighter, have them cut the triangle in half, and color one half of the triangle. Is this still a right triangle? (No, not a right angle.) This is a smaller angle than the right triangle, so I think it is very cute. Angles that are smaller than right angles are called acute angles. Have the students cut the remaining angle in half again, and color. Is this angle acute? (Yes, it is still smaller than the right angle). Have the students make a guess with a partner as to how far they could go before the angle was not acute anymore. Show some of the attempts and talk about which ones are correct, which ones are incorrect. You can also simply do this on the overhead as a group (keep dividing and discussing). | ||
* Review right triangles, right angles, acute triangles, acute angles. Have students draw another right triangle on graph paper. This time, have students ADD a line extending the triangle to widen it. Ask students if this is still a right triangle (no, it does not have a right angle anymore). Tell them that anytime an angle is MORE than 90 degrees, it is too large to be a right angle, and we call that obtuse. Continue to have them widen the triangle to see how far they think it can go before it is no longer considered obtuse. Also, ask them how SMALL they can make it before it will not be considered obtuse, and will be considered right or acute again. | * Review right triangles, right angles, acute triangles, acute angles. Have students draw another right triangle on graph paper. This time, have students ADD a line extending the triangle to widen it. Ask students if this is still a right triangle (no, it does not have a right angle anymore). Tell them that anytime an angle is MORE than 90 degrees, it is too large to be a right angle, and we call that obtuse. Continue to have them widen the triangle to see how far they think it can go before it is no longer considered obtuse. Also, ask them how SMALL they can make it before it will not be considered obtuse, and will be considered right or acute again. | ||
− | * Use Time Delay to teach angles | + | * Use Time Delay to teach angles |
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− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | |
===Additional Resources=== | ===Additional Resources=== | ||
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* Show students a picture of a happy face. Using paint or ink, mark one eye and half of the mouth, and then fold it length-wise in half. Ask the students if they think that the picture is the same on both sides of the fold. Unfold the picture and see what pattern the ink or paint made. Do the same thing, this time fold the picture width-wise. Ask the students again if they think that the picture is the same on both sides of the fold. Unfold the picture and see what pattern the ink or paint made. Tell students that when you can fold a picture and have both sides match up, that picture has symmetry, it matches. The line you can fold it on is called the line of symmetry. That line may NOT be in more than one place on a picture. Hand out or try the same thing with several pictures. See if students can find a line of symmetry or more than one line of symmetry in the pictures. | * Show students a picture of a happy face. Using paint or ink, mark one eye and half of the mouth, and then fold it length-wise in half. Ask the students if they think that the picture is the same on both sides of the fold. Unfold the picture and see what pattern the ink or paint made. Do the same thing, this time fold the picture width-wise. Ask the students again if they think that the picture is the same on both sides of the fold. Unfold the picture and see what pattern the ink or paint made. Tell students that when you can fold a picture and have both sides match up, that picture has symmetry, it matches. The line you can fold it on is called the line of symmetry. That line may NOT be in more than one place on a picture. Hand out or try the same thing with several pictures. See if students can find a line of symmetry or more than one line of symmetry in the pictures. | ||
* Using wikistix, have students try to find lines of symmetry on different shapes. Once they place the wikistix, have them fold the shape along the wikistix and see if the shape is the same along the fold. If not, they must replace the wikistix in a different area and try again. If it works, they can draw the line with pen or pencil. | * Using wikistix, have students try to find lines of symmetry on different shapes. Once they place the wikistix, have them fold the shape along the wikistix and see if the shape is the same along the fold. If not, they must replace the wikistix in a different area and try again. If it works, they can draw the line with pen or pencil. | ||
− | * Multiple exemplar training | + | * Multiple exemplar training |
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− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies. | |
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| style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | | style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | ||
− | * Model-Lead-Test determining if number is x or y for coordinate points | + | * Model-Lead-Test determining if number is x or y for coordinate points |
* Task analysis for finding coordinate points on graph: | * Task analysis for finding coordinate points on graph: | ||
** Determine if each point is x,y. | ** Determine if each point is x,y. | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | |
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* Task analysis: Identify a face in the figure, find the area of each face in the figure, add all faces together to find the surface area | * Task analysis: Identify a face in the figure, find the area of each face in the figure, add all faces together to find the surface area | ||
* Explicit use of the formulas | * Explicit use of the formulas | ||
− | * Model-Lead-Test: Locate plane figures in environment such as desk, wall, door, piece of paper then measure and find area | + | * Model-Lead-Test: Locate plane figures in environment such as desk, wall, door, piece of paper then measure and find area |
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− | + | Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | |
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| style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | | style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | ||
− | * Model-Lead-Test various examples of how to find area | + | * Model-Lead-Test various examples of how to find area |
* Task analysis of finding area of shapes | * Task analysis of finding area of shapes | ||
** Base x height | ** Base x height | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | |
===Additional Resource=== | ===Additional Resource=== | ||
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| style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | | style="background-color:#FFFFFF;" colspan=3|'''Suggested Instructional Strategies:''' | ||
− | * Model-Lead-Test: Use math tools (e.g., tangrams, Legos, stickers) to demonstrate the transformation of the shape. Demonstrate one transformation at a time. | + | * Model-Lead-Test: Use math tools (e.g., tangrams, Legos, stickers) to demonstrate the transformation of the shape. Demonstrate one transformation at a time. |
* Use most-to-least prompting to teach students to demonstrate transformations | * Use most-to-least prompting to teach students to demonstrate transformations | ||
* Given a picture or drawing of a shape, students use whatever tool is appropriate to transform the shape. | * Given a picture or drawing of a shape, students use whatever tool is appropriate to transform the shape. | ||
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|} | |} | ||
− | + | <nowiki>*</nowiki> Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | |
===Additional Resources=== | ===Additional Resources=== | ||
[http://www.mathisfun.com/geometry www.mathisfun.com/geometry] – Point & click to transform the shape | [http://www.mathisfun.com/geometry www.mathisfun.com/geometry] – Point & click to transform the shape | ||
− | [http://www.eduplace.com/kids/mw/swfs/robopacker_grade4.html | + | [http://www.eduplace.com/kids/mw/swfs/robopacker_grade4.html www.eduplace.com/kids/mw/swfs/robopacker_grade4.html] – Transform shapes to create a robot |
Revision as of 13:28, 12 November 2013
Contents |
CCC Mathematics: Geometry
CCSS: K.G.2 Correctly name shapes regardless of their orientations or overall size. | |||
CCC: | K.GM.1a1 | Recognize two- dimensional shapes (e.g., circle, square, triangle, rectangle) regardless of orientation or size. | |
Strand: Geometry | Family: Recognizing, Describing, Naming and Classifying | ||
Progress Indicator: E.GM.1a Recognizing, describing (using spatial language) and naming shapes regardless of orientation or size and locating shapes in the environment | |||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: K.G.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as above, below, beside, in front of, behind, and next to. | |||
CCC: | K.GM.1a2 | Recognize two-dimensional shapes in the environment regardless of orientation or size. | |
Strand: Geometry | Family: Recognizing, Describing, Naming and Classifying | ||
Progress Indicator: E.GM.1a Recognizing, describing (using spatial language) and naming shapes regardless of orientation or size and locating shapes in the environment | |||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
| |||
Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: K.G.1 Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as above, below, beside, in front of, behind, and next to. | |||
CCC: | K.GM.1a3 | Use spatial language (e.g., above, below, etc.) to describe two-dimensional shapes. | |
Strand: Geometry | Family: Recognizing, Describing, Naming and Classifying | ||
Progress Indicator: E.GM.1a Recognizing, describing (using spatial language), and naming shapes regardless of orientation or size and locating shapes in the environment | |||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
| |||
Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
Additional Resources
http://www.kidzone.ws/prek_wrksht/shapes.htm http://www.storyplace.org//preschool/activities/shapesonstory.asp
CCSS: K.G.6 Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" | |||
CCC: | K.GM.1c1 | Compose a larger shape from smaller shapes | |
Strand: Geometry | Family: Constructing/Building | ||
Progress Indicator: E.GM.1c Composing two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter circles) | |||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
Task Analysis
| |||
Suggested Supports and Scaffolds:
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CCSS: K.G.6 Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" | |||
CCC: | 1.GM.1b1 | Identify shapes as two-dimensional (lying flat) or three-dimensional (solid). | |
Strand: Geometry | Family: Recognizing, Describing, Naming and Classifying | ||
Progress Indicator: E.GM.1b Analyzing and comparing two- (and later) three-dimensional shapes using informal language (e.g., flat, solid, corners) to describe their differences and similarities, as well as their component parts (number of sides, vertices) and other attributes (e.g., sides of equal length) | |||
Essential Understandings | Concrete Understandings:
|
Representation:
| |
Suggested Instructional Strategies:
| |||
Suggested Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | |||
CCC: | 2.GM.1a4 | Identify two- dimensional shapes such as rhombus, pentagons, hexagons, octagon, ovals, equilateral, isosceles, and scalene triangles. | |
Strand: Geometry | Family: Recognizing, Describing, Naming and Classifying | ||
Progress Indicator: E.GM.1a Recognizing, describing (using spatial language) and naming shapes regardless of orientation or size and locating shapes in the environment | |||
Essential Understandings | Concrete Understandings:
|
Representation:
| |
Suggested Instructional Strategies:
| |||
Suggested Supports and Scaffolds:
|
* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | |||
CCC: | 2.GM.1b3 | Distinguish two- or three- dimensional shapes based upon their attributes (i.e., #of sides, equal or different lengths of sides, # of faces, # of corners). | |
Strand: Geometry | Family: Recognizing, Describing, Naming and Classifying | ||
Progress Indicator: E.GM.1b Analyzing and comparing two- (and later) three-dimensional shapes using informal language (e.g., flat, solid, corners) to describe their differences and similarities, as well as their component parts (number of sides, vertices) and other attributes (e.g., sides of equal length) | |||
Essential Understandings | Concrete Understandings:
|
Representation:
| |
Suggested Instructional Strategies:
| |||
Suggested Supports and Scaffolds:
|
CCSS: 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | |||
CCC: | 2.GM.1e1 | Draw two-dimensional shapes with specific attributes. | |
Strand: Geometry | Family: Constructing/Building | ||
Progress Indicator: E.GM.1e Drawing and identifying shapes with specific attributes (e.g., number of sides or equal angles) not determined by direct measuring) | |||
Essential Understandings | Concrete Understandings:
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Representation:
| |
Suggested Instructional Strategies:
.1 .2
| |||
Suggested Supports and Scaffolds:
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CCSS: 2.G.3 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, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | |||
CCC: | 2.GM.1f2 | Partition circles and rectangles into 2 and 4 equal parts. | |
Strand: Geometry | Family: Geometric Problems | ||
Progress Indicator: E.GM.1f Partitioning shapes into 2, 3, or 4 equal parts and describing the parts (halves, quarters, fourths, thirds) | |||
Essential Understandings | Concrete Understandings:
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Representation:
| |
Suggested Instructional Strategies:
| |||
Suggested Supports and Scaffolds:
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 2.G.3 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, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | |||
CCC: | 2.GM.1f3 | Label a partitioned shape (e.g., one whole rectangle was separated into 2 halves; one whole circle was separated into three thirds). | |
Strand: Geometry | Family: Geometric Problems | ||
Progress Indicator: E.GM.1f Partitioning shapes into 2, 3, or 4 equal parts and describing the parts (halves, quarters, fourths, thirds) | |||
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CCSS: 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having 4 sides) and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals that do not belong to any of these subcategories. | |||
CCC: | 3.GM.1h1 | Identify shared attributes of shapes. | |
Strand: Geometry | Family: Recognizing, Describing, Naming and Classifying | ||
Progress Indicator: E.GM.1h Describing, analyzing, comparing, and classifying two-dimensional figures (triangles, quadrilaterals) using shared attributes | |||
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CCSS: 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape. | |||
CCC: | 3.GM.1i1 | Partition rectangles into equal parts with equal area. | |
Strand: Geometry | Family: Geometric Problems | ||
Progress Indicator: E.GM.1i Partitioning shapes into equal parts with equal areas and recognizing that each part is a unit fraction of the whole | |||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 4.G.2 Classify two dimensional 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 angles as a category, and identify right angles. | |||
CCC: | 4GM.1h2 | Classify two-dimensional shapes based on attributes (# of angles). | |
Strand: Geometry | Family: Recognizing, Describing and Naming and Classifying | ||
Progress Indicator: E.GM.1h Describing, analyzing, comparing, and classifying two-dimensional figures (triangles, quadrilaterals) using shared attributes | |||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
Additional Resource
http://www.pdesas.org/module/content/resources/13281/view.ashx
CCSS: 4.G.1 Draw points, lines, line segments, rays, angels, perpendicular, and parallel lines. Identify these in two-dimensional figures. | |||
CCC: | 4GM.1j1 | Recognize a point, line and line segment, and rays in two-dimensional figures. | |
Strand: Geometry | Family: Recognizing, Describing and Naming and Classifying | ||
Progress Indicator: E.GM.1j Recognizing and drawing points, lines, line segments, rays, angles, and perpendicular and parallel lines and identifying these in plane figures | |||
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CCSS: 4.G.2 Classify two-dimensional 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 angles as a category, and identify right triangles. | |||
CCC: | 4GM.1j4 | Categorize angles as right, acute, or obtuse. | |
Strand: Geometry | Family: Recognizing, Describing and Naming and Classifying | ||
Progress Indicator: E.GM.1j Recognizing and drawing points, lines, line segments, rays, angles, and perpendicular and parallel lines and identifying these in plane figures | |||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
Additional Resources
http://www.mathplayground.com/measuringangles.html
CCSS: 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts; identify line-symmetric figures and draw lines of symmetry. | |||
CCC: | 4.GM.1k1 | Recognize a line of symmetry in a figure. | |
Strand: Geometry | Family: Transforming and Graphing | ||
Progress Indicator: E.GM.1k Recognizing and drawing lines of symmetry in a variety of figures | |||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies.
CCSS: 5.G.1 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 – 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., x-axis and x-coordinate, y-axis and y-coordinate). | |||
CCC: | 5.GM.1c3 | Use order pairs to graph given points. | |
Strand: Geometry | Family: Transforming and Graphing | ||
Progress Indicator: M.GM.1c Demonstrating the use of a coordinate system by locating/graphing a given point or polygon using ordered pairs | |||
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CCSS: 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | |||
CCC: | 6.GM.1c7 | Use coordinate points to draw polygons. | |
Strand: Geometry | Family: Transforming and Graphing | ||
Progress Indicator: M.GM.1c Demonstrating the use of a coordinate system by locating/graphing a given point or polygon using ordered pairs | |||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | |||
CCC: | 6.GM.1d1 | Find area of quadrilaterals. | |
Strand: Geometry | Family: Geometric Problems | ||
Progress Indicator: M.GM.1d Solving area, surface area, and volume problems by composing and decomposing figures | |||
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* Calculator
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CCSS: 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world mathematical problems. | |||
CCC: | 7.GM.1h2 | Find the surface area of three-dimensional figures using nets of rectangles or triangles. | |
Strand: Geometry | Family: Geometric Problems | ||
Progress Indicator: M.GM.1h Solving real-world area, surface area, and volume problems using different strategies (formulas and decomposing figures) | |||
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CCSS: 7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | |||
CCC: | 7.GM.1h3 | Find area of plane figures and surface area of solid figures (quadrilaterals). | |
Strand: Geometry | Family: Geometric Problems | ||
Progress Indicator: M.GM.1h Solving real-world area, surface area, and volume problems using different strategies (formulas and decomposing figures) | |||
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Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | |||
CCC: | 7.GM.1h4 | Find area of an equilateral, isosceles, and scalene triangles. | |
Strand: Geometry | Family: Geometric Problems | ||
Progress Indicator: M.GM.1h Solving real-world area, surface area, and volume problems using different strategies (formulas and decomposing figures) | |||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
Additional Resource
http://www.mathplayground.com/howto_area_triangle.html
CCSS: 8.G.4 Understand that a two-dimensional 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 two-dimensional figures, describe a sequence that exhibits the similarity between them. | |||
CCC: | 8.GM.1g1 | Recognize congruent and similar figures. | |
Strand: Geometry | Family: Recognizing, Describing and Naming and Classifying | ||
Progress Indicator: M.GM.1g Demonstrating congruence and similarity using a variety of two-dimensional figures | |||
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CCSS: 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | |||
CCC: | H.GM.1a2 | Find the missing side lengths of a two-dimensional right triangle (Pythagorean Theorem). | |
Strand: Geometry | Family: Constructing – Establishing a Figure | ||
Progress Indicator: H.GM.1a Applying the Pythagorean Theorem | |||
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CCSS:' G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformation that will carry a given figure onto another.
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry onto itself. | |||
CCC: | H.GM.1c1 | Construct, draw, or recognize a figure after its rotation, reflection, or translation. | |
Strand: Geometry | Family: Transforming and Graphing | ||
'Progress Indicator:'' H.GM.1c Applying understanding of rotations, reflections, and translations to construct figures (e.g., using coordinates, models, drawings, transparencies, dynamic geometry software)' | |||
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* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
Additional Resources
www.mathisfun.com/geometry – Point & click to transform the shape www.eduplace.com/kids/mw/swfs/robopacker_grade4.html – Transform shapes to create a robot