## Quilts and Geometry |

## Class DescriptionThis delightful class encourages students to understand the connection between mathematics and the craft of quilting. Students will be introduced to traditional patchwork quilts, their characteristics, and patterns. Each student creates a paper quilt block by manipulating and transforming a simple square. The project explores mathematical abstraction and provides a model for students to explore several different mathematical concepts. Grade Level: 1–3 LINK: Art Class: Radial Symmetry ## State Standards, Benchmarks, and GLEs
VA-CE-E6 Students will identify relationships among visual arts, other arts, and disciplines outside the arts VA-CA-E1 Students will view works of art and express observations about how the elements and principles of design are used in the works
Reason with shapes and their attributes. 1.G.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 1.G.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional 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. 1.G.3. Partition circles and rectangles into two and four equal shares, describe the shares using the words
Comprehensions and Collaboration 1.SL.1. Participate in collaborative conversations with diverse partners about a. Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). b. Build on others’ talk in conversations by responding to the comments of others through multiple exchanges. c. Ask questions to clear up any confusion about the topics and texts under discussion. 1.SL.2. Ask and answer questions about key details in a text read aloud or information presented orally or through other media. 1.SL.3. Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood. Presentation of Knowledge and ideas 1.SL.4. Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly. 1.SL.6. Produce complete sentences when appropriate to task and situation. (See grade 1 Language standards 1 and 3 on page 26 for specific expectations.)
Vocabulary Acquisition and Use 1.L.6. Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g.,
2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words
Comprehensions and Collaboration 2.SL.1. Participate in collaborative conversations with diverse partners about a. Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). b. Build on others’ talk in conversations by linking their comments to the remarks of others. c. Ask for clarification and further explanation as needed about the topics and texts under discussion. 2.SL.2. Recount or describe key ideas or details from a text read aloud or information presented orally or through other media. 2.SL.3. Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a topic or issue. Presentation of knowledge and ideas 2.SL.4. Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences. 2.SL.6. Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 2 Language standards 1 and 3 on page 26 for specific expectations.)
Vocabulary Acquisition and Use 2.L.6. Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g.,
3.G.1. 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. 3.G.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Number and operations – fractions Develop understanding of fractions as numbers. 3.NF.1. Understand a fraction 1/ 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual Measurement and data Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.7. Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8. Solve real world 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.
Comprehension and collaboration 3.SL.1. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on b. Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). c. Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others. d. Explain their own ideas and understanding in light of the discussion. 3.SL.2. Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. 3.SL.3. Ask and answer questions about information from a speaker, offering appropriate elaboration and detail. Presentation of knowledge and ideas 3.SL.4. 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. 3.SL.6. Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 on page 28 for specific expectations.)
Vocabulary Acquisition and Use 3.L.6. Acquire and use accurately grade-appropriate conversational, general academic, and domain specific words and phrases, including those that signal spatial and temporal relationships (e.g.,
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