NCDPI AIG Instructional Resource: Background Information s3

NCDPI – AIG Instructional Resource: Background Information

Resource Title: Beautiful Symmetry

Subject Area/Grade Level (s): Math/4 Time Frame: two days

Common Core Standard Addressed: Number and Operations - Fractions Extend understanding of fraction equivalence and ordering. 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) 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. 4.NF.2 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. Number and Operations - Fractions Understand decimal notation for fractions, and compare decimal fractions. 4.NF.5 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 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Mathematical Practice 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project Additional Standards Addressed: Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.3 Recognize a line of symmetry for 2D figures. Identify line symmetric figures and draw lines of symmetry. North Carolina Essential Standards – Visual Arts 4.V.1.2 Apply personal choices while creating art. 4.V.1.4 Understand how the Elements of Art are used to develop a composition. 4.V.3.3 Create art using the processes of drawing, painting, weaving, printing, stitchery, collage, mixed media, sculpture, ceramics, and current technology.

Brief Description of Lesson/Task/Activity: Students will apply fourth grade concepts of equivalent fractions, decimals, and symmetry to create artwork. Once all students have created their masterpieces, they will have a conversation to compare and contrast the various pieces. Through teacher questioning, this conversation will lead to a deeper understanding of equivalent fractions and decimal fractions.

Type of Differentiation for AIGs (include all that apply): Enrichment x Extension Acceleration

Adaptations for AIGs: x Content x Process x Product

Explanation of How Resource is Appropriate for AIGs: This activity extends fourth grade fraction concepts by requiring students to utilize the highest level of Bloom’s Taxonomy: creating. Further, the abstractness of the task will lead students to deeply understand the concepts of equivalent fractions and decimal fractions. The open-endedness allows students to create any number of different pieces of artwork based on a single description. Students will be able to choose their artwork design, size, and composition, allowing for personal choices and freedom of expression.

Needed Resources/Materials: • Images of paintings that demonstrate use of symmetry (e.g., pieces by Frank Stella) • images of paintings that demonstrate the artist’s attention to the fractional parts of color (e.g., pieces from Piet Mondrian, Akash Nihalani, Carmen Herrera, Joan Miro) • copies of Masterpiece Description Cards • paint • construction paper (blue, yellow, and red) • one inch color tiles • one inch grid paper • scissors • glue • Symmetry Artist web-tool (http://www.mathsisfun.com/geometry/symmetry-artist.html)

Sources :NA

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project TEACHER NOTES: Standard 4.G.3 is referenced under “Additional Standards” because this task has a loose connection to this standard.

NCDPI AIG Curriculum Resource Outline

STAGE ONE: ENGAGE

Artists from all cultures carefully attend to details when creating masterpieces. For example, when designing paintings, they often think about how to make the parts of the painting symmetrical, creating a sense of harmony and balance. Today we will look at two types of details that artists often utilize: symmetry and precise attention to the fractional parts of each color.

Explain that some artists try to balance the colors in a piece by ensuring that the fractional part of one color is equal to the fractional parts of all other colors in their paintings. Other artists want to draw attention to a specific color, and ensure that the selected color represents a much larger fraction of the painting. Show several pieces of art, where the artist paid close attention to the fractional parts of each color (e.g., pieces from Piet Mondrian, Akash Nihalani, Carmen Herrera, Joan Miro). Have students discuss the fraction that each color represents.

Next, show examples of how artists used symmetry in their paintings. (e.g., pieces by Frank Stella). Because fourth grade students have only been exposed to “reflection symmetry” by examining lines of symmetry in shapes, it may be necessary to define rotational symmetry and translation symmetry.

STAGE TWO: ELABORATE

Explain the following task to students: Today you will create a piece of art that incorporates both symmetry and attention to the fractional parts of each color. You will select a description card to determine the fraction of each color in your artwork. Your masterpiece can be as big or as small as you please as long as it meets the criteria on your card and demonstrates symmetry.

Once students select their description cards, have them silently think about the following questions:  What is this task asking you to do?  Look at your description card. Which color will you use the most? The least?  What mathematics will you need to use in order to create your artwork?

As students work, it may be necessary to elicit and extend thinking by asking question, which may include:  What type of symmetry will you incorporate into your design?  How will you decide on the size of your artwork? What mathematics do you need to use in order to decide on the size?  How can your knowledge of equivalent fractions help with this task?  What tools can you use to ensure that your fractional parts are correct (grid paper, color tiles, ruler)?  Is it possible to make a piece that is a different size but still matches your description? What is the smallest/largest piece you can make?  How could using an equation to represent your artwork help you with this task (the fractional parts must equal one whole)?

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project After students have completed their artwork, do a gallery walk so that all students can observe the symmetry and fractional parts of each color in the artwork. Then, engage students in a discussion to explore strategies used when creating their pieces. Have students explain how they determined the total size for their piece and how they determined what the fractional parts would look like. Strategies may include using common denominators or reducing a fraction to its simplest form. Make sure students use mathematics (drawings, words, equations, models) to prove their thinking. Ensure that students who had description cards containing decimals have an opportunity to share their strategies as well. Compare and contrast the strategies for working with fractions to the strategies for working with decimals. Have students discuss whether it is easier to create a masterpiece using a decimal description card or fraction card (justify thinking).

Read each description card aloud, and ask the group to determine which description went with each painting. Ask questions such as:  Originally, the group said that this painting was 1/4 yellow, but the card says 2/8. How do we know this is the correct card?  What mathematics did you use to match the description cards?  How did you use knowledge of equivalent fractions to match the cards?  Is it easier to find the matches to the decimal cards or fraction cards? Why?

Observe that different masterpieces are different sizes. Draw attention to the description cards, and ask if it is possible to create a differently- sized piece that still meets the description? Challenge students to find larger and smaller dimensions that will still meet the same description (students will need to draw upon their knowledge of equivalent fractions/decimals to solve this challenge).

STAGE THREE: EVALUATE

The student’s understanding of symmetry will be evaluated based on their completed artwork and ability to describe the symmetry using specific mathematical vocabulary. The student’s understanding of fraction and decimals concepts (i.e., the sum of the parts must equal a whole and equivalent fractions) will be evaluated based on the accuracy of the fractional parts in their artwork. Understanding of fraction and decimal concepts will also be evaluated through one-on-one and whole group discussions. Students should be able to use appropriate vocabulary, thoroughly explain solution strategies, and justify why two fractions/decimal fractions are equivalent.

TEACHER NOTES: If students are struggling to create artwork that matches the exact fractional parts of their description cards, suggest that they begin by planning their work on grid paper or with color tiles.

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project