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Hands-on Minds-on Activities that Address New and Relocated TEKS

Hands-on Minds-on Activities that Address New and Relocated TEKS. All handouts are available at www.cosenzaassociates.com Click on Our Work: Publications and Events, Events and Conferences, CAMT 2014. Gary Cosenza Cosenza & Associates, LLC. CAMT 2014 Fort Worth, Texas.

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Hands-on Minds-on Activities that Address New and Relocated TEKS

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  1. Hands-on Minds-on Activities that Address New and Relocated TEKS All handouts are available at www.cosenzaassociates.com Click on Our Work: Publications and Events, Events and Conferences, CAMT 2014. Gary Cosenza Cosenza & Associates, LLC CAMT 2014 Fort Worth, Texas

  2. Hands-on Minds-on Activities that Address New and Relocated TEKS Several Student Expectations are new to Texas or new to a grade level. In this session we will explore the use of pictorial models, graphic organizers, number lines, and manipulatives to address some of the new or relocated content in grades 3-5. The activities are designed to provide students with the opportunity to gain conceptual knowledge of mathematics while developing procedural fluency.

  3. Impact of Hands-on Minds-on Mathon Student Achievement Research shows that student understanding and mathematical literacy skills improve when students do hands-on minds-on math and make real-world connections.

  4. Focus on Fractions 3.2AThe student is expected to construct concrete models of fractions. NT 3.3A The student is expected to represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines. How is it different? Specificity has been added for the fractions that students are expected to model. Fractions are greater than zero and less than or equal to one. The denominators may be 2, 3, 4, 6, or 8. Concrete models should be linear in nature to build to the use of strip diagrams and number lines. What is new? Students are expected to represent fractions using pictorial models, including strip diagrams and number lines.

  5. Focus on Fractions 3.2B The student is expected to compare fractional parts of whole objects or sets of objects in a problem situation using concrete models. NT 3.3H The student is expected to compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models. How is it different? The revised SE adds specificity to the number of fractions a student compares. It also adds specificity to the types of fractions being compared: two fractions having the same numerator or denominator. Fractions should have denominators of 2, 3, 4, 6, or 8. What is new? Students justify conclusions about their comparisons using symbols, words, and pictorial models.

  6. Focus on Fractions 3.2C The student is expected to use fraction names and symbols to describe fractional parts of whole objects or sets of objects. NT 3.3C The student is expected to explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number. NT 3.3D The student is expected to compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b. How is it different? Fractions should have denominators of 2, 3, 4, 6, or 8. Students are expected to describe or explain the fraction 1/b as the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number. A fraction may a part of a whole object or part of a set of objects. What is new? Students are expected to compose and decompose fractions. For example, 7/8=1/8+6/8; 7/8=2/8+5/8; and 7/8 = 3/8 + 4/8..

  7. Focus on Fractions 3.2D The student is expected to construct concrete models of equivalent fractions for fractional parts of whole objects. NT 3.3F The student is expected to represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines. How is it different? The denominators may be 2, 3, 4, 6, or 8. Objects, also called concrete models, that are linear in nature build to the use of strip diagrams as a pictorial model and number lines. What is new? The revised SE includes the use of pictorial models, such as strip diagrams, and number lines.

  8. Focus on Fractions NT 4.3A The student is expected to represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b. NT4.3D The student is expected to compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <. How is it different? When paired with revised SE 4(1)(D), students may represent a/b as a sum of fractions 1/b using concrete and pictorial models, which includes improper fractions when a>b. What is new? The revised SE builds on revised SE 3(3)(H) where students compare two fractions having the same numerator or denominator.

  9. Focus on Fractions NT 4.3B The student is expected to decompose a fraction in more than one way into a sum of fractions with the samedenominator using concrete and pictorial models and recording results with symbolic representations. NT4.3D The student is expected to compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <. How is it different? This SE builds on revised SE 4(3)(A) that requires students to describe fractions as a sum of unit fractions, such as 5/2=1/2+1/2+1/2+1/2+1/2. In this SE, students are expected to also express 5/2=3/2+2/2; 5/2=1/2+4/2; 5/2=2/2+2/2+1/2; and 2 ½=1+1+1/2. What is new? Students are expected to use concrete models such as fraction strips or fractions bars and pictorial models such as strip diagrams and to record the appropriate number sentences.

  10. Focus on Fractions NT 4.3C The student is expected to determine if two given fractions are equivalent using a variety of methods. How is it different? Methods may include concrete models suchas fraction strips and fraction bars andpictorial models such as strip diagrams. Methods also include numeric approaches. What is new? With the current SE 4(2)(A), students are expected to generate equivalent fractionsrather than verify equivalence.

  11. Focus on Fractions NT 4.3E The student is expected to representand solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. How is it different? This SE is coming to grade 4 from the current grade 5 SE 5(3)(E). Objects that build to the number line include fraction strips and fraction bars and other linear fraction models. Pictorial models include sketches of the linear fraction models and strip diagrams. What is new? Properties of operations with the additionand subtraction of fractions with equal denominators connects to the decomposingof fractions included in revised SE 4(3)(B).

  12. Focus on Fractions NT 4.3F The student is expected to evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole. How is it different? For example, when estimating 7/8+6/8, one might estimate 7/8 as 1 and 6/8 as ½ since the estimate for 7/8 is a bit larger than 7/8. The estimated sum would be 1 ½.

  13. Focus on Fractions NT 5.3H The student is expected to represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. How is it different? The revised SE represents a subset of the Current 6.2A. Within the Revised TEKS (2012), fluency with fraction and decimal addition and subtraction occurs in grade 5. “Procedural fluency refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently” (National Research Council, 2001, p. 121). Pictorial models may include strip diagrams.

  14. Focus on Fractions NT 5.3I The student is expected to represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. How is it different? The revised SE represents a subset of the current 7(2)(A). When paired with revised SE 5(1)(A), the expectation is that students solve problems. The intent of this SE is not a sole focus on the computation. Within the Revised TEKS (2012), fluency with fraction multiplication occurs in grade 6.

  15. Focus on Fractions NT 5.3J The student is expected to represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models. How is it different? The revised SE represents a subset of the current 7(2)(A). When paired with revised SE 5(1)(A), the expectation is that students solve problems. The intent of this SE is not a sole focus on the computation. Within the Revised TEKS (2012), fluency with fraction division occurs in grade 6. A unit fraction is a fraction with a numerator of 1. Students first see unit fractions in grade 3 with revised SE 3(3)(C).

  16. Focus on Fractions NT 5.3L The student is expected to divide whole numbers by unit fractions and unit fractions by whole numbers. How is it different? The revised SE represents a subset of the current 7(2)(B). When paired with revised SE 5(1)(A), the expectation is that students solve problems. The intent of this SE is not a sole focus on the computation. Within the Revised TEKS (2012), fluency with fraction division occurs in grade 6.

  17. Representing Fractions - Engage • Complete the activity sheet. • What do students need to know and be able to do to complete this activity? • How can you use this type of activity in your situation?

  18. Representing Fractions - Explore • Complete the activity sheet. • What do students need to know and be able to do to complete this activity? • How can you use this type of activity in your situation?

  19. Representing Fractions – Explain Foldable: Fractions on a Number Line • Begin with 3 sheets of colored paper. • Layer them so that the bottom edges are about one inch apart. • Fold the top down so that the top edges make 3 more flaps at the top of the layered stack. • Staple the top twice to hold the layered stack in place. Foldable Video

  20. Representing Fractions - Elaborate • Complete the activity sheet. • What do students need to know and be able to do to complete this activity? • How can you use this type of activity in your situation?

  21. Kids Doing MathHands-on Fractions Contact Information: Gary Cosenza gary@cosenzaassociates.com www.staarmission.com • Cosenza & Associates, LLC

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