Math (TAG): Fractions

Suggested Time Frame: 25 Instructional Days

        

Focus TEKS

Represent Fractions (Concrete, Pictorial, Number Lines, Strip Diagrams – Including Improper Fractions and Mixed Numbers)

  • 3.7A represent fractions of halves, fourths, and eighths as distances from zero on a number line; – S RC1
    • 2.9D determine the length of an object to the nearest [whole, half or fourth inch] marked unit using rulers, yardsticks, meter sticks, or measuring tapes
    • 3.3A 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; – S RC1
    • 3.3B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line; S RC1

Generalizing and Explaining – Composing and Decomposing (Including Improper Fractions – any denominator)

  • 3.3D 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; – S RC1
    • 3.3C 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; – S RC1
    • 3.6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape. – S RC3
  • 4.3A  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 S
  • 4.3B  decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations S

Relating Fractions and Decimals

  • 4.2G  relate decimals to fractions that name tenths and hundredths R

Problem Solving (Specific Denominators)

  • 3.3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8; – S RC1

Representing Equivalent Fractions (Objects, Pictorial Models, Number Lines, Strip Diagrams, with denominators of 2, 3, 4, 6, and 8)

  • 3.3F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines; – R RC1

Generalizing and Explaining Fraction Equivalence (any denominator)

  • 3.3G explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model; – S RC1

Comparing with Reasoning (any denominator)

  • 3.3H 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. – R RC1

Add and Subtract Fractions with Like Denominators

  • 4.3E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations; – R RC2
    • 4.3F 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; – S RC2
Computational Fluency TEKS

Multiplication and Division Facts and Computation

  • 3.4F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts. S
  • 4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings S
  • 4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15 S
Spiral Review TEKS

Reviewing 2-D and 3-D Figures

  • 3.6A  classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language R
  • 4.6D  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 R
    • 3.6B  use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories S
      • 4.6B  identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure S
        • 4.6C  apply knowledge of right angles to identify acute, right, and obtuse triangles S
  • 4.6A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines; – S RC3

Perimeter and Area

  • 3.6D  decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area S
  • 3.6E  decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape S
  • 3.7B  determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems R

Place Value Understandings

  • 4.2A interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left; – S RC1