Math: Fraction Concepts

Suggested Time Frame: 22 Instructional Days

        

Focus TEKS

Represent Fractions and Introduce Fraction Notation

  • 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
    • 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

Unit Fractions

  • 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

Fraction Equivalence

  • 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
    • 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

Compare Fractions

  • 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

Problem Solving

  • 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
Numeracy TEKS

Developing Strategies for Multiplying and Dividing within 100 (Suggested: 15 days)

  • 3.4F recall facts [twos, fours, fives, eights and tens facts in this unit] to multiply up to 10 by 10 with automaticity and recall the corresponding division facts;- S RC2 [Including the Use-Ten and Doubling Strategies for Multiplication; Including the Think Multiplication Strategy for Division]
    • 3.4D determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10 [arrays representing twos, fours, fives, eights, and tens facts in this unit]; – S RC2
    • 3.4E represent multiplication facts [twos, fours, fives, eights and tens facts in this unit] by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting; – S RC2
    • 3.4H determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally; – S RC2

Counting Patterns (Suggested: 5 days)

  • RRISD 3.5 Skip count by whole numbers starting from 0 and other starting numbers and describe patterns observed while counting; [Skip count by tens and hundreds within 1,200.]
Spiral Review TEKS

Grade 2 Adding and Subtracting with 2-Digit Numbers (Suggested: 10 days)

  • Computation
    • 2.4B add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations
  • Problem Solving
    • 2.4C solve one-step and multi-step word problems involving addition and subtraction within 1,000 [200 in this unit] using a variety of strategies based on place value, including algorithms
    • 2.4D generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000 [200 in this unit].
  • Representing
    • 2.7C represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

Grade 2 Geometry and Measurement (Suggested: 10 days)

  • Geometry
    • 2.8A create two-dimensional shapes based on given attributes, including number of sides and vertices
    • 2.8B classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language
    • 2.8C classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices
    • 2.8D compose two-dimensional shapes and three-dimensional solids with given properties or attributes
    • 2.8E decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts
  • Measure Length
    • 2.9D determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes
  • Measure Area
    • 2.9F use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit

Counting Quantities (Suggested: 2 days, using both numeracy and spiral review time)

  • RRISD 3.1 Organize and count a collection of objects and create a recording of how the objects were counted
    • 3.1C  select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
    • 3.1E  create and use representations to organize, record, and communicate mathematical ideas;
  • Counting Coins (Make this the focus on 1 day of Counting Collections)

    • 2.5A determine the value of a collection of coins up to one dollar [pennies, nickels, dimes, and quarters]
      • 2.5B use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins

Telling Time (Ongoing)

  • 2.9G read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m.