Math: Developing Fraction Number Sense through Equivalence and Comparisons

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
  • 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

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
• 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

Solving Problems (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
• 2.9D determine the length of an object to the nearest [whole, half, fourth, or eighth inch] marked unit using rulers, yardsticks, meter sticks, or measuring tapes

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

Multiplication and Division Facts (Build Up and Build Down Multiplication Fact Strategies)

• 3.4F recall facts [sixes and nines facts in this unit] to multiply up to 10 by 10 with automaticity and recall the corresponding division facts;- S RC2
  • 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 sixes and nines facts]; – S RC2
  • 3.4E represent multiplication facts [sixes and nines 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

Operations and Algebraic Reasoning

• Problem Solving (All four operations)
  • 3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction; – R RC2
    • 3.4B round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems; – S RC2
  • 3.4K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts. – R RC2
  • 3.8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals. – S RC4
• Representations (Pictorial and Symbolic)
  • 3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations; – R RC2
  • 3.5B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations; – R RC2
  • 3.5E represent real-world relationships using number pairs in a table and verbal descriptions. – R RC2