Student Actions

Teacher Actions

• Demonstrate a deep, conceptual understanding of number lines as they make connections between whole numbers and fractions.  

• Develop mathematical reasoning as they predict and explore where a fraction may lie on a number line.

• Apply a variety of models to justify their reasoning for comparing fractions.

• Develop procedural fluency as they compare and order fractions using a number line that is accurately spaced and labeled.

• Communicate mathematically with peers using academic vocabulary, such as less than, greater than, equal to, numerator, denominator, whole, etc. 

• Pose purposeful questions to help students recall prior knowledge and justify their thinking.Questions may include asking students how models and number lines help us compare and order fractions and how they know the difference between two fractions’ values. 

• Apply mathematical representations purposefully to help students understand the concept of comparing fractions of the same whole.

• Support productive struggle as students explore using number lines and manipulatives to compare and order fractions. 

Key Understandings

Misconceptions 

• Fractions represent parts of numbers and can be found on a regular number line.

• Fractions are equal parts of a whole.

• The larger the denominator, the smaller the fraction pieces (unit fraction).

• A variety of models are useful when ordering and comparing fractions, such as fraction bars, circles, number lines, and grids.

• Each part of the fraction model must be equal to one another.

• Evenly spaced tick marks on a number line help determine the denominator. 

• Labeling the fractions on the number line helps when comparing and ordering fractions.

• Recognize that comparisons are valid only when the two fractions refer to the same whole.

• Understand comparisons symbols >, =, or <

• Fractions only fall between 0 and 1 on a number line.

• Denominators never matter when ordering and comparing fractions.

• The number of tick marks on a number line is the same as the denominator, (e.g. A number line has 9 tick marks starting at “0” and ending at “1”.) Students may think the number line is divided into ninths instead of eighths.

• A whole cannot be described as a fraction. For example, Students may not think 8/8 is the same as 1 whole.

• The relative size of a whole isn't necessary to know to determine what size the fraction is.

• The fraction with the larger denominator as being larger, applying their whole number understanding to comparing and ordering fractions 

  Knowledge Connections

Prior Knowledge

Leads to 

• Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. (2.N.3.1)

• Construct equal-sized portions through fair sharing (length, set, and area models for halves, thirds, and fourths). (2.N.3.2)

• Represent and rename equivalent fractions using fraction models (e.g., parts of a set, area models, fraction strips, number lines). (4.N.3.1)

• Use models to order and compare whole numbers and fractions less than and greater than one, using comparative language and symbols. (4.N.3.3)