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4-N-2-2

Page history last edited by Tashe Harris 6 years, 2 months ago

4.N.2.2 Use benchmark fractions (0, ¼, ⅓, ½, ⅔, ¾, 1) to locate additional fractions on a number line. Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols.

In a Nutshell

Using benchmark fractions as points of reference, students will correctly locate additional fractions on a number line. Students will use models to compare and order whole numbers , fractions less than one and fractions greater than one. Fractions greater than one should be represented as a fraction in which the numerator is greater than the denominator. The comparisons should be expressed in word form (‘seven-eighths is less than one’) and symbolically (5/4 > 3/4 , 4/2 = 2).

Student Actions	Teacher Actions
Develop mathematical reasoning by comparing and ordering whole numbers and fractions (less than one and greater than one), using models and number lines. Develop a deep and flexible conceptual understanding of fractions as numbers by recognizing benchmark fractions and the relationships between them, and applying that knowledge to locate additional fractions on a number line. Develop the ability to communicate mathematically by using “less than”, “greater than”, and “equal to”, as well as the appropriate symbols, to describe relationships between fractions and whole numbers.	Use and connect mathematical representations by modeling the comparison of whole numbers, fractions less than one, and fractions greater than one, using manipulatives, pictorial representations, number lines, and symbolic notation. Implement tasks that promote reasoning and problem solving by introducing real-world problem scenarios which require students to interpret and compare whole numbers and fractions. Support productive struggle in learning about number relationships by providing a variety of challenging tasks in which students must compare and order fractions and whole numbers. Pose purposeful questions by asking students to explain and justify their reasoning.
Key Understandings	Misconceptions
Because benchmark fractions are easily recognized, they can be used as points of reference to facilitate comparing and ordering other numbers, both whole numbers or fractions. Comparisons of fractions and whole numbers can be appropriately expressed using both words and comparison symbols (<, >, =). Whole numbers, fractions less than one, and fractions greater than one are all numbers which can be compared and ordered. The results of the comparison and ordering can be effectively represented using models or number lines.	Fractions can’t be written to represent more than one whole. Numerators have to be less than denominators. Mixed numbers and fractions greater than one are not related. Fractions having numerators greater than the denominators are written incorrectly ('improper').