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Divide unit fractions by whole numbers and whole numbers by unit fractions using visual fraction models.
Clarifications:

Essential Understandings

Concrete:

  • To show whole numbers divided by unit fractions, use fraction manipulatives to model the wholes. Use a template to guide placement of the unit fractions to illustrate that every whole can be represented in terms of groups of unit fractions (e.g., 3 ÷ 1/2 is 3 wholes divided into 6 groups of 1/2).

    3/(1/2) = ?
  • Count the number of groups of the unit fraction to determine the quotient.
Representation:
  • Understand the following concepts and vocabulary: fraction, whole number, divide, ÷.
  • Use visual representations to model whole numbers and groups of unit fractions.
  • Count the number of groups of the unit fraction to determine the quotient.

Access Point #: MAFS.5.NF.2.AP.3a (Archived Access Point)
Access Point Standards

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.5.NF.2.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Access Point Information
Number:
MAFS.5.NF.2.AP.3a
Category:
Access Points
Cluster:
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (Major Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Access Point Courses
  • Grade Five Mathematics (#5012070): The benchmarks in this course are mastery goals that students are expected to attain by the end of the year. To build mastery, students will continue to review and apply earlier grade-level benchmarks and expectations.
  • Access Mathematics Grade 5 (#7712060): Access Courses:

    Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities. 

  • STEM Lab Grade 5 (#5020120): This course offers students an opportunity to deepen science, mathematics, engineering, and technology skills.  The primary content focus will be to expand knowledge of current grade level standards in mathematics and science by applying that content in a real world, hands-on situation involving engineering and technology.  For fifth grade, themes will focus on the investigation of number sense, measurement, geometry, and physical science concepts.

    Students will participate in various hands-on STEM activities in this supplemental course to assist in the mastery of current grade level mathematics and science standards.

    Instructional Practices 
    Teaching from a range of complex text is optimized when teachers in all subject areas implement the following strategies on a routine basis:

    1. Ensuring wide reading from complex text that varies in length.
    2. Making close reading and rereading of texts central to lessons.
    3. Emphasizing text-specific complex questions, and cognitively complex tasks, reinforce focus on the text and cultivate independence.
    4. Emphasizing students supporting answers based upon evidence from the text.
    5. Providing extensive research and writing opportunities (claims and evidence).

    Science and Engineering Practices (NRC Framework for K-12 Science Education, 2010)

    • Asking questions (for science) and defining problems (for engineering).
    • Developing and using models.
    • Planning and carrying out investigations.
    • Analyzing and interpreting data.
    • Using mathematics, information and computer technology, and computational thinking.
    • Constructing explanations (for science) and designing solutions (for engineering).
    • Engaging in argument from evidence.
    • Obtaining, evaluating, and communicating information.

    English Language Development (ELD) Standards Special Notes Section:

    Teachers are required to provide listening, speaking, reading and writing instruction that allows English Language Learners (ELL) to communicate information, ideas and concepts for academic success in science and math.  For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success.  The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL's need for communication and social skills.  To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:  {{AzureStorageLink}}/uploads/docs/standards/eld/sc.pdf.

  • Grade 4 Accelerated Mathematics (#5012065): In grade 4 accelerated, instructional time will emphasize six areas: (1) developing the relationship between fractions and decimals; (2) multiplying and dividing multi-digit whole numbers, including using a standard algorithm; (3) adding and subtracting fractions and decimals with procedural fluency, developing an understanding of multiplication and division of fractions and decimals; (4) developing an understanding of the coordinate plane and plotting pairs of numbers in the first quadrant; (5) extending geometric reasoning to include volume and (6) developing an understanding for interpreting data to include mean, mode, median and range.

    Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.

  • Foundational Skills in Mathematics 3-5 (#5012015):

    This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all domains including number sense & operations, fractions, algebraic reasoning, geometric reasoning, measurement and data analysis & probability. Teachers will use the listed standards that correspond to each students’ needs. 

    Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.