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Handout 4.3e:

Number Line Routines

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Below is some of the math that may come up while facilitating a number line routine. However, planning is essential when preparing to facilitate the routine in class. Before you begin, consider what your objectives may be when conducting the routine. Where would you focus with your students?

Foundational Standard: 4.NF. Use 0-2 number lines to represent relative fraction magnitude for fractions less than 1, equal to one, and greater than 1 as well as mixed numbers.

Strategies

Models

Big Ideas

  • Benchmark fractions and the relationship between a fraction and a whole number
  • Using an understanding of partitioning a whole to partition the space between 0 and 1 on the number line
  • Iterate a unit fraction to cover the distance between 0 and 1

Number lines

  • Detailed: all whole numbers are marked
  • Open: no numbers are marked and the mathematician can decided the best numbers to use based on the given problem
  • Double: show two strategies simultaneously and highlight a relationship

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  • Fractions are numbers on the number line
  • Between whole numbers are an infinite amount of fractional numbers
  • Unit fractions can be iterated units of measurement; this context lends itself to the idea of how much space or distance rather than how many parts

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Math | Module 4.3 (Gr 4)

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Handout 4.3f [pg. 1 of 2]:

End of Module Reflection

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Part I:

Review the NYC Department of Education’s Vision for Mathematics and make connections to the vision and the learning experiences offered in this module.

  • In what ways did you enact the vision for math in terms of students, teachers, and content?

NYCDOE Vision for Mathematics Excerpt

We envision a mathematics learning experience where: 

  • Students are empowered to make sense of mathematics both in the classroom and beyond, including developing mathematical thinking and regularly engaging in mathematical collaboration and discourse; 
  • Teachers facilitate instruction that is student-centered, inquiry-based, coherent and in an environment that fosters belonging and high expectations; and 
  • Content that provides opportunities for students to engage in productive struggle with cognitively demanding, mathematical concepts that are connected to one another and the world around them

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Math | Module 4.3 (Gr 4)

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Handout 4.3e [pg. 2 of 2]:

End of Module Reflection

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Part II:

What will you commit to moving forward? Make it manageable for yourself and share your plan with a colleague.

Options to select from:

  1. I will make time to implement interview-based assessments during the year.
  2. I will facilitate Fair Shares problems when appropriate.
  3. I will facilitate number line routines during the appropriate fraction unit.

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Math | Module 4.3 (Gr 4)