Author: Larry Francis

K-8 grade by grade

Keeping in mind that Algebra is the destination for our K-8 math students, this section recommends key activities for each grade that bring the Common Core State Standards in Math (CCSSM) for that grade to life, plus references to H. Wu’s Understanding Numbers in Elementary School Mathematics and Teaching School Mathematics: Pre-Algebra and other relevant books and links.

My goal is three-fold:

  • to give you worthwhile things to do with your students that help them develop the number sense they need to make sense of arithmetic on their way to Algebra,
  • to justify those activities according to the CCSSM, with pertinent citations for each,
  • and to put those activities in the larger context of school mathematics and human cognition by citing relevant pages and passages from the work of H. Wu and others.

Accelerated Remediation at Helman Elementary

Teaching math to kids who have fallen behind means you—and they—have to somehow go faster, not slower, in order to catch up to their classmates and be able to relate to and benefit from their grade-level teacher’s instruction.

This section is my attempt to explain the somehow of accelerated remediation: what I think we did to help our students make such extraordinary gains (nearly 1 nationally normed quartile on average).

Fractions Race for 3 units

This race game uses pattern blocks (yellow hexagons, red trapezoids, blue rhombuses—or rhombi—and green equilateral triangles) as concrete representations of units and fractions of units, specifically halves, thirds, and sixths, per the 3rd grade standards. (We declare that our unit will be the area of the top of a yellow hexagon. So

  • 1 = the area of a yellow hexagon (our unit).
  • 1/2 = the area of a red trapezoid since 2 red trapezoids exactly cover (tile, pave) the top of a yellow hexagon (our unit).
  • 1/3 = the area of a blue rhombus since 3 blue rhombuses exactly cover (tile, pave) the top of a yellow hexagon (our unit).
  • 1/6 = the area of a green equilateral triangle since 6 green equilateral triangles exactly cover (tile, pave) the top of a yellow hexagon (our unit).

pattern-block-sandwich

We use a cube (6-sided) die with faces equal to first 6 members of the sixths family (after 0/6):  1/6, 1/3, 1/2, 2/3, 5/6, and 1.