Great Ideas of Primary Mathematics

CONTENTS OF CURRICULUM UNIT 11.06.06

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Background
  4. Objectives
  5. Tools
  6. Strategies
  7. Activities
  8. Appendices
  9. Endnotes
  10. Annotated Bibliography

Fractions: Building a Strong Foundation Based on Conceptual Understanding

Valerie J. Schwarz

Published September 2011

Tools for this Unit:

Appendices

Appendix 1: Fraction Strips

image 11.06.06.25

Appendix 2:

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Appendix 3:

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Appendix 4:

image 11.06.06.28

image 11.06.06.29

Appendix 5: Implementing District Standards

Below are the state standards that directly correlate to my curriculum unit. My unit is designed to deeply develop conceptual knowledge of fractions, some of which directly correlate to the state standards from grades 2 and 3. By developing a strong conceptual foundation, the goal is that the students will truly understand fractions in a way that enables them to work with fractions flexibly in many contexts. Below are the standards included in my curriculum unit.

Grade 2 Mathematics Standards

2.3 The student will

a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths;

b) write the fractions; and

c) compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths.

Grade 3 Mathematics Standards

3.3 The student will

a) name and write fractions (including mixed numbers) represented by a model;

b) model fractions (including mixed numbers) and write the fractions' names; and

c) compare fractions having like and unlike denominators, using words and symbols (>, , or =).

3.7 The student will add and subtract proper fractions having like denominatorsof 12 or less.

Grade 4 Mathematics Standards

4.2 The student will

a) compare and order fractions and mixed numbers;

b) represent equivalent fractions; and

c) identify the division statement that represents a fraction.

4.5 The student will

b) add and subtract fractions having like and unlike denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;

Comments:

Karen Conte

December 16, 2013 at 4:01 pm

Inspiring unit

I just wanted you to know that I was inspired by your lesson, I started folding paper strips and figuring out how to integrate them into my lessons on fractions. I teach 5th grade but it was very applicable for my students who were not getting it. We use Singapore but your unit gave a better explanation of Fractions using the concrete, pictorial, abstract. I also like your scope and sequence of the lessons. I was using it to reteach the review of mixed numbers, improper fractions, etc. and will follow it more closely when we get to adding fractions after break. I also liked your activities, I only wish there were 'activities' for all of the lessons:)

Frank Peart

October 19, 2015 at 9:25 pm

Your Publication Strengthens

I am about to teach adding like fractions to my fourth grade class, so I was searching for a variety of ways to introduce the activities in a concrete way. Then I came upon your article.It provided a good base on which to start. The sequencing of the activities spot on; I too have been trying such a sequence however, yours is far more activity base. Thanks and I will share.

Cindy Fisher

November 13, 2016 at 5:02 pm

Great reflections and resources

I am researching fraction work in grades 4 and 5, and I had been led to your link. I am so over-the-moon that I found this resource. You provided me with standards-based instruction, order, misconceptions, instructional resources, and so much more. As an intermediate (mostly) special educator in math for grades 4 and 5, my students have many splintered skills and your reflections are spot-on. They will drive my small group instruction. We have already begun the fraction strips, but I am always in search of more connections. I saved your site for future pathways! Thanks again, Cindy

L Lang

January 2, 2019 at 7:28 pm

Great overview of your fractions unit

I've been placed in a 5th grade ELD class. It's a title 1 school predominantly hispanic. It is not what I've been trained to do. Teaching ELD is hard because of language and prior knowledge from prior grades not being there. The school uses the Engage NY math. Students partially understand the information but the school says push them along. In other words if they didn't learn their math tables then just keep going. I'm going to try your unit as a re-teach for them. I will report back when I finish to see if there is positive growth. Even though I'm re-teaching, I'm bucking their system by doing so. They worry about the AZ Merit & Azella tests. They focus on the tests & not really whether the students learned something or not.

Shannon Mills-dyke

November 10, 2022 at 8:20 pm

Year of publication?

Hi, Can I ask what year this was published please. I would like to reference part of your work in one of my university assignments? 2011

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