Formative Assessment: Understanding Fractions

Grades 3-4 / Math / Fractions
CCSS: Math.3.NF.A.1 Math.Practice.MP1 Math.Practice.MP2

Common Core State Standards

Math

Math

3

Grade 3

NF

Numbers & Operations--Fractions

A

Develop understanding of fractions as numbers

1

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.


Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

Download Common Core State Standards (PDF 1.2 MB)

Common Core State Standards

Math

Math

Practice

Mathematical Practice Standards

MP1

Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

Common Core State Standards

Math

Math

Practice

Mathematical Practice Standards

MP2

Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize--to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Download Common Core State Standards (PDF 1.2 MB)

Lesson Objective

Formatively assess understanding of fractions

Length

16 minutes

Questions to Consider

  • Why does Ms. Romano decide to assess her fourth graders' understanding of a third grade content standard?
  • How does Ms. Romano encourage productive struggle during the lesson?
  • What instructional decisions does Ms. Romano make based on her observations during the collaborative work?

Watch all the videos in this series: Formative Assessment Practices to Support Student Learning

Common Core Standards
Math.3.NF.A.1, Math.Practice.MP1, Math.Practice.MP2

Supporting Materials

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  • Formative Assessment: Understanding Fractions Transcript

  • Formative Assessment Process.PDF

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Teaching Practice Formative Assessment: Understanding Fractions

Grades 3-4 / Math / Fractions

Formative Assessment: Understanding Fractions