A Passion for Fractions

Grades 3-5 / Math / Reasoning
CCSS: Math.5.NF.B.4b Math.Practice.MP2 Math.Practice.MP3

Common Core State Standards

Math

Math

5

Grade 5

NF

Numbers & Operations--Fractions

B

Apply and extend previous understandings of multiplication and division

4b

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.


a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)


b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

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)

Common Core State Standards

Math

Math

Practice

Mathematical Practice Standards

MP3

Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)
Lesson Objective
Multiply a fraction by a fraction
Length
13 min
Questions to Consider
Why does Ms. Pittard present students with a variety of solutions?
How does critiquing solutions help students develop an understanding of multiplying fractions?
What can you learn from Ms. Pittard about engaging all students?
Common Core Standards
Math.5.NF.B.4b, Math.Practice.MP2, Math.Practice.MP3

Supporting Materials

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  • A Passion for Fractions Transcript

  • Lesson Plan: Multiplying Fractions.PDF

  • Lesson Plan: Shamrock Smile Mile Worksheet.PDF

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Lesson Idea (Common Core) A Passion for Fractions

Grades 3-5 / Math / Reasoning

A Passion for Fractions