A Melody of Fractions

Posted By: Lourdes Terrero

Author & Illustrator: Ellen Phillips and Nancy Lane

Recommended Grade Level: Fourth Grade

CCSSM Standards:

CCSS.MATH.CONTENT.4.NF.A.1

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

CCSS.MATH.CONTENT.4.NF.A.2

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Common Core Standards for Mathematical Practice:

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Summary: In this story, Sachiko is taking her first piano lesson. She learns the value of the different kinds of notes. In order to understand the number of beats for each note, Sachiko needs to understand equivalent fractions. Her teacher uses fraction strips to show her the number of beats in each note.

Rating: This book is a great demonstration of how math is related to other subjects like music. In this era, a lot of kids like music. It would be interesting for them to see how fractions are so closely related to the beats in musical notes.

Classroom Ideas: This book can be used for introducing fractions and fraction equivalence.

1- Give students a fraction strip model like the one in the story. Make sure the strips are blank. After reading the story and modeling how Sachiko and her teacher filled out the sheet, have students complete the sheet. This is a great way to hold students accountable for their learning and to assess and monitor their understanding of fractions as part of a whole.

2- Students can use the sheet they created in the above activity to find equivalent fractions. For example, 1/2 is equal to 1/4. The fraction strips serve as a great visual for the students.

3- Students can also learn how to compare fractions by using the fraction strips. For example, they can see that 2/4 is smaller than 5/8 by shading in or putting an item over 2/4 and over 5/8 and comparing the sizes.