CCSS.Math.Content.4.NF.B.3b
The standard
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
Common Core State Standards for Mathematics
What this standard means
Students need to break one fraction or mixed number into smaller fractions that have the same denominator. They should write matching equations and show why the parts make the same whole amount, using fraction strips, number lines, area models, or drawings.
Mastery looks like several correct decompositions for the same fraction, not just unit fractions repeated. Students can explain that the denominator stays the same because the size of each piece stays the same. Common trouble spots are changing denominators, forgetting that a whole can be written as n/n, and treating mixed numbers as two separate answers instead of one amount.
Ways to teach it
- Hands-on: Give pairs fraction strips and ask them to build 5/6 in three different ways, then record each as an equation.
- Prompt: Write two different equations for 7/8, then explain how your drawing proves both equations match the same amount.
- Quick assessment: Show 1 3/4 and ask students to write it as a sum of fourths in two different ways.
- Real-world connection: Use a pizza cut into eighths and ask how four people could share 6/8 using different combinations of slices.
Plan a lesson for CCSS.Math.Content.4.NF.B.3b
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