Submitting Organization: Illustrative Mathematics
Grade Levels: 3rd – 5th Grade
Subject Area: Math
Standards Alignment: Common Core State Standards – Mathematics
5.NF.B.4 This connects to the grade 5 content standard 5.NF.B.4, about extending multiplication of whole numbers to multiplying whole numbers and fractions, and to the mathematical practice standard MP.3: Construct viable arguments and critique the reasoning of others.
Description of the Activity: The purpose of this activity is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.
In principle, students have already had a chance to see why multiplication of whole numbers is commutative by looking at arrays or rectangles in third grade. After seeing the kinds of pictures used in this task and its solution, students should also look at rectangles with fractional side lengths to help reinforce their understanding.
- Do you think it always works that you can multiply a fraction and a whole number in either order and get the same answer? Try some other examples to see.
- Draw a rectangle diagram to explain why 3 × 2 = 2 × 3. Can you use a similar diagram to explain why 3 × (2/3) = (2/3) × 3?
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