The Common Core State Standards emphasize the need to make sense of multiplying and dividing fractions: “Students [also] use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense.” (CCSS, page 33)

As the folks at Conceptua Math know, this is most effectively accomplished using story problems. The learning trajectory may begin with finding the fractional part of a whole number.

Miller has 12 toy trucks. One third of the trucks are fire trucks. How many fire trucks does Miller have? Students first find thirds by dividing 12 by 3. The denominator is the divisor. Students learn that dividing by 3 is the same as multiplying by 1/3.

Madeline has 6 remnant pieces of canvas. Each remnant is ¾ meter long. How many meters of canvas does Madeline have? Some students may solve by combining the fourths and then separating into wholes, while others will make wholes as they go. Both strategies show understanding of combining parts of a whole and arranging them into whole units with leftover, or remaining, fractional parts.

Conceptua Math supports the CCSS, both in Content and Mathematical Practices. They use a problem-based approach that is accompanied by visual tools and verbal representations called paraphrases. The deep conceptual understanding of fraction multiplication challenges many students as well as their teachers. Conceptua Math responds to the challenge and provides an excellent resource for truly making sense of fraction and mixed number multiplication.