1. Understanding additive and multiplicative comparisons (C)
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Lesson objective: Extend understanding that while additive comparisons show "n more than," multiplicative , or relative, comparisons show "n times as many" or "n times as large."
Students bring prior knowledge of additive and multiplicative comparisons of whole numbers from 4.OA.A.2. This prior knowledge is extended to additive and multiplicative comparisons involving fractions as students apply comparative reasoning to calculate and analyze points scored in canoe races. A conceptual challenge students may encounter is thinking of multiplication as repetitive addition and not thinking of it as scaling.
The concept is developed through work with tape diagrams and number lines, which help students develop an understanding of multiplication as scaling.
This work helps students deepen their understanding of operations because they will use multiplication of a mixed number to scale a product and compare it to adding the same mixed number.
Students engage in Mathematical Practice 4 Model with mathematics as they use tape diagrams, functions tables and number lines as they incorporate fractions into their understanding of the meaning of scaling products. Students should notice how rapidly each number increases when multiplied by a number greater than one compared to adding the same number.
Key vocabulary:
 additive comparison
 multiplicative comparison
 resizing
 scaling