Lesson objective: Understand that scaling with a positive, non-whole number has the same meaning as scaling with whole numbers.

Students bring prior knowledge of multiplying whole numbers and fractions from 4.NF.B.4. This prior knowledge is extended to multiplying fractions less than one to scale as students scale recipes, both up and down, with whole numbers and mixed numbers. A conceptual challenge students may encounter is understanding multiplication of mixed numbers and thinking that multiplication will always result in a product greater than both factors.

The concept is developed through work with equations using both fractions and whole numbers to scale numbers up and down, which develops understanding that scaling with numbers less than one has the same meaning as scaling with whole numbers.

This work helps students deepen their understanding of the relationship of numbers because scaling with numbers less than one has the same meaning as scaling with whole numbers.

Students engage in Mathematical Practice 4 (model with mathematics) as they develop and solve equations to scale with whole numbers, mixed numbers and fractions less than one, to solve real-world problems.

**Key vocabulary:**

- scaling