Building on their knowledge of multiplication properties and multiplication of fractions, students will explore the concept of multiplication as scaling. Students draw upon their understanding of multiplicative comparison of whole numbers to explore the effects of multiplying fractions and whole numbers. Using visual models and equations, students will solve realworld problems involving multiplication of fractions and mixed numbers.
A misconception about multiplication that may cause students to struggle is assuming that a product will alway be larger than the two factors. This is where the idea of "multiplication as repeated addition" breaks down, as students encounter multiplication situations of scaling up and down.
Key Concepts:
 Scaling does not always make numbers larger.
 Multiplying both fraction components by the same number preserves the relationship between them. This is the same result as multiplying by 1.
 Scaling with positive, nonwhole numbers has the same meaning as scaling with whole numbers.
Prior Knowledge Needed:
 Distinguish between multiplicative comparison and additive comparison of whole numbers; (Grade 4, Unit 7, 4.OA.A.2)
 Multiplicative comparison of whole numbers; (Grade 4, Unit 6 : 4.OA.A.1)
 Multiply whole numbers by a fraction; (Grade 5, Unit 5: 5.NF.B.4a)
Units on the Horizon:
 Solving problems with fractional quantities (Grade 5, Unit 12)
 Ratios (Grade 6, Unit 1)
Lessons

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 ...

Lesson objective: Understand that scaling does not always make numbers larger and that if we multiply a number by a fraction less than one the number will scale down. Students bring prior knowledge of scaling by whole numbers and multiplying fractions b...

Lesson objective: Use the magnitude of the scaling factor to estimate products . This lesson helps to build fluency with multiplication of whole numbers and fractions less than one. Tape diagrams and number lines are used here because they support stude...

Lesson objective: Apply understanding of multiplication of fractions less than one to solve realworld problems. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplying fractions and whole numbers a to ...

Lesson objective: Understand that multiplying both fraction components by the same number preserves the relationship between them and this is the same result as multiplying by one. Students bring prior knowledge of multiplying fractions and whole number...

Lesson objective: Multiply by a fraction equal to one to prove that two fractions are equivalent. This lesson helps to build the procedural skill of generating equivalent fractions by multiplying by a fraction equivalent to one. Equations are used here ...

Lesson objective: Apply knowledge and understanding of fraction and mixed number multiplication to solve reallife problems. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplication of fractions and m...

Lesson objective: Understand that scaling with a positive, nonwhole 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 ...

Lesson objective: Multiply fractions and mixed numbers to scale numbers up and down. This lesson helps to build fluency with multiplication of fractions and mixed numbers. Equivalent fractions are used here because it supports multiplication of mixed nu...

Lesson objective: Solve realworld problems with mixed numbers using an area model. This lesson provides an opportunity for students to apply their knowledge and understanding of multiplying fractions and whole numbers to a reallife situation. Students...