Lesson objective: Apply multiplication and division to generating equivalent fractions.

This lesson provides an opportunity for students to apply their knowledge and understanding of generating equivalent fractions to a mathematical situation. Students are asked to create an equivalent alien juice recipe with given instructions.

Lesson 9 provides students an opportunity to connect the multiplicative relationship between numerators and denominators of equivalent fractions with combining and partitioning equal parts of a whole on their own before explicitly using and practicing an equivalent fraction algorithm, \(\frac{(n\times a)}{(n\times b)}\) in Lesson 10. While using the equivalent fraction algorithm to generate solutions for the task presented in Lesson 9 is modeled in the task solution, students could initially approach the task solely using visual models without a procedure for finding equivalent fractions.

While the conceptual components of this task in this lesson fit squarely in the 4th grade expectations (generate and recognize equivalent fractions), the fractions that are given in the task involve denominators beyond those expected at a mastery level in 4th grade (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.). Used here for instructional purposes, it provides exposure to other denominators (9 and 18) that are likely unfamiliar and may be challenging. This makes the task inappropriate for high-stakes assessment. Teachers who anticipate that their students may struggle with the number selection in this task may want to adapt it for their students.

You may also wish to reverse the order of Lessons 9 and 10 if you wish to make the connection between combining and partitioning equal parts of a whole with the multiplicative relationship between numerators and denominators explicit before the task presented in Lesson 9.

Key Concept students will use:

- a/b = (nxa)/(nxb) because we have n times as many pieces in the whole. Each piece is n times smaller, so we need n times as many of them to cover the same distance or the same area.

Skills students will use:

- generating equivalent fractions (Grade 3, Unit 10)
- combining and partitioning models to generate equivalent fractions
- multiplication and division facts to find missing factor or divisor (Grade 3, Unit 7)

Students engage in Mathematical Practice 5 (use apprpriate tools strategically) as they decide how models, number lines, and fraction sense will help them find equivalence with multiplication or division.

**Key vocabulary: **

- denominator
- divide
- equivalent
- multiply
- numerator