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.

You may 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