For full lesson outline, see Advantage Math.

Standards:

*4.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Objectives:

Math Objective: Students will be able to connect knowledge of repeated addition of unit fractions to multiplying a fraction by a whole number multiplier.
Language Objective: Students will be able to describe the pattern of counting by unit fraction multiples.

Vertical Alignment:

3.NF.1- Fractions as one part of the whole written with numerator and denominator
*4.NF.4- Apply and extend previous understandings of multiplication to multiply a fraction by a whole number
5.NF.4,6- Multiply a fraction or whole number by a fraction including real-world problems
5.NF.5- Interpret multiplication as scaling

Common Misconceptions:

Students may write a fraction multiplication equation and forget to write the multiplication sign. For example, a student may write $LaTeX: 10\frac{1}{6}$ when they should have written 10 × $LaTeX: \frac{1}{6}$ . Remind students that $LaTeX: 10\frac{1}{6}$ really means 10+ $LaTeX: \frac{1}{6}$ .

Lesson Outline:

🚀Launch :

Students: Asked to break apart 7/8 by decomposing it.
Teachers: Students may not understand what the word decompose is, but hopefully they can understand how to break down a number into smaller pieces.
To make remote, record yourself explaining this part of the lesson or do a Zoom/Teams call and teach this part.
Students will reflect on why it is important to understand what makes a larger number.

🤔Explore :

Students need to think about something that makes a number that is larger than 1. How do those larger numbers get to be so large? What makes a number larger?
Some questions you can ask:
- How do those larger numbers get to be so large?
- What makes a number larger?
This is also a good time to restate and show how multiplication and repeated addition are related.

💬Discuss :

Students should discuss and show different ways they can show multiplication, specifically, a whole number multiplied by a fraction, with a model.

✅Exit Ticket:

Students will solve the problem and upload their model that proves their thinking.

Differentiation:

Challenge: Invite students to think of real-world scenarios where a fraction may be repeatedly added, or multiplied by a whole number. Write a word problem using this context to match the multiplication equation 4 × 13.
Struggling: Make connections to the multiplication of a whole number by a whole number. Explain what it means to multiply a fraction by a whole number (e.g., 3 × 1/2.). What is happening when multiplying a fraction by a whole number? Instruct students to model the multiplication expression for 1/2 times 3. What does it look like? What does it mean? Write the repeated addition equation for the problem. Make connections from the model to the repeated addition to the multiplication equation.