Generalize Fraction Multiplication
10 min
Narrative
This Notice and Wonder asks students to consider 2 diagrams representing a shaded region with the same side lengths. The first diagram shows the unit square and the grid lines and the second diagram just shows the side lengths of the shaded region. This prepares students to transition from the gridded diagrams they have worked with in previous lessons to the diagrams they will work with in this lesson. In the Activity Synthesis, students discuss different equations that represent different ways of finding the area.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- In one diagram, you can see the equal pieces.
- The shaded regions have equivalent side lengths, so the areas should be equal.
- You can represent both areas with the expression 21×54.
Students may wonder:
- Do they have the same area?
- How do you calculate the area of the rectangle with no grid lines?
Activity Synthesis (Teacher Notes)
- “How do we know that the shaded regions have the same area?” (54×42=208 and 21×54=104. 208=104 or 21=42, so they must be the same.)
- “How does the first diagram represent this equation: 208=104?” (Each of the 202=101.)
Standards
- 5.NF.4.b·Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
- 5.NF.B.4.b·Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
20 min
15 min
Knowledge Components
All skills for this lesson
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Generalize Fraction Multiplication
10 min
Narrative
This Notice and Wonder asks students to consider 2 diagrams representing a shaded region with the same side lengths. The first diagram shows the unit square and the grid lines and the second diagram just shows the side lengths of the shaded region. This prepares students to transition from the gridded diagrams they have worked with in previous lessons to the diagrams they will work with in this lesson. In the Activity Synthesis, students discuss different equations that represent different ways of finding the area.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- In one diagram, you can see the equal pieces.
- The shaded regions have equivalent side lengths, so the areas should be equal.
- You can represent both areas with the expression 21×54.
Students may wonder:
- Do they have the same area?
- How do you calculate the area of the rectangle with no grid lines?
Activity Synthesis (Teacher Notes)
- “How do we know that the shaded regions have the same area?” (54×42=208 and 21×54=104. 208=104 or 21=42, so they must be the same.)
- “How does the first diagram represent this equation: 208=104?” (Each of the 202=101.)
Standards
- 5.NF.4.b·Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
- 5.NF.B.4.b·Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.