CCSS.Math.Content.5.NF.B.4b
The standard
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.
Common Core State Standards for Mathematics
What this standard means
Students need to connect fraction multiplication to area. They should tile rectangles with unit fraction squares, count the tiles, and then show the same area by multiplying the side lengths. They need to see why 2/3 by 3/4 gives sixths, twelfths, or another unit area based on the grid.
Mastery looks like drawing or using a grid rectangle, labeling side lengths, counting fractional square units, and writing the matching multiplication equation. Students often get stuck choosing the right grid, mixing up side length units with area units, or multiplying numerators and denominators without understanding what the product represents.
Ways to teach it
- Hands-on: Give students grid paper and have them shade a 2/3 by 3/4 rectangle, then count the twelfths inside.
- Prompt: Explain why the area of a 1/2 by 3/5 rectangle is 3/10 square units using a drawing.
- Quick assessment: Ask students to draw a 3/4 by 2/3 rectangle and write the area equation with units.
- Real-world connection: Plan a small garden bed that is 5/6 meter by 3/4 meter, then find its area.
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Related standards
- CCSS.Math.Content.3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
- CCSS.Math.Content.3.MD.C.7c
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to ...
- CCSS.Math.Content.3.MD.C.7a
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
- CCSS.Math.Content.3.MD.C.7b
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent w...