NY Next Generation Math NY-5.NF.4.b
The Standard
Find the area of a rectangle with fractional side lengths by tiling it with rectangles 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.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the area of rectangles with fractional side lengths by tiling with suitable unit-fraction rectangles. They connect the tile count to multiplying the two side lengths.
What Mastery Looks Like
- The student tiles a 3/4-by-2/3 rectangle with 1/4-by-1/3 pieces and counts 6/12 square unit. The student shows that 3/4 times 2/3 gives the same area, 1/2 square unit.
Common Misconceptions
- Students may multiply only the numerators or label area with linear units. They may use tiles whose side lengths do not match the fractional partitions of the rectangle.
How to Assess It
- Ask students to tile and find the area of a rectangle with side lengths 2/3 unit and 3/5 unit, then write the matching product.
Lesson moves
Ways to Teach It
Partition a paper rectangle in two directions to create unit-fraction tiles, then count and multiply to find its area.
Ask students how the denominator of each side length determines the small tile dimensions.
Play model-product match with fractional rectangles, tile counts, multiplication expressions, and areas.
Find the area of a rectangular fabric patch with fractional side lengths using a grid model.
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Printable NY-5.NF.4.b Worksheet
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Related Standards
- NY-3.MD.7.b
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...
- NY-3.MD.7.c
Use tiling to show in a concrete case that the area of a rectangle with whole-number side length a and side length b + c is the sum of a × b and a × c. Use area...
- NY-3.G.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
- NY-3.MD.7.a
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.
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