NY Next Generation Math NY-3.MD.7

NY-3.MD.7 is a cluster heading. These are the individual standards under it.

• 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.

• 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.MD.7.d

  Recognize area as additive. Find areas of figures composed of non-overlapping rectangles, and apply this technique to solve real world problems.

01

What Students Need to Do

Students connect rectangle area with multiplication and addition. They tile rectangles, multiply whole-number side lengths, decompose a side, and add nonoverlapping rectangle areas to find composite areas.

02

What Mastery Looks Like

A student shows that a 7-by-6 rectangle has area 42 by multiplying and by adding areas 7 × 4 and 7 × 2. The student finds a composite figure's area by summing nonoverlapping rectangular parts.

03

Common Misconceptions

Students may add side lengths instead of multiplying, omit the square-unit label, or double-count overlapping regions. They may decompose a figure with gaps or use the distributive property without preserving both dimensions.

04

How to Assess It

Give students a 7-by-6 rectangle and ask them to split 6 into 4 and 2, find both partial areas, and explain why the sum equals the whole area.

1. 01

   Tile a rectangle, organize the tiles into rows and columns, and connect the count to a multiplication equation.

2. 02

   Ask students why 7 × (4 + 2) gives the same area as 7 × 4 + 7 × 2.

3. 03

   Play area decomposition by drawing rectangle cards, splitting one side, and matching partial-area equations to each figure.

4. 04

   Find the area of a floor plan made from nonoverlapping rectangles and total the spaces for new flooring.

• NY-5.MD.5

  Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

• NY-1.OA.5

  Relate counting to addition and subtraction.