CCSS.Math.Content.3.MD.C.7c
The standard
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 represent the distributive property in mathematical reasoning.
Common Core State Standards for Mathematics
What this standard means
Students need to see a rectangle as two smaller rectangles put together. They use tiles, grid paper, or drawn area models to show that a side length can be split, like 7 as 4 + 3, and the total area still matches the two partial products added together.
Mastery looks like drawing or building a rectangle, splitting one side, labeling both parts, and writing an equation such as 5 × 7 = 5 × 4 + 5 × 3. Students often mix up side lengths and area, count border squares, or forget that both smaller rectangles share the same other side length.
Ways to teach it
- Have students build a 4 by 9 rectangle with square tiles, split the 9 side into 5 and 4, then record both areas.
- Ask students to explain in writing why 6 × 8 can be shown as 6 × 3 plus 6 × 5.
- Show a gridded 3 by 7 rectangle split into 3 by 2 and 3 by 5, and ask students to write the matching equation.
- Connect to a garden bed by drawing a 5 by 12 rectangle split into flowers and vegetables, then finding each area and the total.
Plan a lesson for CCSS.Math.Content.3.MD.C.7c
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Related standards
- CCSS.Math.Content.5.NF.B.4b
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 i...
- 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
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
- 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...