3.MD.C.7.B

*This standard is part of a major cluster

Standard

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 whole-number products as rectangular areas in mathematical reasoning.

Standard Unpacked

Area is the two-dimensional space inside a region. Area is measured by covering and so students should use tiles or square units to cover objects to find the area. Formulas should not be introduced at this grade level.

This standard builds on 3.MD.7.A where students began to explore tiling to find area. Through that exploration, students may have begun by counting each individual square progressing toward counting each row (skip counting), and finally discovering the connection to multiplication. This standard focuses on understanding that you can multiply to find the area of an array or rectangle. This is NOT to be confused with the formula (l × w), and then to apply that understanding to solving real world problems.

An important concept and opportunity for standard integration while developing this standard is to also help students understand the meaning of multiplication while they work with the basic multiplication facts.

Bypassing developing conceptual understanding of area to a formula could cause misconceptions for understanding the difference with area and perimeter. When student’s develop formulas, they gain conceptual understanding of the ideas and relationships involved, and they engage in “doing mathematics.” Also, there is less likelihood that students will confuse area and perimeter or that they will select the incorrect formula (Van de Walle, 2012).

Students should solve real world and mathematical problems which provide a context to make meaningful connections.

Example:
Drew wants to tile the bathroom floor using 1 foot tiles. How many square foot tiles will he need?

Students might solve problems such as finding all the rectangular regions with whole-number side lengths that have an area of 12 area-units, doing this for larger rectangles (e.g., enclosing 24, 48, 72 area-units), making sketches rather than drawing each square. Students learn to justify their belief they have found all possible solutions. (Progressions for the CCSSM, Geometric Measurement, CCSS Writing Team, June 2012, page 18)

Questions/ Activities to check for understanding and increase rigor:

•  Your grandfather is building a miniature car out of wood. He cuts two larger rectangles for the sides and two smaller rectangles for the front and back. The total area for the car surface is 54 square units. What could the areas for the sides and front/back pieces be?

•  An object has an area of 12 square centimeters. What could the length and width be?

•  Design a shape that has a total area of 60 sq. units and is made up of both squares and rectangles (at least one of each).

•  Explain the relationship between the two strategies for finding area: counting square units and multiplying the side lengths together? Use an example to support your answer.

•  If a rectangle has an area of 36 square inches, what could the length and width be? What would the length and width be if the shape were a square?

•  Kelly’s kitchen has a length of 10 ft. and width of 20 ft. Her living room has a length of 32 ft. and width of 40 ft. What is the total square feet of her kitchen and living room area?

•  Tommy’s bedroom is a rectangle with side lengths of 10 feet and 17 feet. He wanted to calculate the area by multiplying the side lengths, but he thinks it would be easier to break the 17 into 10 and 7 before multiplying. Can Tommy do this? Explain why it would or would not work.

Level 1
Entering / Level 2
Emerging / Level 3
Developing / Level 4 Expanding / Level 5
Bridging
Domain: Reading / Identify side lengths to find areas of rectangles
in the context of solving real world and mathematical problems by reading story problem to student and asking student to point to side lengths. / Identify side lengths to find areas of rectangles
in the context of solving real world and mathematical problems by reading the problem aloud and asking student to name side lengths. / Identify side lengths to find areas of rectangles
in the context of solving real world and mathematical problems by choral reading the problem with a partner and highlighting the side lengths. / Identify side lengths to find areas of rectangles
in the context of solving real world and mathematical problems by reading and discussing the problem in a cooperative group and drawing a picture labeling the side lengths. / Identify side lengths to find areas of rectangles
in the context of solving real world and mathematical problems by reading the problem independently and justifying their thinking in words, numbers and/or pictures. / Level 6 Reaching

ELD Standard #3: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Mathematics.