3.MD.7 - About the Math, Learning Targets, and Rigor

Grade 3 Measurement

3.MD.C.7

Full Standard

Relate area to the operations of multiplication and addition.

    1. 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.
    2. 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.
    3. 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.
    4. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

3rd Grade Students Learning 3rd Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of measurement, data and geometry.

 

 

Learning Targets

  • Tile to find the area of a rectangle.
  • Explain the relationship between tiling and multiplying side lengths to find the area of rectangles.
  • Solve area word problems by multiplying.
  • Use area models to explain the commutative property.
  • Use area models to explain the distributive property.
  • Decompose an irregular figure into non-overlapping rectangles.
  • Explain area as additive (when decomposing irregular figures)
  • Solve area word problems with regular and irregular figures.

 

About the Math

Area is the two-dimensional space inside a region. Area measures the amount of space covered. So students should use tiles or square units to cover objects to find the area. Formulas should not be introduced at this grade level. Essential vocabulary for this standard includes: area, area model, distributive property, and additive. Visit the online dictionary Links to an external site. for vocabulary support.

NOTE: Work with this standard is an excellent opportunity for reinforcing the distributive property. Work with decomposing area should first begin with simple rectangles before shifting to more complicated figures such as those pictured to the right from the Illustrative Mathematics Project.

 

Other Common Misconceptions

Students often confuse area and perimeter. A thorough understanding of these two concepts is needed so students see how area and perimeter are related. Students may not realize that two figures can have the same area but different perimeters. Use pentominoes to explore how the same area of 5 square units can have different perimeters.

 

 

Progression of Standard within Grade 3

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Within Grade
Quarter 1 Quarter 2 Quarter 3 Quarter 4
   
  • Tile to find the area of a rectangle.
  • Explain the relationship between tiling and multiplying side lengths to find the area of rectangles.
  • Solve area word problems by multiplying.
  • Use area models to explain the distributive property.
  • Decompose an irregular figure into non-overlapping rectangles.
  • Explain area as additive (when decomposing irregular figures)
  • Solve area word problems with regular and irregular figures.

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grade Levels
Grade 2 Grade 4
  • Partition rectangles into rows and columns ( 2.G.A.2 )
  • Apply the area formula for rectangles in real world and mathematical problems (4.MD.3)

 

 

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