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

Grade 3 Measurement

3.MD.C.7

About the Math

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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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

  • Use centimeter or inch grid paper (found here in your resource bank) and have students "tile" a rectangle. Students should trace the outline of the rectangle and label the side lengths and find the area. Teacher should record on chart paper the different rectangle dimensions and area. Then ask "What pattern do you notice?" The discussion should be centered around when multiplying the two side lengths produces the area.
  • The teacher should outline 3-4 different rectilinear shapes on the centimeter grid paper (see link above) and then distribute a copy to each student. Students should work in partners to find the area. Teacher should observe different strategies. During the debrief, select and sequence student work from the physical models of "tiling" or "counting" to the subdivision into rectangles and use of the L x W and additive reasoning. Students can then create their own rectilinear shapes on the centimeter paper and challenge a partner to find the area.
  • Write 9x4=(5x4)+(4x4) and ask students to turn and talk about "What do you see happening here?" The discussion can be about reviewing the distributive property and how it can help.  The teacher should outline 3-4 different rectangles on the centimeter grid paper (see link above) and then distribute a copy to each student.  Challenge students to "make one cut" in each rectangle to show how the distributive property could help to find the total area.
  • 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.
  • Kim's bedroom has a length of 12 ft. and a width of 8 ft. Kevin's bedroom has a length of 9 ft. and a width of 11 ft. Kevin thinks that the area of their bedrooms is the same but Kim says her bedroom has a larger area.  Who is correct?  Use what you know about area to defend your thinking.

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides.  These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 12 • Perimeter and Understanding Area and Basic Facts (3s)

Find Area by Tiling and Connect to Multiplying Side Lengths:

Solve Area Word Problems by Multiplying:

Module 13 • Area & Perimeter and Basic Facts (6s)

Area and the Distributive Property:

Relate Area to Multiplication and Addition by Decomposing Shapes:

 

 

Additional Tasks and Lesson Seeds

These links provide instructional ideas connected to this standard. Mizuno baseball glove

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages

 

Teaching Student-Centered Mathematics    

 

K-3

234 (Two-Piece Shapes, Activity 8.8)
235 (Rectangle Comparison- No Units, Activity 8.9)
236 (Fill and Compare, Activity 8.11)
237 (Rectangle Compare- Square Units, Activity 8.12)

 

Teaching Student-Centered Mathematics  

 3-5

265 (Fixed Areas, Activity 9.8)

288-289 (Expanded Lesson: Fixed Areas)
  Hands-On Standards 3-4 132-135 (Finding Area)
  Groundworks Reasoning About Measurement

3

 72-79
  Brain-Compatible Activities for Mathematics 2-3 99-102
  Developing Mathematics with Base Ten   85-87

Math In Practice

Teaching Third-Grade Math

 3 Module 14

 

More Ideas

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

 

Independent Practice/Homework

These resource sheets can be used for independent practice or homework. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

 

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Assessment

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 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.

 

Learning targets identify what students should be able to do. The rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

 

 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.  

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.