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

Full Standard

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Measurement Topic

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

Learning Targets

• Explain the area formula.
• Explain the perimeter formula.
• Use area formula to solve problems including unknown length or width problems.
• Use perimeter formula to solve problems including unknown lengths or width problems.
• Subdivide shapes into rectangles to solve problems with area and perimeter.

About the Math

The area of a rectangle is the region inside the rectangle. The formula for area is A = l x w. Students can find a missing side if they know the length of one side and the area for the figure. Students need to use the relationship between multiplication and division to solve problems involving finding the missing side. The perimeter of a rectangle is the distance around it. The formula for finding perimeter is P = l + w + l + w or P = 2 l + 2 w. Students can find the missing side using the perimeter and the known side. Students need to remember that there are two sides that have the same length or width. Students can build on standards taught in 3rd grade to subdivide a shape into rectangular pieces to find area and perimeter. Focus for instruction should be understanding the concepts of area and perimeter and not just knowing the formulas. Essential vocabulary for this standard includes: area, perimeter, length, width, unit, and square unit. 

Progression of Standard within Grade 4

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

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.

TASKS

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

• Provide students with 36 colored tiles. Ask students to identify the different rectangles squares that could be created that have an area of 36 square units. After students identify the dimensions of the figures, they should use the formula to calculate the perimeter of each figure. Which figure created the greatest perimeter? Which figure created the smallest perimeter?
• Students will use colored tiles to create the image shown on the slides Links to an external site.. Encourage students to explore and explain which colored tile could be removed so that the area of the figure changes but the perimeter remains the same.
• How could you go about finding the area of your rectangular classroom? What information do you need and what steps would you take to solve?
  
• A rectangular figure has a perimeter of 35cm. What could the lengths of the sides be? Give two possibilities.
• The floorplan of a building has an area 1200 square feet. How many rooms could the building have, and what would the area of each room be?
• A construction worker laid 54 square feet of hardwood in the rectangular family room of a new house. What could possible perimeters of the room be?
• The areas of two shapes are each 40 square inches, but the perimeters are very different. Sketch the two shapes and calculate the perimeters.
• Imagine a rectangle with an area of 28 square centimeters. If the length of the rectangle is 3 centimeters shorter than the width, find the dimensions of the rectangle.
• A rectangle has a length of 3 cm and a width of 2 cm, with an area of 6 sq.cm. Double the length and width. What is the area of this rectangle? How does that affect the area? Try doubling the side lengths again and describe the pattern you see.

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.

Additional Tasks 

  These links provide instructional ideas connected to this standard. 

• Karl's Garden Links to an external site. (Illustrative Math)
• Area and Perimeter Links to an external site.(Georgia Department of Education, pg. 40-46)
• Parking Lot Links to an external site. (Georgia Department of Education, pg. 47-53)
• Yard Crashers Download Yard Crashers
  (Utah Core Academy Lesson)
• Designing Your Own Bedroom Download Designing Your Own Bedroom
  (Utah Core Academy Lesson)
• You Are the Architect Download You Are the Architect
  (Utah Core Academy Lesson)
• How Much Does Boog Weigh? Download How Much Does Boog Weigh?
  (Utah Core Academy Lesson)
• Grandpa's Playground Download Grandpa's Playground
  (Utah Core Academy Lesson)
• Double Trouble Download Double Trouble
  (Utah Core Academy Lesson)

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	3-5	Tangram Areas, Activity 9.4, Page 262 Fill and Compare, Activity 9.5, Page 263 Fixed Perimeters, Activity 9.7, Page 265 Fixed Areas, Activity 9.8, Page 265 Expanded Lesson Fixed Areas, Page 288
	Hands-On Standards	3-4   5-6	128-131 (Perimeter of Shapes) 132-135 (Finding Area) 140 (Area of a Triangle) 134-137 (Perimeter and Area, Area of a Parallelogram)
	Groundworks Reasoning About Measurement	4 5	88-111 88-95
	Groundworks Reasoning About Measurement ​	3 5	72-79 80-87
	Brain-Compatible Activities for Mathematics	4-5	99-102
	Developing Mathematics with Base Ten	2-6	18-21 85, 87
	Problem Driven Math	4 5	103-105 112, 118
	Roads to Reasoning	4 5	52, 82 39, 40, 52, 63, 83
	Super Source Color Tiles Super Source Base Ten Blocks	3-4	22-25, 30-33 18-21
	Math In Practice Teaching Fourth-Grade Math	4	Module 12

Centers

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

• Choosing a Pool and a Garden Download Choosing a Pool and a Garden
  (HCPSS-adapted print resource)
• Puppy Fencing Download Puppy Fencing
  (HCPSS-adapted print resource)
• Soccer Party  Download Soccer Party 
  (HCPSS-adapted print resource)
• Tangram Center Download Tangram Center
  (print resource)
• Tangram Center Download Tangram Center
  (answer key)
• Perimeter Polygons Download Perimeter Polygons
  (print resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

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

• Area and Perimeter a Links to an external site.
• Area and Perimeter b Links to an external site.
• Area and Perimeter c Links to an external site.
• Apply Area and Perimeter Formulas to Create and Measure Rectangles Links to an external site.
• Reason About Dimensions, Area, and Perimeter Links to an external site.
• Apply Area Formula to Solve Problems Links to an external site.
• Apply Area and Perimeter Formulas to Solve Problems Links to an external site.
• Apply Area and Perimeter Formulas to Solve Problems_2 Links to an external site.
• Apply Area and Perimeter Formulas to Solve Problems_3 Links to an external site.

Learning Targets

• Explain the area formula.
• Explain the perimeter formula.
• Use area formula to solve problems including unknown length or width problems.
• Use perimeter formula to solve problems including unknown lengths or width problems.
• Subdivide shapes into rectangles to solve problems with area and perimeter.

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

Rubric for Tasks Links to an external site.

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.