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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Standard 3 : Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (Major Cluster)Archived
Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.3.MD.3.5 : Recognize area as an attribute of plane figures and understand concepts of area measurement.
    1. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
    2. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
  • MAFS.3.MD.3.6 : Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
  • MAFS.3.MD.3.7 : 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.
Cluster Information
Number:
MAFS.3.MD.3
Title:
Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (Major Cluster)
Type:
Cluster
Subject:
Mathematics - Archived
Grade:
3
Domain-Subdomain
Measurement and Data
Cluster Access Points

This cluster includes the following Access Points.

Cluster Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Original Student Tutorials
  • Ariana Explores Area: Ariana explores Area as she plants vegetables in her rectangular garden boxes. Help Ariana cover rectangles with unit squares without gaps or overlaps and count the squares to find the area with this interactive tutorial.

  • Terrific Tiling: Learn how tilling can be used to find the area of different rectangular rooms in this interactive tutorial.

  • Golden Gardening Girls: An Area Adventure: Explore the relationships between tiling an area, multiplication arrays and calculating area using a formula in this interactive tutorial.

  • Building a Square Garden: Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

  • Techies Talk Area: Discover how square units can be used to cover the interior of a rectangle and measure its area of a rectangle in this interactive tutorial.

Formative Assessments
  • Using Arrays to Model the Distributive Property: Students are presented with a rectangular area model and asked to write an equation that represents the distributive property.

  • Cover Me: Students determine the area of a rectangle in two different ways.

  • Decompose Shapes to Find Area: Students are given a rectilinear shape and asked to find its area.

  • Area of a Butterfly Garden: Students are asked to find the areas of two rectangular figures and are observed to determine if they use multiplication.

  • Using Tiles of Different Sizes: Students consider whether tiling a rectangle with different sized tiles is appropriate when calculating area.

  • Unit Square: Students are asked to explain how the area of a rectangle can be calculated and their responses are examined for references to the unit square as the unit of measurement.

  • Overlapping Tiles: Students are asked to evaluate another student's area calculation that involves overlapping tiles.

  • Calculating Area: Students discuss the meaning of area and are asked about the kinds of figures for which area can be calculated.

  • Dawn’s Vegetable Garden: Students are given a diagram showing a garden shaped like an irregular hexagon and are asked to find the area by counting the number of unit squares the figure contains.

  • Area of a Right Trapezoid: Students determine the area of a right trapezoid.

  • How Many Square Units?: Students determine the area of a right triangle.

  • Fenced Dog Run: Students are given a diagram showing a rectangular dog run and asked to find its area.

Lesson Plans
  • Area of Rectangles: A More Efficient Way?: In this lesson, students will connect the concepts of counting each square unit and multiplying the side lengths to compute the area of a rectangle. They will extend this knowledge by computing a side length, when given only the area and the other side length.

  • Make A Mighty Monster: Practice with Area and Perimeter: In this culminating activity, students will use their knowledge of area and perimeter to create a "Mighty Monster" following specific criteria. Given a designated area, students will make their monster on centimeter grid paper and calculate both the area and perimeter of each body part, as well as the combined area and perimeter of the entire figure.

  • "This is InTENTS!": This STEM challenge will engage the students in the ways to create different rectangles that have the same area, but different perimeters. They will also explore how to use scientific processes to test their designs with hypothesis, records, data, and a conclusion. This STEM challenge combines architectural engineering with life science and measurement skills for math.

  • No Cracks Allowed: An EGG-cellent STEM Design Challenge with Surface Area and Gravity: STEM design! EGG-cellent! Students will use hands-on inquiry to find out more about gravity and how surface area can oppose it. Through trial and error based on collected data, students will design, create, and drop a vehicle carrying precious "cargo" from a ten-foot ladder, using a parachute to ensure a safe landing. When completed, students should have a better understanding of how gravity interacts with falling objects and how the surface area of a parachute can oppose those interactions.

  • Blowin' Around the House: In this engineering design challenge, student teams will design a house that will withstand high winds.

  • Area Architects, Lesson 1: In this unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area. Using all five lessons will allow the students to discover, explore and eventually relate area to multiplication and addition. This lesson is the first lesson of the unit. In Lesson 1, students will develop strategies for finding area by counting square units. Students will learn the importance of accurately measuring area by exploring the concepts of area in realistic applications.

  • Area: Add or Multiply?: This lesson is designed to encouage students to make connections to their prior knowledge of multiplying using rectangular arrays to finding the area of rectangles by multiplying the side lengths. Students will be led to "discover" the formula for finding area.

  • From Arrays to Areas: Students will be asked to use different strategies to figure out the area of rectangles.. Students progress from playing a game with arrays, to creating rectangles with square tiles, and finally to exploring the area formula.

  • All About Area: This lesson is an introductory lesson about area at the third-grade level. Students will play a game to learn the definition of area, build with square tiles to discover we measure area with square units, and then put this knowledge in practice to complete two worksheets.

  • Best Vegetable Garden: The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Treehouse Makeover MEA: In this Model Eliciting Activity, MEA, The Shady Oak Treehouse Club is doing a makeover and needs help choosing flooring. Students will be asked to figure area, calculate cost, and add installation fees to cost. The students will then rank the flooring and choose the best one for the makeover. The data provided is: a model of the treehouse (in square yards), flooring price per square yard, and ratings for ease of cleaning, comfort, and color choices. In the twist, student will be provided with an installation fee for each flooring material and must decide if, and how, to change their procedure with the new information.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • Area Architects, Lesson 3: In this unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area and relate area to multiplication and addition. This lesson is the third of a five-lesson unit.

    In this lesson, students will apply strategies learned for finding the area of rectangles with whole-number side lengths after creating floor plans for their dream home on 1-inch grid paper, and represent whole-number products as rectangular areas.

  • Area: We Need to Know: In this lesson students build on their knowledge of area by finding the area of a variety of composite figures and create a composite shape when given an area.

  • Area of Rectangles: A More Efficient Way?: In this lesson, students will connect the concepts of counting each square unit and multiplying the side lengths to compute the area of a rectangle.

  • Count Those Square Units: Students count unit squares to find the area of rectangles and play a matching game for practice.

  • Animal Habitat MEA: Animal Habitat MEA is where the students will help a pet store choose which habitat they should buy to house their snake and lizard families. The students will solve an open-ended problem and give details on the process that they used to solve the problem.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • What Does Your Garden Grow?: In this model eliciting activity students use data about the temperature and water requirements of plants to figure out when the plants should be planted. They also use data such as space requirements and time until harvest to make judgments about which plants would best suit the needs of students planning a school garden in Florida.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

  • Playground Protection: In this Model Eliciting Activity, MEA students will decide which type of protective surface should be put in under a new playground unit. They will consider many factors before ranking their decisions about the best surface.

    Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

  • Make A Mighty Monster: Practice with Area and Perimeter: In this lesson, students will use their knowledge of area and perimeter to create a "Mighty Monster”. Given specific criteria related to area and perimeter, students will make their monster on centimeter grid paper and calculate both the area and perimeter of each body part to explore the differences between the two types of measurement.

  • No Spare Space: In this lesson, the students are employees of a fencing company. They are working with a customer to try and get the best deal and design of a fence that will fit the customer's area needs. Students will have to use reasoning skills in order to fill in missing information. Students will also discuss whether or not their designs have met the needs of the customer.

  • Area Architects, Lesson 2: In this unit on area, students explore geometric measurement by becoming "Area Architects" to learn the concepts of area and relate area to multiplication and addition. This lesson is the second of a five-lesson unit. In this lesson, students will develop strategies for finding the area of rectangles 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.

  • Area Architects, Lesson 5: In this unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area and relate area to multiplication and addition. This lesson is the fifth and final lesson of the unit. In this lesson, students will recognize area as additive. Students will find areas of rectangular figures by decomposing them into non-overlapping parts in order to solve a real-world problem. This lesson is focused on single-digit x single-digit dimensions using proper units for dimensions (e.g. ft, yd, m) and square units for the area (e.g. sq. ft, sq. yd, sq. m).

  • Area Architects, Lesson 4: In this 5-lesson unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area and relate area to multiplication and addition. In this 4th lesson, students will use tiling to show in a concrete case that the area of a rectangle can be found using the distributive property of multiplication. This lesson is focused on single-digit x single-digit dimensions using proper units for dimensions (e.g. ft, yd, m) and square units for the area (e.g. sq. ft, sq. yd, sq. m).

  • Area and Perimeter of Rectangles Investigations: Students will determine the validity of the statement, "All rectangles with the same area will have the same perimeter" through two investigations.

  • Area Designers: This hands-on lesson makes a real-world connection for students in measuring area by counting square units. Students become area designers during an activity that illustrates area, and then make a real-world connection with area when they are shown a residential blueprint. Students gain practice determining the area and recording the area of rectangular rooms in square units.

  • Area Isn't Just for Squares: This lesson helps students make the connections between area and multiplication using square tiles.

  • House Building Architects: In this lesson, students are tasked with drawing a house based on given directions. The directions include the area and perimeter of particular features of the house. This resource is recommended as a review of perimeter and area.

  • Squiggly's New Space: A Deeper Look at Area and Perimeter: Students will use guided discovery to find a formula for both area and perimeter in order to more efficiently solve area and perimeter problems.

Problem-Solving Task
  • The Square Counting Shortcut: This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. However, students should not be discouraged from using individual counting to start if they are stuck. Often students will get tired of counting and devise the shortcut method themselves.

Professional Development
  • What Does It Mean To Measure?: This is a professional development session from the Learning Math series from Annenberg. Learners will begin to explore the questions "What can be measured?" and "What does it mean to measure something?" Learners identify measurable properties of objects such as weight, surface area, and volume, and discuss which metric units are appropriate for measuring these properties. Learners will also learn that measurement is, by its nature, approximate. Finally, learners will consider how to make measurements using nonstandard units. This session features a number of problems for learners to solve and open-ended questions to discuss, videos that demonstrate measurement techniques, and an interactive activity that asks learners to construct shapes using different size triangles to foster understanding of area and perimeter. There are also nine homework problems in which learners are asked to generate different measurements, graph measurements, and evaluate the appropriateness of the measurements generated using a data chart. Many of the professional development activities can be used directly in the classroom.

Tutorial
  • Connecting area to multiplication: In this tutorial video from Khan Academy, students who understand how to count unit squares to find the area of a rectangle can explore the connection between this method and the area formula for rectangles (length times width or base times height).

Worksheet
  • Junior Architects: Finding Perimeter and Area: In this worksheet, students are directed to find the perimeter and area for a clubhouse in the form of rectangles, composite figures, and other polygons. The second sheet urged them to make their own designs for a clubhouse and find the perimeter and area. This resource is recommended as an introduction or review of perimeter and area.

    (Found under "Finding Perimeter and Area" on NCTM's Illuminations)