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

Students are presented with a rectangular area model and asked to write an equation that represents the distributive property.

Type: Formative Assessment

Students determine the area of a rectangle in two different ways.

Type: Formative Assessment

Students are given a rectilinear shape and asked to find its area.

Type: Formative Assessment

Students are asked to find the areas of two rectangular figures and are observed to determine if they use multiplication.

Type: Formative Assessment

Students consider whether tiling a rectangle with different sized tiles is appropriate when calculating area.

Type: Formative Assessment

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.

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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.

Type: Formative Assessment

Students determine the area of a right trapezoid.

Type: Formative Assessment

Students determine the area of a right triangle.

Type: Formative Assessment

Students are given a diagram showing a rectangular dog run and asked to find its area.

Type: Formative Assessment

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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 the scientific method 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.

Type: Lesson Plan

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.

Type: Lesson Plan

In this engineering design challenge, student teams will design a house that will withstand high winds.

Type: Lesson Plan

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.

Type: Lesson Plan

This lesson is designed to connect the operation of multiplication to the concept of area. It begins with a review of counting squares in a rectangle to find the area then gradually moves to multiplying the sides. Finally, students will determine dimensions based on the area of the rectangle.

This lesson addresses parts a and b of the standard:

a.) 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

b.) 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)

Type: Lesson Plan

Students will be asked to use different strategies to figure out the area of rectangles and use real-world experiences. Students progress from using tiles and array models, using the distributive property of multiplication, to the use of area models and finally to exploring the area formula.

Type: Lesson Plan

This lesson is an introductory lesson about area at the third grade level. It addresses only part a and b of this standard During this lesson students will are given a choice of different units (one smaller, one larger) in order to determine the area of a given rectangle. Efficiency is a goal of this lesson, as well as students understanding the concept of why we multiply the length times the width in order to determine the area.

Type: Lesson Plan

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.

Type: Lesson Plan

In this garden of veggies, students will find the area to determine which vegetable garden beds should be created and where they should be located. Students will submit a letter to the client explaining their procedure for choosing the garden beds and layout.

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.

Type: Lesson Plan

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 and comfort. In the twist, student will be provided with an installation fee for each flooring material and must decide 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. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Students count unit squares to find the area of rectangles and play a matching game for practice.

Type: Lesson Plan

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

Type: Lesson Plan

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

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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).

Type: Lesson Plan

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).

Type: Lesson Plan

Students will determine the validity of the statement, "All rectangles with the same area will have the same perimeter" through two investigations.

Type: Lesson Plan

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.

Type: Lesson Plan

This lesson helps students make the connections between area and multiplication using square tiles.

Type: Lesson Plan

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.

Type: Lesson Plan

Students will use guided discovery to find a formula for both area and perimeter in order to more efficiently solve area and perimeter problems.

Type: Lesson Plan

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.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Explore the relationships between tiling an area, multiplication arrays and calculating area using a formula in this interactive tutorial.

Type: Original Student Tutorial

Learn to identify one square unit that can be used to measure area in this brief interactive tutorial.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

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.

Type: Problem-Solving Task

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.

Type: Professional Development

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).

Type: Tutorial

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)

Type: Worksheet