<p>Students will explore the concept of area. Students will:&nbsp;<br>- select the appropriate units of measure for area for a given shape or region.&nbsp;<br>- understand the difference between the estimated and actual area.&nbsp;<br>- develop various ways for determining the area of irregular shapes.&nbsp;<br>- apply multiplication to the areas of rectangles and squares.&nbsp;</p>

<p>- How precise should measurements and calculations be?&nbsp;<br>- In what ways are the mathematical attributes of objects or processes measured, calculated, and/or interpreted?<br>- What does it mean to analyze and estimate numerical quantities?&nbsp;<br>- What makes a tool and/or strategy suitable for a certain task?&nbsp;<br>- When is it appropriate to estimate versus calculate?&nbsp;<br>- Why does "what" we measure affect "how" we measure?</p>

<p>- Area: The number of square units needed to cover a flat surface.&nbsp;<br>- Estimate: A rough judgment or calculation.&nbsp;<br>- Square Unit: A unit used to measure area.</p>

<p>- standard measuring tools (ruler, yardstick, meter stick)<br>- grid paper (M-4-1-2_Square Centimeter Grid Paper.doc and M-4-1-2_Square Inch Grid Paper)<br>- large sheets of grid paper (optional)<br>- Shape 1 (M-4-1-2_Shape 1)<br>- Shape 1 with Unmarked Square Inches (M-4-1-2_Shape 1 with Unmarked Square Inches)<br>- Shape 1 with Square Inches (M-4-1-2_Shape 1 with Square Inches)<br>- Shape 1 with Square Centimeters handout (M-4-1-2_Shape 1 with Square Centimeters)<br>- construct drawings of a square foot, a square yard, and a square meter on chart paper for students to see their relative sizes<br>- chart paper<br>- construction paper<br>- 3 x 5 inch index cards (optional)<br>- Pattern-block pieces (optional)<br>- rulers with inches and/or centimeters<br>- various rectangles cut out with similar or equal areas<br>- Area Four Square activity (M-4-1-2_Area Four Square and KEY)<br>- Area Chart (M-4-1-2_Small Group Area Chart)</p>

<p>- Observe students' interactions and responses to questions as they are determining which shape has a greater area.&nbsp;<br>- Assess students' use of effective strategies for calculating the estimated area of a shape using square centimeters.&nbsp;<br>- Examine students' engagement while identifying which rectangle is larger, and observe their ability to use multiple strategies.&nbsp;</p>

<p>W: Inform students they will learn about the area of two-dimensional shapes, building on the concept of measurement. Discuss the definition of area with students.&nbsp;<br>H: Show students models of square units, including centimeters, inches, and feet. Discuss why it is impossible to display a square mile in a classroom. Have students choose an appropriate unit to measure classroom objects.&nbsp;<br>E: Compare two different shapes and discuss how to determine which one has the larger area. Have students create shapes and compare them. Display an irregular shape and explain which unit of measurement is best for calculating its area. Discuss how students will find an estimate rather than an exact area. Allow students to discover the best way to find the area.&nbsp;<br>R: Provide students with two rectangles of various sizes and rulers to decide which is larger or if they are the same. Students can use any way they want to do so. Distribute grid paper to help them.&nbsp;<br>E: Have students complete the Area Four Square assignment to evaluate their understanding.&nbsp;<br>T: Allow students to regularly draw a shape on graph paper so that the rest of the class can estimate its area. Make a list of classroom items to measure and identify the areas with standard and nonstandard units. Have students try to find shapes that are of a given area.&nbsp;<br>O: This lesson focuses on the area of two-dimensional shapes to enhance understanding of measurement concepts.&nbsp;</p>

<p><strong>"In this lesson, we will continue to investigate the concept of measuring. We shall specially examine the area of two-dimensional shapes. Area is the number of square units required to cover a flat surface. Small shapes’ areas can be measured in square centimeters, square inches, or smaller square units. Larger shapes’ areas can be measured in square feet, square yards, square meters, or larger square units. Calculating the area of a shape is useful for figuring how much carpeting or tile is needed to cover a floor or how much wallpaper is required to cover a wall. Remember, area is a two-dimensional measurement because it is a measurement of two dimensions: length and width."</strong><br><br>Show students models of square units. You can draw different square units on chart paper or build them with rulers and yardsticks. Include examples of square inches and square centimeters (M-4-1-2_Square Centimeter Grid Paper and M-4-1-2_Square Inch Grid Paper). Measure out a square foot on chart paper for students to see, or tape four rulers together. Repeat the same process to show students what a square yard and a square meter look like. Ask students why a square mile or square kilometer model cannot be shown in the classroom. After students have seen the visual representations for square units, allow them to select an appropriate unit to measure the areas of various shapes in the classroom. Classroom shapes to measure include the size of a bulletin board, the top of a student desk, the top of your desk, a computer screen, and the classroom floor.<br><br>On construction paper, design two shapes that are different in areas. Examples include both regular and irregular shapes. Show the figures to students. <strong>"How do we determine which of these two shapes has the larger area? Remember, area is the number of square units required to cover a two-dimensional surface.”</strong> Post students' suggested methods on the board, and demonstrate how each method can be used to determine which shape has the larger area. Students could suggest filling both shapes with square tiles, counting the number of square tiles, and comparing the results. At this point, it's a good idea to remind students that square tiles are a standard unit of measurement. This method also gives an estimated area. Another method may be to cut one shape into pieces and stack them on top of the other shape. Students can then compare the area of the shapes.<br>Ask each student to draw a two-dimensional shape on a piece of construction paper. Collect them. Pick two shapes at random and ask partners to determine which has the larger area. Encourage students to come up with as many different approaches as possible for validating their responses. Keep track of pupils' progress while they work. Ask questions like the ones listed below.&nbsp;<br><br>What is area? (<i>the measure of the surface of an object</i>)<br>Which square units are best choice to measure the area of these shapes?&nbsp;<br>(<i>square inch, square centimeter, square millimeter, etc.</i>)&nbsp;<br>What approach did you use to determine which shape has the greater area?&nbsp;<br>Is there any other method you could use?&nbsp;<br>If required, have students trade shapes with their partners and repeat the process to reinforce understanding.<br><br><strong>"If you wanted to calculate the area of this shape, would you be able to get an accurate or estimated answer? Prepare to offer your ideas and engage in discussions with the students around you."</strong> (M-4-1-2_Shape 1) After a thought-pair-sharing time, encourage students to present their ideas in class. Teach student that calculating the area of an irregular form will result in an estimated response. Discuss which standard unit of measurement, square inches or square centimeters, would provide the most accurate estimate and why. (Square centimeters provide a more accurate estimate because the pieces are smaller and fit better into the shape's surface.)<br><br><strong>"Remember that the standard unit of measurement is a square, such as square inches. We can't find entire squares, so we'll have to estimate the area, which is the number of whole squares we think will cover the two-dimensional shape. How can we do this and get a reasonable outcome?"</strong><br><br>Create a way for students to calculate the estimated area of a shape using square inches. A transparency can be created; portions of square inches can be chopped to fit the shape. Alternatively, cut out the shape and trace it on square inch paper (M-4-1-2_Shape 1 with Unmarked Square Inches). <strong>"We can count the square inches."</strong> (<i>There are 20.</i>)<strong> "Is it accurate to estimate the area of this form as 20 square inches? Discuss with the students around you and be prepared to share your ideas.”</strong> After students have had time to think-pair-share, have them share their ideas with the class. <strong>"Twenty square inches is not a good starting point for estimating the area of the two-dimensional object, but we can improve our accuracy. This number would show an overestimated area. Take a look at all the square units that are not on the shape's surface. To achieve a more accurate estimate of the area, we have to combine partial pieces until they equal the area of one square inch."</strong> Show students the Shape 1 with Square Inches handout. (M-4-1-2_Shape 1 with Square Inches). <strong>"Look at how I numbered the pieces to indicate which partial parts would make about one square inch. My new estimated answer is about 11 square inches. If necessary, I can cut out the shape and trace it on square inches of paper. Now, you and a partner will apply a similar technique to calculate the estimated area of this shape using the standard unit of measurement, square centimeters. Remember to combine partial pieces until they equal the area of one square centimeter in order to get a more accurate estimated area.”</strong> Distribute the Shape 1 with Square Centimeters handout (M-4-1-2_Shape 1 with Square Centimeters) to each pair of students. Give students time to determine the estimated area. Monitor student performance and provide guidance as needed. While students are working, offer them questions like the ones mentioned below to test their understanding.<br><br>What does the area of a shape represent? (<i>measurement of the inside of the shape</i>)&nbsp;<br>What are some of the standard units of measurement you can use to calculate the area of a two-dimensional shape? (<i>square inches, centimeters, feet, meters, etc.</i>)&nbsp;<br>What did you do first? Why?&nbsp;<br>Do you have to count each square to calculate the area of a two-dimensional shape? Is there another strategy you could try? (<i>You can do multiplication.</i>)&nbsp;<br>What do you think would be a good estimated area? What are you basing your answer on?&nbsp;<br>What if you have leftover parts of square centimeters? How can you use these pieces to calculate a more accurate area? (<i>Use square millimeters.</i>)<br>How are square centimeters similar to square inches? (<i>They both measure areas of surfaces.</i>)&nbsp;<br>Which will provide a more accurate representation of the shape's area? Why?&nbsp;<br>For students who complete quickly and demonstrate understanding, have them design irregular shapes and swap with a partner to determine the area. <strong>“This activity showed us how we can find the area of a shape using standard units of measures. The shapes we used were irregular two-dimensional shapes. Now let’s look at determining the area of two common two-dimensional figures: rectangles and squares.”</strong><br><br>Students are given a pair of rectangles that are either the same or very close in area. These rectangles can be cut from construction paper or drawn on paper. Some suggested pairings are as follows: 4 × 10, 5 × 8, 5 × 10, 7 × 7, 6 × 8, 12 × 4, 4 × 5, and 12 × 2. Students are also given a drawing of a single square unit and a ruler to measure the proper unit. <strong>"Your task is to use your rulers to discover, in any way that you can, which rectangle has a larger area or if they have the same area. You are not allowed to clip out the rectangles. You can draw on them if you want. Use words, pictures, and numbers to explain your findings."</strong><br><br>Not every student will take a multiplicative approach. To count a single row of squares along one edge and then multiply by the length of the other edge, consider the first row as a unit that is repeated to fill up the rectangle. Many students will try to draw in all of the squares. To help transition from the requirement to see all of the square units, one option is to cut out strips (rows of squares) and fill in the rectangle. At this point, providing students with grid paper and units may be helpful. The rectangle below contains an eight-square-unit row, and three strips of eight squares are required to fill it. A visual that will help students focus on what the dimensions of the rectangle is the following “<i>L</i>”.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_1.png" width="193" height="79"><br><br>Notice how the "<i>L</i>" allows students to visualize the square units that are not drawn.&nbsp;<br><br>Encourage students to trade rectangle pairs and repeat the process. After several attempts, students may be able to refine their thinking and adjust strategies to improve their performance.<br><br>To check student understanding, have them complete the Area Four Square activity (M-4-1-2_Area Four Square and KEY). <strong>"In this lesson, we learned about the area of two-dimensional shapes. The area of a shape can be calculated using both standard and nonstandard units of measurement. Sometimes an area is an estimated value because of the units used and the actual shape of the object. Choosing the appropriate unit of measurement is important not only when determining area but when calculating any measurement."</strong><br><br><strong>Extension:</strong><br><br>Use the following strategies and activities to meet the needs of your students during the lesson and throughout the year.<br><br><strong>Routine:</strong> Hang a large piece of graph paper in one area of the room. Throughout the year, ask a student to draw a shape on it. Then, ask students to estimate the area of the shape by counting squares. Then, have a small group select the area and demonstrate their method to the rest of the class.&nbsp;</p><p><br><strong>Small group:</strong> Ask students to assist create a list of two-dimensional, non-curved items in the classroom whose areas can be calculated using a standard unit of measurement. Remind students that area is only applicable to two-dimensional shapes. Explain to students that they will work in pairs to choose two things from the list and measure their area. Students will measure each object using various standard and nonstandard units. Units can consist of square tiles, triangles, and rhombi from pattern-block sets, as well as 3 × 5-inch index cards. Distribute a chart (M-4-1-2_Small Group Area Chart) to each student to record.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_2.png" width="1315" height="224"><br><br>Choose one of the shapes created by the students and demonstrate the procedure to the group. Explain why certain measures on the chart will provide more accurate estimates than others. Allow students time to complete the work. Monitor student interaction and clarify any misunderstandings that arise. Bring the small group back together and discuss the findings. Ask each student to speak finish the stem below: Area is …<br><br><strong>Expansion:</strong> Have students who have demonstrated proficiency look for different shapes with the same area. Students can be given a specified area, such as 12 square units, and challenged to find as many different shapes with that area as possible. Students may use grid paper or square tiles (pattern-block pieces). Once students have mastered discovering as many different shapes as possible, urge them to focus only on finding as many different rectangles as possible in that area. If students are given 12 square units, they can create the following rectangles: 1 × 12, 2 × 6, and 3 × 4. Start with numbers like 24 and 36 square units. Ask students how they know whether they have found all possible rectangles with a particular area.<br>This lesson is intended to further explore the concept of measurement, with a particular focus on the area of two-dimensional shapes. Students will be introduced to the many units of measurement that can be used to calculate the area of shapes. Students will begin to understand the need of selecting an acceptable unit to measure the area of chosen items. Estimated areas will be discussed, and students will see how the shape's features, together with the units used, might result in an approximated area. Students will use various strategies, such as counting square units and multiplication, to calculate the area of irregular shapes, as well as rectangles and squares.</p>