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# Finding Area

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Students will be able to add and multiply square units in order to find the area of a rectangle.

(10 minutes)
• Pick up six square tiles. Using a projector, display three of them in a connected row, and display the other three in a scattered group. Ask students to identify which group shows an area, or square unit total, of three. (You'll be defining the term "area" more clearly later on in the lesson.)
• After hearing their answers, explain that both groups have a total area of three. Each tile is a square unit, and regardless of how they're positioned, three tiles will always equal three square units.
• On your display, write "3 sq. units" above the row of tiles and "1 sq. unit" above each tile in the scattered group.
(15 minutes)
• Display a 4 square unit rectangle (e.g. four rows of one block, 2 rows of 2 blocks, or 1 row of 4 blocks). Ask students what they think the area of the shape is. Have those who volunteer answers explain their reasoning.
• After hearing their responses, display a different 4 square unit rectangle. Ask students to compare this rectangle to the previous one. Ask them what they think the area of this rectangle is.
• After hearing their responses, display the final 4 square unit model. Remind students that the area of a figure is the sum of its unit squares. Ask students to count the number of unit squares in this model as you point at each of its tiles.
• Make sure that students understand that all three of the models have an area of 4 square units.
• Ask the class for suggestions on more efficient ways to find area.
• Once a student suggests multiplication, begin modeling an example of it on the board. As you're making the model, explain that rows and columns can be used as part of multiplication equations. These equations, in turn, can be used to find the areas of shapes.
• Draw an arrow going across each row of your model, then number each row. For example, if you're using a model with two rows of three blocks, you'd draw two arrows and number them "1" and "2." Above the model, you'd write "2 rows of ___."
• Circle one of the rows to show how many units are in each row. Continuing the previous example, you'd fill in the blank with "3." This results in the statement "2 rows of 3."
• Replace the words "rows of" with a multiplication symbol, and you'll end up with "2 x 3." The answer to this equation, six, is the area of the shape.
• Explain that the area of a shape is equal to its length multiplied by its width. Write "Area = Length x Width" on the board.
(10 minutes)
• Have students partner up. Let them know that for this portion of the lesson they'll be working with a classmate to create various rectangular shapes using square tiles, recreate the shapes on graph paper, and write matching multiplication equations.

• Distribute one-inch square tiles and a sheet of one-inch graph paper to each pair.
• Ask students to use their tiles and construct a rectangle with an area of 6 square units.
• Once students have finished, allow volunteers to share their model with the class by drawing it on the board.
• Have students share until all four possible models have been represented on the board.
• Ask partners to copy and shade in their rectangles on their graph paper.
• Have each pair write a multiplication equation to go with their shape. Then, have them find and record its area. For example, a pair with a model that has one row of six would write "6 x 1 = 6" and "Area = 6 sq. units."
(15 minutes)
• Have students repeat the activity on their own, with rectangles of varying sizes and areas.
• Remind students to save space on their graph paper by drawing their shapes close to one another.
• Enrichment: Give advanced students an extra challenge by having them work out different multiplication equations on another sheet of graph paper. Some problems you can assign are: 9 x 6 = ___, 3 x 7 = ___, 5 x 12 = ___, and 8 x 4 = ___. Ask them to find and record the area of each answer by decomposing a factor. For example, 9 x 6 = (5 x 6) + (4 x 6) = 30 + 24 = 54. Area = 54 sq. units. Students should also draw and label a visual representation for each problem. (A 9 x 6 array would be divided into two sections: one labeled "5 x 6" and another labeled "4 x 6.")

• Support: If there are only a few struggling students, give them one-on-one support. If there are multiple students in need of assistance, pull them aside for small group instruction. Briefly review the lesson with them and, if needed, reduce their workload.
• An interactive whiteboard could be used to present visual aids in a more streamlined manner. Its square shape tool could be used to represent square inch tiles within the lesson. Visual representations can be made in advance and hidden behind the shade tool. The clone tool would allow for the infinite creation of square tiles when putting together visual models.
(10 minutes)
• To assess their understanding, sit near pairs during Independent Working Time and make visual observations.
• Prior to closing the lesson, ask each student to create a model with an area of 16 square units. Allow volunteers to share multiplication equations that match their models.
(5 minutes)
• Ask students to share what methods they thought were most useful for finding area.
• Collect student work, and review it later to identify any students who need additional support.

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