Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 by Judith A. Muschla, Gary Robert Muschla, Erin Muschla-Berry Read Free Book Online Page A
the classroom, measure various rectangles and squares on the classroom floor and mark the corners of the figures with masking tape, for example a 2-meter-by-1-meter rectangle, a 2-yard square, and a 4-foot square. Also designate the surfaces of various objects such as desks, tables, bulletin boards, books, windowsills, and the door to the classroom for measurement. Be sure to find the areas of these figures prior to the activity.
Procedure
1. Explain to your students that they will be using meter sticks, yard sticks, and rulers to find the areas of various figures. Remind them that areas are measured in square units.
2. Show your students the figures that they will be measuring. Tell them that they will need to use the appropriate tool—a meter stick, yard stick, or ruler (in inches or centimeters)—to find as closely as possible the number of unit squares that will cover each particular figure, without any gaps or overlaps.
3. Instruct groups to designate a recorder who will write down the number of square units needed to cover each figure.
4. To avoid congestion and idle “waiting around,” have groups work at different parts of the classroom, measuring different figures.
5. Remind students that they should try to be as accurate as possible in measuring and then counting the number of unit squares they find in each figure.
Closure
Discuss your students' results. Which group's results were closest to the actual area of each figure? What, if any, problems did students have in measuring the figures? How did they resolve the problems? Emphasize that the area of a plane figure can always be found by counting the unit squares that cover the area completely.
5-Inch Square
10-Centimeter Square
Measurement and Data: 3.MD.7
“Geometric measurement: understand concepts of area and relate area to multiplication and to addition.”
7. “Relate area to the operations of multiplication and addition.
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.
c. “Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths and is the sum of and Use area models to represent the distributive property in mathematical reasoning.
d. “Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real-world problems.”
Background
The area of a rectangle can be found by counting the number of tiles that cover it with no part of the tiles overlapping. Think of a rectangle as being a grid, consisting of rows and columns.
In the example below, because the rectangle has 3 rows with 4 squares in each row, the area is or 12 square units.
The way to express the area of a rectangle can vary. The rectangle above may be decomposed into two rectangles as pictured below. The 4 columns can be redrawn as resulting in a 1-by-3 rectangle and a 3-by-3 rectangle. ( Note: To avoid confusion with terminology, a square is a special type of rectangle.)
The area of the previous rectangle can be found by using the distributive property: The sum of nonoverlapping parts can be used to find the total area, showing that area is additive.
Activity 1: Tiling and Finding Area
Students will tile a 3-inch-by-5-inch index card, and then find the area by multiplying the lengths of its sides. They will solve a real-world problem by multiplying the sides of a rectangle to find area.
Materials
One 3-inch-by-5-inch index card; about 20 1-inch square color tiles for each student.
Procedure
1. Explain that students will find the area of an index card by tiling
Procedure
1. Explain to your students that they will be using meter sticks, yard sticks, and rulers to find the areas of various figures. Remind them that areas are measured in square units.
2. Show your students the figures that they will be measuring. Tell them that they will need to use the appropriate tool—a meter stick, yard stick, or ruler (in inches or centimeters)—to find as closely as possible the number of unit squares that will cover each particular figure, without any gaps or overlaps.
3. Instruct groups to designate a recorder who will write down the number of square units needed to cover each figure.
4. To avoid congestion and idle “waiting around,” have groups work at different parts of the classroom, measuring different figures.
5. Remind students that they should try to be as accurate as possible in measuring and then counting the number of unit squares they find in each figure.
Closure
Discuss your students' results. Which group's results were closest to the actual area of each figure? What, if any, problems did students have in measuring the figures? How did they resolve the problems? Emphasize that the area of a plane figure can always be found by counting the unit squares that cover the area completely.
5-Inch Square
10-Centimeter Square
Measurement and Data: 3.MD.7
“Geometric measurement: understand concepts of area and relate area to multiplication and to addition.”
7. “Relate area to the operations of multiplication and addition.
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.
c. “Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths and is the sum of and Use area models to represent the distributive property in mathematical reasoning.
d. “Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real-world problems.”
Background
The area of a rectangle can be found by counting the number of tiles that cover it with no part of the tiles overlapping. Think of a rectangle as being a grid, consisting of rows and columns.
In the example below, because the rectangle has 3 rows with 4 squares in each row, the area is or 12 square units.
The way to express the area of a rectangle can vary. The rectangle above may be decomposed into two rectangles as pictured below. The 4 columns can be redrawn as resulting in a 1-by-3 rectangle and a 3-by-3 rectangle. ( Note: To avoid confusion with terminology, a square is a special type of rectangle.)
The area of the previous rectangle can be found by using the distributive property: The sum of nonoverlapping parts can be used to find the total area, showing that area is additive.
Activity 1: Tiling and Finding Area
Students will tile a 3-inch-by-5-inch index card, and then find the area by multiplying the lengths of its sides. They will solve a real-world problem by multiplying the sides of a rectangle to find area.
Materials
One 3-inch-by-5-inch index card; about 20 1-inch square color tiles for each student.
Procedure
1. Explain that students will find the area of an index card by tiling
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