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 B

(covering it with 1-inch squares).
2. Explain that students should cover the index card with the 1-inch squares completely, without leaving any gaps or having overlapping squares. After they have completed their tiling, ask: How many 1-inch squares were needed to cover the index card? (Students should have found 15.) Note that this is the area of the index card.
3. Tell your students to find the area of the index card by multiplying its length times its width.
4. Ask your students to compare the areas by tiling and multiplying. (Both are 15 square inches.)
5. Now pose this problem: Mrs. Williams is planning to change her kitchen floor. She needs to buy 1-foot square tiles to cover the floor, which is 9 feet by 10 feet. What is the area of the floor? (90 square feet) How many tiles does she need? (90)
Closure
Ask your students questions such as the following: Does multiplying the length times the width of a rectangle always result in the area of a rectangle? (Students should realize this is true, because the width represents the number of rows, and the length represents the number of squares in each row. The product shows the number of squares needed to tile the rectangle, which is the number of square units.) Is finding the area of a rectangle by multiplying its length by its width easier than counting tiles? Ask your students to explain their answers.
Activity 2: Decomposing Areas
Working in pairs or groups of three, students will decompose area models to represent the distributive property.
Materials
Graph paper; reproducible, “The Area of the Sums,” for each pair or group of students.
Procedure
1. Explain that rectangles can be decomposed (separated) into smaller rectangles. The area of the original rectangle is equal to the sum of the areas of smaller rectangles.
2. Distribute copies of the reproducible. Explain that at the top is a rectangle whose area is 6 square units. Below it are two different ways to decompose the rectangle into two smaller rectangles. ( Note: If students point out that in the first example the original rectangle is decomposed into a rectangle and a square, remind them that a square is a special type of rectangle.)
3. Instruct your students to draw a rectangle that has two rows, each with five squares, on their graph paper.
4. Instruct them to decompose this rectangle into two smaller rectangles and find the area of each pair. There are three ways to do this. They should find all three.
Closure
Discuss the ways the rectangle can be decomposed. Ask your students: Do you think the sum of the areas of the smaller rectangles will always equal the area of the original rectangle? Why?
Answers
There are three ways to decompose the rectangle: a 2-by-1 and a 2-by-4 rectangle; a 2-by-2 and a 2-by-3 rectangle; a pair of 1-by-5 rectangles.
The Area of the Sums

Measurement and Data: 3.MD.8
    “Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.”
8. “Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.”
    Background
    While the area of a polygon (a closed plane figure whose sides are line segments) is the number of square units needed to cover the flat surface, the perimeter of a polygon is the distance around the figure.
    Two rectangles may have the same area but different perimeters. For example, a 4-by-5 rectangle and a 2-by-10 rectangle both have an area of 20 square units, but the perimeters are 18 units and 24 units respectively.
    Two rectangles may have the same perimeters but different areas. For example, a 1-by-6 rectangle and a 3-by-4 rectangle both have a perimeter of 14 units, but their areas are 6 square units and 12 square units respectively.
Activity 1: Area and Finding Perimeter
Working in