Practice with Perimeter & Area

Gianni’s Pizza Gianni & Jen were asked to design two rectangular pizzas, each with an area of 36 in2, but each with a different perimeter. Use square tiles to complete this task. 9 9 9 Encourage participants to use the tiles!

Gianni’s Pizza What is the area for each pizza? 9 9 What is the perimeter for each pizza? 9

Rectangles, Rectangles, Rectangles Use 20 square tiles to create a rectangle. Participants will use the square tiles to create rectangles. Remind participants of the importance of using manipulatives in order for them to develop their understanding of perimeter and area. Give each participant 20 square tiles. Have them complete Activity 1: Rectangles, Rectangles, Rectangles from the Periemter_Area activities sheet. Model how to complete the activity using 20 tiles to make a rectangle. Participants will keep data on a chart in their foldable booklet.

Rectangles, Rectangles, Rectangles Use 20 square tiles to create a rectangle. Just show them this ONE example! How many different rectangles can you make?

Same Perimeter, Same Area Draw a shape with a perimeter of 12 centimeters. P = 12 A = 8 Participants have used manipulatives for the last 2 activities. Now they will work with paper and pencil. Give each participant 3 or 4 sheets of centimeter grid paper. Directions: Draw a shape on centimeter grid paper with a perimeter of 12 centimeters. Record the area inside the shape. Draw as many shapes as you can with a perimeter of 12. Record the areas inside the shapes. Repeat steps above with shapes having a perimeter of 14. Repeat steps above with shapes having a perimeter of 18. Write a general statement (based on your work above) about area with shapes having the same perimeter. If a shape has a perimeter of 24, what are the dimensions of the shape with the largest area? If a shape has a perimeter of 36, what are the dimensions of the shape with the largest area?

Draw a shape with a perimeter of the dice. Racing Rectangles Draw a shape with a perimeter of the dice. P = 12 A = 8 This will be a second paper and pencil activity Give each participant a Racing Rectangle Activity Sheet. Number of Players: Two Materials: Two dice or number cubes, game-grid, crayon per player Directions: Each player has a different color marker or crayon In turn each player rolls the dice. A player outlines and colors a rectangle on the grid board to match the cubes. (Ex. a roll of 6 and 3 = a 6 x 3 rectangle or a 3 x 6 rectangle). The player writes the area ( total number of squares) in the center of the rectangle. A player loses a turn when he rolls and cannot fit his rectangle on the gridboard. The game is over when neither player can draw a rectangle. The winner is the player with the most squares colored on the gridboard.

Create rectangle with tiles. 15 Rectangles Tiles Create rectangle with tiles. 15 This will be a Manipulative Activity Give each participant a Periemter_Area activities_2 hand-out Materials Needed: Numbers 1-50 in a bag Square tiles Grid paper Directions: Write the numbers from 1 through 50 on small pieces of paper and drop them into a paper bag. Have each participant draw two pieces of paper. Then have participants work with a partner. Participants start with one of the papers and selects that number of square-inch tiles The partner pair will build as many different rectangles as possible with that number of tiles. Using grid paper, they draw each rectangle and record the area (total number of tiles), length, width, and perimeter for each rectangle. They repeat the process with each paper they selected from the bag.

Perimeter How can you find the perimeter of each of these shapes? This slide is a lead up to deriving perimeter formulas.

Perimeter Add all sides! Can you write a FORMULA for perimeter of any: Triangle? Quadrilateral? Pentagon? Deriving the formula or perimeter seems somewhat silly. Perimeter means to add all sides. Since it is unknown if any figure is regular or not (all sides equal or not), the formula for a triangle is Tp = s1 + s3 + s3. Then the formula for ANY quadrilateral is Qp =s1 + s3 + s3 +s4. There are special quadrilaterals, look at a square. We know all 4 sides are equal, so the formula for a square could be Qp =s1 + s3 + s3 +s4 or 4s (all 4 sides equal so 4 times 1 side is same as 4 sides added together. Talk about the formula for a rhombus, then rectangle and parallelogram before pentagon.

Area How can you find the area of each of these shapes? Give the participants manipulatives (polygon shapes), and tiles. Encourage their use. It might be necessary to lead a discussion about how to define “different” before students begin working. How will students know when they have found all the different rectangles? When students have completed gathering all the data for the numbers one through one hundred, ask them to discuss how all of these data might be represented or displayed. Then ask them what patterns they can find. Can they make any generalizations?

Area Formulas Square Rectangle Parallelogram Triangle Trapezoid Deriving the formula for area formulas is important

Area of a square 3 units 3” 9 square units in square 1 2 3 4 5 6 7 8 9 Deriving the formula for area formulas is important 9 square units in square 3” or 3 units on each side 3 x 3 = 9

Area of a square Suppose square was 4 cm on each side. What is the area? Suppose square was 6 feet on each side. What is the area? Deriving the formula for area formulas is important

Area of a square Formula is side times side (S x S) Or Side squared (S2) Deriving the formula for area formulas is important

Area of a Rectangle 3” 4” 3 units 4 units 1 2 3 4 5 6 7 8 9 10 11 12 Deriving the formula for area formulas is important 12 square units in the rectangle 3” or 3 units on top (width) 4” or 4 units on side (height) 3 x 4 = 12

Area of a Rectangle Suppose a rectangle had a width (top) 5 cm and height (side) of 3 cm. What is the area? Suppose a rectangle had a width of 6 feet and a length of 2 feet. What is the area? Use length, width, height interchangeably. These are words that are seen in different problems. Recommend they DRAW the problem! Suppose a rectangle had a length of 8” and a width of 8”. What is the area?

Area of a Rectangle Formula is TOP times SIDE Or Length times Height L x H L x W The formula can be written in many ways. Discuss with the group.

Area of a Parallelogram What is the relationship between a rectangle and a parallelogram? Talk about a rectangle and a parallelogram. Give each participant a sheet of grid paper and a pair of scissors. Have them draw re parallelogram (pretty large one). Ask them to cut out their parallelogram. Now, can they cut the parallelogram into two pieces to make a rectangle?

Area of a Parallelogram Help the participants to see that is they cut a triangle from the end, they can move it to the other side to form a rectangle. Ask them what they can say bout a rectangle and a parallelogram. Now talk about the formula for the area of a rectangle… What is the formula for the area of a parallelogram?