SUCH A SQUARE! TEACHER NOTES Area - TeachTransform · 2 Scary Jerry also has a rectangular garden of square grape plants. The garden of grapes has 3 rows: one row of grapes is for

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How-To Guide

1. Place students in pairs and distribute materials.2. Project Such a Square! Example #1. 3. Work through the problem with your students. Have students model the problem using

the 1” cubes or tiles.

4. Explain that area is another way to measure a rectangle. Instead of finding the distance around the figure (perimeter), we can also measure a figure by finding the number of squares that can be used to cover the figure. How many squares did it take to make the rectangle? 20. So what is the area of the rectangle? 20.

5. Now make the rectangle again. Instead of using random colors, make each row a different color.

6. Explain to students that there are easier ways of finding the area than having to count each individual square. Connect finding area to finding the number of squares in an array.Questions to ask:• How many squares are in each row? 5• How many rows are there? 4• You said that the area of the rectangle was 20. How can you make 20 with the

numbers 5 and 4? Multiply them.Explain that another way to find the area of a rectangle is to count the number of squares in each row and multiply that by the number of rows, just like they did when finding the number of objects in an array. Then write:

4 rows with 5 in each row 4 × 5 = 20

Scary Jerry has 20 gourds.On Such a Square!, students should outline a 4 by 5 rectangle, color it in, and fill in the blanks to find area.

7. Project Such a Square! Example #2. Work through the problem with your students. 8. Students should work in pairs to solve the rest of the problems. Note that students may

choose to draw their rectangles at various places on the grid. As long as the dimensions are correct, the location and orientation do not matter.

Setting Up For Instruction

• Gather a set of 1” cubes or tiles for each student. Each pair of students will need about 100 cubes or tiles in assorted colors.

• Gather 1 set of colored pencils or markers for each pair of students.

• Gather 1 piece of construction paper for each pair of students to use as a problem-solving mat.

• Make 1 copy of Such a Square! for each student.

• Prepare both Such a Square! Examples so they can be projected using your classroom technology.

SE 3.6C, 3.4D, 3.4E, 3.4F, 3.1A, 3.1B, 3.1C, 3.1D, 3.1E

Thought Extenders

• What does area mean?

• How is area different than perimeter?

• Can you think of a real-life situation where you would need to find the area of an object instead of the perimeter?

• How many squares did it take to make the rectangle?

• How many are in each row?

• How many rows are there?

• What multiplication fact can you use to find the area?

SUCH A SQUARE! TEACHER NOTES (PG. 1 OF 2)

Area

Perimeter

Area (regular)

Area (composite)

Time

Teacher-facilitated

Small Group

Tutoring/Intervention

Centers

Below & On Grade Level

On Grade Level

On Grade Level & Advanced

Challenge Problems

Purpose This Ramp Up activity acts as a bridge between the 2nd-grade concept of area (covering a rectangle with squares, then counting the squares) and 3rd-grade concept of area (multiplying the number of squares in each row by the number of rows). It also bridges to the array model for multiplication.


What is Area? (3.1F, 3.1G)

In the first section of this book, students used perimeter to measure rectangles. They found the length (or distance) around the figure. In this section, they measure rectangles by finding the number of squares it takes to cover a rectangle with no overlaps and with squares that are all the same size.

In 2nd grade, students found areas of rectangles by covering them, which is a fairly informal way to find area. In 3rd grade, students begin to systematize the calculation of area by counting the number of squares in each row by the number of rows. Then they multiply to find the area.

The beauty of this method of understanding area is that students are using the same model to find area that they used to understand their basic multiplication facts. Remind students that when they began learning multiplication, they explored arrays. They calculated the total number of objects in an array using a similar method to how they are now finding the areas of rectangles. So understanding area reinforces multiplication fact fluency and vice versa.

It might be tempting to teach students to find area of rectangles by multiplying length × width. Try to resist the urge, because the 3rd -grade TEKS don’t require this level of abstraction. In fact, the TEKS are clear that area is found by using the “number of rows times the number of unit squares in each row.” No mention is made of length and width, and the formula for area of rectangles is not even on the 3rd -grade STAAR Reference Materials. Although in many cases the TEKS ask math students to move from concrete to abstract concepts quickly, in the case of area they don’t. Let students be concrete with area for one more year. It will be the 4th-grade teacher’s job to connect the concrete and pictorial models to the abstract calculation.

SUCH A SQUARE! TEACHER NOTES (PG. 2 OF 2)

Making Vocabulary Accessible (ELPS 1C, IF, 4C, 4F)

Some students, especially English Language Learners (ELLs), may not be familiar with some of the vocabulary in this book. You can support their success in several ways.

• Provide labeled pictures. In Such a Square! these pictures might be of buttons, plates, earrings, necklaces, shelves, a cabinet. You know best which words might be unfamiliar to your students. For Playground Design you might provide pictures of the different pieces of playground equipment.

• Place realia around the room, or go outside! Make labels objects for each of the objects in the activity. Put students in groups of 3 – 4. Each group should take their label to the object it matches.

• Take realia a step further in Playground Design and take students outside to the playground with their labels. Have groups go to the equipment that their label matches. Don’t have some of this equipment? Work with students to guess what the words mean. Give hints to help them make educated guesses: “It is very tall. You climb to the top. You sit down, and then move quickly to the bottom.” Allow students to stop you at any point to guess.

• Once they’ve been provided with this background knowledge, have students add these words to their personal dictionary or math journals. Of course, you will want to have students include academic math vocabulary as well so they can be independent, self-reliant learners!

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1 Scary Jerry has a set of square building blocks. He put his building blocks in 4 rows. He has 5 building blocks in each row to make a rectangle. How many building blocks does he have? What is the area of the rectangle made from the blocks?

rows with in each row

× =

The area is square units.

Scary Jerry has square building blocks.

SUCH A SQUARE! EXAMPLE #1


2 Scary Jerry also has a rectangular garden of square grape plants. The garden of grapes has 3 rows: one row of grapes is for making grape juice, one row is for making raisins, and one row is for eating. He has 6 plants in each row. What is the area of the garden?

rows with in each row

× =

The area is square units.

Scary Jerry has square grape plants blocks.

SUCH A SQUARE! EXAMPLE #2


1 Scary Jerry has a set of square building blocks. He put his building blocks in 4 rows. He has 5 building blocks in each row to make a rectangle. How many building blocks does he have? What is the area of the rectangle made from the blocks?

4 rows with 5 in each row

4 × 5 = 20

The area of the rectangle is 20 .

Scary Jerry has 20 square building blocks.

2 Scary Jerry also has a rectangular garden of square grape plants. The garden of grapes has 3 rows: one row of grapes is for making grape juice, one row is for making raisins, and one row is for eating. He has 6 plants in each row. What is the area of the garden?


3 × 6 = 18


Scary Jerry has 18 square grapes.

Directions: Use models and pictures to solve the following problems. Sketch the rectangle on grid paper, write down the number of rows, and then find the answer.

SUCH A SQUARE! ANSWER KEY (PG. 1 OF 4)


3 Scary Jerry’s sister Skinny Jenny also likes square things. She arranges the buttons to make a rectangle. There are 6 buttons in each row. Her button drawer fits exactly 2 rows of red buttons, 2 rows of yellow buttons, and one row of orange buttons. What is the area of the rectangle of buttons? How many square buttons are in Skinny Jenny’s drawer?


5 × 6 = 30


Skinny Jenny has 30 square buttons.

4 Skinny Jenny also has a rectangular drawer for her tiny square plates, and her square plates completely fill the drawer. She has 7 rows of tiny square plates with 9 plates in each row. What is the area of the drawer? How many square plates does Skinny Jenny have?


7 × 9 = 63


Skinny Jenny has 63 tiny square plates.




5 Addie the jewelry collector has a collection of square earrings. She arranges them to make a rectangle. There are 5 rows of earrings with 5 earrings in each row. How many earrings does she have in her collection?


5 × 5 = 25


Addie has 25 square earrings.

6 In her living room, Addie also has a cabinet full of tiny drawers to keep her tiny necklaces. The front of the cabinet has 9 rows, and each row has 3 square drawers. How many drawers does the cabinet have?


9 × 3 = 7


The cabinet has 27 square drawers.




7 Mr. Beasley loves books in the shape of squares. (Kind of silly, huh?) He arranges them in a rectangle. There are 8 rows and there are 7 books in each row. What is the area of the rectangle of books? How many books are in the rectangle?


8 × 7 = 56


Mr. Beasley has 56 square football cases.

8 Mr. Beasley has a smaller collection of square flags from countries around the world. Each flag is a one-foot square. He lays the flags out on the floor to make a rectangle. He has enough to flags to make 7 rows with 3 flags in each row. What is the area of the rectangle of flags? How many flags does Mr. Beasley have?


7 × 3 = 21


Mr. Beasley has 21 square flags.



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SUCH A SQUARE! TEACHER NOTES Area - TeachTransform · 2 Scary Jerry also has a rectangular garden of square grape plants. The garden of grapes has 3 rows: one row of grapes is for