3.MMT.4 RAMP UP TEACHER NOTES (PG. 1 OF 2) Area

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1 3.MMT.4 RAMP UP TEACHER NOTES (PG. 1 OF 2) Area SE 3.6C, 3.4D, 3.4E, 3.4F, 3.1A, 3.1B, 3.1C, 3.1D, 3.1E Purpose This activity acts as a bridge between the 2 nd -grade concept of area (covering a rectangle with squares, then counting the squares) and 3 rd -grade concept of area (multiplying the number of squares by the number of rows). It also bridges to the array model for multiplication. 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 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 3.MMT.4 Ramp Up for each student. Prepare both 3.MMT.4 Ramp Up Examples so they can be projected using your classroom technology. 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? How many rows are there? What multiplication fact can you use to find the area? How-To Guide 1. Place students in pairs and distribute materials. 2. Project 3.MMT.4 Ramp Up 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? 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? 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 and multiply that by the number of rows, just like they did when finding the number of objects in an array. Then write: = 20 Scary Jerry has 20 gourds. On 3.MMT.4 Ramp Up, students should outline a 4 by 5 rectangle, color it in, and fill in the blanks to find area. 7. Project 3.MMT.4 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. PAGE 33

2 3.MMT.4 RAMP UP TEACHER NOTES (PG. 2 OF 2) 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 2 nd grade, students found areas of rectangles by covering them, which is a fairly informal way to find area. In 3 rd grade, students begin to systematize the calculation of area by counting the number of squares 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 3 rd -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. No mention is made of length and width, and the formula for area of rectangles is not even on the 3 rd -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. 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 3.MMT.4 these pictures might be of buttons, plates, earrings, necklaces, shelves, a cabinet. You know best which words might be unfamiliar to your students. For 3.MMT.6 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 3.MMT.6 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! PAGE 34

3 3.MMT.4 RAMP UP EXAMPLE #1 1 Scary Jerry has a set of square building blocks. He put his building blocks in 4 rows. He has 5 building blocks to make a rectangle. How many building blocks does he have? What is the area of the rectangle made from the blocks? The area is square units. Scary Jerry has square building blocks. PAGE 35

4 3.MMT.4 RAMP UP EXAMPLE #2 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. What is the area of the garden? The area is square units. Scary Jerry has square grape plants blocks. PAGE 36

5 3.MMT.4 RAMP UP ANSWER KEY (PG. 1 OF 4) 1 Scary Jerry has a set of square building blocks. He put his building blocks in 4 rows. He has 5 building blocks to make a rectangle. How many building blocks does he have? What is the area of the rectangle made from the blocks? = 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. What is the area of the garden? = 18 The area of the rectangle is 18. Scary Jerry has 18 square grapes. PAGE 37

6 3.MMT.4 RAMP UP ANSWER KEY (PG. 2 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. 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? = 30 The area of the rectangle is 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. What is the area of the drawer? How many square plates does Skinny Jenny have? = 63 The area of the rectangle is 63. Skinny Jenny has 63 tiny square plates. PAGE 38

7 3.MMT.4 RAMP UP ANSWER KEY (PG. 3 OF 4) 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. How many earrings does she have in her collection? = 25 The area of the rectangle is 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? = 7 The area of the rectangle is 27. The cabinet is 27 square drawers. PAGE 39

8 3.MMT.4 RAMP UP ANSWER KEY (PG. 4 OF 4) 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. What is the area of the rectangle of books? How many books are in the rectangle? = 56 The area of the rectangle is 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 onefoot square. He lays the flags out on the floor to make a rectangle. He has enough to flags to make 7 3 flags. What is the area of the rectangle of flags? How many flags does Mr. Beasley have? = 21 The area of the rectangle is 21. Mr. Beasley has 21 square flags. PAGE 40

9 3.MMT.4 RAMP UP (PG. 1 OF 4) Name: 1 Scary Jerry has a set of square building blocks. He put his building blocks in 4 rows. He has 5 building blocks to make a rectangle. How many building blocks does he have? What is the area of the rectangle made from the 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. What is the area of the garden? PAGE 41

10 3.MMT.4 RAMP UP (PG. 2 OF 4) Name: 3 Scary Jerry s sister Skinny Jenny also likes square things. She arranges the buttons to make a rectangle. There are 6 buttons. 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? 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. What is the area of the drawer? How many square plates does Skinny Jenny have? PAGE 42

11 3.MMT.4 RAMP UP (PG. 3 OF 4) Name: 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. How many earrings does she have in her collection? 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? PAGE 43

12 3.MMT.4 RAMP UP (PG. 4 OF 4) Name: 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. What is the area of the rectangle of books? How many books are in the rectangle? 8 Mr. Beasley has a smaller collection of square flags from countries around the world. Each flag is a onefoot square. He lays the flags out on the floor to make a rectangle. He has enough to flags to make 7 3 flags. What is the area of the rectangle of flags? How many flags does Mr. Beasley have? PAGE 44