Solving for Area

1. Solving for Area Unit of Study 11: Understanding Area Global Concept Guide: 2 of 3

2. Content Development “Do not make the mistake of bypassing formula development with your students, even if your annual testing programs allow students access to the formulas during the test. When students develop formulas, they gain conceptual understanding of the ideas and relationships involved, and they engage in ‘doing mathematics’… students who understand where formulas come from do not see them as mysterious; they tend to remember the formulas. This reinforces the idea that mathematics makes sense.” -Van De Walle “It is important for students to know that when finding the area of a plane shape, they are measuring the amount of a region in a space. Whether finding the area of a hand-drawn rectangle or a wall that needs to be painted, the surface to be measured is flat. The shape also has sides which contain the region. Therefore, the area of the shape is a region in the plane. Area is used in many fields of employment, such as painting, interior design, and carpentry. It is a tool that can be used to measure not only a plane shape, but (the face of) a three-dimensional shape as well. Area can be measured using any kind of tessellating shape. However, the square unit is the standard unit. It is one unit on each side.” - GoMath TE p. 409A

3. Day 1/2 • Essential Question: How can you apply efficient strategies to solve area problems? • Give students an index card, grid paper, square tiles and rulers to solve the following problem: • “Riley the dog is having accidents in his crate, so his owner is going to cover the floor with newspaper. If an index card is a model for the floor with a scale of 1in.=1ft., how many square feet of paper does she need to cover the floor of the crate?” • While students are working, monitor, select and sequence students to share strategies starting with the most concrete strategies. Facilitate discussion about connections between the different strategies. The last strategy that should be shared should be the one closest to the area formula. Use that as a springboard for discussion about the formula. • Have students select 3 area problems from #2-7 on GoMath pg. 419 to test whether the area formula works with all rectangles. All students should complete question 9. • After testing the formula, have students select the best tool to measure and find the area of various sized rectangles around the classroom. Introduce components from GoMath lesson 10.6 and incorporate throughout the rest of this GCG. • GoMath p.422-423 has additional problems for application of the formula. • By the end of day 2, students should be able to justify and apply the formula for the area of rectangles.

4. Day 3 • Essential Question: How can you apply the formula for area to real world problems? • Give each group of students four different sizes of construction paper rectangles, color tiles, sheets of copy paper and rulers. Pose the problem, • “You have four photos of different sizes. You want to place the photos, without overlapping , onto a rectangular scrapbook page. What are the dimensions of the smallest rectangular scrapbook page that you could use?” • Differentiation could include graph paper, color tiles or altering the task to determining the area for each photo. • Facilitate a discussion to compare different strategies, dimensions of scrapbook pages and the physical arrangement of the pictures. • Use additional problems from GoMath p. 424.

5. Day 4 • Essential Question: What is the relationship between area and perimeter? • On day 4, students will apply their understanding about the formula of area as they explore the relationship between perimeter and area. • Provide students with just the “Unlock the Problem” and “Try Another Problem” from GoMath SE p. 435-436. Facilitate discussion on different strategies students used, focusing on the way they organized their information as well as any generalizations/patterns students may have noticed. Generalizations may include the following: • As the length of a rectangle increased, the width decreased and visa versa • The square for a given perimeter will have the greatest area • Rectangles can have the same perimeter, but different areas • A rectangle for a given area that is a square will have the smallest perimeter. • The closer the measurements for length and width are to each other, the greater the area of the rectangle. • Students can continue to explore the relationship between perimeter and area and see if their generalizations are verified on problems 1-4 on Go Math SE p. 437. • By the end of day 4, students should be able to explain the relationship between perimeter and area.

6. Day 5Enrich/Reteach/Intervention • Essential Question: How can you apply the relationship between perimeter and area to solve real world problems? • Reteach – Provide students with more opportunities to make connections between concrete models and the formula for area. • Reteach Activity TE p.421B • GoMath Reteach Lesson 10.7 p.R89 • Online Florida Interventions Skill 47 • Core – • Grade 5 Excursion Modify Perimeter and Area Royally TE p. TR 1 and SE p. 111-112 • Enrich: • Enrich Activity TE p. 421B, Enrich Activity TE p. 431B • Enrich Book Lesson 10.4 p.E86 • Grade 5 Excursion Modify Perimeter and Area Royally TE p. TR 1 and SE p. 111-112

7. Literature for your Classroom Library