Filling and Wrapping 1.2 Making Rectangular Boxes Three-Dimensional Measurement

Please take out… Filling and Wrapping Book Your investigation note sheets A pencil And remember to be respectful so that everyone has an equal opportunity for learning today!

1.1 Review Making cubic boxes Cube Unit cube Net How is the area of a net related to a cube?

1.2 Making Rectangular Boxes Today we are learning about rectangular boxes, as opposed to the cubic boxes we made yesterday. (Remind students to write Investigation 1.2 on their note sheets). Using what we’ve learned yesterday, and thinking about a packaging designer, how might you describe these boxes? How many faces are there? What do they look like? How many edges does the box have? How many vertices does it have? Will a different box have a different number of faces, edges, or vertices?

1.2 Objectives: WALT… Visualize a net as a representation of a rectangular prism Understand the relationship between the area of the net and a rectangular prism Give students time to write the objectives on their note sheets.

1.2 Success Criteria Define and describe a rectangular prism Create two or more nets for a rectangular prism Explain how the area of a net is related to the surface area and the space inside of a rectangular prism

1.2 Vocabulary Rectangular prism: a three-dimensional shape with 6 rectangular faces Remember: a square is a rectangle. Provide time for students to add the vocabulary term to their notes sheet. While students are writing, the teacher should draw the rectangular prism from the book problem on the board. While students are waiting for everyone to finish writing, prompt them to look at the rectangular prisms (boxes). Using your knowledge about cubes and nets from yesterday’s lesson, what might you know about a rectangular box?

Problem 1.2 On grid paper, draw two different nets for the rectangular box on the board. Cut each pattern out and fold it into a box. Describe the faces of the box formed from each net you made. What are the dimensions of each face? Find the total area of each net you made in Question A. How many centimeter cubes will fit into the box formed from each net you made? Explain your reasoning. Suppose you stand the rectangular 1 centimeter x 1 centimeter x 3 centimeter box on its end. Does the area of a net for the box or the number of cubes needed to fill the box change? Why or why not? Many boxes are not shaped like cubes. The rectangular box below has square ends, but the remaining faces are non-square rectangles. Read through each problem. Ask if there are any questions in what the problems are asking. Remind students that if they need help, they need to raise their hands and stay quietly in their seat until a teacher comes to assist them. Think.Pair.Share. Students will have 10 minutes to work independently, 10 minutes to work together, and 5-10 minutes to share/discuss as a class. While students are working, the teacher should circulate around the room and ask: How do you know your net will create the rectangular box? What is the same/different in all of the nets? How is the area of each net related to the number of squares that would cover the rectangular box? Answers will vary. See Teacher’s Guide for specific examples. Four rectangular faces are congruent, with a length of 3 cm and a width of 1 cm. The remaining two faces are also congruent, with a length of 1 cm and a width of 1 cm. The area for each net is 14cm2. 3 cm cubes. One cube will cover the square end and fill one third of the box so two more will fill the box. No. If the position of the box is changed, the area of a net for the box and the number of cubes needed to fill the box remain the same.

Let’s share! What was the area of your net? How did you find that measure? What do you think the total area of the box’s surface will be? Why? How do these areas compare? Why does it make sense that these two measures are the same? Area: 14 cm2 Add the areas of each rectangle. The area of the rectangles is 3 and the squares is 1. ( 3 + 3 + 3 + 3 + 1 + 1) Yesterday’s exit slip was to write about the relationship between the area of a net and the number of faces in a cube. Recall that the area of the net was 6 because there were 6 square units. How many faces does a cube have? 6. They are equal! Some of you said the areas were the same, but we have to specific that the area of the net is equal to the surface area of the cube, not it’s area—that would be the space inside. Thus, how does the area of a rectangular net relate to the box’s surface area?

EXIT SLIP Sketch a rectangular prism (box) with: Length: 6 cm Width: 2 cm Height: 2 cm Label the dimensions and identify the box’s area. Height Height Width Width Length Length