Guided Lessons

Information Gaps and Finding the Area

Facilitate rich maths conversations with this lesson on finding the missing information in problems related to the area of rectangles and squares. It may be taught by itself or used as support to the lesson Finding Area: Furnishing A Room.
This lesson can be used as a pre-lesson for theFinding Area: Furnishing A RoomLesson plan.

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This lesson can be used as a pre-lesson for theFinding Area: Furnishing A RoomLesson plan.

Students will be able to find the area of rectangles and squares.

Language

Students will be able to ask for necessary information and explain their reasoning when solving area problems using peer interaction and sentence frames.

(3 minutes)
• Present students with a situation that is unsolvable due to a lack of complete information. For example, "Ms. McClosky wants to buy a small table for her students' reading corner. She wants to make sure it will fit in the space she has in her classroom. The area of one table she is considering is 600 square inches. What are the dimensions of the table?"
• Define and explain any unfamiliar words in this word problem.
• Have students turn and talk to a nearby partner about the problem. Invite students to share any concerns they have with the problem and what they need to solve it.
• Record students' input and guide them to the understanding that even though they could come up with possible factors that MayBe the width and length of the table, they will not be sure of the dimensions unless one of the sides is given (i.e., we need to know what either the width or length is in inches to be able to calculate the unknown dimension).
(8 minutes)
• Invite volunteers to read aloud the content and language objectives for the lesson. Ask students to repeat them to a partner. Answer any questions students may have regarding the lesson.
• Explain that first students will learn/review some key maths vocabulary necessary to master today's lesson. Emphasize that students will be working hard on their maths conversation skills so it is important for them to know the correct terms to use as they talk to each other about the problems.
• Distribute a copy of the Glossary worksheet to each student. On the document camera, introduce each tiered word by reading aloud the definition and describing the image if available.
• Tell students to write "Example" as the title for the far right column on the glossary. Model to students how to write an example for each word (e.g., for the word area, write "Area = width x lengthOr A = 3 x 4 = 12 square units").
• Place students into partnerships and have them add examples for the remaining words in the the glossary and then glue the glossary into their maths journals.
• Have a few students share their examples with the whole group once everyone has completed the glossary using the sentence frame, "An example of ____Is..."
• Remind students to use the glossary as a resource as they work on the day's lesson.
(10 minutes)
• Ask students to point to the formula for AreaIn their glossary. Teach students the connection between multiplication and division using the term Inverse operationIn the glossary. Remind students that addition and subtraction are inverse operations and show them an example of each (e.g., 100 – 35 = 65And 35 + 65 = 100; 12 x 3 = 36And 36 ÷ 3 = 12).
• Tell students that they must remember the importance of keeping the unit of measurement consistent in each problem. For example, if the rectangle is being measured in inches, the answer must also be stated in inches.
• Model to students how to solve the following problem: "What is the area of a square room that has the length of 6 feet? Draw a square and label the sides as 6 feet. Ask for student input for how to solve it (e.g., multiply 6 by 6 to get 36 square feet).
• Ask students to consider the possibility of the problem: "What is the area of this square room?" Draw the same square but do not label the sides. Ask students to turn to a partner and state what information is needed, using the sentence starter: "In order to solve for the area of the square, we need to know..." Have students share out their conversations.
• Model another problem with a rectangle. Read aloud the following problem: "What is the area of a rectangle that has the width of 8 inches?" Ask students if they can solve this problem.
• Instruct students to talk to their partner as they consider what the information gap is or what information is missing in order to solve it. Provide students with the following sentence stems/frames to use as they discuss:
• "The information gap is..."
• "We know the ____Of the rectangle, but we do not know the..."
• "If we knew the ____, we could solve the problem."
• "To solve for the area of the rectangle, we need to know..."
• Confirm or correct students' sentences and model how to solve for the problem if the missing information were provided (e.g., the length of the rectangle is 7 inches).
• Show one more problem with an information gap that will require students to use the inverse operation, such as: "The area of the rectangle is 66 square meters. What is the length of the rectangle?"
• Have students use the displayed sentence stems/frames to discuss with a partner. Invite a few students to share their discussions (e.g., "We know the area of the rectangle, but we do not know the width. If we had the width, we could solve the problem.").
• Give students the missing information: "The width of the rectangle is 6 meters. Then, have them work with a partner to solve for the problem using inverse operations. Confirm or correct students' solutions. Explain that since Area = Length x Width, Length = Area divided by Width, and therefore we must calculate 66 divided by 6 to get the length of 11 meters."
(10 minutes)
• Tell students that they will participate in an Information Gap activity in which they will each get a card that either has a question and image or a "data card" that has one piece of information about the geomtery problem. Students will be placed into A–B partnerships. Partner A will get the card with the question and some information, while Partner B will get the missing piece of information.
• Tell students that it is essential that they Do notRead their card out loud but instead read it silently to themselves. Partner A will be responsible for thinking of what key information is needed to close the information gap and be able to solve the problem. Partner B is required to ask Partner A to explain why they need the specific information.
• Display the Information Gap Cards for Area directions on the document camera and review the steps with students. Note: Make sure the steps are visible throughout the activity.
• Invite one student volunteer to model how to do the activity with you, using the questions and sentence starters as a guide. Model your thinking aloud as Partner A and have the student play the role of Partner B.
• Place students in A–B partners. Give each student one Information Gap Card and have them do the activity while referring to the steps.
• Listen in on students' conversations to check for accuracy of sentences and terms.
• Remind students that some of the cards have them solving for the area of a rectangle while others ask for the width or length of a square or rectangle. Tell them to carefully read the question and look at the shape before asking for missing information.
• Collect the cards and redistribute them to students, making sure that they receive the opposite role (A or B) so they each have the chance to ask for the missing information or to ask for an explanation of the missing information.
• Provide sentence stems for the Partner A to use as they explain their reasoning:
• "I need this information because..."
• "With this information, I can..."

Beginning

• Allow students to explain the process of solving the problems in their home language before rephrasing using sentence stems/frames in English.
• Have students work in a small, teacher-led group during group work.
• Create and display a word/phrase bank with helpful terms from the lesson for students to refer to, with images if applicable.
• Place students in specific partnerships based on their language needs.

• Have students share their answers aloud without referring to the sentence stems/frames for support.
• Allow learners to utilize glossaries and dictionaries for challenging words.
• Have learners repeat instructions and key vocabulary for the class.
(5 minutes)
• Distribute whiteboards and markers to students. Tell them to draw a shape and ask a problem related to area that has an information gap For example, draw a rectangle that has a width of 10 centimeters and ask for the area.
• Have them show their problem to a classmate and instruct the classmate to ask for the missing piece of information.
• Tell the author of the problem to give the missing information to their classmate (provided they asked correctly) and then have the classmate solve the problem.
• Circulate to check on students' understanding.
(4 minutes)
• Have students reflect on the following questions in small groups:
• How was your experience in finding the missing information?
• What are some other times in your life you might need to use these skills?
• Display and read aloud these sentence stems to help students discuss:
• "Finding the missing information was..."
• "I might need to use these skills when I..."