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Area with Decimals and Fractions
Students will be able to find the area of rectangular shapes with one fractional dimension using the area equation.
- Display a visual of a location with a sketch of a rectangle to show a portion of the location. Make sure it's a familiar location for your students (e.g., a gymnasium, tennis court, etc.). Add two-digit whole numbers for the dimensions. (Tip: you can take pictures of familiar locations to the students, project them on the board, and then write out dimensions.)
- Ask students to calculate the area of the rectangle on their whiteboards. Tell them to share their answers with their elbow partners when they are finished.
- Call on students to share their calculations. Choose a student to show their method for calculating the area of the rectangle.
- Explain to students that while the examples involved dimensions with whole numbers, they will find the area of locations with dimensions that are fractions or decimals by using the using the area equation.
Explicit Instruction/Teacher modeling(8 minutes)
- Define dimensions as the size measured in length or width when relating to area.
- Review that the area equation helps us determine the area of rectangular shapes and define it as length (l) x width (w).
- Remind students about some of the decimal fractions, which are fractions whose denominator is some power of ten. Review how to convert a fraction, such as 2/4 into a decimal (0.50) and explain how this is a decimal fraction.
- Display the same picture from the Introduction section but change the dimensions so that one is a fractional unit. Tell students that the first dimensions were rounded and now you want to use the exact dimensions. Find the area for the problem using the area equation.
- Model how you solved the problem using key vocabulary and sequencing words (e.g., "First, I changed the ½ in the dimension 33 ½ ft to 0.50 to change the whole dimension to 33.50 ft. Then, I multiplied 33.50 ft by 29 ft to get an area of 971.5 feet squared.").
Guided Practice(18 minutes)
- Post the photos of the locations (see materials section) around the room and separate students into groups of four.
- Conduct a jigsaw activity where groups of 3–4 students choose one of the posted pictures on the wall and find the area. Have them use a sheet of poster paper, draw their own rectangle with the labeled dimensions, and then solve for the area.
- Tell students that the presenter will be chosen randomly, so they should practice their explanations aloud within their group. Number each group member 1–4 and choose a random number. The student who has that number will present their group's area to the class.
- Choose one member of each group to present and have them explain how they found the area of the rectangle. For example, "I converted the fraction ¼ in the width to 0.25 to change my the width from 10 ¼ ft to 10.25 ft. Then, I used the area equation and multiplied 23 ft x 10.25 ft. I used the standard algorithm to solve my multiplication problem and got the area of 235.75 feet squared."
- Ask clarifying questions (e.g., "What do you mean by...?") or offer suggestions ("I like ____, but what about adding/subtracting ____.") to gather more information and model how to actively listen to a presenter.
Independent working time(10 minutes)
- Have students choose a photo from a group they were not a part of and have them calculate the area on a sheet of copy paper.
- Tell students to show their work and explain the steps they used to solve the area problem.
- Assign students different partners to share their answers and tell partners to offer feedback. For instance, have partners ask clarifying questions ("What do you mean by...?") or offer suggestions ("I like ____, but what about adding/subtracting ____.").
- Model again how to use these questioning skills with a confident student presenter by asking them questions about their area solution.
- Provide visuals and definitions for difficult vocabulary and sentence stems for ELs and students with disabilities.
- Allow students to multiply more simplistic numbers and decimal fractions that are more obvious (e.g., halves).
- Have students model their thinking aloud by allowing them to share their explanations. Use some of their language and write it on the board for other students to consider.
- Ask students to estimate the products before performing the calculations to verify their answers. Allow them to explain their rationale to the class.
- Challenge them to calculate the area of three-digit by a two-digit mixed number (i.e., 133 x 97 ⅓).
- Allow students to use the internet to research the dimensions of what might fit in a given area.
- Give them the chance to look up vocabulary terms and their meanings.
- Distribute an index card and write the dimensions of a rectangle that is two-digits by a mixed number with a decimal fraction (e.g., 50 m x 9 ½ m) on the board. Have students:
- Draw the rectangle it represents.
- Label the rectangle with the dimensions.
- Convert the fraction to a decimal.
- Solve for the area.
- Ask students to think about what would fit in the area and share their ideas with a partner.
Review and closing(5 minutes)
- Ask volunteers to share their index card answers with the class by explaining how they got their answers.
- Choose a volunteer to share what would fit in the determined area (e.g., pool, playground area, etc.). Have students put a thumb up if they agree and a thumb down if they disagree. If students disagree, have them say why and offer an alternative explanation.