# Illustrating Areas in Fractional Units

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Students will be able to illustrate area for rectangular shapes with side lengths that include fractions.

(5 minutes)
• Review area (the amount of space within a given border) and it’s formula (A = l x w) with your students.
• Think aloud calculations for a rectangular shape with whole number length and width (like 4 units by 6 units = 24 units squared).
• Illustrate the area with a 4 by 6 array to your students, but note something interesting happens when you calculate area for a rectangle with fractional length and width (like 2¾ units by 6 units).
• Have your class turn and tell a neighbour what they think happens to the area when one side length includes a fraction. Allow several students to share their ideas with the whole class.
• Explain today’s lesson objective is to illustrate area easily when fractions are included in a side length. Using area models makes finding areas fun and easy to see!
(10 minutes)
• Hand out and preview the Area Models in Fractional Units worksheet with your students. Note to your class how you can see the whole area is made up of two parts: A whole number part (4 units x 6 units) and a fractional part (6 units x ½ units).
• Explain that adding the fractional part and the whole number part gives you the entire area. Lead your class through the calculations and answer any clarifying questions.
(5 minutes)
• Pose the following problem to your class and solve it together using area models, "Find the area for a rectangle with side lengths of 8 units and 2 ⅖ units." You should have calculations of (8 x 2) + ( 8 x ⅖ ); 16 + 16/5 ; 16 + 3 ⅕ = 19 ⅕ units squared.
• Carefully point out to your students how you can see the two separate parts of the area for each calculation: the whole number part (8 x 2) and the fractional part ( 8 x ⅖ ). Answer any clarifying questions.
(15 minutes)
• Release students to complete the Area Models in Fractional Units worksheet.

Enrichment:

• Students can try each exercise where both sides include a whole number and a fraction.

Support:

• Have students draw only the dimensions for each exercise, so as to clearly see the area in two parts: Whole number and fractional. Then they can move to solve one exercise at a time.
• For review practise, students can do the Multiplying Fractions with Whole Numbers worksheet for additional practise in multiplying fractions (see suggested media).
(5 minutes)
• Show your students a model based on the worksheet example and have them point and tell you the factors for the fractional and whole number parts of the area. If proficient, have them give you the sum of both products.
(10 minutes)
• Post two extra problems to find the area of a rectangle with dimensions of 3 ¼ units and 10 units.
• Allow students to explain each step (i.e. draw an area model, add the dimensions, see the two parts) through to solution for each one, handing off to a peer as needed.

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