Dear Parents and Caregivers, We appreciate the support you give to your child in learning mathematics. We would like to share some information to help you better understand Arizona’s College and Career Ready Standards. This is one of a series of letters intended to help you understand the work your child is bringing home. We will highlight new language and strategies we will use to build understanding, help students make sense of numbers and know common methods we learned in school. This letter is about finding the area of rectangles in third grade. End-­‐of-­‐year goals Students in third grade recognize area as an attribute of two-­‐dimensional figures. They measure the area of a shape by finding the total number of same-­‐size units of area required to cover the shape without gaps or overlaps. A square with sides of equal length is the standard unit for measuring area. They understand that rectangular arrays can be decomposed (taken apart) into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication. Vocabulary •
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Area: the measure, in square units, of the interior region of a two-­‐dimensional figure Array: an arrangement of objects into equal rows or columns Dimensions: measurements of a figure, such as length and width Two-­‐dimensional figure: a figure having length and width, such as a rectangle Decompose a figure: to take apart a two-­‐dimensional figure into smaller areas Square measure: a unit, such as a square meter, or a system of units used to measure area (u2) Recognizing Area Students develop an understanding of area of rectangles by using square units to measure area. They will fill an area with the same-­‐sized square units and count the number of square units. Units may be square inches, square feet, square centimeters, square meters, or improvised units. Students may use tiles to fill rectangles and draw the units and rectangles on graph paper. 5 4 one square unit Modeling area using tiles and graph paper helps students connect the process of adding up the rows or columns of square units to find the area with using the length and width dimensions of the rectangle to find the area using an equation (Area= length times width; A = l • w). Students will solve real-­‐world problems using their understanding of these ideas. •
Tim and Terry painted a wall in their bedroom. Tim painted a section of the wall that was 8 feet tall by 4 feet wide. Terry painted the other section of the wall that was 8 feet tall by 6 feet wide. What is the area of the wall that was painted? Mesa Pubic Schools/Grade 3/Rectangular Area/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014). A student might draw and label a rectangle to model this problem. They could use the equation for area to find the area of each rectangle and add them together or apply the distributive property to find the total area. (8 • 4) + (8 • 6) = 32 + 48 = 80 square feet Distributive property: 8 feet (8 • 4) + (8 • 6) = 8 (4 + 6)= 8 • 10 = 80 square feet (ft.2) 4 feet 6 feet Students will also solve problems that require them to decompose a figure into different rectangles. • Sara has a piece of fabric she wants to use in her sewing project. The model below shows her fabric piece. She needs 100 square inches to make her project. Does she have enough fabric? Explain how you know. Area = (12 • 3) + (8 • 7) = 36 + 56 = 92 in2 “ I made two rectangles from the fabric. One rectangle is 12” by 3”. The other rectangle is 8” by 7”. Then I found the area of each rectangle and added them together. Sara will not have enough fabric because 92 square inches is less than the 100 square inches she needs.” Some problems may ask students to apply their understanding of area by creating rectangles of the same perimeter and different areas or of the same area and different perimeters. For example, the table below shows some possible dimensions of a rectangle with the area of 24 square units. Area Length Width 24 square units 1 unit 24 unit 24 square units 2 units 12 units 24 square units 3 units 8 units 24 square units 4 units 6 units 24 square units 6 units 4 units 24 square units 8 units 3 units 24 square units 12 units 2 units 24 square units 24 units 1 unit How to help at home • Set aside time every day for your child to learn and practice the multiplication facts. •
Watch the videos about arrays and multiplication at http://learnzillion.com/lessonsets/58-­‐understand-­‐area-­‐and-­‐arrays •
Remember, mistakes are a part of learning. Mesa Pubic Schools/Grade 3/Rectangular Area/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014). Perimeter 50 units 28 units 22 units 20 units 20 units 22 units 28 units 50 units