12/17/2023 0 Comments Expression for area of a rectangle![]() ![]() Rectangle A has a vertical side length of 3 and horizontal side length of 2. ![]() For example, if they choose 2 as the value for \(x\), \(5(3 \boldcdot 2 + 8)\) is 70, and \(15 \boldcdot 2 + 40\) is also 70.ĭescription: A rectangle is partitioned by a vertical line segment creating two smaller rectangles, A and B. No matter what value they choose, the expressions will yield the same value. Ask each pair of students to choose any number, and evaluate both \(5(3x+8)\) and \(15x+40\) using the value they chose for \(x\). However, we want to reinforce what equivalent means here. For example, we can see that \(5(3x+8)\) and \(15x+40\) are equivalent because they both represent the area of figure G. When appropriate, encourage students to use the word term to refer to things like \(3a\), \(6p\), and \(15x\).įinally, we want to make the point another way that each pair of expressions they wrote are equivalent to each other. Likewise, we take \(2(3x +4)\) to be a product because we note that 2 is multiplied by the quantity \(3x + 4\), which contains a sum and a product.) Ask students why we consider one expression for area “a sum” and the other “a product” even though both expressions contain sums and products. (For example, we take \(6x + 8\) to be a sum because we are adding two terms \(6x\) and 8, even though \(6x\) is actually a product of 6 and \(x\). Remind students about the term “coefficient” and the convention of writing the coefficient before the variable. The purpose of the discussion is to help students understand the distributive property and how it can be used to generate equivalent expressions. The vertical side is labeled 5 and the top horizontal side lengths are labeled 3 x and 8. Rectangle F is partitioned by a vertical line segment into two smaller rectangles. The vertical side is labeled m and the top horizontal side lengths are labeled 6 and 8. Rectangle E is partitioned by a vertical line segment into two smaller rectangles. The vertical side is labeled 6, and the top horizontal side lengths are each labeled 4. Rectangle D is partitioned by 3 vertical line segments into 4 equally sized rectangles. ![]() The vertical side is labeled r and the top horizontal side lengths are each labeled 1. Rectangle C is partitioned by 2 vertical line segments into three equally sized rectangles. The vertical side is labeled one third and the top horizontal side lengths are labeled 6 and x. Rectangle B is partitioned by a vertical line segment into two smaller rectangles. The vertical side is labeled 3 and the top horizontal side lengths are labeled "a" and 5. Rectangle A is partioned by a vertical line segment into two smaller rectangles. Description: Six different sized rectangles labeled A, B, C, D, E, and F. ![]()
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