A ratio compares two numbers by division. The ration of two numbers a and b, where b cannot equal (undefined, no solution). One may think of a ratio as a multiplicative relationship. For example, if the ration of the number of boys to the number of girls in a class is 2:1, then the number of boys is two times the number of girls.
A ration that compares quantities measured in different units is called a rate. A rate with a denominator of 1 unite is a unit rate. One can write ratios and find unit rates to compare quantities. One may also convert units and rates to solve problems.
Guided Practice: Comparing Unit Rates (Problem 1) and Got It, page 117.Have students learn new vocabulary: ratio, rate, unit rate, conversion factor, and unit analysis.Solve problems #23 and 24 together.
Independent Practice: Page 119 (11-16), page 120, #36.
Allow students remaining 30 minutes of class to take assessment to cover sections 2.3-2.5.
A proportion can produce an infinite number of equivalent ratios. Any two of these can be use to write a proportion. A proportion is an equation that states that two ratios are equal. For example, where b and d cannot equal 0. One can read this as “a is to b as c is to d.
Direct Instruction: Introduce essential vocabulary for the section including, proportion and cross products.
Guided Practice: Page 124-126, Problems 1-3.Work through Got It 1-3 for additional practice.
Independent Practice: Page 127 (10-13, 18-21, 26-29, 31, 32)
Similar figures have the same shape but not necessarily the same size. In similar figures, the measure of corresponding angles are equal, and corresponding side lengths are in proportion. The order of the letter when you name similar figures IS important because it tells which parts of the figures are corresponding parts.
Guided Practice: Page 131, Problems 1-4 and Got It set for additional practice.
Independent Practice:page 134: 6-10, 23.
One can solve a problems involving percent using either proportions or the percent equation, which are closely related. If we are to write a percent as a fraction, we can use a proportion to easily solve the problem.
Guided Practice:Page 138, Problems 1-4.Helps student determine percent using proportion, using percent equation and finding part/base.Got It for additional practice.
Independent Practice: Page 141 (#10-28, even. Work together to solve “Error Analysis” on page 142. Have students copy percent equation to work Kuta homework part finding the part, whole, and percent of several given expressions.
One can determine the percent change when he or she knows the original amount and how much it has changed by. If a new amount if greater that the original amount, the percent change is denoted as an increase. Likewise, if there is a decrease in amount, this is denoted as a decrease.
Direct Instruction:Review Key Concept page 144 (equation to employ)
Guided Practice: Work through Problems 1-4 on pages 145-147.
Independent Practice:Page 148, 7-15, 37.