OUR STANDARDS
6.RP.A.1 – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." For every vote candidate A received, candidate C received nearly three votes." Learning Targets: I can use a variety of representations for ratios (pictures, illustrations, etc.). I can write a ratio in different forms – as a fraction (a/b), with a colon (a:b), and in word form (a to b I can use models and pictures to develop a ratio. 6.RP.A.2 – Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar." "We paid $75 for 15 hamburgers, which rate of $5 per hamburger." Learning Targets: I can explain the concept of unit rate. I can describe a ratio relationship using rate language. I can calculate unit rate when given certain quantities. 6.RP.A.3 – Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot pairs of values on the coordinate plane. Use tables to compare ratios. Learning Targets: I can create a table by using equivalent fractions. I can find a missing value from a table of ratios. I can solve proportions using equivalent ratios (ex. by using simple proportions ½ = c/4). b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Learning Targets: I can solve unit rate problems (including unit pricing and constant speeds) I can solve real-world problems using ratio and rate. Solve a unit rate problem by reasoning about tables of equivalent ratios, tape diagrams, double line diagrams, or equations. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent Learning Targets: I can explain how ratio and percent are related. I can find a percent of a quantity as a rate per 100 using ratios. I can solve problems involving finding the whole given a part and the percent by reasoning about tables or equivalent ratios, tape diagrams, double line diagrams, and equations. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Learning Targets: I can convert units to solve real-world problems using multiplication and division in multiple ways (proportions, multiplication, division, and moving decimals). I can convert measurement units using ratio reasoning within customary units. Ratio and Rate Help What's a Ratio? A ratio expresses the relationship between 2 related amounts. For instance, in a recipe, the amount of each ingredient that you add is related to the amounts of the other ingredients used. If you're making bread that has 2 cups of flour and 1 cup of water, you could write this as the ratio 2:1 (2 to 1). This information is helpful if you wanted to double the recipe because you'd know that if you doubled the flour to 4 cups, you'd also need to double the water to 2 cups. Ratios are used in lots of other situations as well. For example, imagine that you're given a picture containing 2 triangles and 7 circles, and asked to write the ratio of triangles to circles. You'd simply count the number of each type of shape and write the ratio, which is 2:7. If you'd been asked to write the ratio of circles to triangles instead, it would be 7:2. It's important to note that ratios can also be written as fractions. For instance, 2:7 would be 2/7 and 7:2 would be 7/2. You'll see why this is critical in the next section. Understanding Unit Rates You can think of a unit rate as yet another way of expressing a ratio. To calculate a unit rate, write the ratio as a fraction, and then divide the top number by the bottom number. This will tell you how many of the units on top there are for each bottom unit. Let's use an example to make this a bit more concrete. Going back to the triangles and circles, recall that we said the ratio of triangles to circles was 2:7 or 2/7. To find the unit rate, solve 2 ÷ 7 to get a decimal that rounds to 0.3. This means there are about 0.3 triangles for every 1 circle. You can also reverse this by stating the unit rate in terms of the ratio of circles to squares (7:2 or 7/2). Since 7 ÷ 2 = 3.5, you can also say there are 3.5 circles for every 1 triangle. Unit rates are commonly used for situations that involve rates of speed. For instance, let's say you can ride your bike 20 miles every 2 hours, which can be represented by the ratio 20:2. To find the unit rate of speed in miles per hour (mph), write the ratio as a fraction and divide: 20/2 = 20 ÷ 2 = 10. This means that you're riding your bike at a speed of 10 mph if you cover 20 miles every 2 hours.
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April 2015
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