This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.
Unit 2: Introducing Ratios
Lesson 10: Comparing Situations by Examining Ratios
In previous lessons, students learned that if two situations involve equivalent ratios, we can say that the situations are described by the same rate. In this lesson, students compare ratios to see if two situations in familiar contexts involve the same rate. The contexts and questions are:
Two people run different distances in the same amount of time. Do they run at the same speed?
Two people pay different amounts for different numbers of concert tickets. Do they pay the same cost per ticket?
Two recipes for a drink are given. Do they taste the same?
In each case, the numbers are purposely chosen so that reasoning directly with equivalent ratios is a more appealing method than calculating how-many-per-one and then scaling. The reason for this is to reinforce the concept that equivalent ratios describe the same rate, before formally introducing the notion of unit rate and methods for calculating it. However, students can use any method. Regardless of their chosen approach, students need to be able to explain their reasoning (MP3) in the context of the problem.
Students must calculate the volume of a cone in this real world task.
Unit 3: Unit Rates and Percentages
Lesson 5: Comparing Speeds and Prices
Previously, students found and used rates per 1 to solve problems in a context. This lesson is still about contexts, but it's more deliberately working toward the general understanding that when two ratios are associated with the same rate per 1, then they are equivalent ratios. Therefore, to determine whether two ratios are equivalent, it is useful to find and compare their associated rates per 1. In this lesson, we also want students to start to notice that dividing one of the quantities in a ratio by the other is an efficient way to find a rate per 1, while attending to the meaning of that number in the context (MP2).
Calculating rates per 1 is also a common way to compare rates in different situations. For example, suppose we find that one car is traveling 30 miles per hour and another car is traveling 40 miles per hour. The different rates tell us not only that the cars are traveling at different speeds, but which one is traveling faster. Similarly, knowing that one grocery store charges $1.50 per item while another charges $1.25 for the same item allows us to select the better deal even when the stores express the costs with rates such as “2 for $3” or “4 for $5.”
This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.
The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task.
The purpose of the task is for students to compare signed numbers in a real-world context.
The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together.
This short video and interactive assessment activity is designed to teach third graders about comparing numbers using greater than and less than.
This short video and interactive assessment activity is designed to teach fourth graders about comparing values of two numbers.
Many students will not know that when comparing two quantities, the percent decrease between the larger and smaller value is not equal to the percent increase between the smaller and larger value. Students would benefit from exploring this phenomenon with a problem that uses smaller values before working on this one.
The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one.
This short video and interactive assessment activity is designed to teach second graders about comparing and writing decimal inequalities in word problems.
This short video and interactive assessment activity is designed to teach third graders about comparing the values of numbers to 1,000 - word problems.
In this task students are required to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.
In this task students are required to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.
In this video from Cyberchase, Harry must score a total of 50 points in various events to qualify for the Northern Hemisphere games in New Orleans.
An interactive applet and associated web page that demonstrate the concept of complementary angles (angles that add to 90 degrees). The applet shows two angles. You can drag the endpoints of each angle and the other angle changes so that they always add to 90 degrees. They are drawn in such a way that it is visually obvious that together they form a right angle, although they are separate on the page. The angle measure readouts can be turned off for class discussions. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
This short video and interactive assessment activity is designed to teach fourth graders about finding and completing the number patterns.
This short video and interactive assessment activity is designed to teach third graders about finding and completing the number patterns.