This resource is intended for students to work with a partner to determine equivalent fractions to find the sum. Students need to have a background knowledge of connecting fractions and decimals, along with equivalent fractions prior to this activity. It may be helpful to have each row be printed on different colored paper, so it may help organize their thinking.

This resource is part of Tools4NCTeachers.

Math games are fun, motivating, and provide opportunities for students to build number concepts, reasoning, and fluency. These games may be used as math stations or as whole group learning opportunities. This file contains directions and materials for Cluster 2 math games.

Distributions and Variability

Type of Unit: Project

Prior Knowledge

Students should be able to:

Represent and interpret data using a line plot.
Understand other visual representations of data.

Lesson Flow

Students begin the unit by discussing what constitutes a statistical question. In order to answer statistical questions, data must be gathered in a consistent and accurate manner and then analyzed using appropriate tools.

Students learn different tools for analyzing data, including:

Measures of center: mean (average), median, mode
Measures of spread: mean absolute deviation, lower and upper extremes, lower and upper quartile, interquartile range
Visual representations: line plot, box plot, histogram

These tools are compared and contrasted to better understand the benefits and limitations of each. Analyzing different data sets using these tools will develop an understanding for which ones are the most appropriate to interpret the given data.

To demonstrate their understanding of the concepts, students will work on a project for the duration of the unit. The project will involve identifying an appropriate statistical question, collecting data, analyzing data, and presenting the results. It will serve as the final assessment.

Students will apply what they have learned in previous lessons to analyze and draw conclusions about a set of data. They will also justify their thinking based on what they know about the measures (e.g., I know the mean is a good number to use to describe what is typical because the range is narrow and so the MAD is low.).Students analyze one of the data sets about the characteristics of sixth grade students that was collected by the class in Lesson 2. Students construct line plots and calculate measures of center and spread in order to further their understanding of the characteristics of a typical sixth grade student.Key ConceptsNo new mathematical ideas are introduced in this lesson. Instead, students apply the skills they have acquired in previous lessons to analyze a data set for one attribute of a sixth grade student. Students make a line plot of the data and find the mean, median, range, MAD, and outliers. They use these results to determine a typical value for their data.Goals and Learning ObjectivesDescribe an attribute of a typical sixth grade student using line plots and measures of center (mean and median) and spread (range and MAD).Justify thinking about which measures are good descriptors of the data set.

In this lesson, students are given criteria about measures of center, and they must create line plots for data that meet the criteria. Students also explore the effect on the median and the mean when values are added to a data set.Students use a tool that shows a line plot where measures of center are shown. Students manipulate the graph and observe how the measures are affected. Students explore how well each measure describes the data and discover that the mean is affected more by extreme values than the mode or median. The mathematical definitions for measures of center and spread are formalized.Key ConceptsStudents use the Line Plot with Stats interactive to develop a greater understanding of the measures of center. Here are a few of the things students may discover:The mean and the median do not have to be data points.The mean is affected by extreme values, while the median is not.Adding values above the mean increases the mean. Adding values below the mean decreases the mean.You can add values above and below the mean without changing the mean, as long as those points are “balanced.”Adding values above the median may or may not increase the median. Adding values below the median may or may not decrease the median.Adding equal numbers of points above and below the median does not change the median.The measures of center can be related in any number of ways. For example, the mean can be greater than the median, the median can be greater than the mean, and the mode can be greater than or less than either of these measures.Note: In other courses, students will learn that a set of data may have more than one mode. That will not be the case in this lesson.Goals and Learning ObjectivesExplore how changing the data in a line plot affects the measures of center (mean, median).Understand that the mean is affected by outliers more than the median is.Create line plots that fit criteria for given measures of center.

This single player game helps students develop an understanding of the partial quotient strategy for division. It can also help students develop and understanding of division with and without remainders.

Lesson plan where students are asked to consider how to draw a perfect circle, and learn to do so using a line segment called a radius. They also learn to fold a circle in two directions symmetrically to find its center. This activity is motivated by a CYBERCHASE episode in which the CyberSquad set out to rescue a magic ring from Hacker and deposit it in a safe place.

In this video segment from Cyberchase, the CyberSquad is trapped in one of the Spheres of Fears, and they are trying to get through a gate to escape. The key to the gate is locked inside a can, and in order to access the key they must attach the correct label to the can. After guessing incorrectly on the first try, the CyberSquad decides to take some measurements to find the correct label. Using two circles nearby, they compare the diameter of each circle to its circumference. They realize there is a special relationship between the circumference of a circle and the length of its diameter. Teaching tips are also provided that discuss frame, focus and follow-up suggestions for using this video in a math lesson.

This resource is part of Tools4NCTeachers.

This file contains easy to implement math center ideas for Kindergarten, Cluster 3.

This resource is part of Tools4NCTeachers.

Math games are fun, motivating, and provide opportunities for students to build number concepts, reasoning, and fluency. These games may be used as math stations or as whole group learning opportunities. This file contains directions and materials for Cluster 3 math games.

This resource is part of Tools4NCTeachers.

Math games are fun, motivating, and provide opportunities for students to build number concepts, reasoning, and fluency. These games may be used as math stations or as whole group learning opportunities. This file contains directions and materials for Cluster 3 math games.

This resource is part of Tools4NCTeachers.

Math games are fun, motivating, and provide opportunities for students to build number concepts, reasoning, and fluency. These games may be used as math stations or as whole group learning opportunities. This file contains directions and materials for Cluster 4 math games.

This resource is from Tools4NCTeachers.Math games are fun, motivating, and provide opportunities for students to build number concepts, reasoning, and fluency. These games may be used as math stations or as whole group learning opportunities. This file contains directions and materials for Cluster 5 math games

This resource is from Tools4NCTeachers.Math games are fun, motivating, and provide opportunities for students to build number concepts, reasoning, and fluency. These games may be used as math stations or as whole group learning opportunities. This file contains directions and materials for Cluster 6 math games

This resource is from Tools4NCTeachers.Students need distributed practice of newly-learned skills to develop fluency, build proficiency, and deepen understanding. This file contains directions for activities which may be used as Cluster 4 games or math stations.

This resource is from Tools4NCTeachers.Students need distributed practice of newly-learned skills to develop fluency, build proficiency, and deepen understanding. This file contains directions for activities which may be used as Cluster 6 games or math stations.

This resource is from Tools4NCTeachers.Students need distributed practice of newly-learned skills to develop fluency, build proficiency, and deepen understanding. This file contains directions for activities which may be used as Cluster 6 games or math stations.

This geometry concentation game is from Tools4NCTeachers.Math games are fun, motivating, and provide opportunities for students to build number concepts, reasoning, and fluency. This game may be used as math stations or as whole group learning opportunity.

This resource is from Tools4NCTeachers.  In this game, students toss pennies and dimes onto a target on the floor.  After tossing their coins, they determine the total value of the coins landing on their target.  The student with the greater amount wins.