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# Sixth Grade Mathematics Resources

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**Equivalent Expressions with the Distributive Property**

**Source: PBS Learning Media**

**Resource Type: Video**

This animated *Math Shorts* video explains how the distributive property can help students model and create equivalent expressions. In the accompanying classroom activity, students play a quick game where they identify common factors within an expression and work on a series of problems that expand their understanding of how to apply the distributive property.

*Skills: Apply the properties of operations to generate equivalent expressions.*

*Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).*

*Georgia Standards: MGSE6.EE.3, MGSE6.EE.4 *

**One-Variable Equations: How Much Did He Read?**

**Source: PBS Learning Media**

**Resource Type: Video**

Visualize a word problem in multiple ways to develop your problem solving skills. This video focuses on converting a problem with fractions into a one-variable equation and alternately modeling it using unit blocks.

*Skill: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.*

*Georgia Standard: MGSE6.EE.7 *

**Areas of Irregular Shapes: Building Sailboats**

**Source: PBS Learning Media**

**Resource Type: Video**

Learn how wooden boat builders use a variety of mathematical concepts when custom designing their vessels. This video focuses on how area, volume, and measurements of irregular shapes are used in the engineering process, taking math out of the classroom and into real world problem solving.

*Skill: Find area of right triangles, other triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.*

*Georgia Standard: MGSE6.G.1 *

**Source: PBS Learning Media**

**Resource Type: Video**

Use your spatial reasoning skills to calculate the surface area when given a 3D figure. This video focuses on a right rectangular prism and shows you how unit blocks can help you visualize, then calculate the surface area.

*Skill: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems.*

*Georgia Standard: MGSE6.G.4 *

**Source: PBS Learning Media**

**Resource Type: Video**

In this video, learn how to find the greatest common factor of two numbers. Then, see how this can be used to solve problems with large numbers. In the accompanying classroom activity, students learn to find prime factors using factor trees. They then learn how prime factors, a Venn diagram, and simple multiplication can help them find the greatest common factor of two numbers. The lesson challenges students to find the greatest common factor of increasingly large numbers. It also pushes them to think about how prime factors are the building blocks of composite numbers.

*Skill: Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100. *

*Georgia Standard: MGSE6.NS.4 *

**Source: PBS Learning Media**

**Resource Type: Video**

Exploring positive and negative integers and how we use them in the real world. This I <3 Math episode explains the difference between positive and negative numbers and how these numbers can be represented on a number line.

*Skills: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.*

*Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.*

*Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.*

*Georgia Standards: MGSE6.NS.5, MGSE6.NS.6*

**Source: PBS Learning Media**

**Resource Type: Game**

Play a fast-paced video game that involves finding rational numbers on the number line. This game from Math Snacks focuses on using what you know about positive and negative numbers and fractions to place them correctly on the variable number line and retrieve pearls. This resource is part of the Math at the Core: Middle School collection.

*Skills: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.*

*Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.*

*Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.*

*Display numerical data in plots on a number line, including dot plots, histograms, and box plots.*

*Georgia Standards: MGSE6.NS.5, **MGSE6.NS.6, **MGSE6.SP.4*

**Locating Points on the Cartesian Graph**

**Source: PBS Learning Media**

**Resource Type: Interactive**

In this interactive, students use clues and logic to plot the location of aquatic animals on a Cartesian graph that represents the four cardinal directions. The three riddles in the interactive, including one that requires students to understand rate, have randomized values so that students can practice placing points at different locations on the graph. The accompanying classroom activity provides students with a review of locating points on a Cartesian graph. A response sheet helps students work with the interactive. This resource is part of the Math at the Core: Middle School Collection.

*Skills: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.*

*Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.*

*Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.*

*Georgia Standards: MGSE6.NS.6, MGSE6.NS.8*

**Logical Leaps | Rational Numbers on the Number Line**

**Source: PBS Learning Media**

**Resource Type: Interactive**

In this interactive, use logic to solve riddles involving a wallaby jumping contest. Then, place each contestant’s jump—a fraction, mixed number, or decimal between –5 and +5—at the correct point on the number line. Backward jumps are represented by negative numbers and forward jumps by positive numbers. Numbers are randomized so that riddles can be solved and wallabies placed on the number line multiple times. The accompanying classroom activity includes a fraction/decimal concept review and a response sheet to accompany the online work. This resource is part of the Math at the Core: Middle School Collection.

*Skill: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.*

*Georgia Standard: MGSE6.NS.6*

**The Number Line: Rational Numbers and Football**

**Source: PBS Learning Media**

**Resource Type: Interactive**

In this interactive, students add and subtract plays on a football field to practice working with negative and positive integers on the number line. Each set of randomized drives consists of seven to nine plays and ends with a touchdown. Plays are represented with equations. When students place the football at the correct point for each play, the answer to the corresponding equation is automatically filled in. The accompanying activity suggests ways that teachers can integrate the interactive into the classroom setting. This resource is part of the Math at the Core: Middle School Collection.

*Skills: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.*

*Understand ordering and absolute value of rational numbers.*

*Georgia Standards: MGSE6.NS.6, MGSE6.NS.7 *

**Source: PBS Learning Media**

**Resource Type: Video**

This animated Math Shorts video explains absolute value, as demonstrated on the number line and through a real-life example. In the accompanying classroom activity, students watch the video and then play a game in which they move a penny along a number line in positive and negative directions. As they play, they use absolute value to track the total distance that the penny moves. To get the most from the lesson, students should be comfortable determining distance between positive and negative numbers on a number line.

*Skill: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.*

*Georgia Standard: MGSE6.NS.7c *

**Horizontal and Vertical Distances on the Cartesian Graph**

**Source: PBS Learning Media**

**Resource Type: Interactive **

In this interactive, students use logic and mathematical skill to place aquatic animals at locations on a Cartesian graph with cardinal directions. Then, they determine both the vertical and horizontal distances between points. The riddles in the interactive, including one that requires an understanding of rate, have randomized values so that students can practice placing points at different locations and calculating different distances. The accompanying classroom activity provides a review of concepts related to determining the distances between points on a Cartesian graph and a response sheet to help students work with the interactive. This resource is part of the Math at the Core: Middle School Collection.

*Skills: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.*

*Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.*

*Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.*

*Georgia Standards: MGSE6.NS.8, MGSE6.NS.6, MGSE6.G.3*

**Source: PBS Learning Media**

**Resource Type: Interactive Lesson**

In this blended lesson supporting literacy skills, students watch videos and complete interactive activities to learn how much water various activities use and explore ways that they can conserve water resources. Students develop their literacy skills as they explore a mathematics focus on using fractions to convert units of measurement. During this process, they read informational text, learn and practice vocabulary words, and explore content through videos and interactive activities.

*Skill: Given a conversion factor, use ratio reasoning to convert measurement units within one system of measurement and between two systems of measurements (customary and metric); manipulate and transform units appropriately when multiplying or dividing quantities.*

*Georgia Standard: MGSE6.RP.3d *

**Source: PBS Learning Media**

**Resource Type: Video**

Watch and listen as the assistant general manager of a major league baseball team explains how he uses math in this video from KAET, Arizona PBS.

*Skills: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.*

*Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.*

*Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.*

*Summarize numerical data sets in relation to their context.*

*Georgia Standards: MGSE6.SP.1, MGSE6.SP.2, MGSE6.SP.3, MGSE6.SP.5*

**Animals Offer Hope to Cancer Patients**

**Source: PBS Learning Media**

**Resource Type: Video with Lesson**

In this video and accompanying lesson from SciTech Now, students will consider how qualitative data is collected and practice analyzing datasets inspired by research on whether a media program from the San Diego Zoo Kids program has a positive impact on kids who watch it while receiving medical care.

*Skills: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.*

*Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.*

*Summarize numerical data sets in relation to their context.*

*Georgia Standards: MGSE6.SP.2, MGSE6.SP.3, MGSE6.SP.5*

**The Lowdown | Real-World Data Sets: Low- and High-Paying Jobs**

**Source: PBS Learning Media**

**Resource Type: Interactive**

In this interactive, two infographics display the 10 lowest- and highest-paid jobs in the United States in 2012, based on figures provided by the US Bureau of Labor Statistics. In the accompanying classroom activity, students examine the data in the interactive to determine how different the top of the pay scale is from the bottom. Given salary ranges for positions on the top and bottom of the corporate ladder, students construct and analyze box plots to see just how wide the disparity is. This resource is part of the Math at the Core: Middle School Collection.

*Skills: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.*

*Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.*

*Display numerical data in plots on a number line, including dot plots, histograms, and box plots.*

*Summarize numerical data sets in relation to their context.*

*Georgia Standards: MGSE6.SP.2, MGSE6.SP.3, MGSE6.SP.4, MGSE6.SP.5*

**Source: PBS Learning Media**

**Resource Type: Interactive**

Flip a virtual coin to introduce or explore the concept of probability. This interactive exercise focuses on determining probabilities associated with repeated coin tosses and building tree diagrams to take math out of the classroom and into the real world. This resource is part of the Math at the Core: Middle School Collection.

*Skill: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.*

*Georgia Standard: MGSE6.SP.4*