**Title:** How Far Can You Leap?

**Description:**
This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?"
This is a College- and Career-Ready Standards showcase lesson plan.
**Standard(s): **

[MA2015] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7-RP1]

**Subject:**Mathematics (6 - 7)

**Title:**How Far Can You Leap?

**Description:**This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?" This is a College- and Career-Ready Standards showcase lesson plan.

**Title:** Getting into the Electoral College

**Description:**
In this unit of 3 lessons from Illuminations, students are engaged in activities involving percentages, ratios, and area, with a focus throughout on building problem-solving and reasoning skills. They are designed to be used individually to fit within curriculum being covered at the time of an election. Additionally, the lesson extensions include many ideas for interdisciplinary activities and some possible school-wide activities.
**Standard(s): **

[MA2015] ALC (9-12) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama)

**Subject:**Mathematics

**Title:**Getting into the Electoral College

**Description:**In this unit of 3 lessons from Illuminations, students are engaged in activities involving percentages, ratios, and area, with a focus throughout on building problem-solving and reasoning skills. They are designed to be used individually to fit within curriculum being covered at the time of an election. Additionally, the lesson extensions include many ideas for interdisciplinary activities and some possible school-wide activities.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** A Swath of Red

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate in the 2000 presidential election using a grid overlay. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States.
**Standard(s): **

[MA2015] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7-SP2]

**Subject:**Mathematics

**Title:**A Swath of Red

**Description:**In this lesson, one of a multi-part unit from Illuminations, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate in the 2000 presidential election using a grid overlay. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Inclined Plane

**Description:**
In this multiple-day activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved.
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Mathematics,Science

**Title:**Inclined Plane

**Description:**In this multiple-day activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Paper Pool: Analyzing Numeric and Geometric Patterns

**Description:**
This page provides an overview of a four-lesson Illuminations unit plan titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit plan provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. This investigation includes student resources for the Paper Pool project, preparation notes, answers, and a holistic-by-category scoring rubric with guidelines for how it can be used to assess the project. Samples of two students' work and comments from a teacher accompany the suggested rubric. This resource references the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns,'' and '' Go the Distance.''
**Standard(s): **

[MA2015] (6) 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. [6-RP3]

**Subject:**Mathematics

**Title:**Paper Pool: Analyzing Numeric and Geometric Patterns

**Description:**This page provides an overview of a four-lesson Illuminations unit plan titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit plan provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. This investigation includes student resources for the Paper Pool project, preparation notes, answers, and a holistic-by-category scoring rubric with guidelines for how it can be used to assess the project. Samples of two students' work and comments from a teacher accompany the suggested rubric. This resource references the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns,'' and '' Go the Distance.''

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** First Class First? Using Data to Explore the Tragedy of the Titanic

**Description:**
In this Science NetLinks lesson, students analyze and interpret data related to the crew and passengers of the Titanic. They draw conclusions to better understand the people who were lost or saved as a result of the disaster, and whether or not social status affected the outcome.
**Standard(s): **

[MA2015] AL1 (9-12) 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3]

**Subject:**Mathematics, Social Studies

**Title:**First Class First? Using Data to Explore the Tragedy of the Titanic

**Description:**In this Science NetLinks lesson, students analyze and interpret data related to the crew and passengers of the Titanic. They draw conclusions to better understand the people who were lost or saved as a result of the disaster, and whether or not social status affected the outcome.

**Thinkfinity Partner:**Science NetLinks

**Grade Span:**9,10,11,12

**Title:** Linking Length, Perimeter, Area, and Volume

**Description:**
In this four-lesson unit, from Illuminations, students explore ratio, proportion, scale factor and similarity using perimeter, area, volume and surface area of various rectangular shapes. Students use an online interactive applet to explore how the perimeters, areas, and side lengths of similar rectangles are related.
**Standard(s): **

[MA2015] (7) 2: Recognize and represent proportional relationships between quantities. [7-RP2]

**Subject:**Mathematics

**Title:**Linking Length, Perimeter, Area, and Volume

**Description:**In this four-lesson unit, from Illuminations, students explore ratio, proportion, scale factor and similarity using perimeter, area, volume and surface area of various rectangular shapes. Students use an online interactive applet to explore how the perimeters, areas, and side lengths of similar rectangles are related.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Purple Prisms

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students investigate rectangular prisms using an online, interactive applet. They manipulate the scale factor that links two three-dimensional rectangular prisms to learn about edge lengths and surface area relationships.
**Standard(s): **

[MA2015] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7-G1]

**Subject:**Mathematics

**Title:**Purple Prisms

**Description:**In this lesson, one of a multi-part unit from Illuminations, students investigate rectangular prisms using an online, interactive applet. They manipulate the scale factor that links two three-dimensional rectangular prisms to learn about edge lengths and surface area relationships.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Can It Be?

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. They listen to the story The Phantom Tollbooth, by Norton Juster, and then explore and interpret the concept of averages.
**Standard(s): **

[ELA2015] (8) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of Grades 6-8 text complexity band independently and proficiently. [RL.8.10]

**Subject:**Language Arts,Mathematics

**Title:**Can It Be?

**Description:**In this lesson, one of a multi-part unit from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. They listen to the story The Phantom Tollbooth, by Norton Juster, and then explore and interpret the concept of averages.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** How Much is a Million?

**Description:**
This lesson focuses students on the concept of 1,000,000. It allows students to see first-hand the sheer size of a million while at the same time providing students with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and mass of 1,000,000 grains of rice.
**Standard(s): **

[MA2015] (8) 6: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. [8-EE4]

**Subject:**Language Arts,Mathematics

**Title:**How Much is a Million?

**Description:**This lesson focuses students on the concept of 1,000,000. It allows students to see first-hand the sheer size of a million while at the same time providing students with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and mass of 1,000,000 grains of rice.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Ratios

**Description:**
This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for surface area and volume when comparing a model to a full-size object.
**Standard(s): **

[MA2015] (6) 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. [6-RP3]

**Subject:**Mathematics

**Title:**Ratios

**Description:**This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for surface area and volume when comparing a model to a full-size object.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** The Ratio of Circumference to Diameter

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula.
**Standard(s): **

[MA2015] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7-G4]

**Subject:**Mathematics

**Title:**The Ratio of Circumference to Diameter

**Description:**In this lesson, one of a multi-part unit from Illuminations, students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Constant Dimensions

**Description:**
In this Illuminations lesson, students measure the length and width of a rectangle using both standard and non-standard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising.
**Standard(s): **

[MA2015] (7) 10: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7-EE4]

**Subject:**Mathematics

**Title:**Constant Dimensions

**Description:**In this Illuminations lesson, students measure the length and width of a rectangle using both standard and non-standard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Capture - Recapture

**Description:**
In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of tagged items to the number of items in a sample is the same as the ratio of tagged items to the total population.
**Standard(s): **

[MA2015] AL2 (9-12) 14: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* [A-SSE4]

**Subject:**Mathematics

**Title:**Capture - Recapture

**Description:**In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of tagged items to the number of items in a sample is the same as the ratio of tagged items to the total population.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8,9,10,11,12

**Title:** Bean Counting

**Description:**
By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The number-sense of recognizing equivalent fractions is useful when students study slope and proportions.
**Standard(s): **

[MA2015] ALC (9-12) 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama)

**Subject:**Mathematics

**Title:**Bean Counting

**Description:**By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The number-sense of recognizing equivalent fractions is useful when students study slope and proportions.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8,9,10,11,12

**Title:** How Can Math Help You Cook?

**Description:**
You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy!
**Standard(s): **

[MA2015] (6) 6: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. [6-NS3]

**Subject:**Cross-Disciplinary - Informal Education , Health - Nutrition , Mathematics - Applied Mathematics , Mathematics - Arithmetic , Mathematics - Measurement , Science - Biological and Life Sciences , Science - Biology , Science - Chemistry , Science - General Science , Adult & Family Literacy - Lifeskills , Informal Education - Health/Wellness/Nutrition/Cooking

**Title:**How Can Math Help You Cook?

**Description:**You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy!

**Thinkfinity Partner:**Wonderopolis

**Grade Span:**K,PreK,1,2,3,4,5

**Title:** How Can Math Help You Cook?

**Description:**
You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy!
**Standard(s): **

[MA2015] (6) 6: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. [6-NS3]

**Subject:**Cross-Disciplinary - Informal Education , Health - Nutrition , Mathematics - Applied Mathematics , Mathematics - Arithmetic , Mathematics - Measurement , Science - Biological and Life Sciences , Science - Biology , Science - Chemistry , Science - General Science , Adult & Family Literacy - Lifeskills , Informal Education - Health/Wellness/Nutrition/Cooking

**Title:**How Can Math Help You Cook?

**Description:**You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy!

**Thinkfinity Partner:**Wonderopolis

**Grade Span:**K,PreK,1,2,3,4,5

**Title:** Calculation Nation

**Description:**
Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.
**Standard(s): **

[MA2015] DM1 (9-12) 1: Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers. (Alabama)

**Subject:**Mathematics

**Title:**Calculation Nation

**Description:**Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8,9