Illustrative Math Alignment: Grade 6 Unit 3

July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

May 2014. In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opportunity to apply the concept of currency exchange.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

This is part of a collection of math quizzes on the topic of Equations with Percents.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Percents.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Percents.

Related Resources

Quiz Library

ary">click on this link.

This 45-minute SAT Math prep lesson focuses on ratios, proportions, and percents—key concepts that appear throughout the Problem Solving and Data Analysis domain of the SAT. These topics account for approximately 29% of the SAT Math section and often appear in real-world scenarios involving recipes, maps, discounts, and data comparisons. In this lesson, students will learn to simplify ratios, solve proportions using cross multiplication, calculate percent increase and decrease, and solve percent-based equations involving unknowns.

This 45-minute SAT Math lesson focuses on mastering percents, percent increase and decrease, percent error, and reverse percent problems. Students will learn to convert between fractions, decimals, and percents, and apply key percent formulas to real-world and test-style problems. The lesson includes a warm-up activity, five instructional examples, a five-problem review section, and a 10-question SAT-style quiz with detailed solutions. Students also learn how to recognize percent-related language on the SAT and determine the correct solving strategy.

Topic

Fractions

Description

The term Percent represents a fraction with a denominator of 100, showing a proportion out of 100. Examples include 1% = 1/100, 5% = 5/100, and 25% = 25/100. Percentages are a real-world application of fractions and decimals, often used in data analysis, finance, and everyday calculations.

Topic

Fractions

Description

The term Percent Error describes the difference between an estimated value and the actual value, expressed as a percentage of the actual value. The example provided shows an estimated value of 100 versus an actual value of 107, resulting in a percent error of approximately 6.54%. This concept links fractions, percentages, and error analysis, which are important in measurement and data accuracy.

Topic

Fractions

Description

The term Percentage refers to converting fractions and decimals into their equivalent percentages. Examples include 1/2 = 50%, 0.4 = 40%, and 1/3 ≈ 33.3%. This concept connects fractions, decimals, and percentages, emphasizing their equivalence and usage in various contexts.

Topic

Fractions

Description

The term Percentage Decrease refers to the reduction in value expressed as a percentage of the original value. The example shows a decrease from 75 to 50, calculated as (75 - 50) / 75 * 100%, which equals 33.3%. This term applies percentages to real-world contexts like discounts and data analysis, building on fraction concepts.

Topic

Fractions

Description

The term Percentage Increase refers to the increase in value expressed as a percentage of the original value. The example shows an increase from 25 to 40, calculated as (40 - 25) / 25 * 100%, which equals 60%. This term reinforces the application of percentages and fractions in scenarios like profit and growth analysis.

This is the transcript for the video of same title. Video contents: Why do rivers meander instead of traveling in a straight line? In going from point A to point B, why should a river take the circuitous route it does instead of a direct path? Furthermore, what information can the ratio of the river's length to its straight-line distance tell us? In this segment the geological forces that account for a river's motion are explained. In the process, the so-called Meander Ratio is explored. Students construct a mathematical model of a meandering river using the TI-Nspire. Having built the model, students then use it to generate data to find the average of many Meander Ratios. The results show that on average the Meander Ratio is equal to pi.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

This is the transcript that goes with the video segment entitled Video: Percents: Applications of Percent -- Grade.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Calculating Commissions and Tips.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Calculating Tax.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Calculating the Whole Given a Percent.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Estimating Percents.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Fraction-Percent Conversion.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Multiple Percents.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Percent Decrease.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video: Percents: Percent Increase.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Percent of a Difference.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Percent of a Number.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Percents and Multiples of Numbers.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Probabilities and Percents.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Simple Interest.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Percents: The Percent One Number is of Another.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Percents: Visual Models for Percents.

To see the complete collection of video transcriptsy, click on this link.

To see the complete collection of videos in the Video Library, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorials: Ratios, Proportions, and Percents: Calculating Percents.

To see the complete collection of video transcriptsy, click on this link.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items. Let's look at an example.

Topic

Percents

Description

The video explains how to find the percent of a number by converting percents to fractions or decimals and performing multiplication. Examples include voter turnout in elections, body water composition, and ocean salt concentration. Key concepts include percent conversion and checking calculations using reverse operations. Applications include real-world scenarios such as population statistics and scientific measurements.

Topic

Percents

Description

This video covers calculating percent decreases in scenarios such as price reductions, vehicle depreciation, and cube dimension changes. Examples demonstrate the relationship between linear decreases and their exponential effects on surface area and volume. Applications include consumer goods, real estate, and geometry.

Topic

Percents

Description

The video explains how to calculate simple interest using a formula involving principal, rate, and time. Examples include savings account growth, stock investments, and rare coin valuation. Applications include financial planning and historical item appraisal.

Topic

Percents

Description

This video covers tax calculations for purchases, property, and VAT. Examples include grocery bills, iPad purchases, and real estate property taxes. Applications highlight the importance of understanding tax rates for budgeting and financial management.

Topic

Percents

Description

The video demonstrates calculating tips and commissions using percentages. Examples include restaurant tips, real estate commissions, and catering costs. Applications focus on service industry calculations and earnings management.

Topic

Percents

Description

This video demonstrates how to handle multiple percentage changes applied sequentially, including discounts and price fluctuations. Examples include double-discounted items, stock price variations, and gasoline price changes. Applications emphasize consolidating multiple percents into single calculations for efficiency in financial and retail scenarios.

Topic

Percents

Description

The video explores percent-based probabilities in scenarios like dice rolls. Examples include calculating probabilities of specific outcomes and estimating occurrences over multiple trials. Applications include games of chance and statistical analysis.

Topic

Percents

Description

The video explains the distinction between percent growth and multiple growth. Examples include doubling heights, stock price increases, and oil price changes. Applications emphasize clear understanding of percent versus multiplier concepts in finance and everyday math.

Topic

Percents

Description

This video demonstrates solving for the whole when given a percent and a part. Examples include lemonade recipes, mixing paint, and counting UFOs. Techniques involve writing equations using decimals for percents and solving for the unknown total. Key vocabulary includes part, whole, and equation setup, with practical applications in recipes, art, and problem-solving.

Topic

Percents

Description

The video discusses finding a percent difference when given a part that is not the focus of the percent. Scenarios include bus usage in schools, basketball free throws, and salmon spawning. It emphasizes adjusting percentages for complementary parts before solving equations. Applications highlight real-world uses in demographics, sports, and environmental studies.

Topic

Percents

Description

This video focuses on calculating what percent one number is of another, using ratios and fractions. Examples include ratios in milk composition and inverses such as determining larger percents over 100. Applications show comparisons and understanding proportional relationships in varied contexts.

Topic

Percents

Description

Visual models such as grids and rectangles are used to represent percents and fractions for solving problems like transport usage, car distribution, and sales discounts. Examples include using grids to represent percentages of populations or products. Applications include educational tools and practical estimation.

Topic

Percents

Description

This video teaches estimation techniques for calculating percents without a calculator. Examples include estimating fish populations, race participants, and cyclists. Visual aids like rectangles partitioned into fractions assist with rounding percents for quick calculations. Applications focus on efficient mental math for real-world approximations.

Topic

Percents

Description

The video explores converting fractions to percents for simplified calculations. Examples include determining cargo contents, rose sales, and motorcycle proportions. Fraction-percent equivalence simplifies arithmetic and provides quick insights into ratios and totals. Applications include logistics, commerce, and urban planning.

Topic

Percents

Description

This video applies percents to measure slopes or grades, using ratios for rise over run. Examples include road inclines, ski slopes, and cycling paths. Applications showcase percents in engineering, sports, and transportation, emphasizing their practicality in measuring inclines accurately.

Topic

Percents

Description

The video explains how to calculate percent increases, focusing on changes in school enrollments, asset values, and cube dimensions. Examples highlight the non-linear effects of changes on surface area and volume. Applications include finance, education, and geometry, emphasizing understanding growth trends.

Topic

Ratios

Description

Ratios are connected to percentages in this video. Examples include finding percentages of items in collections. It develops a formula for converting part-to-whole ratios into percentages.

Relevance to the Topic: This video is a crucial resource for understanding the concept of Ratios. It delves into mathematical foundations by exploring how ratios function in real-life scenarios, such as scaling, comparisons, or visual representations. The mathematical principles demonstrated include proportional reasoning, equivalence, and fraction comparisons.