Illustrative Math Alignment: Grade 6 Unit 3

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

Topic

Ratios and Fractions

Description

In many scenarios, ratios are expressed using whole numbers, yet there are instances, like in recipes, where fractions play a significant role. This example illustrates a ratio involving fractions and demonstrates how to convert it into a ratio with whole numbers. Students will engage in understanding the process of converting these fractions to whole numbers, enhancing their comprehension of ratios and their practical applications such as cooking or mixing. The focus is on the fundamental skill of fraction conversion and applying it in a ratio context.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

This is part of a collection of math examples that focus on ratios and rates.

February 2023. In this issue of Math in the News we look at NFL statistics for the number of concussions. The NFL now tracks concussion, and this is an opportunity to analyze this data and draw conclusions.

Note: The download is a PPT file.

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February 2012. In this issue we look at unemployment statistics from the Bureau of Labor Statistics.

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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.

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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.

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Topic

Multiplication and Division

Description

A Division Strategy involves deciding how to divide two numbers, often using visual aids. For example, 18 ÷ 3 = 6 is illustrated using arrays or equal groups to find the quotient. Strategies help break down division problems into steps. This term focuses on methods to solve division, aiding problem-solving and conceptual understanding.

Topic

Multiplication and Division

Description

A multiplication strategy involves deciding how to multiply two numbers. For example, 4 • 5 = 20 can use an array for support. This connects multiplication reasoning with tools like arrays and mental strategies.

Topic

Addition and Subtraction

Description

Subtraction Strategy: Choosing how to subtract two or more numbers effectively. The example illustrates counting down on a number line for 10 - 3 = 7. This term emphasizes strategic thinking in subtraction, aiding problem-solving and mental math skills.

Topic

Addition and Subtraction

Description

Definition: Subtraction Strategy: Choosing how to subtract two or more numbers effectively. The example illustrates counting down on a number line for 10 - 3 = 7. This term emphasizes strategic thinking in subtraction, aiding problem-solving and mental math skills.

Topic

Addition and Subtraction

Description

An Addition Strategy involves choosing how to add two or more numbers, such as using a number line. In the example, 5 + 2 = 7 is calculated by moving two steps forward on a number line starting from 5. Teaching strategies for addition fosters problem-solving skills and offers multiple approaches to understanding arithmetic operations.

Topic

Addition and Subtraction

Another factor in the mortgage crisis was the use of adjustable rate mortgages Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Applications: Data Analysis, Segment 4: What is an Adjustable Rate Mortgage?]: https://www.media4math.com/library/algebra-applications-data-analysis-segment-4-what-adjustable-rate-mortgage

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 solving problems involving unit rates, dimensional analysis, and unit conversions. Students will learn how to calculate speed, cost per item, and population density, as well as how to convert between units using proportion and dimensional analysis. The lesson also includes multi-step word problems that combine rate calculations with percent-based reasoning—realistic scenarios frequently tested on the SAT.

Topic

Linear Functions

Description

The term is "Rate of Change," defined as the slope, interpreted as the rate at which the dependent variable changes relative to the independent variable. An example is speed as a rate of change of distance over time. This term highlights the application of slope in real-world scenarios, making the concept more tangible and relatable.

This is the transcript for the video of same title. Video contents: Another factor in the mortgage crisis was the use of adjustable rate mortgages. Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis.

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 to the video entitled "Video Tutorial: Counting Strategies."

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This is the transcript that goes with the video segment entitled Video Tutorial: Ratios and Rates: Converting Measurement Units.

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This is the transcript that goes with the video segment entitled Video Tutorial: Ratios and Rates: Rates and Slopes of Lines.

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This is the transcript that goes with the video segment entitled Video Tutorial: Ratios and Rates: Rates from Data.

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This is the transcript that goes with the video segment entitled Video Tutorials: Ratios and Rates: Ratios and Decimals.

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

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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.

What Are Ratios?

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

Topic

Counting

Description

This video combines skip counting and counting on strategies for faster and more accurate counting. Examples include determining total tennis balls, milk gallons, and shoes. Vocabulary includes skip counting, combinations, and accuracy, emphasizing real-world problem-solving applications.

Topic

Ratios

Description

This video demonstrates calculating rates from data sets, focusing on patterns like distance-time relationships and wages. Examples include determining car speeds, hourly wages, and unit costs of gasoline. Data tables are used to visualize and compute rates.

Topic

Ratios

Description

Rates are linked to slopes in linear functions. The video explores calculating rates of change for graphs of speed, savings growth, and loan repayment. It highlights using the slope formula to interpret and solve practical problems.

Topic

Ratios

Description

This video covers converting units using rates, with examples like speed conversion, currency exchange, and calculating seconds in a year. It emphasizes multiplication by conversion rates to transition between units effectively.

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.

Topic

Ratios

Description

This video illustrates converting ratios to percents using visual aids like area models and grids. Examples include determining percentages of colored eggs, fruit types, and combinations of colored lights.

Topic

Ratios

Description

The video explores working with ratios involving decimals, such as finding unit costs or recycling rates. Scientific notation and multi-step conversions are used to calculate speeds of spacecraft like Voyager I.

Topic

Ratios

Description

The video covers practical applications of ratios for measuring slopes of roofs and ramps. Examples include comparing roof pitches, calculating base lengths of roofs, and determining ramp heights. Ratios provide clarity for gradual slopes.

Topic

Ratios

Description

The video focuses on unit rates, where the denominator equals one. It includes practical examples like finding the cost per pound of bananas or determining hourly wages. Applications extend to conversions and scaling calculations for various real-world tasks.

Topic

Topic: Inequalities

Topic

Topic: Inequalities

Topic

Equations

Description

The video investigates the geometry of river meanders using the concept of the meander ratio, calculated as the ratio of a river’s sinuous length to its straight-line length. It uses a TI-Nspire calculator to simulate river paths and compute ratios. Key vocabulary includes meander ratio, sinuous length, and geometric modeling. Applications highlight the mathematical modeling of natural phenomena and the occurrence of pi in nature.

This is part of a collection of math worksheets on the topic of unit rates.

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