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6th Grade Unit 3: Ratios

Page history last edited by Brigit Minden 11 months ago

6th Grade Unit 3: Ratios
Unit Driving Question How can ratios be applied in real-world situations? Essential Questions How can we compare quantities? How do we use the relationship between ratio and rates to solve problems? How and when are percents useful in real-world scenarios? Big Ideas Ratios are used to compare quantities. Unit rates compare quantities with different units where the second quantity in the comparison is one. A percent represents a ratio of a number to 100.
Useful Websites
The following apps, websites, and smartboard lessons can be used throughout the unit, as needed, during small groups, lessons, to reinforce standards. They are also useful for students who may need reinforcement, remediation, or differentiation. Virtual Nerd: Virtual Nerd provides video tutorials as a supplemental resource for both students and teachers. Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard so that students may study at their own pace both in and outside of the classroom. Mr.Naussbaum.com: MrNussbaum.com offers interactive games specifically designed to pinpoint one or several essential concepts to make the learning process more interactive and enjoyable. Interactive Sites for Education: These interactive activities work great on your interactive whiteboard, computer, laptop, or Chromebook for whole group or small group instruction or use in the computer lab or at home for individual learning. Most of these activities are Flash-based. This means that they will NOT work on iPads unless you are running an app that allows Flash to play such as Puffin. Kahoot: Kahoots are fun, learning games best played in a group setting. Players answer questions on individual devices (Ex: Chromebook, iPads) while games are displayed on a shared screen (Ex: Smartboard or TV). Choose a Kahoot to match your desired skill or create your own. Zapzapmath: Zapzapmath has over 150 math lessons designed to incorporate higher order thinking skills in the fields of creation, evaluation, and analysis. This is combined into a game-based system of fun math learning. Mr.Anker Tests: Interactive activities and games for dozens of math skills. Most of these activities run on Flash.

Launch Task

1 Lesson

What Kind and How Many? (Open Up): This Warm-Up from the lesson Introducing Ratios and Ratio Language listed under Big Idea 1 provides students with a set of tiles and asks them to sort the tiles in different ways. You can extend this task by asking students to compare categories using the number of items in each category they create.

Big Ideas for Development Lessons

3-4 Weeks (approximately 1 week per big idea)

Big Idea 1: Ratios are used to compare quantities.

OAS-M: 6.N.3.1, 6.N.3.3, 6.A.1.2

Key Resources

Introducing Ratios and Ratio Language (Open Up): For this lesson, the teacher and students will need to bring a collection of items to class, such as trading cards or coins. The Warm-Up for this task is used as the Initial Task for this unit. In Activity 1, students will sort the teacher’s collection of items and discuss different ways to write a ratio. In Activity 2, students will determine ratios for their own collections. The Cool-Down asks students to write two ratios for the given picture.
Color Mixtures (Open Up): In the Warm-Up, students participate in a number talk about how changing a factor affects the product of two numbers. In Activity 1, students investigate mixtures and equivalent ratios using blue and yellow food coloring and water. A digital version of this experiment is also available. Activity 2 asks students to determine which student in the given scenario has created the perfect purple water based on their experience from Activity 1. The Cool-Down ends the lesson by having students answer questions about a recipe for orange water. This would be a good way to check for understanding.
Equivalent Ratios (Open Middle): Students create equivalent ratios for 2:3 using only the whole numbers 1 through 9.
Representing Ratios with Tables (Open Up): In the Warm-Up, students analyze a growing pattern. Activity 2 uses ratio tables to investigate equivalent ratio used to make a trail mix recipe. This activity can be extended by having students plot the points from the table on a graph to find other equivalent ratios. The Cool-Down provides another opportunity to complete a ratio table using measurements from a cookie recipe.
Comparing Situations by Comparing Ratios (Open Up): The Warm-Up, Activity 1, and Activity 2 asks students to compare ratios in a given situation using what they have learned about equivalent ratios. The level of difficulty increases with each task. The method for comparing ratios in the Cool-Down is similar to Activity 2 meaning that students must find an equivalent ratio for both ratios in the given situation in order to compare them. All of these tasks provide double number lines to represent ratios in the solutions, but ratios table may also be used as a representation.
Using Proportional Reasoning (MARS): Students reason about mixtures and concentrations using part-to-part and part-to-whole ratios. This activity includes two assessment tasks to assess a student’s understanding of mixtures and concentrations and card sort.
Mix it Up: Making Sense of Percent Concentrations (NCTM): In this activity, students will adequately estimate percent concentration in final mixes based on percents in component mixtures, develop a formula and strategy for calculating percent concentration in a final mix based on the component mixes, critique the correctness of their own and other groups' formulas and strategies, and solve related word problems.

Big Idea Probe

Ratios Probe

Evidence of Understanding

Recognize that ratios can be expressed using multiple representations.

Recognize that ratios can represent part-to-part and part-to-whole relationships between quantities.

Describe the similarities and difference between mixture and concentration using ratios.

Use tables and graphs to investigate problems involving ratios.

Use equivalent fractions to compare ratios.

Discuss the use of multiplicative comparison when working with ratios.

Big Idea 2: Unit rates compare quantities with different units where the second quantity in the comparison is one.
OAS-M: 6.N.3.2, 6.N.3.3, 6.GM.4.1, 6.GM.4.2
Key Resources Interpreting Rates (Open Up): In the Warm-Up, students get to brainstorm in a group about phrases they have encountered that compare “something per something.” In Activity 1, students investigate the two possible unit rates for a given ratio. Activity 2 introduces the term “unit rate” and students calculate both unit rates for each scenario. The Cool-Down has students complete a table and explain the meaning of the unit rates in the table. Solving Rate Problems (Open Up): In the Warm-Up, students are asked to identify what fractional part of a whole is shaded on a 100 grid. Activity 1 is a card sort activity in which students determine unit rates to investigate good and bad deals. In Activity 2, students convert between customary and metric units. It may be best to complete this activity after students have more experience converting units in the lesson, Converting Units. The Cool-Down provides another problem for students to determine the best deal. Anchoring Units of Measurement (Open Up): In Activity 1, students are given string to estimate standard units of length including 1 centimeter, 1 foot, 1 inch, 1 meter, and 1 yard. Activity 2 is a card sort in which students match units of length, volume, and weights or mass to common benchmarks used to estimate those units of measure. The Cool-Down has students choose the appropriate unit of measure for three given situations. What’s Your Rate? (Illuminations): Students use unit rates and unit conversions to make predictions based on data collected by the students. Click Battle (Desmos): Students will explore unit rate through this online activity. Desmos Click Bots are battling it out to see who can click the most in a specified time frame. Students decide who would win based on bots given rates. Big Idea Probe Unit Rates Probe	Evidence of Understanding Recognize and apply unit rates in real-world situations. Identify the unit rate for a given ratio using tables and graphs. Use unit rates to compare real-world relationships. Explain unit rate as it relates to ratios.
Big Idea 3: A percent represents a ratio of a number to 100.
OAS-M: 6.N.3.1, 6.N.3.3, 6.N.1.3, 6.N.1.4, 6.A.3.1, 6.A.3.2
Key Resources What are Percentages? (Open Up): The Warm-Up asks students to think about problems involving dollars and cents to prepare them for the activity included in this lesson. In the Activity, students use the value of U.S. coins to understand the concept of percent. The Cool-Down asks students to apply what they know about percents in relation to the value of U.S. coins. Percentages (Open Middle): Students try to make a correct sentence using percents and numbers 0 through 9, at most one time each. Related Percentages (Open Middle): Students try to make a correct number sentences that are related using percents and numbers 0 through 9 as many times as they want. Exam Scores (Illustrative Mathematics): In this task, students use percents to answer questions about exam scores. Percent of a Number (GeoGebra): This applet helps students develop a method for finding a percent of a number by allowing students to locate the percentage on a number line. Big Idea Probe Percentages Probe	Evidence of Understanding Recognize a percent as a part-to-whole ratio in which the whole is 100. Explore applications of percents in real-world situations. Use equivalences between fractions, decimals, and percents to solve real-world problems. Use equations to solve real-world problems involving percents.
Unit Closure 1 Week (includes time for probes, re-engagement, and assessment)
Painting a Room (Open Up): In this lesson, students use what they know about ratios, unit rates, converting units, and percentages to solve a problem about painting a room. On the Bus Performance Assessment (covers 6.N.3.1, 6.N.3.3, and 6.N.3.4): For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.