Unit 3 Ratios and Rates Math 6

Transcription

1 Number of Days: 20 11/27/17 12/22/17 Unit Goals Stage 1 Unit Description: Students study the concepts and language of ratios and unit rates. They use proportional reasoning to solve problems. In particular, students solve ratio and rate problems using tape diagrams, tables of equivalent ratios, double number line diagrams, and graphs. Materials: unit cubes, centimeter cubes, graph paper, calculators Standards for Mathematical Practice SMP 1 Make sense of problems and persevere in solving them. SMP 2 Reason abstractly and quantitatively. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. SMP 8 Look for and express regularity in repeated reasoning. Standards for Mathematical Content Clusters Addressed [m] 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. Transfer Goals Students will be able to independently use their learning to Make sense of never-before-seen problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Making Meaning UNDERSTANDINGS Students will understand that Ratio concepts and ratio reasoning are used to solve real-world problems. When two quantities are related proportionally, the ratio of one quantity to the other is constant as the numerical values of both quantities change by the same factor. Ratios and rates can be represented visually. KNOWLEDGE Students will know The definition of academic vocabulary words, such as ratio, rate, unit rate, ratio tables, tape diagrams, double number line diagrams, percent, unit analysis, and conversion factor. A ratio is a comparison of two quantities. A rate is a specific kind of ratio that compares two quantities that have different units. A unit rate refers to the numerical part of the rate. The word unit is used to highlight the 1 in per 1 unit of the second quantity. A percent represents a rate per 100. Common percent equivalencies, such as 50% is ½, 100% is 1, 150% is 1 ½, and 200% is 2. Common conversion factors, such as 12 in. = 1 ft., 1 gallon = 4 quarts, and 1 m = 100 cm. ESSENTIAL QUESTIONS Students will keep considering How are ratios and rates different? How do you use ratios and rates to solve real world problems? How do ratios relate to percents? Acquisition SKILLS Students will be skilled at and/or be able to Use ratio language to describe a ratio relationship. Compute unit rates, including ratios of fractions. Reason with ratios and rates using tape diagrams, double number lines, ratio tables, and graphing in the coordinate plane. Find the whole, given a part and the percent. Find a percent of a quantity as a rate per 100. Use ratio reasoning to convert measurement units. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 6/23/17

2 Assessed Grade Level Standards Standards for Mathematical Practice SMP 1 Make sense of problems and persevere in solving them. SMP 2 Reason abstractly and quantitatively. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. SMP 8 Look for and express regularity in repeated reasoning. Standards for Mathematical Content [m] 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. 6.RP.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. a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2 Posted 6/23/17

3 Assessment Evidence Unit Assessment Evidence of Learning Stage 2 Claim 1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Concepts and skills that may be assessed in Claim1: 6.RP.A The student uses ratio language to describe a ratio relationship. The student determines the unit rate associated with a real-world ratio. The student finds missing values in tables of equivalent ratios. The student plots coordinate pairs to represent equivalent ratios. The student makes tables of equivalent ratios relating quantities with whole-number measurements. The student solves real-world problems involving unit rate. The student solves mathematical problems involving finding the whole, given a part and the percent. The student solves real-world and mathematical problems involving finding a percent of a quantity as a rate per 100. The student uses ratio reasoning to manipulate and transform units appropriately when multiplying or dividing quantities. Claim 2: Students can solve a range of wellposed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Standard clusters that may be assessed in Claim 2: 6.RP.A Claim 3: The student can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. Standard clusters that may be assessed in Claim 3: 6.RP.A Claim 4: The student can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Standard clusters that may be assessed in Claim 4: 6.RP.A Other Evidence Formative Assessment Opportunities Informal teacher observations Checking for understanding using active participation strategies Exit slips/summaries Tasks Modeling Lessons (SMP 4) Formative Assessment Lessons (FAL) Quizzes/Chapter Tests SBAC Interim Assessment Blocks Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website M Mathematics Curriculum Documents LONG BEACH UNIFIED SCHOOL DISTRICT 3 Posted 6/23/17

4 1 day I will explore ratios and rates by participating in the Opening Task. OPENING TASK Nana s Paint Mixup In this Opening Task, students will watch a video, and then you will orchestrate a whole-class discussion. This task is a gateway into the entire unit of ratios and rates. Teacher s Directions for Nana s Paint Mixup 4-5 I will explore ratio concepts in realworld situations by Using ratio language to describe a relationship between two quantities. (SMP 6) Explaining the concept of a ratio and using ratio language to describe a ratio relationship between two quantities. (SMP 3) Using visual models such as tape diagrams, double number lines, and ratio tables to compare ratios. (SMP 5) Graphing the pairs of values from a ratio table on the coordinate plane. o How do you find equivalent ratios? o What are the different ways to represent ratios? o How can two different ratios describe the same relationship? o Why can you multiply or divide both terms of a ratio by the same number without changing the value of the ratio? o How are ratios related to fractions? o How are ratios related to division? o Compare and contrast the different visual models (tape diagrams, double number lines, and ratio tables) for ratios. o Synergy Item Bank: Item ID 50180, 52288, 53066, 53157, Section 5.1 (Activities 1, 3, and 4; Examples 1, 2, and 3) Section 5.2 (Activity 1; Examples 1, 2, and 3) Section 5.4 (Activities 1, 2, and 3; Examples 1 and 2) Finding Equivalent Ratios Task Desmos: Tile Pile Procedural Skills and Fluency: Ratios Activity On the Bus Task Mangos for Sale Task Speed Conversions Task Modeling: Nana s Chocolate Milk (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 4 Posted 6/23/17

5 I will explore unit Section 5.3 rate concepts in (Activities 2 and 3; real-world Examples 2 and 3) situations by 4-5 Explaining the concept of a unit rate a/b associated with a ratio a:b with b 0, and using rate language in the context of a ratio relationship. (SMP 3) Interpreting and analyzing what the unit rate means in the context of the problem. (SMP 2) Using visual models such as tape diagrams, double number lines, and tables of equivalent ratios to find unit rate. (SMP 5) Connecting unit rate to tables and graphs in problems involving unit pricing and constant speed. o What is a unit rate? o How is finding an associated rate or unit rate helpful when making comparisons between quantities? o Compare and contrast ratio, rate, and unit rate. o Compare and contrast different visual models (tape diagrams, double number lines, and ratio tables) for rates. o What patterns do you see when using a double number line? (SMP 7) o How can you use rates to describe real-life problems? o Synergy Item Bank: Item ID 51908, 51911, 52970, 53062, 53063, 53308, Introductions to Tape Diagrams Walk-a-thon Task The Escalator Task Ticket Booth Task Truffles Task Voting for Two Task Modeling: Sugar Packets (SMP 4) mypd Course #3480: Facilitating a Three-Act Math Task: SMP 4 Modeling: Super Bear (SMP 4) 2 I will check my understanding of ratios and rates by participating in the FAL. FORMATIVE ASSESSMENT LESSON (Choose one) Maximizing Profit: Selling Soup (SMP 1, 2, 3, 4, 5, 6, 8) Sharing Costs Equitably: Travelling to School (SMP 1, 2, 3, 4, 6) Using Proportional Reasoning (SMP 1, 2, 3, 4, 5, 6, 7, 8) LONG BEACH UNIFIED SCHOOL DISTRICT 5 Posted 6/23/17

6 I will explore Section 5.5 percent and solve (Activities 1, 2, and 3; percent partwhole Examples 1, 2, and 3) problems Section 5.6 by (Activities 1, 2, 3, and 4; Examples 1, 2, 3, 5, 6) 3-4 Introducing percent of a quantity as a rate per 100. Knowing how to convert between percents and fractions. Using visual models, such as percent grids, tape diagrams, double number lines, and ratio tables. (SMP 5) Using benchmark percents, such as 1%, 10%, 25%, 50%, 75%, and 100%. Applying estimation strategies to assess the reasonableness of the answer. (SMP 5) o Why is 100% equal to 1? o What would be a good estimate for 52% of 209? Why? o Synergy Item Bank: Item ID 52286, 52962, Percents Task Percentages Task Percents on a Linear Model 5 (Double Number Line) Related Percentages Duplicating Dollars Task 2-3 I will convert measurement units by Using unit analysis to decide which conversion factor to apply. Using ratio and rate reasoning to multiply or divide by one or more conversion factors. o What is a conversion factor? o Why does a conversion factor always equal 1? o Synergy Item Bank: Item ID 52964, 52968, Section 5.7 (Activity 3; Examples 1, 2, and 4) STEM Video: Human Circulatory System Why The Metric System Matters STEM Video Performance Task: Unit Conversion Mistakes LONG BEACH UNIFIED SCHOOL DISTRICT 6 Posted 6/23/17

7 1 day I will prepare for Incorporating the Standards for Mathematical Ch. 5 Study Help (p. 216) the unit Practice (SMPs) along with the content standards to Ch. 5 Review assessment on review the unit. (p ) ratios and rates by... Procedural Skills and Fluency: Ratios Concentration Tape Diagrams, Double Number Lines, and Ratio Tables Review Activity Modeling: Can you Earn $10/Hour Selling Lemonade? Unit Assessment 1 day Students will take the Synergy Online Unit Assessment. Unit Assessment Resources (Word or PDF) can be used throughout the unit. At this point, all standards addressed in the Math 6 SBAC Interim Assessment Block Ratio and Proportional Relationships have been covered. This block may now be administered. LONG BEACH UNIFIED SCHOOL DISTRICT 7 Posted 6/23/17