Unit Plan including Common Core Standards
Unit Title:
Grade Level/Course:
Big Idea
Essential Questions:
Ratio and Proportion Time Frame: 5 weeks
Math 6 A ratio relates two or more quantities, and when two ratios are equivalent, the data are said to be proportional. Proportions allow us to scale up or down data while keeping the ratio intact. What is a unit rate? Are these data proportional? Which method is most helpful in each situation? Am I looking at an absolute comparison or a relative comparison? What is a ratio? Instructional Activities: Activities/Tasks
Units have many types of lessons that have different purposes: Hook: Making Lemonade GeTng General #3: Double Number Lines to solve ProporMons Concept #1: RaMos with Tape Diagrams GeTng Fluent: Solving proporMons Concept #2: Absolute vs. RelaMve Diffrence GeTng Precise #1: Rate and Speed problems Copyright – Irvine Math Project -­‐ All Rights Reserved Concept #3: What does it mean to be proporMonal? GeTng Precise #2: Conversions GeTng General #1: Using Equivalent FracMons to solve proporMons GeTng Precise #3: Percent problems GeTng General #2: Cross-­‐products of proporMons are equal Robust DifferenM-­‐
aMon: Real World Problem Solving with RaMos and proporMons 1 st
21 Century
Skills:
Learning and Innovation:
Critical Thinking & Problem Solving
Communication & Collaboration
Creativity & Innovation
Information, Media and Technology:
Online Tools
Software
Essential
Academic
Language:
Tier II:
Absolute Relative Per Speed
Common Core Math Standards Taught and Assessed Hardware
Tier III:
Equivalent Fractions Cross-­‐products Ratio Percent Unit Rate Convert Proportion
6 Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
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.”
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.”1
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.
6 Expressions and Equations
Represent and analyze quantitative relationships between dependent and independent variables.
9.Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express
one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the
relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a
problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent
the relationship between distance and time. Copyright – Irvine Math Project -­‐ All Rights Reserved 2 Opportunities for listening, speaking, reading, writing, and thinking:
-­‐Emphasize salient points to assist the listener in following the main ideas and concepts. (L/S 1.4) -­‐Use simple, compound, and compound-­‐complex sentences; use effective coordination and subordination of ideas to express complete thoughts. (W OLC 1.1) -­‐Write persuasive compositions: a) State a clear position on a proposition or proposal and b) support the proposition with organized and relevant evidence (6 W 2.5 a & b) -­‐Connect and clarify main ideas by identifying their relationships to other sources and related topics (6 R 2.3) Resources/
Text(s) Titles: Textbook Materials:
Mathematical Tools/ Manipulatives: Calculators, rulers, Media/Technology: BrainPop lessons on Ratio and Proportions Supplementary Materials: hot wheels, pretzels, stop watches, balls, stop watches, digital camera Mini-­‐white boards & Markers Differentiated
Instruction:
English Learner Supports -­‐Word Wall vocabulary -­‐Development of Academic Language through concrete objects and visuals -­‐Student Discourse Strategies -­‐Sentence Frames -­‐Thinking Maps -­‐Language Objectives
Special Need Students Special Needs-­‐ -­‐Manipulatives and Visuals -­‐Student Discourse GATE-­‐ -­‐Big Idea -­‐Details -­‐Patterns -­‐Language of the Discipline -­‐Unanswered Questions Copyright – Irvine Math Project -­‐ All Rights Reserved 3 Objectives, Assessment, Depth of Knowledge & Means to get students there
Knowledge Type & Claim Content Objective Time Topic & Teaching Strategy Formative Assessment (in addition to that explained in Teacher Directions while conducting lesson) Students explain how different ratios of sugar to water affected taste. Concept/ RK By using different ratios to make 1 day 2,3 and taste-­‐test lemonade, students will use tape diagrams to explain the concept of ratios. 5, 7 Concept 1,3 3,4 Students draw tape diagrams to explain the ratio of boys to girls 3.4 Students can compute both the absolute and relative differences of scenarios. 1,3,4,8 Students explain, in writing, what it means for data to be proportional. Students use thumbs up/down to identify if Concept 1,3 Concept 1,2,3 Hook Lesson: Making Lemonade -­‐Students will use different ratios of sugar to water to make and test lemonade. Students will draw tape diagrams (see end of document for example) to represent the mixtures and to understand the idea of ratios. See Activity Making Lemonade. -­‐See BrainPop video “ratios” Students will study color 1 day Tape Diagrams to represent Ratios combinations used to color -­‐Students will do an activity called Mixture Blues and jeans to compare ratios. then draw tape diagrams to represent each ratio. See activity Mixture Blues (http://www.learner.org/courses/learningmath/algebr
a/session4/part_b/index.html). -­‐Students will practice the idea of tape diagrams on the CC activity Ratios of Boys to Girls (10 minutes) -­‐Ratio Practice: Textbook Practice Students will compare absolute 1 day Absolute vs. Relative difference. and relative statements made -­‐Students will look at statements made about activities about scenarios to explain the students participate in to determine and understand difference between additive and the difference between absolute (additive) differences multiplicative change. and relative (multiplicative) differences. -­‐See Activity Which is more: 12 girls or 10 girls (http://www.learner.org/courses/learningmath/algebr
a/session4/part_a/index.html) -­‐See CC activity Games at Recess (10 minutes). Students will understand and 4 days What does in mean to be Proportional? explain what it means for data -­‐Have students participate in a series of activities to be proportional by comparing where 1 task is proportional and 1 is not. Have them and contrasting the tables, record a t-­‐chart and graph for each and then compare scenarios and graphs of 2 data and contrast to understand why all of the tasks 1’s sets. were proportional (by looking at the scenario, the Math Practice Copyright – Irvine Math Project -­‐ All Rights Reserved 4 RK/P 1 Students will discover that proportions and comprised of equivalent fractions and use that information to solve for a missing number in a proportion. Students will discover that the cross-­‐products of proportions are equal and use that information to solve for a missing number in a proportion. RK/P 1 RK 4 Students will apply their knowledge of proportions to create a body to match a given-­‐
sized head shot of themselves. Concept 2 Students will study a scenario comparing two rates to build a double-­‐sided number line to represent the proportion. table, the y-­‐intercept and the graph) and tasks 2’s were not. Once they understand and can write summary statements about what it means for data to be proportional, give scenarios, tables and graphs and have students decide if the data is proportional. (See IMP Intervention Unit Proportions 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 3.1, 3.3 & 7.2) 2 days Equivalent Fractions -­‐Have students discover that proportions are comprised of equivalent fractions. -­‐Have students use equivalent fractions to solve problems involving proportions. -­‐See IMP intervention Unit Proportions 3.4, 4.2 & 5.1 -­‐For Practice, See Textbook (non-­‐word problems) a situation is proportional or not. 3, 7 Students use equivalent fractions to solve a proportion. 2 days Cross Products to solve Proportions -­‐ Have students discover that the cross-­‐products of proportions are equal. (See IMP Intervention Unit Proportions 5.2, 5.3) -­‐Practice using cross-­‐products to solve problems involving proportions-­‐ See textbook practice and/or IMP Intervention Unit Proportions 7.1 See BrainPop video-­‐ Proportions 2 days Picture Perfect Proportions -­‐Take (BEFORE THIS DAY) a head shot and full body length shot of each student. Have them use proportions to draw the body to match their head shot. See IMP Intervention Unit Proportions 6.1 -­‐Practice solving proportions (numbers only) 3, 8 Students use cross products to solve a proportion. 1, 4 -­‐Students create a body to match their new head photo. 1 day 7 Student draw a double sided number line and label it appropriately. Copyright – Irvine Math Project -­‐ All Rights Reserved Double-­‐sided Number Line -­‐Use a scenario, such as measuring the rebound of a bouncing ball from a given drop height, to help students understand how to create a double-­‐sided number line. 5 Procedures 2 RK 2,4 RK 2 RK 2 -­‐Have students practice creating a double-­‐sided number line and estimating the value of the missing quantity (See IMP Intervention Unit Proportions 7.3). Students will build double-­‐sided 2 days Practice: Solving Proportions with a double-­‐sided number lines to write and solve number line proportions. See IMP Intervention Unit Proportions 8.1, 8.2, 9.1 Students will participate in 2 Rate and Speed Problems activities involving rates and days -­‐Have students use a double-­‐sided number line to record the rates on a double-­‐
record data for walking rates or other rates. (See sided number line. Activity Top Speed). -­‐See CC activities Friends on Bikes, Running at a Constant Speed, First Rate (mathematics.org/problems-­‐of-­‐the-­‐month/pom-­‐
firstrate.pdf) and Movin’ Groovin (http://insidemathematics.org/problems-­‐of-­‐the-­‐
month/pom-­‐movinngroovin.pdf). Note: Each problem will likely take 10-­‐20 minutes. -­‐Practice solving rate problems using proportions. See textbook practice sections Students will use double-­‐sided 2 days Conversion Problems number lines and proportions to -­‐Have students create a double-­‐sided number line solve problems involving using known conversions (e.g., 12 inches = 1 foot). See conversions. Carr pg. 25 -­‐IMP activity Change of Units -­‐Practice conversions by setting up double-­‐sided number lines. See textbook practice 2 days Percent Problems Students will use double-­‐sided number lines and proportions to Have students practice setting up the double-­‐sided solve problems involving number line, estimating and writing and solving the percentages. proportions for all types of percent problems (always present a mix of problem types (i.e., discount, interest, interest, tips) so it is one concept!!!) See IMP Intervention Unit Percent 6.2, 7.1, 8.1 Copyright – Irvine Math Project -­‐ All Rights Reserved 1 Students correctly solve problems. 4 Observe students working on problems -­‐Ask probing questions for students to explain thinking. 4 Observe students working on problems -­‐Ask probing questions for students to explain thinking. 4 Students give accurate estimates for percent discounts 6 RK 4 All Students will apply their knowledge of ratios and proportional relationships to solve differing levels of problems involving proportions. Codes: RK-­‐ Relational Knowledge C-­‐Conceptual Knowledge P-­‐Procedural Fluency M-­‐Memorization Claim 1: Concepts/Procedures Claim 2: Problem Solving Claim 3: Communicating & Reasoning Claim 4: Model and Data Analysis 2 days 1 day Copyright – Irvine Math Project -­‐ All Rights Reserved See textbook practice Robust Differentiation: Proportion Stations for Problem Solving See CC activities Jim and Jesse’s Money, Currency Exchange, Mixing Concrete, Truffles (http://insidemathematics.org/common-­‐core-­‐math-­‐
tasks/6th-­‐grade/6-­‐2009%20Truffles.pdf) and Measuring Mammals (http://insidemathematics.org/problems-­‐of-­‐the-­‐
month/pom-­‐measuringmammals.pdf). Summative Assessment: Mix of all 4 claims 1, 4 Observe students working on problems -­‐Ask probing questions for students to explain thinking. 7