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- From: CRS Collaboration
- Contributed By: Joe Schlessinger
A critical part of any scientific experiment is collecting and analyzing data (as seen in the WHAT'S UP IN THE ENVIRONMENT? Web site, long-term projects). In this lesson, students learn first-hand about the strengths and weakness of qualitative and quantitative data by gathering and analyzing data collected from a classroom poll. Using what they’ve learned, students design and conduct a poll of their own. As an assessment piece, students can use what they’ve learned to teach their peers about qualitative and quantitative data, or stage a debate over the merits of qualitative versus quantitative data.
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Lesson Plan Quadratic Functions
This lab is based on one from Illowski and Dean's Collaborative Statistics book. Students collect data and then calculate the measure of central tendency and dispersion. They create a histogram and a box plot. They look at outliers and use Chebyshev’s theorem to look at the dispersion of the data. Student Learning Objectives • The student will construct a histogram and a box plot. • The student will calculate univariate statistics. • The student will examine the graphs to interpret what the data implies.
Explore the graph the inverse of an exponential function and match it to a logarithmic function.
Teacher Guide for the lesson on adding, subtracting, and multiplying complex numbers.
Materials needed for this specific lesson:
1. Percentages Worksheet (see Lesson 1 Resources folder).
Procedure:
Begin the lesson by reviewing the various methods for finding percent of a number. Spend as much time as necessary to ensure that students have fully understood and are fluent with the process of deriving percent of a number and percent of change.
Two common methods for finding percent of a number are: the percent equation (Part = %(as a decimal) x Number or p=%b) and the percent proportion (part/base = %/100, where part is the portion and base is the original number).
After ensuring that students can accurately perform these calculations, distribute the Percentages Worksheet. Ensure that students understand what is being asked of them in the first question. If they have already done this for their circle graph for the previous unit, tell them to double check their answers. After they have found all of these percentages, they should answer questions 1 - 3 on the bottom of the worksheet.
Once the class has finished this worksheet, lead a discussion comparing and contrasting different percentages of budget categories. Also, lead a discussion about the notion of sales tax on food and gasoline. The discussion about gasoline sales tax should include the fact that many European nations view the gasoline tax as a "sin tax", much on the same order as cigarettes and alcohol, as mass transit is much easier on the European continent than in the United States. Ask the students to think about what changes that might make on consumer behavior if the US had a similar tax rate on gasoline. Would these be good or bad changes, and why?
The following is a set of suggested activities for a third grade curriculum unit on the Earth/Sun/Moon system. The goal is to provide students with an understanding of the motions of the three objects in the system and the way in which they determine the periodic changes we observe. In particular, students should develop an understanding of the way the Earth's daily rotation determines the cycle of light and dark that we call day and night; the way the Moon's motion about Earth determines the monthly cycle of lunar phases; and the way the Earth's orbital motion around the Sun determines the annual cycle of seasons. We also discuss how eclipses - solar as well as lunar - come about. The cyclic changes we discuss are a visible and essential part of students' experience. In finding that they can systematically state, quantify, and model these changes, and that they can furthermore comprehend the astronomical phenomena that underlie them, students acquire not only a familiarity with scientific methods and facts but also a sense that these methods render the physical universe they inhabit essentially comprehensible. This in itself is an important aspect of teaching the unit, and we have attempted to structure the activities to make it explicit. The activities are constructed to fulfill the requirements of the North Carolina Standard Course of Study objectives for third grade science. Included in these is an understanding of some aspects of the nature of Light. Several of the activities address this - they occur early in the Unit, as the facts about light are used extensively in the following Activities. As a study of light this is woefully incomplete; some related enrichment activities are included for teachers interested in taking this to slightly greater depth.
Students must first know the order of operations, at least enough to know that 2x+4 is the same as 4+2x. That's because both expressions would be acceptable answers to a scenario with an initial value of 4 and a rate of 2.
Group Size: Any
Learning Objectives:
Students will be able to identify rate and initial value in story problem scenarios involving linear patterns. Students will be able to write numeric and algebraic expressions evaluating the output of a linear pattern for different (known or unknown) inputs in the context of story problems.
Guiding Question:
In a story problem, how can I tell whether to a given number should be added or multiplied in my answer expression? What's the shortest way to summarize everything I know about a linear pattern?
Materials:
1). Student handouts Optional but recommended: 2). Elmo/document camera 3). Student response whiteboards
Procedures:
Begin with a review of Order of Operations. For this lesson, students just need to know that 2+4x and 4+2x are the same. An optional Order of Ops drill practice Powerpoint is attached. For #1-4, display teacher blacklines on Elmo/document camera. If no Elmo is available, make copies and hand them out. Try to use questioning techniques that are open-ended and stretch students to deeper levels of reasoning. For example, if two students have different answers for a question, display both answers and ask the class to compare the reasoning processes underneath both. Beginning with #5, allow students to work in small groups on remaining questions.
Assessment:
Whiteboard responses will give you a quick sense of each student's comprehension.
Attached Files:
| 1.6Lesson--StudentHandout.pdf |
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| 1.6Lesson--StudentHandout.docx |
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| 1.6Lesson--TeacherMaterials.docx |
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| 1.6Lesson--TeacherMaterials.pdf |
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| 1.6OrderofOpsDrill.ppt |
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| 1.6OrderofOpsStudentSheet.pptx |
Students learn to translate between table, graph, and algebraic equation for linear patterns. The lesson focuses student attention on identifying the rate of change and initial value in each representation. Lesson comes with short PowerPoint slides designed to help the teacher move among students watching them work as they complete an Understanding Check at the end of the lesson.
Students use real-world knowledge and hands-on algebra tiles to learn the basics of equation-solving. The lesson progressive from a concrete scenario involving downloading music to abstract representations with variables. A companion PowerPoint slideshow scaffolds discussion and demonstrates proper use of algebra tiles.
Hooks students through an exciting number trick. Explores why number tricks work through a pictorial approach (algebra tiles), leading to the concept of operations that "undo" each other. Translates this concept to an understanding of canceling in algebraic expressions. Teaches students how to take a two-step expression and undo it. Finishes by asking students to creatively design their own number trick so everybody can try out someone else's.
This is the PowerPoint of the lesson on the area of sectors and arc length.
Lesson on how to use midpoint formula
This lesson plan introduces students to the single event of probability. A variety of experiments are included for theoretical probability. Links and resources are included.
Graphic Organizer for cup/pint/quart/gallon.
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Using a 1-100 (10 x10) Number Chart on paper, students create their own Times Tables by pointing,counting, and coloring the numbered boxes. This creates simple geometric color patterns that enable students to learn, predict, and prove arithmetic calculations and "families" of numbers. Students actually create their own "Math Tools for Fun at School"...
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Environmental issues are often at odds with commerce. In the case of packaging, while environmentally friendly packaging is socially responsible, it is often hard to do in a cost effective manner. In this lesson, students have to balance the need for secure packaging with environmental and economic concerns. They will work together in groups of 3–4 students to create a mailing package for a fragile substance. In this case, students will be using a cookie as their substance. After the packages are finished, take them to the post office and mail them back to the students. When the packages arrive, schedule a second session to evaluate the results. Students will score their packages using a rubric. . BY ERIN DENNISTON Provided by Kenan Fellows Program.
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Our Changing Earth: Earthquakes, Volcanoes, and Tsunamis is a 6th grade Science unit to teach students how these three events have changed and still change and shape our earth. This unit is inter-disciplinary covering math, science, language arts, and technology.
A series of four short videos explaining the basics of multiplying and dividing fractions and decimals.
Lasting Ideas & Results:
(1) Multiplying, Dividing, and Simplifying Fractions and Decimals
Essential Question(s):
(1) How do you multiply fractions? (2) How do you divide fractions? (3) How do you multiply decimals? (4) How do you divide decimals?
Desired Learner Outcomes:
| Students will be able to… | Students will know… |
|---|---|
| (1) Multiply and divide fractions and decimals. | (1) When they can cross cancel fractions. |
| (2) Manipulate fractions before and after dividing and multiplying. | (2) The basic rules for multiplying and dividing fractions and decimals. |
Summative
| Describe Performance Tasks | Explain &/or Reference Criteria |
|---|---|
| e.g., quiz | e.g., use Answer Key attached |
Procedures:
Go to the Math Videos-Dividing and Multiplying Decimals and Fractions folder to view all four videos.
Each video may be used individually at learning centers, for homework, or review.
This lesson may be followed by the Fraction Modules Lesson.
Visualizing and understanding rational numbers through number lines, diagrams, and problems.
Lasting Ideas & Results:
(1) What is a rational number?
(2) What are integers?
(3) Visualizing fractions as part of a whole
Essential Question(s):
(1) How do numbers relate to one another?
(2) How do you rank fractions?
(3) How do you solve absolute value problems?
Desired Learner Outcomes:
| Students will be able to… | Students will know… |
|---|---|
| (1) Use a number line to answer simple problems | (1) The definition of integers and rational numbers |
| (2) Visualize fractions | (2) The physical relation of fractions on a number line |
| (3) Rank fractions | |
| (4) Find the opposite of a given number or equation | |
| (5) Solve simple absolute value equations |
Summative
| Describe Performance Tasks | Explain &/or Reference Criteria |
|---|---|
| e.g., quiz | e.g., use Answer Key attached |
Procedures:
Access the Integers and Rational Numbers video.The video is 13 minutes in length and discusses integers and the rational numbers including such topics as locating numbers on the number line, equivalent fractions, absolute value, ranking fractions, and negatives.
Incorporate into a full class session or assign for homework.
A presentation explaining how to work with improper fractions and mixed numbers including many practice problems.
Lasting Ideas & Results:
(1) How to work with improper fractions and mixed numbers.
Essential Question(s):
(1) What is an improper fraction?
(2) What is a mixed number?
(3) What is a fraction?
(4) How do you convert from an improper fraction to a mixed number?
(5) How do you convert from a mixed number to an improper fraction?
Desired Learner Outcomes:
| Students will be able to… | Students will know… |
|---|---|
| (1) Move back and forth between mixed numbers and improper fractions. | (1) What mixed numbers and improper fractions are. |
| (2) Visualize mixed numbers and improper fractions |
Procedures:
Open the Converting Fractions and Mixed Number Presentation and present to your students.
This lesson is made up of a couple of grids for students to complete to help them understand how to convert from fractions to decimals and percents.
Lasting Ideas & Results:
Finding patterns when working with numbers.
Essential Question(s):
(1) What patterns can I learn about fractions, percents, and decimals that will facilitate understanding? (2) How do you convert from a fraction to a decimal and from a fraction to a percent? (3) What patterns can be detected?
Desired Learner Outcomes:
| Students will be able to… | Students will know… |
|---|---|
| (1) Convert fractions to decimals. | (1) The relationship between fractions and decimals, and fractions and percents |
| (2) Convert fractions to percents. |
Procedures:
Download the Converting Fractions to Decimals to Percents Worksheet and distribute to students for completion as classwork or homework.
An interactive program that uses pattern blocks of various shapes to facilitate understanding of geometry and fractions.
Lasting Ideas & Results:
Complex geometric figures and fractions of complex figures.
Essential Question(s):
(1) How do you use simple shapes to make complex figures?
(2) How can you simple shapes relate to complex figures as fractions?
Desired Learner Outcomes:
| Students will be able to… | Students will know… |
|---|---|
| (1) Use simple shapes to understand how complex figures are made. | How complex figures are made from simple shapes |
| (2) Determine what fraction of a complex figure a certain number of simple shapes are |
Procedures:
- (1) Using Pattern Blocks
- Ask students: Have you ever used pattern blocks to think about fractions? Then present this exploration for small group or individual classwork.
- Tell students: Now that you are familiar with pattern blocks, you can use them to multiply fractions and whole numbers. Then present this exploration.
- Ask students to think about what they already know about how whole number multiplication works. How is multiplying fractions different than multiplying whole numbers? How is it the same?
- (3) Dividing Fractions
- Ask students: How is dividing fractions different from dividing whole numbers? How is it the same? What strategies did you use to solve?
- (4) e-Notebook
- Students will complete the questions for this lesson in the e-Notebook worksheet. This may be classwork, homework, or small group work.
(2) Multiplying Fractions
(1) The instructor can score students’ exercise results to assess understanding of simple fractional operations.
How to add fractions.
Lasting Ideas & Results:
(1) Understanding how to add fractions with the same denominator (2) Understanding when to find a least common denominator (3) Understand how to find a least common denominator
Essential Question(s):
(1) What is the rule for adding fractions (2) How to evaluate an addition problem (3) How do you find equivalent fractions? (4) How to add once you find a common denominator (5) How to draw a pictorial representation of a fraction
Desired Learner Outcomes:
| Students will be able to… | Students will know… |
|---|---|
| (1) Identify equivalent fractions | (1)The rule for adding fractions |
| (2) Multiply and divide in order to find equivalent fractions | (2) The process for adding fractions |
| (3) Add and subtract fractions |
Procedures:
Play the Adding and Subtracting Fractions video for students. This video introduces the basics of adding and subtracting fractions by solving several simple equations. Appropriate as whole class activity, small group activity, or individual assignment.
Materials:
Adding and Subtracting Fractions video
Brandon Beaudoin, Kristofer Kraul, Austin Smith
This unit focuses on gathering, organizing and displaying data. The unit also addresses creating line graphs, circle graphs, bar graphs and pictographs with emphasis on labeling each graph correctly. In addition, this unit will develop and enhance mathematic arguments and proofs in regards to analyzing graphs. This unit also teaches probability skills and concepts. Prediction, testing probabilities and finding outcomes are developed through game play and instructor modeling of lessons.
This unit focuses on the use of common fractions and improper fractions. It allows students to further their understanding of adding and multiplying fractions as it relates to geometry. This unit allows students to develop their understanding of geometric figures as they explore area and perimeter in the real world.
STEW Level A Exemplar
