lesson planning project
TRANSCRIPT
6th Grade Math: Equivalent Ratios
Standards:
• 6.4(E) Represent ratios and percents with concrete models, fractions, and decimals.
• 6.4(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute.
• 6.4(B) Apply qualitative and quantitative reasoning to solve prediction and comparison of real-‐world problems involving ratios and rates
Unit Focus:
The focus of this unit is to develop an understanding of ratios and rates. Students learn that ratios compare the same types of measures and represent part:whole and part:part relationships. They also learn that ratios that compare different types of measures are called rates. Students apply these concepts to a variety of real world and mathematical situations, including problems involving measurement conversions and percents. In the culminating performance task, students plan a recipe, using ratios to find the quantities, unit rates, and costs of ingredients for different numbers of servings.
Objectives/Outcomes:
Students will be able to…
• Identify and write ratios. • Represent ratios with concrete models. • Represent ratios with fractions and decimals. • Represent percents with concrete models. • Represent percents with fractions and decimals. • Generate equivalent ratios. • Use ratio and rate reasoning to solve real-‐world and mathematical
problems. • Solve unit rate problems (including unit pricing and constant speed). • Solve percent problems, including finding a percent of a quantity as a
rate per 100 and finding the whole, given the part and the percent. • Use multiple representations such as tape diagrams, double number
line diagrams, or equations to solve rate and ratio problems.
Prior Knowledge Required:
• Students will be able to multiply fractions. • Students are able to find equivalent fractions without manipulatives.
Big Ideas:
• Connecting ratio and rate to whole number multiplication and division • Using concepts of ratio and rate to solve problems
Essential Questions:
• When is it useful to be able to relate one quantity to another? • How are ratios and rates used in everyday life? How would life be different
without ratios and rates?
Academic Vocabulary:
• Ratio • Rate • Compare • Equivalent • Quantity
Content and Pedagogy:
Ratio: A ratio expresses the relationship between two quantities. Ratios compare two measures of the same types of things. Examples: the number of one color of marble to another color of marbles, or the number of cats to dogs.
Ratios can compare parts to a whole (part:whole). Example: 12 of the 15 students are playing soccer (12/15).
Ratios can also compare a part of one whole to another part of the same whole (part:part). Example: The ratio of green marbles in the jar to red marbles in the jar is 4:2.
Ratios can be expressed in following notation: x:y, x/y, or x to y.
Rate: When a ratio compares two different types of measures, it is called a rate. Examples: 5 gallons of paint are needed to paint 8 walls (5:8). 3 shirts for $20 (3/$20)
Unit Rate: A unit rate is a rate which compares a quantity to one of the other quantity. Examples: Miles per hour, cost per foot, eggs per carton.
Proportion: A proportion is an equation written in a form that states that two ratios are equal. A/B = C/D
Anticipated Student Preconceptions/Misconceptions:
• Students may be confused about the order of the quantities. For example, a comparison of 2 wins to 3 losses is written as 2:3, and not 3:2. It is helpful if students begin labeling the quantities of the things they are comparing both in writing and orally.
• Students may have difficulty distinguishing a part:part ratio from a part:whole ratio. For example, “There are 12 girls compared to 11 boys in the class (12:11), but 12 of the 23 students in the class are girls (12:23).”
Lesson One Sequence:
Briefly introduce the concept of ratio and the key vocabulary and notation associated with it.
Nearpod Presentation:
• The presentation begins by having students explain in picture, numbers, or words what ratio means.
• The definition of ratio is given, along with a pictorial and numerical representation.
• Simplifying ratios is discussed. If two ratios simplify to the same things, then they are equivalent.
• To find an equivalent ratio, multiply or divide the given ratio by a form of “1”. • Student practice: You mix green paint in the ratio of 2 parts blue to 5 parts
yellow. What is the ratio of blue to yellow paint? Students respond by writing their answer on the iPad screen, and press “submit”.
• The next slide shows the correct answer. • Equivalent ratios can be organized using a table. • Student practice: Complete the ratio table for orange paint mixed from 3
parts red to 8 parts yellow. Students will fill in the table to create equal ratios.
• The next slide shows the correct answers, along with teacher explanation.
View a teaching video on ratios:
• At the learnalberta.ca website there are a variety of teaching videos. This is a Mathematics-‐Grade 6 Spy Guys Ratio video. http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonsshell03.swf
• http://www.youtube.com/watch?v=eT1yYqmjHPY • http://www.youtube.com/watch?v=yztq_ELjfSw&feature=related
(Teaching videos focusing on the definition of ratio and the ways that a ratio can be expressed.)
Revisit student ideas:
• Are there any ideas that need to be refined based on the activities and the videos?
• Do students want to contribute additional thoughts to the chart about ratios?
• Do they want to delete flawed ideas from the chart?
Extended Learning/Practice (homework):
• Students find three examples of ratios in the real world. They can find examples on the internet, in newspapers, or in their own homes. For each, they write down the ratio and discuss its meaning. Example: The ratio of citizens who voted in the last election compared to those who didn’t vote was 1:6. Analysis: Not very many people voted. A few people are making decisions for the whole city. Example: Two of my sisters have jobs after school. The ratio of their hourly pay is $7:$10. Analysis: The sister who makes $7 an hour could ask for a raise in her hourly rate, but she is younger and has less experience, so it is probably fair.
Lesson Two Sequence:
• In this lesson, the focus is on writing ratios that accurately represent mathematical, tabular, or pictorial situations. In the next lesson, students will be asked to express ratios in simplest form.
• Students work in groups of 3 to briefly share their “ratios in the real world homework”. Each group shares one good example with the rest of the class. Student 1 reads the example so that the teacher can record it on the board. Student 2 tells which notation to use in the written ratio. Student 3 explains the meaning of the ratio and any inferences that can be made. This activity reviews the previous lesson, and pre-‐assesses student readiness for writing ratios.
• Students practice writing ratios based on the following types of problems: o Pictures of objects in scattered arrangements
o Working backward: In the diagram, what does the ratio ___:___ represent
o Shapes divided into equal parts with some parts shaded. Write the ratios for shaded to non-‐shaded or shaded to total.
Technology resources:. These resources facilitate students model with mathematics (SMP.4) The first one may be very useful for students with disabilities or ELLs.
• http://www.thinkingblocks.com/ThinkingBlocks_Ratios/ TB_Ratio_Main.htmlInteractive site where students are taught how to use blocks to model ratio problems. Problems may ask students to find one of the two quantities in the ratio, the difference between the two quantities, or the total. Provides a video with step-‐by-‐step clear, visual, auditory demonstration of using blocks to solve ratio problems. Teachers can use to guide instruction with block manipulatives , or students can virtually manipulate blocks. http://illuminations.nctm.org/LessonDetail.aspx? id=L722 Pairs (or groups) of students use a cup of beans to find ratios to express the number of marked beans in the cup compared to the total number of beans in the cup. Theoretically, each sample should be essentially the same. The decimal representation of each ratio confirms that ratios are, indeed, approximately equivalent.
• http://www.math-‐aids.com.Ratios/ Practice sheets that use shapes to help students explore ratio relationships.
**Note: Some students may benefit from using actual manipulatives that they can move around.
Assessment:
Exit ticket: We know that all ratios can be written in fraction form. Are all fractions ratios? Why or why not? (Students write a response, explaining their thinking on a card or paper scrap. After putting their names on them, they turn them in on their way out.)
Extended Learning/Practice (homework):
• Students write ratios in the form requested for 6 different situations. • Students create a ratio problem for someone else to solve. Include pictures of
objects, the question (what ratio the student wants the solver to find), and the form in which the student wants the ratio written.
CEP 800: Lesson Planning Project
1. Content: The focus of this unit is to develop an understanding of ratios and rates. Students learn that ratios compare the same types of measures and represent part to whole and part to part relationships. They also learn that ratios that compare different types of measures are called rates. Students apply these concepts to a variety of real world and mathematical situations, including problems involving measurement conversions and percents. In the culminating performance task, students plan a recipe, using ratios to find the quantities, unit rates, and costs of ingredients for different numbers of servings.
The students learned about fractions in the previous unit, and struggled greatly with the concept. Therefore, they are likely to have some difficulty with ratios and rates as well. To help them be more successful, manipulatives and models will be essential to helping them understand the concept, and will be used wherever possible throughout the unit.
Texas State Standards:
• 6.4(E) Represent ratios and percents with concrete models, fractions, and decimals.
• 6.4(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute.
• 6.4(B) Apply qualitative and quantitative reasoning to solve prediction and comparison of real-‐world problems involving ratios and rates
2. Technology:
I believe that technology is a very effective way of teaching new things in the classroom. The teacher is able to take a different approach, and the students are exposed to so many different ways of finding information and presenting it. Technology should promote a change in the way that information is learned. If it is easier for a teacher to just print out information and have the students read it and complete a worksheet, it really is not effective. The use of technology in the classroom should give a student a different opportunity to learn by being actively engaged in what they are doing. It is important that the use of technology is fun, but entertainment should not be the primary focus. Teachers can use Power Point in the classroom in various different ways. First and foremost, this program can be used to present information to the students in a slide show format. The teacher can include pictures, internet links, video clips, and sound to the presentation to make it more interesting to the audience. Not only is a Power Point slideshow a better
visual for students, but it is also very easy to create and edit. Recently, I discovered a new spin on Power Point that will forever change the way that I use Power Point in my classroom. I was introduced to Nearpod during at a faculty meeting by another staff member who had discovered it and wanted to share it with all of us. Nearpod allows you to take your Power Point Presentations and upload them to their app, and use them in a more interactive way. You can create multiple choice and open-‐ended questions to include in the presentation to use to check for understanding. Each student will have their own device (ie. iPad, iPod, smart phone), and they will need to download the app. They will login using a class code to be able to view the presentation. Once logged in, I will begin my presentation. The students are able to view it directly in front of them on their device. Along the way there are questions that students can answer, and I can see their responses on my screen. The teacher can see instantly whether the students understand, or if the content needs further explanation. In addition, there are several math websites available that have interactive lessons that are similar to using math manipuatives. Websites such as Thinking Blocks and Illuminations are excellent math resources to be used, and I did have my students use these sites when I taught this lesson.
3. Pedagogy: In creating this lesson for students with special needs, I focused on the cognitivism learning theory, which focuses on how the mind processes and uses information. Within cognitivism, tasks are analyzed and then broken down into smaller steps or chunks. Information is then taught from the most simple to the most complex based on the learner's prior knowledge. Cognitive learners use schema or mental maps to help organize information and tie the material to existing knowledge to aid memorization. This method pays attention to the learner's specific differences by accommodating and approaching information in various ways.
This lesson would be considered to be active learning because they are engaged in listening, reading, writing, and solving problems throughout the lesson. I begin the lesson by having students explain what a ratio is by using numbers, pictures, or words. This assesses their prior knowledge to the subject. I begin the lesson by giving students the definition, along with pictorial and numerical representations. I take this information and build onto it, having students practice reading a word description, and translating it into a number ratio. We then go on to build ratio tables, and determine the relationships between the numbers, and how they are equivalent.
This type of presentation will appeal to both visual learners and auditory learners, because students will be able to see the information, and hear the teacher explain the information. They also have the opportunity for
independent practice, and instant feedback. Following the presentation, students will be able to generate equivalent ratios.
4. Content & Pedagogy: I chose this particular strategy when working with struggling learners to help them stay engaged throughout the presentation, but it also allows me to check how they understand the content. Had it been a regular old fashioned Power Point, I may not have their full attention throughout. Furthermore, to check for understanding, I would have called on one student. Using Nearpod, I am able to see the responses of all of the students.
One of the benefits of the Nearpod app is that students are not able to scroll ahead in the presentation. The teacher is in full control at all times. Furthermore, the app is the only thing that is open on the iPad when the presentation is running. Unlike on the computer, where student often minimize the screen, and try to work on other things or websites while the teacher is talking. If the student exits the presentation, the teacher is notified. This keeps the students on task, and they can be held accountable if they are not doing what they are supposed to be doing.
In addition, this technology is useable by all students of different abilities. It is very easy to use, and students don’t have to be able to type fast to respond to questions, and there isn’t a great deal of reading. They can use their finger or a stylus to respond to questions on the touch screen.
5. Technology & Pedagogy: The technology that I chose compliments the teaching strategies well, because it introduces the content in a fun and engaging manner, and then students have the opportunity to practice problems using interactive math manipulatives. The content is also taught to the level of the students in a special education classroom. The introduction breaks down the different aspects of ratios and rates, defining the vocabulary words, presenting pictures and models, and slowly putting the topics into practice by writing ratios, and then later solving problems. The lesson gradually builds onto the topic at an appropriate pace for students with learning disabilities.
6. Technology & Content: It is sometimes difficult to incorporate technology into a math class. I am always looking for new math websites that my students can use that act as manipulatives. I also use Educreations and Powtoon to create “how to” videos, and post them to my class website. Students are then able to view the videos at home when they are completing their homework or studying for a test. The great thing about videos is that they can be paused and played over and over again.
For this lesson, technology was used to introduce the topic of equivalent fractions, and students used the Thinking Blocks and Illuminations websites
to work out practice problems involving equivalent ratios and solving unit rates. It is very important for students with learning disabilities to be able to use manipulatives when learning about a new math topic. These websites allow them to solve problems using maniputlaives, while also breaking down pieces of the problem in a more logical way.
7. Assessment: As discussed before, using Nearpod, I was able to assess student understanding of the content through the use of multiple choice and open ended questions at different points throughout the presentation. This was a great way for me to know whether I needed to revisit topics, or if it was appropriate to move on. Furthermore, after students have the opportunity to practice using the ratios and rates website learning tools, they will complete an exit ticket about relating ratios and rates to real life situations.