Using Children's Books to Understand Probability, Percent, Ratios, and Circles
The beginning of this unit plan can be found here.
Lesson 3
Today's
lesson can be approached in two different ways and I want to do it
both ways. I want my students to be able to understand a percent as a
ratio and also a proportion as a ratio. In the book Pythagoras
and the Ratios: A Math Adventure ratios
are presented using only two but since in this unit we are working
with probability problems which can deal with more than one I need to
introduce this also. Today's lesson has a moment where the students
can show me their transfer ability and critical thinking skills. In
today's lesson I am going to ask the students to answer a question
which we have not covered yet but they have all of the tools to
solve. I think it is important to ask these questions periodically
because in the real world examples students are shown almost always
are similar but not the same as the problems they will be asked to
solve. Again this lessons activating strategy is also the exit ticket
because I am using the activating strategy is the goal we are working
towards. The lesson will be differentiated in two ways. The first
being when I walk around I will spend more time with the students who
usually struggle. Also the students are encouraged to ask someone
else in the class for help if they are struggling. This allows for
more than one teacher in the room.
I
like this lesson because it show the circular form of mathematics but
also we can take each concept of the previous two lessons and turn
them into ratios. Ratios is not a hard concept but is a different
concept. Again this lesson for some students should be a review
because they have learned this topic in previous concepts but it is
something they will see every day in real so it is an important
topic. Finally this is the middle of the unit so I need to bring
energy to today's lesson.
Standards:
- Journalism
- CFU 3005.3.4 Use a variety of strategies when appropriate (e.g., comparisons, anecdotes, detailed descriptions) to provide facts, details, reasons, and examples that support the thesis. (This along with the previous lesson about percentages show the same information in two different ways which help to support. Also ratios provide more information that percents in a given topic so therefore supply more support.)
- CFU 3005.6.3 Recognize clear or subtle and implied relationships among ideas (e.g., cause/effect, comparative, sequential) in complex informational and technical texts. (Ratios imply a relationship between two items but they again can be used to provide misleading information. The relationship is 4:8 can be written as a ratio of 1:2.)
- Finite Mathematics
- CLE 3182.5.3 Organize data for problem solving. (Again this supports the whole unit because we need to organize the ratios to solve proportion problems. It supports the lesson because organization in determining correct ratios.)
- CLE 3182.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning. (Student need to understand what a colon means when writing ratios. Also they need to understand how ratios justify creating pie charts for the unit.)
Objectives
- TSWBAT create ratios using word problems.
- TSWBAT take percentages and proportions and turn them into ratios
Assessment/Evaluation
- The informal assessment will occur while I am walking around the classroom and observing their work. The formal assessment will occur when I look over the exit ticket for today and then when they complete the unit project.
Materials
- Pythagoras and the Ratios: A Math Adventure
- Pythagoras and the Ratios: A Math Adventure PowerPoint
- SmartBoard
Activating Strategy
- I will start the lesson in the PowerPoint by asking two questions. What is a ratio and what does it look like? Yesterday we took a problem out of the book Probably Pistachio and wrote it in a percentage. What would that percentage look like if you wrote it as a ratio?
Instructions
I
would start off today by going over their homework and making sure
they were sound with turning probability into percents. I would start
today's lesson with the activating strategy. What is a ratio and what
does it look like? Yesterday we took a problem out of the
book Probably
Pistachio and
wrote it in a percentage. What would that percentage look like if you
wrote it as a ratio? The next thing I would do would be to start
reading Pythagoras
and the Ratios: A Math Adventure. I
would read up until page 6. After reading page 6 I would ask the
students if they saw how the two widths were related. I would then
ask how the two lengths were related. I would continue reading until
page 8 and there I would introduce ratios by looking at the diagram
on page 8. We would discuss the differences between a ratio and a
percent and the difference between a ratio and a proportion. If they
cannot figure it out I will ask some prompting questions to help
facilitate the conversation. The next thing I am going to do is read
the rest of the book. After the book I am going to ask them what they
thought about the book and if anyone can think of any ratios in their
own lives? After we discuss this for a couple of minutes we are going
to move on to working some ratio problems. I am going to ask them to
turn 35%, 20%, and 45% into a ratio. They might struggle with this
because we have only introduced ratios with two numbers from the
book. I am going to let them struggle with this for a couple of
minutes then if a student was able to accomplish this task I will let
them explain what they did. If not I will explain this thought
process to them. We will then work a problem dealing with 3
proportions. I will ask them to write 1/5, 2/5, ¾ in a ratio. We
will then discuss with a student who could accomplish the task
letting us know what they did. The next problem will be 2/4, 1/3,
7/6. What are these numbers written as a ratio? We will then discuss
again. The final thing will be the exit ticket. The exit ticket will
be answering the activating strategy.
Book
- The book I am going to use is called Pythagoras and the Ratios: A Math Adventure and it supports my lesson in a couple of ways. The first thing it does is introduce the word ratios to my students. The next thing it shows is how to create and display ratios with a division sign or a colon sign. It reminds students of the greatest common divisor which is a term they have already learned. It also shows the students how ratios are used in real life. Again this is really important to me so it follows this lesson's goals and also my unit's goals. Also in the back of the book it gives some historical context information which I will not read but the students could read on their own for more information.
Background
- The : symbol is just used to replace the division symbol when the numbers are written side by side.
- A ratio is called the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.
Reflection
- In this lesson I really need to stress how a ratio is not a number out of another number but rather a number compared to another number. If I confuse them on this which is a really easy misconception to have then they will struggle. I need to be very precise in my language so I do not confuse them. I also need to remind them why we present the same thing in different ways in mathematics.
- Today is the middle of the lesson so the students might have forgotten our first lesson which I need to remind them of because that is our ultimate goal. Also since it is the middle of the unit the students might have started to drag so I need to make sure that the students are participating and I need to make sure I am bringing energy into the classroom. Otherwise I might lose them and today is hump day of the lesson so if we get over it the students can see the finish line.
Continue on to Lesson: 1, 2, 3, 4, 5
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