This study was conducted in an online course environment.
Subject: Numbers and Operations
Topic: Ratio and Proportion
Age: 12-13 years
Real World Motivation
Mathematics and real-life are closely related. It is important to see mathematics in life and to be able to transfer mathematical knowledge to daily life. Seesaw is playground equipment in which two people sit on opposite ends of a plank balanced in the middle so that one end goes up as the other goes down. However, it is very difficult for children with a large weight difference to play on the seesaw at the same time. In this study, students will understand the mathematics behind the seesaw and try to find a solution to this problem by developing a movable seesaw.
Goals of the lesson
By the end of the lesson the students will be able to:
- Understand the link between mathematics and real life
- Create a movable seesaw by using waste materials
|Mathematics||Understand the inverse proportion of two multiples in real life, find one of two inversely proportional multiplicities when the other is given, formulate and solve the problems related to inverse proportion and make an interpretation about the solution|
|Science||Understand the idea behind a simple machine will, notice the interdisciplinary link between science and math, create a simple machine on their own, develop a strategy to maintain the balance on seesaw|
|Technology||Search for the information about the seesaw on the internet, use technology for learning and assessment|
|Engineering||Use materials, tools and ingredients in order to produce a certain product in a correct way, develop a strategy for movable seesaw design|
|21st Century Skills||Information literacy: in order to make well-founded judgements about balancing, students find, use and evaluate the necessary mathematical knowledge. Creativity: in seesaws, we see in life, the distances of the seats to the equilibrium point are equal and stable. In this study, students will develop an original seesaw model by going beyond the existing one. Productivity: in order to develop the product, students will create a plan, implement this plan and use time efficiently.|
|UNIT CONCEPTS AND SYMBOLS||TEACHING METHODS AND TECHNIQUES||TOOLS AND MATERIALS||SAFETY PRECAUTIONS|
|Inverse proportion Proportionality constant Leverage system||Problem solving Direct instruction Class discussion Inquiry-based instruction||Computer Zoom application Web tools|
Household waste / recycling materials (e.g. wooden stick, plastic bottle, rope) Ruler Scissors Band Glue
|Students were asked to carry out project studies in a home environment under the supervision of their parents.|
Introduction: Guessing Part (15 minutes)
The sales prices of four different olive oils are given below. Which one is economical? Why?
|2 L 41.80 TL||500 mL 10.5 TL||750 mL 15.55 TL||250 mL 5.30 TL|
Make a guess (30 minutes)
Q1.If someone is climbing a ladder in four by four at 18 steps, how many steps does a person take when climbing it in three by three?
|Guess||Examine the given situation||Solution||Your answer|
|Will the number of steps increase or decrease? ||What are the variables in this question? What is the total number of steps of the ladder? You can draw a shape.||Try to climb the same ladder three by three.|
Q2. A sum of money will be equally distributed to each child. The amount of money per child according to the number of children is given in the table.
|the number of children||The amount of money per achild|
|Guess||Examine the given situation||Solution||Your answer|
|X is greater than 60 or not.||What are the variables in this question? |
What is the total amount of money? You can calculate.
|Try to distribute the total money to 15 children.|
Students think, share and discuss their ideas.
Lecture (60 minutes)
The video about the topic is watched by students. Then, the teacher explains the subject and solves the problems in task and more.
EBA – TERS ORANTI KONU ANLATIM VİDEOSU (INVERSE PROPORTIONALITY SUBJECT VIDEO) (click for the video)
Two quantities are said to be inversely proportional when the value of one quantity increases with respect to a decrease in another or vice-versa. This means that these two quantities behave opposite in nature. For example, the time taken to complete a task decreases with the increase in the number of workers finishing it and the time taken to complete a task would increase with the decrease in the number of workers.
Inverse proportionality is the relationship between two variables when their product is equal to a constant value. When the value of one variable increases, the other decreases, so their product is unchanged.
A single tap can fill an empty pool in 120 minutes. Let’s examine the relationship between the number of taps and the filling time of the pool.
|Number of taps||1||2||3||…|
|Pool filling time (min)||120||60||40||…|
Let’s multiply the number of taps and the time which the pool is filled:
1.120 = 2.60 = 3.40 = Number of taps . Pool filling time
The product of inversely proportional multiplicities is constant.
DRILL AND PRACTICE (30 mınutes)
After the lecture, the teacher projects the questions one by one on the screen, gives time to the students to solve and mark, and then the teacher solves it by explaining. Depending on the level of students, questions can be taken from the following source:
Formative assesment: Indiviual work:
Interdisciplinary work is carried out at this stage (30 minutes)
The photo below is reflected on the board. Students are asked the following questions.
- What are the differences or similarities of these objects?
- Is it possible to give these objects a name?
- If it is possible, what would you name it?
After the answers are discussed, the teacher explains:
“These objects are examples of leverage used in daily life. Bars that can rotate around a support point are called levers. Levers are a variety of simple machines. Simple machines are the mechanisms that facilitate the daily work of people, provide ease of work and consist of very few parts.”
In order to see the inverse proportion idea behind the leverage system, the videos given below are whatched and online game is played.
5 kg x 4 = 10 kg x 2
(The presentation phase of the project was done in the online course environment. – 30 minutes)
Making a movable seesaw
It is very difficult for children with a large weight difference to play on the seesaw at the same time. Because of that, you are expected to design a movable seesaw. the distance between the sitting part and the equilibrium point must change in order to make people with having different weights play on it.
The points to take into account:
- People who have different weights (e.g. grandparent and grandchildren) can sit and play on together. Being movable is especially important for this substance.
- The equilibrium point must be stable.
- It must look like a seesaw.
- The seesaw should be able to move up and down.
- Prepare your design as a model.
Try to use the household waste / materials (e.g. wooden stick, plastic bottle, rope) while preparing the design
MONITORING THE DESIGN PROCESS
At this stage, students are assisted in the design process in a home environment under the supervision of their parents. Also, they are asked to take photos and send their progress while working on the project.
PRESENTATION OF THE PRODUCT
At this stage, students present their products in an online course on the Zoom platform. Students have the opportunity to examine other designed products.
EVALUATION OF THE PROJECT
Each project is evaluated in two stages: peer evaluation and teacher evaluation. Peer evaluation is done via Google Form (The evaluation form has been translated into English.)
|TEACHER PROJECT EVALUATION FORM|
|Should be improved||Acceptable||Very good|
|Does the model look like a seesaw?|
|Is the seesaw movable? (up-down)|
|Was waste material used?|
|Is the seesaw suitable for the use of different weights?|
|Was the project presentation clear and understandable?|
Students are given a summative assessment to demonstrate what they know and can do. The inverse proportion exercise containing 10 questions in the eba.gov.tr system is given to the students as homework.