Mathematics 7

Mathematics 7

Content Standards:  The learners should have knowledge and understanding of 

1. data collection and sampling techniques, and the presentation of data in appropriate tables and graphs,
2. interpretation of statistical graphs. 

Performance Standards: By the end of the lesson, the learners are able to 

• collect data and organize data in a frequency distribution table,
• represent and interpret data in different types of graphs. (DP) 

Learning Competencies and Objectives: By the end of the lesson, the learners … 

Organize statistical data in a frequency distribution table. 

1. Correctly identify and describe a frequency distribution table.
2. Correctly organize data using a frequency distribution table. 

Use appropriate graphs to represent organized data: pie graph, bar graph, line graph, histogram and stem-and-leaf plot. 

1. Correctly use different graphs for their specific purpose. 
2. Properly create a graph based on the given data. Interpret statistical graphs.

Day 1

Review: Let the students do the activity below.

Answer the following:

1. What is 25% of 600?

2. What is 10% of 5% of 200?

3. Mr. De La Cruz, receives Php 20,000 in his salary per month. if he save 15% of it, how much he save per month?

Lesson Proper: 

“Do you feel motivated to present gifts during special events? If so, do you expect to receive anything in return? Do you think giving is preferable to receiving at special events?”

Suppose that in a survey on gift giving, 71% of the respondents polled said that it is "better to give" gifts, while 29% said it is "better to receive." 

This survey shows that statistics has become a helpful tool in many aspects of our lives, such as in medicine, psychology, education, sociology, and other academic areas, to discover ways to improve human lives.

Suppose you are keeping track of how much money you have saved each week. You are able to save for the last three years or 156 weeks. What do you think is the best method to organize these numbers?

To answer the question, you are going to study one of the ways of data collecting and arrangement. This is known as a frequency distribution table. In this lesson, you will learn how to organize and describe data in a frequency distribution table correctly.

A statistical table is used to organize data and to display it graphically. 

The frequency distribution table is a statistical table that deals with the frequency or number of occurrences of a given variable for a specific experimental unit.

The parts of a simple frequency distribution table are as follows:

Category	Frequency	Relative Frequency	Percentage

 

• The category column refers to the things being considered. 
• The frequency is the number of times each category appears on the data set. 
• The relative frequency is the part of measurements compared to the whole sample. To get the relative frequency, divide the frequency of each fruit by the total frequency. Remember that the sum of all relative frequencies must be equal to 1. 
• The percentage represents the measurement's portion to the overall sample, expressed in hundreds (%). Likewise, the sum of the percentages must be equal to 100%.

Example:

Category	Frequency	Relative Frequency	Percentage
Eggplant	5	0.20	20%
Carrot	4	0.16	16%
Cabbage	3	0.12	12%
Zucchini	6	0.24	24%
Green Peas	4	0.16	16%
Bell Pepper	3	0.12	12%
Total	25	1.00	100%

Worked Example:

After a survey, Gina gathered data about the fruit preferences of some Grade 7 students. The result is presented in the table below.

 

Orange	Apple	Banana	Orange	Mango
Mango	Orange	Orange	Banana	Apple
Apple	Banana	Apple	Orange	Orange

1. How many of each fruit are there in the data gathered? 
2. Create a frequency distribution table of the data gathered.

Solution: Step 1. Start by transforming the raw data (ungrouped data) into grouped data by considering the frequency per fruit. 

Step 2. Determine the categories. Based on the raw data, the fruit categories are apple, orange, banana, and mango. 

Step 3. Count the frequency per fruit. The frequency of oranges is 6, apples is 4, mangoes is 2, and bananas is 3. The total frequency is 15, which is the sum of all these frequencies.

Fruit	Frequency	Relative Frequency	Percentage
Orange	6
Apple	4
Mango	2
Banana	3
Total	15

Step 4. Compute for the relative frequency. To get the relative frequency of each category, we divide each frequency by 15. The formula is given by: 

Fruit	Frequency	Relative Frequency	Percentage
Orange	6	0.40
Apple	4	0.27
Mango	2	0.13
Banana	3	0.20
Total	15	1.00

Step 5. Compute for the percentage. Compute the percentage by multiplying the relative frequency by 100 or just simply move the decimal point two decimal places to the right.

Fruit	Frequency	Relative Frequency	Percentage
Orange	6	0.40	40%
Apple	4	0.27	27%
Mango	2	0.13	13%
Banana	3	0.20	20%
Total	15	1.00	100%

Day 2

Lesson Activity

A. Using the examples above, answer what is being asked in each item. 

1. Complete the frequency distribution table below. 

   Category	Frequency	Relative Frequency	Percentage
   Male	45
   Female	37
   Total	82

   2. Create a frequency distribution table with the given               data below:

Red	Orange	Yellow	Blue	Red
Violet	Yellow	Orange	Blue	Green
Green	Yellow	Blue	Orange	Blue
Blue	Violet	Violet	Green	Red

B. Group Task: To be done in groups. (15 pts per item) 

Directions: Read and analyze the following word problems, then answer the questions that follow. Be guided by the rubric below.

Criteria	Points	Accumulated
Accuracy of Solution	8
Proper use of statistical data and symbols	6
Total	15

1. Donna conducted a survey about the preferred Student Government presidents of Grade 7 students from a school. Among the 140 respondents, 15% preferred Lloyd, 20% for Emily, 15% for Anne, 15% for Patricia, 30% for Emmanuel, and the rest for Keith. Help Dona create a frequency distribution table of the data.
2. The Supreme Student Government (SSG) conducted a survey about those students who wanted to join the Senior High School Promenade in February. They gathered the following data: 40 will attend, 25 will not attend, and the rest are still undecided.

      a. If there are 135 Senior High School Students, how many are           still undecided? 

      b. What is the percentage of students who will: 

            i. attend? 

           ii. will not attend? 

          iii. not decided? 

      c. Create a frequency distribution table for the problem.

Day 3 PIE GRAPH

    For better visualization of data, graphs can be used for illustration. Pie graph or pie chart is an example of data presentation to illustrate the frequency distribution. 

    A pie graph is a circular graph that shows how the categories are distributed. It shows the division of a whole into its parts. It is used to convey information on different categories, like business, sciences, and education. 

    To draw a pie graph, assign one sector of a circle to each category. The angle of each sector should be proportional to the relative frequency in that category. Since one full circle has 360°, we can find the angle for each category by multiplying the relative frequency by 360°. Below are examples of pie graphs.

                    Figure 1         Figure 2

• In Figure 1, the chart shows the distribution of different kinds of fruits. 
• In Figure 2, the breakdown of the 24-hour schedule of a person is shown.

2. Worked Example Consider the data below. Suppose you have conducted a survey of your friends to find what kind of movie they like and listed down all the responses using the frequency distribution table as shown below.

Favorite Type of Movie
Action	Comedy	Drama	Romance	SciFi
5	4	6	4	1

Create a pie chart to represent the data.

1. Put your data into a table (like above), then add up all the values to get a total: 

   Favorite Type of Movie
   Action	Comedy	Drama	Romance	SciFi	Total
   5	4	6	4	1	20

2. Divide each value by the total and multiply by 100 to get the percent.

   Favorite Type of Movie
   Action	Comedy	Drama	Romance	SciFi	Total
   5	4	6	4	1	20
   25%	20%	30%	20%	5%	100%

3. To find out how many degrees for each sector or “pie slice”, multiply each ratio of different movies.
   
   
   
4. Draw a circle and create sectors “pie slice” using a protractor based on the obtained angle measures. 

3. Lesson Activity 

Perform the following activities following the steps from the examples and be guided by the rubric.

Criteria	Points	Accumulated
Accuracy of Solution	7
Correct Distribution of Data in percent	5
Proper use of mathematical symbol	2
Correct interpretation and final answer	6
Total	20

A survey was conducted on 50 Grade 7 learners to determine what is their favorite fruit. The results were gathered and organized using a Frequency Distribution Table, as shown below. Complete the table and create a pie graph out of it.

Grade 7 Favorite Fruits
Mango	Guava	Apple	Banana	Grape	Total
15	14	6	6	9

 

Making Generalizations

1. Learners’ Takeaways 

KWL – Activity 

PENTOWRITE: This activity will be answered individually to monitor each learner about their understanding of the lesson. 

What I Know	What I’m Learning	My New Learnings

2. Reflection on Learning 

1. Why do we need to use a pie chart in presenting a set of data? 
2. When do we choose a pie chart to present the data?

DAY 4 Evaluation Learning

1. Formative Assessment

1. Complete the frequency distribution table below:

   Category	Frequency	Relative Frequency	Percentage
   Male	26
   Female	31
   Total	57

2. Fifty Grade 7 learners were asked about their favorite destination in the Philippines every summer vacation. The table shows the result. Construct a pie chart out of the given data and explain each part of the pie chart based on the distribution of the data. 

Destination	Number of Students
El Nido	8
Boracay	5
Baguio	14
Bohol	11
Cebu	12

2. Homework (Optional)

The data below is the result of the voting during the Grade 7 parents' meeting on the agreement of the asynchronous class.

Responses	Frequency	Relative Frequency	Percentage
Strongly Agree	10
Agree	8
Disagree	9
Strongly Disagree	8
Total	35

a. Complete the frequency distribution above to determine the relative frequency and percentage of each category. 

b. Construct a pie chart to represent and explain the data graphically.

Learning Resources:

Byju’s The Learning App. Types of Graphs. Retrieved December 2023 from https://byjus.com/maths/types-of-graphs/

Dummies. (2016). The Basics of Pie Chart. Retrieved 19 December 2023 from ummies.com/article/academics-the-arts/math/pre algebra/the basics-of-pie-charts-168778/ 

Hoyland, S. Study.com (2023). Frequency Distribution in Statistics: Table and Examples. Retrieved 20 December 2023 from https://study.com/learn/lesson/frequency-distribution-table.html Nivera, G. C. (2018). 

Grade Mathematics: Patterns and Practicalities (pp. 435-436). Don Bosco Press. 

Pierce, R. Math is Fun. (2022). Frequency Distribution. Retrieved 20 December 2023 from https://www.mathsisfun.com/data/frequency-distribution.html

Pierce, Rod. "Data Graphs (Bar, Line, Dot, Pie, Histogram)" Math Is Fun. Ed. Rod Pierce. 20 Dec 2023. 20 Dec 2023 http://www.mathsisfun.com/data/data-graph.php StatisticsHowTo.com. (2023). 

Frequency Distribution Table: Examples, How to Make One Retrieved 19 December 2023 from https://www.statisticshowto.com/probability-and-statistics/descriptive-statistics/frequency-distribution-table/

Grade 7 Lesson Exemplar