Unit Plan on Order of Operations

UNIT 1:	TOPIC: Comprehension of Whole Numbers			TIME FRAME: 15days
Stage 1 DESIRED RESULTS / OUTCOMES
Content Standard: The learner understands the concept of exponents and base, order of operations (PEMDAS) of whole numbers and enjoys relating it to a variety of problem situation.			Performance Standard: The pupil solves real life problems involving order of operations of whole numbers and computes them using a variety of strategies.
Essential Understanding: - Math terms such as expression, equation, evaluate are very important terms for the succeeding lessons . Most of these terms are often use in giving instructions such as in order of operations and word problems. - In evaluating expressions with more than two operations, follow the PEMDAS rule. - There are various strategies in solving word problems.			Essential Questions: - Why do I need to know some Math Terms? - How does understanding order of operations rule help in performing expressions with more than two operations? - What information and strategies would you use to solve a multi-step word problem?
Prior Knowledge: Misconceptions: - In evaluating number with exponent, just multiply the base and the exponent. - In evaluating expressions with more than two operations, start performing from left to right. - Only one strategy can be used in solving word problems.			Transfer Goals: Use operations of whole numbers with more than two operations in solving real-life problems.
Students will know: (Cognitve) - Exponent and Base - Order of Operations - Multi-Step Word Problems The students must be able to: (Affective) - show honesty and precision in solving problems - manifest patience in solving problems - exhibit orderliness and cleanliness in one’s work - manifest thriftiness in budgeting money			Students will be able to do: (Psychomotor) - give the meaning of expression, equation, exponent, and base - translate the mathematical expression into word expression and vice-versa - find the value of a number involving exponents - use order of operations to find the value of a mathematical expression - apply the order of operations in solving two to three-steps word problems - use varied strategies in solving multi-step word problems - cite situations where order of operations whole numbers can be applied
Stage 2: ASSESSMENT EVIDENCE
Product or Performance Task Goal: Proficiency in performing operations of whole numbers and order of operations; develop strategies for selecting the appropriate computational and operational method in problem-solving situation. Role: Family Budget Manager Audience: Family Members Situation: You are responsible for managing your family’s checkbook for one month. During this time period, you will make deposits, make withdrawals from the ATM (Automatic Teller Machine) and write checks in order to pay various bills. You will begin with a balance of P45, 000. Your task is the following: 1. Solve the problems that require you to use your mathematical skills. 2. Order all of the transactions by date. 3. Enter each transaction in the checkbook register. 4. Tally your results. Be sure you are using the correct operation in your checkbook register. 5. Check your work. Remember, you must come out with the correct balance at the end of your register Rubric for the project will be used to score the output.		Evidence at the level of Understanding: Explaining the concept of exponent, expression, equation; the steps in solving expressions with more than two operations and steps in solving word problems. Interpreting diagrams, tables, pictures and problem situations involving whole numbers Applying operations of whole numbers and order of operations in solving word problems. Showing Empathy by describing how one feels when there are no orders/steps to be followed in solving problems. Manifest Self-Knowledge by suggesting ways to help improved one’s mathematical skills		Evidence at the level of Performance Calculation Skills Clear presentation of Solution Creative Accurate Drill: Completeness of Work Accurate Mange Time Wisely Oral/Written Explanation Correct Response Thorough-use vivid and precise language Illustrative Group work: Teamwork is visible Mange Time Wisely Complete and Correct Output Performance Task: - Creativity in Presenting the Solution - Concept Accuracy - Teamwork
OTHER EVIDENCES OF UNDERSTANDING - oral and written explanation - quizzes - boardwork - hands-on activity - simulation and games - drills - think-pair-share
Stage 3: LEARNING PLAN
TEACHING/LEARNING SEQUENCE: USE OF THREE Is INTRODUCTION OF ESSENTIAL QUESTIONS: Session 1: “MATH is FUN” 1. Ask the students to give a meaning to each letter of the word MATH. Then compose a CHANT using the acronym formed. In the content of the chant, they should include the math terms they will encounter and how are these terms relevant to them. Process the children after they have performed the chant. 2. Tell the students that they are going to learn order of operations of whole numbers in the whole unit and they are going to apply these to various situations. Introduce the essential questions and performance task to the students. Essential Questions: - How does understanding “order of operations rule” help in performing expressions with more than two operations? - What information and strategies would you use to solve a multi-step word problem? INTERACTIONS: Session 2: “ Expression, Equation, Exponent, and Base Guess the 4E’s Game” 1. Post pictures on the board. Tell the students to guess what each picture tells. Give a clue to the students. They are all math terms. 2. Ask each group to write the meaning of the words in a barbell diagram. Post their works on the board for other students to see and the teacher will lead the discussion. 3. The teacher will post numbers, operation symbols, grouping symbols on the board, tell the students to form an expressions and equations. Then ask them to differentiate expressions and equations. 4. In their math drill, students will write at least 2 math expressions and 2 math equations, then evaluate. Session 3: Translating Mathematical Expressions to Word Expressions and Vice-Versa “Translate My Words” July 15 – 17 1. Group Contest: Each group will be provided with quadrant chart. The quadrant chart has the symbol addition, subtraction, multiplication, and division. Ask each group to write terms related to addition, say, plus, increase of, more than, etc. The group who has the most number of terms given wins the game. 2. Divide the class into groups of four. Read an example equation to the class and as a group try to translate the equation using the number disks. Ex. The sum of x and 5 3. After everyone understands the task, read a different expression to the students. 4. After reading the expression, have the students show the expression using their group’s manipulative. 5. Have one person from each group raise their hand when the group has an answer and the teacher can check for correctness. 6.After a correct answer is found, have all of the groups correct their answer and discuss any questions that might arise. 7. 7. 7. 7.Continue giving expressions to the groups until you feel that they have an understanding of the translations. 8. Pair work: Ask students to answer page 18-19 “Let’s Work Together” of their book. Session 4 : Drill ( July 18 ) 1. Test the understanding of the students by asking them to answer page 19-20. 2. Showing of solution through board work. Ask two or three students to explain their work. 3. Summarize the concept learned on Expression and Equation in foldable form: Format is hamburger fold. Session 5: Exponent and Base 1. Show a multiplication sentence such as 6 x 6 x 6 x 6. And ask: How many times does the digit 6 used as a factor? What is the shortcut way in writing repeated multiplication? 2. Ask volunteer to write 6x6x6x6 in another way using exponents. Point out which is the base, and exponent. 3. Brain Buzz: With their partner, share their knowledge on what they have understood about exponent and base. 4. Give examples on the board and ask students to evaluate the given expression. Remind them that the given example is a mathematical expression. Ask volunteer to demonstrate how to evaluate numbers with exponent. 5. Play expo-bingo for drills. 6. Group work: Give a word problem to each group involving exponents. 7. Challenge the students to do the activity for mastery provided by the teacher. 8. Journal Log: How is the use of exponents relevant to me? Session 6: Order of Operations 1. Instruct the students to read what they have written in their journal log about exponents. 2. Ask: Did you help your mother in some household chores? If so, what kind of household chores were you involved in? Write down the steps you take in doing the household chores. Ex. Washing Clothes. And ask how does the order of the steps you take affect the result? How about in Math, if there is more than one operation in an expression, what do we do? 3. Pair work: Give a mathematical expression, say, 4 + 5 x 9 – 4, first ask the students to use paper and pen method in solving the expression. The second one is to use scientific calculator. Let them compare the answers. Ask: Are they the same? If so, why are they same? If not, why are they different? 4. Tell the students that there is a rule to follow in performing more than two operations with whole numbers. The acronym is PEMDAS. Ask the students what does the acronym stand for? What does this mean? In what instance do we apply PEMDAS? 5. Works in group of three. Look at the five number sentences in the table. Pupil A is to work them out from left to right without using a calculator. Pupil B is to work without using a calculator. Pupil C is to work them out using a calculator by keying in the number sentences from left to right. Have them discuss the results. 6. After answering the activity, process the students by asking: a. What have you realized after performing the activity? b. How many operations are involved? c. Which operation was done first? d. Which operation was done next? e. Were you able to follow PEMDAS thoroughly? What would happen if you don’t follow it? 7. Drill on performing expression with four operations. Name which operations should be done first, second, third, and so on. 8. Challenge the students to do mental math in answering the given expressions as shown in the flashcard. Give the students another exercise for mastery. 9. Solicit ideas from the students: What grouping symbols do you know? How are they used? Post an expression containing grouping symbols and exponents on the board, and ask the students to do it by pair. Have them discuss the problem. Ask volunteer to demonstrate how to perform expressions with grouping symbols. Then process the children for further understanding. 10. By pair: Ask each student to make an expression with four operations then solve. Have one student explain his work while the other one listens, then exchange role. After that answer some exercises on the book for mastery. 11. Tell the students that in the next activities, they will apply the understanding they have gained on order of operations. Session 7: Problem Solving: 1. Discuss and illustrate some of the problem-solving strategies below. a. Make an equation b. Solving Backwards c. Draw a Picture or Graph d. Look for Patterns e. Block Model Approach f. Make an Organized List 2. Read the problems on the board. Identify the strategies that are more appropriate for solving problems. How do you know which strategy is best used for the given problem? Specify that making an equation is the most appropriate. Discuss and illustrate the four steps in problem solving: a. Explore b. Plan c. Solve d. Examine 3. Let us now apply the strategy in solving problem. Give the students the worksheet for activity 15. Allow them to work in groups of three. Ask the students to to present and explain their answers on the board. How useful is order of operations in solving problems? 4. Discuss another strategy in solving problems. Handout word problems to the students. Allow them to discuss the problems with their group mates. INTEGRATION: 1. In the next activities, we will fuse what we have learned. With your foldables, summarize the concept learned on expressions, equations, exponents, order of operations. Write down their applicability to real life. 2 . Time to reflect. What did you learn from the previous lessons? What topic do you like most? What topic do you like least? 3. Students will share their reflections in their group. Ask some volunteers to share it in the class. 4. The students will have 3 weeks to complete the project at home. They were encouraged to complete their tasks prior to the due date. Closure: Close the topic and relate back to how order of operations is used in real life situations.

Solving Backward

LC: Solve word problems by working backwards.

I. Learning Objectives: After the activity, pupils shall be able to

EOC1 solve word problems by working backwards.

EOP2 demonstrate accuracy in writing the equation

EOA3 solve with confidence.

II. Learning Content:

Topic: Working Backwards

Concept: When solving a problem by starting at the end and working

backwards, any mathematical operations you

come across will have to be reversed.

Skill: solving correctly

Values: confidence

Material: problems written in cartolina

Resources: www. lessonpage.com

MTG Pop Sheets

III. Learning Experience:

Classroom Routine: Checking of Attendance and I.D.

A. Introduction: Back Me Up!

Activity 1. Who can recite the alphabet backwards?

Activity 2: Who can write his name backward in 15 seconds?

· What comes to your mind when you hear the word

“backward”?

· In Math, is there an instance where in we solve backwards?

· What is the opposite of addition? multiplication?

B. Interaction: Pairwork

Activity 3:

Jimmy had a certain amount of money. He spent P54 on books

and received another P300 from his father. He then had P580 left.

How much did he have at first?

a. Can someone give an example of a word or words that imply addition or subtraction?

b. Can you state the ways you could solve a problem?

c. What have you noticed in the given problem?

d. How would you solve when the unknown is in the beginning of the problem?

e. What symbol do you represent for the unknown?

f. What do you think is the mathematical sentence?

Let X the amount he had at first

X – P54 + P300 = P580

X= P580 –P300 + P54 = P334

g. Is the answer reasonable?

C. Integration:

1. Generalization:

· When do we solve backwards?

· How do we solve backwards?

2. Evaluation: Quiz

a. N + 45 - 66 x 8 = 88, what is N?

b. Subtract 14 from a number, the result is 51. What is the number?

3. Reflection:

How can you gain confidence in solving problems?

IV. Assignment: Drill Notebook

I. Write an equation, then solve by working backwards.

There were some apples in a box. Tom took 15 apples and Janet took 27 apples out of the box. Mrs. Tan put in 20 more apples

and threw away 9 rotten apples. There were 60 apples left in the

box. How many apples were there at first?

II. Answer briefly.

Did you find difficulty in solving the problem?

Which word/phrase distracts you most?

Kinds of Angles

LC: Visualize, name, and classify different kind of angles.

I. Learning Objectives: By using arm movements, pupils shall be able to:
C: classify angles as right, obtuse, acute, straight, or reflex.
C: identify the parts of the protractor.
P: demonstrate different kinds of angles using arm movements.
A: show enthusiasm by participating well in the activity.

II. Learning Content:
Topic: Kinds of Angles
Concept: Acute Angle – an angle that measures below 90 degrees.
Right Angle – an angle that measures exactly 90 degrees.
Obtuse Angle – an angle that measures more than 90 degrees but below 180 degrees.
Straight Angle – an angle that measures exactly 180 degrees.
Reflex Angle – an angle greater than 180 degrees.
Skill: Classifying Angles
Values: enthusiasm
Materials: model of different kinds of angles
Resources: Kotah, M. (2005), Soaring 21st Century
http://www.education.com/activity/fourth-grade/page7/
Glencoe, Mathematics Connection and Application

III. Learning Experience:
Classroom Routine - checking of attendance, ID, etc.
A. Introduction:
1. Prelection:
a. Review: Brainstorming (by pair)

With your protractor make a list of observations based on the physical appearance of the protractor.

The list may include the following:
- It is shaped like a semi circle (although some protractors can be a full circle)
- It looks like a ruler
- It has numbers labeled from 0 to 180
-There are two rows or scales of numbers
-The upper scale starts with 0 on the left side and increases to 180
on the right the lower scale starts with 180 on the left side
and decreases to 0 on the right
-The upper scale measures angles with openings on the left
- The lower scale measures angles with openings on the right
- The protractor is clear so that the angle can be seen and measured
accurately

2. Preview:
a. Motivation:
· Who can draw a picture of an angle on the board?
· Can you define it by your own words?
· What the word angle sounds like? Hint: Its part of your body.
· Explain that word angle comes from the word ankle, and that your foot makes
an angle with your leg.

b. Presentation of the day’s lesson

B. Interaction:
Activity 1: By pair
1. Measure students' angles. Show the students how to make an angle with your arms. Have one student in a group and have his right arm up level to his shoulder. Use a protractor to measure the angle.


· What did you notice on the position of the angle?
· What kind of angle is this?
· Can you identify right angles in the classroom?
2. Ask the student to put his arm a little bit down. This is an acute angle.

· What happens to the opening of the angle?
· What would happen to the measurement of the angle? Would it go up higher
or lower?
· What kind of angle is this?
3. Ask anyone to make an angle more than 90 degrees using their arms.

· What did you notice on the opening of the angle?
· What kind of angle is this?

4. Let the students figure out how 180 degrees would look like. Hint: Let them
realize that the measure of the two right angles is 180 degrees.


Activity 2: Drill
Teacher will give an angle measurement and students will demonstrate
through arms movements.

C. Integration:
1. Generalization: Journal-Writing
· What are the different types of angles?
· How do we measure angles?

2. Valuing:
· How do you find the activity today?

3. Action: List down a real life situation where you could use your knowledge
about angles.


IV. Evaluation: Fixing the Skills
Answer page 343 letter E – F.

A. Fill in each blank with the correct answers to complete the sentence.

1. A right angle has a measure of ______.
2. A straight angle has a measure of ____.
3. An acute angle measures between ____ and ____.
4. An obtuse angle measures between ____ and ____.

B. Classify each angle as acute, right, obtuse, or straight. (see page 115 of your book)



V. Assignment:
Invent a cheer utilizing arm movements that demonstrate the different kinds of angles. This will be performed on Monday.

Criteria:
Concept Accuracy: 20 points
Creativity: 20 points
Props/Costume 10 points

Addition of Similar Fractions

LC: Add and subtract similar fractions in simple form without regrouping.

I. Learning Objectives: Using a model, pupils shall be able to:
C: analyze the steps in adding/subtracting similar fractions.
P: perform addition and subtraction similar fractions correctly.
A. show patience while learning the skills.

II. Learning Content:
Topic: Adding and Subtracting Similar Fractions
Concept: To add or subtract fractions with like denominators, add the
numerators. Use the same denominator in the sum or
difference.
Skill: Adding and Subtracting Similar Fractions
Values: Patience
Material: 2 by 3 grid, flashcards of fractions
Resources: Kotah, M. (2005), Soaring 21st Century
Glencoe, Mathematics Applications and Connections
www.lessonplanpage.com

III. Learning Experience:
Classroom Routine - checking of attendance, ID, etc.

A. Introduction:
1. Prelection:
a. Drill: Flashcard Drill on Reducing Fraction to Lowest Term.
· 25/75
· 36/48
· 150/250

2. Preview:
a. Motivation:
· Cake was dessert for supper. Two thirds of it was left over. If a visitor arrives and is offered one third of the cake, then what portion of the cake is left over?
· Kim bought some special plastic sticker to use for decorating her walls. She used 2/6 for one wall and 3/6 for another wall. How many of her plastic stickers did she use?

b. Presentation of the day’s lesson

B. Interaction:

Activity 1: Pairwork.
Procedures:
· Draw a 2 x 3 grid as shown below.
· Shade three squares with blue.
· Then, color 2 squares with red.

Questions for Discussions:

· What fraction does color blue represent?
· What fraction does color red represent?
· How many squares are colored? What fraction would that represent?
· If you color four more squares, what fraction would that represent?
· What is the addition sentence?
· What have you noticed with the sum?

C. Integration:
1. Generalization: writing
· How are similar fractions added/subtracted?

2. Reflection:
· In solving the fractions, which step do you find difficult?

3. Action:
· What would you do to lessen your difficulty?

IV: Evaluation: Quiz
a. Perform the indicated operations. Reduce to lowest term if
necessary.

· 2/3 + 1/3
· 11/18 + 1/19

V. Assignment: Answer in your drill notebook.
1. Solve each equation. Write the solution in simplest form.
· a + 2/5 = 4/5
· 8/9 – c = 4/9

2. Solve each problem.
· How much longer than 7/16 inch is 15/16 inch?
· How much more is ¾ cup than ¼ cup?

Surface Area of a Cube

LC: Finding the surface area of a cube.

I. Learning Objectives: After the activity, pupils shall be able to:
C: discover surface area formula of a cube.
P: solve for the surface area of a cube.
A: follow instructions properly.

II. Learning Content:
Topic: Surface Area of a Cube
Concept: SA = 6 faces x area of each square
SA = 6s2
Values: following instructions properly
Materials: oslo paper, masking tape, scissor,
Resources: Apistar, E. (2005), Soaring 21st Century
Torres, H. (2009) Number Smart
http://www.education.com/activity/fourth-grade/page7/

III. Learning Experience:
Classroom Routine - checking of attendance, ID, etc.
A. Introduction:
1. Preview:
a. Motivation: Game Ka Na Ba? ( group of 4 )
I have two flat surfaces.
0 edges and 0 vertices
Which space figure am I?

I have 5 faces and 5 vertices.
How many edges do I have?
Which space figure am I?

I have 6 faces and 12 edges
I am not a rectangular prism
Which space figure am I?

I have a flat surface and curved surface.
Which space figure am I?

b. Presentation of the day’s lessons.

B. Interaction:
Cooperative Learning:

What you will do:
1. Draw the figure below in an oslo paper.
(show the flat figures of a cube with 10cm each side)
2. Be sure to copy the correct measurement.
3. Cut the figure.
4. Form a three-dimensional figure by putting masking tape on each edges.
(they should form a cube)

· What shape did you form?
· How many edges/sides are there in a cube?
· How many faces are there in a cube?
· How do we get the area of each face?
· What is the total area of all the faces?
· How do we get the surface area of a cube?

C. Integration:
1. Generalization:
· What is the formula in finding the surface area of a cube?
2. Valuing:
- How important is following instructions?
3. Action:
Explain in your own words on how you get the formula SA=6s2.

IV. Evaluation:
Rubrics:
Teamwork: 5 pts.
Getting the correct answer 15 pts.

V. Assignment: Find the surface area of each cube with the given side.
1. 12mm
2. 110cm
3. 1.5 ft

Changing Percent to Fraction

LC: Change percent to fraction and vice-versa.

I. Learning Objectives: After the activity, pupils shall be able to:
C: analyze the process in changing percent to fraction and vice-versa.
P: convert percent to fraction and vice-versa with accuracy.
A: do the activity joyfully.

II. Learning Content:
Topic: Changing Percent to Fraction and Vice-Versa
Concept: To express percent as a fraction,
express the percent as a fraction with a denominator of 100.
Then, simplify. To express a fraction as a percent, write a
a proportion and solve it.
Skill: Changing fraction to decimal and vice-versa
Values: Doing work joyfully.
Materials: ball, wastebasket
Resources: Apistar, E. (2005), Soaring 21st Century
Insigne, L. (2003), Math and Me
www. lessonpage.com

III. Learning Experience:
Classroom Routine - checking of attendance, ID, etc.

A. Introduction:
1. Prelection:
a. Review: What does the word percent mean?

2. Preview:
a. Presentation of the day’s lesson
b. Motivation:
· In the word person, 50% of the letter spells the name of a
family member. Ans. Son

· In the word “price”, 80% of the letters spells the word of the primary
food the Filipino eats. Ans. Rice

· In the word fraction, 75% of the letters spells the
word for the meaning of a verb.

In the word muse, 75% of the letters spell the word of the
answer to an addition problem. Ans.sum

B. Interaction:
Activity 1: Work in group of four

a. Stand behind a line 15 feet from a wastebasket.
b. Have each person throw a ball into the basket. Each person will have
five tries.
c. Have one group member record a ratio for the total number of baskets
made out of the total number of tries.
e. Calculate the percent of baskets made for the group.


Fill in the chart:

Total Number of Baskets Made/Total Number of Tries Percent



· How many shoots have you made?
· How many shoots/baskets have you tried all in all?
· How did you find the percent?

Activity 2: Drill
a. Write as percent:
5/100 ___
5/ 20 ___

b. Write each percent as a fraction in lowest term.
13%
36%

C. Integration:
1. Generalization:
· How do you convert fraction to percent? Percent to fraction?

2. Reflection:
· Did you enjoy the activity?

3. Action
· What should you do to make your work joyful?

IV: Evaluation: Quiz (portfolio)
The circle graph shows the monthly budget for the Aquino family.





a. What fraction in simplest form, represents the portion of the
family budget that is spent on:
- Rent - clothes - utilities
- savings -food

V: Assignment: Enrichment
Do page 198 letter of your book.

Area of a Circle

LC: Derive formula in finding the area of a circle.

I. Learning Objectives: After the activity, pupils shall be able to:
C: derive area formula of a circle.
P: determine the area of a circle using the formula A = ∏ x r2
A: finish the assigned task within the given time frame.

II. Learning Content:
Topic: Area of a Circle
Concept: A = ∏ x r2
Values: sense of responsibility
Materials: paper plates, scissors
Resources: Apistar, E. (2005), Soaring 21st Century
Torres, H. (2009) Number Smart
http://www.education.com/activity/fourth-grade/page7/

III. Learning Experience:
Classroom Routine - checking of attendance, ID, etc.
A. Introduction:
1. Preview:
a. Motivation: Show a circle drawn on centimeter grid
- How many squares are there inside the circle?
b. Presentation of the day’s lessons.

B. Interaction:
Work with a group!
1. Fold your paper plate into eights.
2. Unfold the plate and cut along the creases
3. Arrange the pieces to form a parallelogram as shown below.

a. What is the height of the parallelogram?
b. What is the length of the parallelogram’s base?
c. How would you find the area of the parallelogram?
d. How would you find the area of the circle?
e. What is the formula for it?

Area = base x height = 1/2 circumference x radius = 1/2 [(pi) x 2r] r = (pi)x r2
C. Integration:
1. Generalization:
o How do we derive for the area formula of a circle?

2. Valuing:
· How do you show your sense of responsibility to your groupmates?

3. Action: Find the area of a circle using the formula:
d = 5 in
r =10 in


IV. Evaluation: Criteria
Solution:
10 points – solution is complete, clear, and correct.
5 points – solution is correct but style of presentation is poor.
3 points – solution is incorrect

Teamwork: 5 pts. – each member of the group performs the task
3 pts – 50% of the group performs the task

V. Assignment: ½ crosswise
a. Explain how the area of a parallelogram is related to the area of the
circle?
b. Write in your own words, how to find the area of a circle with a
diameter of 6m.