Basic Education Assistance for Mindanao (BEAM) project. Prior approval must be
given by the author(s) or the BEAM Project Management Unit and the source must
be clearly acknowledged.
Mind Map
The Mind Map displays the organization and relationship between the concepts and activities in this Learning Guide in a visual form. It is included to provide visual clues on the structure of the guide and to provide an opportunity for you, the teacher, to reorganize the guide to suit your particular context.
Stages of Learning
The following stages have been identified as optimal in this unit. It should be noted that the stages do not represent individual lessons. Rather, they are a series of stages over one or more lessons and indicate the suggested steps in the development of the targeted competencies and in the achievement of the stated objectives.
Assessment
All six Stages of Learning in this Learning Guide may include some advice on possible formative assessment ideas to assist you in determining the effectiveness of that stage on student learning. It can also provide information about whether the learning goals set for that stage have been achieved. Where possible, and if needed, teachers can use the formative assessment tasks for summative assessment purposes i.e as measures of student performance. It is important that your students know what they will be assessed on.
1. Activating Prior Learning
This stage aims to engage or focus the learners by asking them to call to mind what they know about the topic and connect it with their past learning. Activities could involve making personal connections.
Background or purpose
Strategy
TRIVIA. This strategy requires an accurate response that will enable the students to
learn and develop their mathematical skills. It is a fun and interesting way of activating the students' comprehension through visuals. This aims to enhance their logical/mathematical and visual/spatial intelligences.
Material
• activity sheet (refer to Student Activity 1 on page 12)
Activity 1: “Multiply By Itself”
Instructions:
1. Organize the class into 10 groups or as desired and distribute the activity sheet.
2. Set a time allotment for them to work for the activity. 3. Let them present their outputs to the class.
Formative Assessment
Ensure the participation of the students in the activity by monitoring their performance. Check their outputs. Refer to page 13 for the answers.
Roundup
The students would have rewritten two factors with the same value into exponential form and determined their product.
2. Setting the Context
This stage introduces the students to what will happen in the lessons. The teacher sets the objectives/expectations for the learning experience and an overview how the learning experience will fit into the larger scheme.
Background or purpose
The students in this stage will be given an overview on how to determine square roots of the numbers and their approximate values.
Strategy
BUZZ SESSION.This strategy aims to maximize students' engagement and to tap their verbal/linguistic and mathematical intelligences through answering questions or solving problems and come up to some kind of conclusion.
Material
• activity sheet (refer to Student Activity 2 on page 14)
Activity 2: “Ir-Rational Balloons”
Instructions:
1. Organize the class into 10 groups or as desired and distribute the activity sheet.
2. Set a time allotment for them to work for the activity.
Formative Assessment
Ensure the participation of the students in the activity by monitoring their performance and progress.
Check their outputs. Refer to the answer key on page 15.
Roundup
The students would have given an overview on how to determine the square roots of the numbers and their approximate values.
3. Learning Activity Sequence
This stage provides the information about the topic and the activities for the students. Students should be encouraged to discover their own information.
Background or purpose
In this stage, students will be able to demonstrate knowledge and skill in solving square roots of positive rational numbers.
They are expected to:
• define square root of a rational number;
• approximate the square root of a positive rational
number;
• identify square roots which are rational and which are
not rational (irrational numbers);
• determine two integers or rational numbers between which it lies, if the square root
of a number is not rational;
• give examples of other irrational numbers; and
• use knowledge related to square roots in problem-solving.
Strategies
INTERACTIVE LECTURE. This strategy provides students with a general outline to give
them a framework for thinking about a subject and to structure their note-taking. This type of lecture involves the students by focusing their attention on key words and emphasizes information transfer at the knowledge, recall, and comprehension levels of learning.
PUZZLE. This strategy is structured for small group work that encourages
participation, cooperative learning and group responsibilities. It caters students whose comprehensions are activated using visuals. This enhances their
logical/mathematical, kinesthetic and spatial intelligences.
PROBLEM SOLVING. Teaching students how to effectively solve problems will
provide them with useful lifelong skills. Problem solving models, so as working mathematical model, break problem solving into a step by step process:
CLARIFY What is the problem asking you to do or find out?
CHOOSE What tools would be effective for solving the problem?
INTERPRET Is this answer reasonable? Can you check it using another method?
Materials
Activity 3: “Form Me”
• activity sheet (refer to Student Activity 2 on page 16) • manila paper
• masking tape • crayon (4-5 pieces)
Activity 4: “Working With Square Root”
• task cards (refer to Teacher Resource Sheet 4 on page 18) • manila paper
• masking tape • marking pen
LECTURETTE 1
Refer to Activity 1. Ask the students to write the expressions below in exponential form and find their products.
1) 2 x 2 2) 7 x 7 3) -9 x -9
Guide questions:
• What do you call the product of these two factors?
Answer: perfect square
• In reverse, what do you call this factor?
Answer: square root
• How would write square root in symbol?
Answer:
• In general, what do you call this symbol?
Answer: radical sign
Let them write the expressions in symbols and give their roots.
a. square root of 4 b. square root of 25 c. square root of 10
Questions:
• Which of the problems above gives a rational square root? which is/are not? • What do you call this non-rational number?
Now, ask them to identify which of the square roots below are rational. Then, find their roots.
1.
18 4.
2 7.
4842.
64 5.
12 8.
1203.
169 6.
625 9.
144•
2 •
12Solutions:
Let the students try to solve the second problem.
Introduce another method of estimation named Successive Division. Example: Approximate
5 to the nearest hundredths place. The integer nearest to
5 is 2.• 22.5
2 = 4.5
2 =2.25
Step 2: Get the average of 2 and 2.5.
• 5 ÷ 2.25 = 2.22... Step 3: Divide 5 by 2.25.
Therefore,
5 lies between 2.22 and 2.25. Get its approximate value.Hence,
5 ≈ 2.23.Activity 3: “ Form Me”
Instructions:
1. Organize the class into 10 groups or as desired.
2. Distribute the activity sheet. Refer to Student Activity 2 on page 16.
3. Set a sufficient time allotment to work for the activity.
4. Check their outputs. Refer to page 17 for the answers.
Activity 4: “Working With Square Root”
Instructions:
1. Reorganize the class into 8 groups and distribute the materials needed. Refer to Teacher Resource Sheet 4 on page 18 for the tasks. Ensure that 2 groups will answer the same task.
2. Set a sufficient time allotment for them to work for the activity.
3. After which, ask the groups with the same task to discuss their output together to reach a consensus.
4. Refer to page 19 for the answer key.
Formative Assessment
Ensure the participation of the students in the activity by monitoring their performance and checking their progress.
Roundup
The students would have defined square root and approximated the square root of a positive rational number, identified square roots which are rational and which are irrational numbers, determined two integers or rational numbers between which it lies if the square root of a number is not rational, given examples of other irrational numbers, and used knowledge related to square roots in problem-solving.
4. Check for Understanding of the Topic or Skill
This stage is for teachers to find out how much students have understood before they apply it to other learning experiences.
Background or purpose
Strategy
BUZZ SESSION. This strategy aims to maximize students' engagement and to tap their verbal/linguistic and mathematical intelligences through answering questions or solving problems and come up to some kind of conclusion.
Materials
• image pictures (refer to Teacher Resource Sheet 6 on
page 20)
• activity sheet (refer to Student Activity 5 on page 21)
• masking tape • manila paper
Activity 5: “Let's Party”
Instructions:
1. Prior to the activity, prepare the image pictures and put inside the envelope. Refer to Teacher Resource Sheet 6 on page 20.
2. Divide the class into 10 learning groups and distribute the materials needed.
3. Set a time allotment for them to work for the activity.
4. Let them present their outputs to the class for comparison and discussion.
Formative Assessment
Ensure the participation of the students in the activity by checking their progress and monitoring their performance.
Check their outputs. Look for the answer key on page 22.
Roundup
The students would have demonstrated knowledge and skill in solving square roots of positive rational numbers.
5. Practice and Application
In this stage, students consolidate their learning through independent or guided practice and transfer their learning to new or different situations.
Background or purpose
The students will solve problems involving square roots in real life situations.
Strategy
TASK CARDS. These specify a task or activity for students to complete individually, in pair or as a small group. Making tasks “real life” tasks make them more meaningful. Task can be issued to practice a newly developed skill. This strategy aims to develop their
logical/mathematical, spatial/visual and interpersonal intelligences.
Materials
• task cards (refer to Teacher Resource Sheet 8 on page 23) • marking pen
Activity 6: “Real Fact”
Instructions:
1. Prior to the activity, prepare the task cards.
2. Divide the class into 8 learning groups and distribute the materials needed. Ensure that two groups will have the same task.
3. Let them write their output on a manila paper and present it to the class.
Formative Assessment
Ensure the participation of the students in the activity by checking their progress and monitoring their performance.
Check their outputs. Refer to the answer key on page 24.
Roundup
The students would have solved problems involving square roots in real life situations.
6. Closure
This stage brings the series of lessons to a formal conclusion. Teachers may refocus the objectives and summarize the learning gained. Teachers can also foreshadow the next set of learning experiences and make the relevant links.
Background or purpose
In this stage, the students will consolidate their learning about the topic.
Strategy
MAZE. This is an exciting game where students are competing to find out their final destination by following the right road trail. This strategy enhances students' logical/mathematical and visual/spatial intelligences.
Materials
• activity sheet (refer to Student Activity 7 on page 25) • crayon
Activity 7: “A-MAZE-iNG”
Instructions:
1. Reorganize the class into 10 groups and give the activity sheet. 2. Set a time allotment for them to work the activity.
3. Let them present their outputs to the class for comparison.
Formative Assessment
Ensure the participation of the students in the game by monitoring their performance. Check their answers using the answer key on page 26.
Roundup
Teacher Evaluation
(To be completed by the teacher using this Teacher’s Guide) The ways I will evaluate the success of my teaching this unit are: 1.STUDENT ACTIVITY 1
Multiply by Itself
What do you call a product whose two factors are the same?
To answer this question, rewrite first the problems in the table into exponential
form as shown in the example and look for their answers in the balloons. Then,
write them in the SOLUTION column. After which, affix each letter in the box
found in each horse that corresponds to your answer.
Item PROBLEM EXPONENTIAL FORM SOLUTION Item PROBLEM EXPONENTIAL FORM SOLUTION
1 2 x 2 22 6 31 x 31
2 -13 x -13 7 -12 x -12
3 5 x 5 8 16 x 16
4 35 x 35 9 27 x 27
5 24 x 24 10 9 x 9
TEACHER RESOURCE SHEET 1
Multiply by Itself
ANSWER KEY
What do you call the product whose two factors are the
same?
Item PROBLEM EXPONENTIAL FORM SOLUTION Item PROBLEM EXPONENTIAL FORM SOLUTION
1 2 x 2 22 4 6 31 x 31 312 961
2 -13 x -13 (-13)2 169 7 -12 x -12 (-12)2 144
3 5 x 5 52 25 8 16 x 16 162 256
4 35 x 35 352 1,225 9 27 x 27 272 729
STUDENT ACTIVITY 2
Ir-Rational Balloons
Directions:
1. Determine each given number in the balloon whether rational or irrational.
2. If rational, rewrite it in RATIONAL COLUMN and give its root. If irrational,
affix it in the IRRATIONAL COLUMN and determine two integers or rational
numbers between which it lies, then write its estimated value.
Question:
●
Do you know how to find two rational numbers where between which the
given square root lies?
If yes, how? ______________________________________________________
_________________________________________________________________
If no, that would be further discussed in the next stage.
1
3
12
9
27
7
4
36
39TEACHER RESOURCE SHEET 2
Ir-Rational Balloons
ANSWER KEY
1
3
12
9
27
7
4
36
39STUDENT ACTIVITY 3
Form Me
Directions:
1. Cut the figures and assemble them to form four pictures of animals. Paste them on a manila paper.
2. Cut also the boxes containing the square roots and determine their roots from the formed figures. Paste them appropriately in the empty boxes within the figure.
3. Then, name and color each animal.
between
7.41 and 7.42
6.78
7
between
5.73 and 5.75
7.87
between
9.69 and 9.70
13
21
6.16
11.40
9
12
144
46
81
169
62
94
38
130
33
55
441
TEACHER RESOURCE SHEET 3
Form Me
Answer Key
TEACHER RESOURCE SHEET 4
Working With Square Root
Directions:
Reproduce 2 copies of each task and cut.
Rodel asks the carpenter to make a square table
that would fit for his laptop. He instructs the
maker that the area of the table should be 576
in
2. How long should be its side?
Our principal plans to fence the surrounding of
the school to avoid students from cutting
classes. It is a square lot with an area of 16,000
m
2
. Find the perimeter of our school that will be
TEACHER RESOURCE SHEET 5
Working With Square Root
ANSWER KEY
Our principal plans to fence the surrounding of the school to avoid students from cutting classes. It is a square lot with an area of 16,000 square meters. Find the perimeter of ourschool that will be covered by the fence?
Given: A = 16,000 m2 Solution: A = s2
16,000 m2 = s2
1600 m2=s40 m = s
P = 4s P = 4 (40m) P = 160 m
Therefore, the perimeter of our school is 160 meters.
Rodelasks the carpenter to make a square table that would fit for his laptop. He instructs the maker that the area of the table should be 576 in2. How long
should be its side?
Given: A = 576 in2 Solution: A = s2
576 in2= s2
576 in2=s24 in = s
Therefore, the side of the table should be 24 inches.
A cylindrical pitcher with a height of 12 inches can be filled with 339.12 in3volume of water. What is its
diameter? Use π= 3.14.
Given: V = 339.12 in3 ; h = 12 in Solution: V = π r2 h
339.12 in3 = (3.14) (12 in) r2
339.12 in3= (37.68 in) r2
339.12in3 37.68in =r
2
9 in2=r3 in = r d = 2r d = 2 (3 in) d = 6 inches
Therefore, the diameter of the pitcher is 6 inches.
A tank can be filled with 5,086.8 ft3of gasoline. If its
length is 20 ft, then what is its radius? Use π= 3.14.
Given: V = 5,086.8 ft3 ; h = 20 ft Solution: V = π r2 h
5,086.8 ft3= (3.14) (20 ft) r2
5,086.8 ft3 = (62.8 ft) r2
5,086.8 ft3 62.8ft =r
2
81 ft2=r9 ft = r
TEACHER RESOURCE SHEET 6
Let's Party
Directions:. Reproduce 10 copies of this sheet and cut each figure.
11
14
16
21
289
196
95
12
56
256
340
1217.5
between
18 & 19
between
19 & 20
between
17.85
between
3.43 & 3.5
17
between
6.31 & 6.33
15.81
between
9.74 & 9.75
between
3.83 & 3.85
250
289
289STUDENT ACTIVITY 5
Let's Party
Directions:
1. Determine who among the “Princesses” are carrying rational or irrational
numbers. Write your answer in the indicated box.
2. Choose among the “Princesses” the exact or approximate value of each
number mentioned above.
3. Cut the figures and pair them accordingly. Then, paste them in a manila
paper as shown in the example below.
Question:
If the square dance floor occupied an area of 225m
2;
a. what is the length of its side?
b. find its perimeter.
3
9
TEACHER RESOURCE SHEET 7
Let's Party
ANSWER KEY
If the square dance floor occupies an area of 225 square meters,
a. what is the length of its side? b. find its perimeter.
Given: A = 225 m2
a. Solution: A = s2
225 m2 = s2
225 m2=s 15 m = sTherefore, the length of the side of the dance floor is 15 meters.
b. Solution: P = 4s P = 4 (15 m) P = 60 m
Therefore, the perimeter of the dance floor is 60 meters.
11
16 14
between
6.31 & 6.33
Irrational
40
between
9.74 & 9.75
Irrational
95
between
3.43 & 3.5
12
Irrational
256
Rational
between
18 & 19
TEACHER RESOURCE SHEET 8
Real Fact
Task Cards
Directions:Reproduce 2 copies of these task cards and cut.
Mr. Enrico wants to put a fence around his square lot.
He asks the carpenter to estimate the materials to be
used. If his lot has an area of 529 m
2, then what is the
total length of the sides that will be covered by the
fence?
Mrs. Jackie bought a round dining table whose area
measures 28.26 square feet. What is the diameter of
TEACHER RESOURCE SHEET 9
Real Fact-Task Cards
ANSWER KEY
TASK 1
The school would like to build a reservoir that will supply water in the campus. It is expected that the tank would hold an approximate volume of 100.48 cubic meters. If the height of the reservoir is 8 meters, what should be its diameter? Use 3.14 as value of π.
Given: V = 100.48 m3; h = 8 meters; π = 3.14
Solution: V = π r2h
100.48 m3= 3.14 (r2) (8 m) 100.48 m3= 25.12 m (r2)
100.48m3 25.12m =r
2
4 m2= r2
4m2=r
2 m = r d = 2r d = 2(2m) d = 4m
Therefore, the diameter of the reservoir is 4 meters.
TASK 2
Mr. Enricowants to put fence around his square lot. He asks the carpenter to estimate the materials to be used. If his lot has an area of 529 m2, then what is the
total length of the sides that will be covered by the fence?
Given: A = 529 m2
Solution: A = s2 529 m2= s2
529m2=s23 m = s length of the four sides
=4 (23 m) = 92 m
Therefore, the total length of the four sides that will be covered by the fence is 92 m.
TASK 3
Mrs. Jackie bought a round dining table whose area measures 28.26 square feet. What is the diameter of the table? Use π= 3.14.
Given: A = 28.26 ft2; π = 3.14
Solution: A = π r2
28.26 ft2= 3.14 r2 28.26ft2
3.14 =r
2
9 ft2 = r2
9ft2=r
3 ft= r d = 2r d = 2 (3 ft) d = 6 ft
Therefore, the diameter of the table is 6 ft.
TASK 4
The sports complex in our city is square in shape. Its area measures 4 hectares.
a. What is the length of its side in meters?
b. Find the perimeter of the sports complex in meters.
Given: A = 4 hec.
Conversion: 4 hec = 40,000 m2 Solution:
a. A = s2
40,000 m2= s2
40,000m2=s200 m = s
Therefore, the length of the side of the square sports complex is 200 m.
b. P = 4s P = 4 (200 m) P = 800 m
STUDENT ACTIVITY 7
A-MAZE-iNG
Directions:
1. Help Mary find her way home by tracing the exact path with a crayon.
2. Along her path is an item number. Find the square root of the number that
corresponds to the item number at the left of the table.
3. Write the solution on a sheet of paper.
1
18
2
21
3
53
4
67
5
69
6
90
7
72
8
105
9
110
10
138
11
150
12
180
13
200
14
250
Problem:
TEACHER RESOURCE SHEET 10
A-MAZE-iNG
ANSWER KEY
2
21
5
69
9
110
10
138
12
180
2.
214 <
21 < 5 A. 21 ÷ 5 = 4.2B. 4.25
2 = 9.2
2 =4.6
C. 21 ÷ 4.6 = 4.56
Therefore,
21 lies between 4.56 and 4.60.5.
698 <
69 < 9 A. 69 ÷ 8 = 8.62B. 8.6282 =16.62 2 =8.31 C. 69 ÷ 8.31 = 8.30
Therefore,
69 lies between 8.30 and 8.31.9.
11010 <
110 < 11 A. 110 ÷ 10 = 11B. 1110
2 =
21 2 =10.5 C. 110 ÷ 10.5 = 10.47
Therefore,
69 lies between 8.30 and 8.31.10.
13811 <
138 < 12 A. 138 ÷ 12 = 11.5B. 11.512
2 =
23.5
2 =11.75 C. 138 ÷ 11.75 = 11.74
Therefore,
138 lies between 11.74 and 11.75.12.
18013 <
180 < 14 A. 180 ÷ 13 = 13.84B. 13.8413
2 =
26.84
2 =13.42 C. 180 ÷ 13.42 = 13.41
Therefore,
180 lies between 13.41 and 13.42.Problem: Mary's square lot has an area of 400 m2. What is the
perimeter of her lot?
Given: A = 400 m2
Find: perimeter
Solution: A = s2
400 m2 = s2
400m2=s 20 m = sP = 4s P = 4 (20 m) P = 80 m
For the Teacher: Translate the information in this Learning Guide into the following matrix to help you prepare your lesson
plans.
Stage
1.
Activating Prior Learning
2.
Setting the
Context
3.
Learning Activity Sequence
4.
Check for
Understanding
5.
Practice and
Application
6.
Closure
Strategies
Activities from the Learning Guide
Extra activities you may wish to include
Materials and planning needed
Estimated time for this Stage
