beam lg gr.5 module 1 - mathematicsematics 5 subsets of whole numbers

BASIC EDUCATION ASSISTANCE FOR MINDANAOLEARNING GUIDE

Elementary Mathematics — Grade FiveWhole Numbers

Module 1 — Subsets of Whole Numbers

COPYRIGHT NOTICE

Section 9 of the Presidential Decree No. 49 provides: “No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office within the work is created shall be necessary for exploitation of such work for profit.” This material has been developed within the 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.

Written, edited and produced by Basic Education Assistance for Mindanao, February 2008

BASIC EDUCATION ASSISTANCE FOR MINDANAO

ELEMENTARY MATHEMATICS — GRADE FIVE

WHOLE NUMBERS

MODULE 1 — SUBSETS OF WHOLE NUMBERS

Information about this Learning GuideRecommended number of lessons for this Learning Guide: 7

Basic Education Curriculum CompetenciesYear 5 mathematics: Subsets of Whole Numbers• Differentiate odd from even numbers

• Give the common factors of given numbers

• Identify prime and composite numbers

• Find prime factors of a number

• Show multiples of a given number by 10, 100

• Find the least common multiple of a set of numbers

• Tell when a number is divisible by another number (Divisibility Rules)

Objectives• Tell which numbers are odd and which are even.

• Differentiate prime and composite numbers.

• Find the factors of given numbers.

• Identify common factors.

• Enumerate multiples of the given numbers.

• Tell the least common multiple of 2 or more given numbers.

• Give the divisibility rule of numbers.

Essential concepts, knowledge and understandings targeted• Differentiating odd and even numbers, prime and composite numbers.

Even numbers are numbers that can be divided exactly by 2, while odd numbers are numbers that will give an extra 1 when they are divided by 2. Prime numbers are numbers with only 2 factors, 1 and itself, while composite numbers are numbers with more than 2 factors aside from 1 and itself.

• Identifying factors and common factors of numbers.

Factors are numbers which when multiplied will give a certain number. A common factor is a number that is a factor of 2 or more numbers.

• Describing multiples and least common multiple of numbers.

The multiples of a number are found by taking the product of any counting number and the given number. Example, the multiples of 3 are 3, 6, 9, 12, etc( these are the products of 3X1, 3X2, 3X3, 3X4, etc.) The least common multiple (LCM) is the smallest multiple common to those 2 or more given numbers.

• Divisibility

Basic Education Assistance for MindanaoLearning Guide, February 2008 3



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Divisibility means dividing a number without any remainder. A number is divisible by another number, if after dividing the answer is exact. There are numbers which are divisible by 2, 3, 4, 5, 6, 7, 8, 9 and 10. A number maybe divisible by more than 1 number.

Specific vocabulary introduced• odd numbers

• even numbers

• prime numbers

• composite numbers

• factors

• multiples

• divisibility rule of numbers

Suggested organizational strategies• Divide the class into smaller groups.

• Prepare necessary materials to be used during the teaching and learning activities.

• Set up the classroom for group activities.

Opportunities for IntegrationOther Subjects

• English - Children are given the opportunity to improve their speaking skill through discussion and reporting. Reading skill is likewise improved by following written directions.

• Art Education - Students are given the time to manipulate on shapes.

• Science - Some problem situations deals with plants and animals.

• Peace Education - Students work cooperatively with other members of the group to produce group outputs.

• Environmental Education - Students maintain cleanliness during group activities.

Multiculturalism

• Activities can be participated by all students of different cultures.

Gender Sensitivity

• All activities can be participated by both boys and girls.

Activities in this Learning GuideActivity 1: Agree or Disagree?

Multiple Intelligences

• Interpersonal

• Verbal/Linguistic




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Skills

• Compare and discriminate between ideas

• Make choices based on reasoned argument

• Interpret facts, compare, contrast

Text Types

• Personal Response

• Exposition

Activity 2: Here I AM


• Interpersonal


• Logical/Mathematical

• Body/Kinaesthetic

Skills

• Order, group, infer causes

• Observation and recall of information


Text Types

• Information Report

• Procedure

Activity 3: Numbers All


• Naturalist

• Interpersonal



• Visual/Spatial

• Intrapersonal

Skills

• Compare and discriminate between ideas

• Seeing patterns

• Solve problems using required skills or knowl5edge





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Text Types

• Discussion

• Observation

• Procedural Recount

Activity 4: Cross-Number Puzzle


• Interpersonal


• Visual/Spatial

Skills

• Mastery of subject matter

• Solve problems using required skills or knowledge


• Interpret facts, compare, contrast

Text Types


• Procedure

Activity 5: Tiling a Floor


• Interpersonal



• Visual/Spatial

Skills


• Solve problems using required skills or knowledge

• Organization of parts

• Use methods, concepts, theories in new situations

Text Types

• Discussion

• Procedure




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Activity 6: Check Me Now


• Interpersonal


• Intrapersonal

Skills


• Observation and recall of information

• Use information

Text Types

• Information Report

• Observation


Key Assessment Strategies• Teacher observation during group activities

• Rubric for Assessing Group Performance and Output

• Peer Assessment (by comparing and reviewing each other's output)

• Student Individual Performance Checklist




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Mind MapThe 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 LearningThe 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.

AssessmentAll 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 LearningThis 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 purposeStudents are expected to have experiences working with whole numbers. These knowledge is a pre-requisite skill in performing the activities on this topic. To activate this knowledge, they will perform an activity using the restructured Agree-Disagree strategy.

StrategyAgree or Disagree (Restructured). A strategy that will help students organize data to support a position for or against an idea. It promotes students' thinking about the content.

A “Don't Know” column is added to find out the concept which the students do not have prior knowledge.




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Materialsenlarged copy of Agree or Disagree Chart, marking pens

Activity 1:Agree or Disagree?1. Divide the class into 5 groups or as desired. Provide an enlarged copy of Agree or

Disagree Chart to each group. Refer to Teacher Resource Sheet 1, page 14.

2. Motivate the students to think and recall their past learning. Let them check the “Agree” column if they are in favor of the idea, “Disagree” if they are against to it and “Don't Know” if they don't have the knowledge yet. This is done on the “BEFORE” columns of the chart.

3. Remind them not to place any mark under the “AFTER” columns yet.

Formative AssessmentDiscuss with the students the items they agree, disagree or they don't know yet as indicated on their charts. This way, all the students will understand each others' work.

RoundupBy carrying out this activity, the teacher will know which items cause problems and may spend time reinforcing them.

2. Setting the ContextThis 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 purposeStudents are presumed to have understood the concept of whole numbers. On this stage, they will group numbers accordingly.

StrategyCooperative learning – Work It Out. This is a teaching strategy in which small teams, with students of different levels of ability, use a variety of learning activities to improve their understanding of a subject. Each member is responsible not only for learning what is taught but also for helping teammates learn, thus creating an atmosphere of achievement. Students work through the task until all the group members successfully understand and complete it. (http://edtech.kennesaw.edu/intech/cooperativelearning.htm)

Materials20 number cards, flip chart/manila paper, masking tape

Activity 2: Here I AMPrepare sets of number cards . (Refer to Teacher resource Sheet 2, page 15)

Directions:

1. Students will examine all their cut outs and discuss how to group them. Encourage each member to share ideas. Clearly write the instructions on the flip chart where they will paste their groupings or you may do this on the board.

2. After grouping the cutouts, they will paste them on a manila paper or flip chart.

3. Instruct them to post their work on the board for everyone to see.


http://edtech.kennesaw.edu/intech/cooperative





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4. Then, call students from any group with different grouping to share how they group their cutouts.

Formative AssessmentStudents' participation and group output can be observed during the activity.

RoundupIt is important to check further if all the students have grouped the numbers accordingly and have given a reason/s on how they grouped them.

3. Learning Activity SequenceThis stage provides the information about the topic and the activities for the students. Students should be encouraged to discover their own information.

Background or purposeOn this stage, they will perform a series of activities that would make them gain knowledge on the subsets of whole numbers like odd and even numbers, prime and composite numbers, common factors and least common multiples of 2 numbers. They will be able also to give the divisibility rules of numbers.

Strategy: Cooperative LearningCommunity Circle. This strategy allows discussion on issues. Students may sit on the floor or chairs facing each other. Observe the 3C's; Cares, Concerns and Celebrations. Reluctant members can be encouraged using the think time, talking sticks.

Think Pair Share. This strategy allows groups to reach consensus, check understanding or this can be used as an introductory activity.

First, students think individually about an issue, question or problem and record response. Next, shares ideas with a partner, discuss and record what had been shared. Then, share with the whole group to reach consensus.

Materials5 bags (20 pebbles in each bag), square cutouts, number cards from 1-10, activity sheets

Activity 3: Numbers AllTask-1: Odd or Even

Give a bag of 20 pebbles to each group and the activity sheet. Refer to Student Activity 3 Task 1, page 17. Students will discover the numbers which can and cannot be paired. All members of the group will take turn in doing this. Reluctant members should be encouraged to take his/her turn in doing the activity. Remind the group to continue performing Tasks A and B on their activity sheet.

For Tasks C and D, give each group a pack of 5 number cards. You may use the 1-digit number cards in Activity 2 or you may prepare another set.

Let each group post and report their outputs.

Task 2: Prime and Composite

Prior to the activity, prepare square cutouts and give ten pieces to each group. Refer to Teacher Resource Sheet 3, page 20.

Instruct them to form a square or rectangular shapes in different ways using 2 cutouts first. Then, let them count the number of rows and columns of each formed shape and




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write them on the appropriate columns of the table on the activity sheet. They will then form a multiplication sentence out of these numbers and write this on the third column. Refer to Student Activity Task 2, page 21 for further instruction.

Task 3: Multiples

Prepare the activity sheet with pictures. Refer to Student Activity 3- Task 3 sheet on page 25. Instruct the students to study the pictures on their activity sheet carefully. Then, they will complete this by following the given instructions. Any group with different answers will be asked to explain their output.

Task 4: Divisibility

Give a set of task cards to each group. Refer to Teacher Resource Sheet 4, page 28. Each member or pair will work on one task. Then, they will share their output with another student or pair and with the whole group. After which, let them summarize their findings by answering the Activity 3-Task 4, Divisibility rules, on page 32.

Formative AssessmentRandomly, the teacher may call students to identify numbers as either odd or even and find the multiples and the least common multiples of 2 numbers. They may be asked also to give 3 or 4 numbers, their multiples and the LCM.

Observation of student's participation during the group activity should be done also. A Student Individual Performance Checklist on page 38 maybe used.

A rubric for assessing group output may also be used. Refer to the rubric on page 38.

RoundupResults of the activities will assist the teacher to determine if the students have gained skills on identifying odd and even numbers, prime and composite numbers and finding the common factors and the least common multiples of 2 numbers. He/She will further know if the students can state the divisibility rules of numbers. Enrichment activities may be given if necessary.

4. Check for Understanding of the Topic or SkillThis stage is for teachers to find out how much students have understood before they apply it to other learning experiences.

Background or purposeAfter performing a series of activities on the different tasks, the students are expected to have gained the necessary knowledge and understanding of the topic. These will be checked further on this stage through the given exercises.

StrategyPuzzle Game. This strategy aims to exercise one's mind. Usually, a problem is given to test one's skill or ingenuity. The end results mirror the performance of the individual member as they enthusiastically contribute to their group answers.

Materialspuzzle cards

Activity 4: Cross-Number PuzzleDistribute the puzzle cards. Students will work by pair or group of 4. Refer to Student Activity 4, page 33.




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Directions:

1. Each pair/small group will think of the different factors/concepts learned in finding the solution to each problem. Then, they will fill in the puzzle card accordingly.

2. Instruct them to compare their finished puzzle with another pair/group and make necessary corrections or agreements if there are any. Then, they will compare outputs again with another pair. This is done until all the puzzle cards have been compared within the whole group.

3. Any member from each group may be asked to answer a question based on the puzzle.

Note: Please refer to Teacher Resource Sheet 5, page 34 for the answer to the puzzle.

Formative AssessmentPeer assessment maybe done as the students exchange, compare and discuss each other's puzzle cards.

Teacher may use the Student Individual Performance Chart on page 37 to assess individual/pair participation and outputs.

RoundupStudents are hoped to have a good understanding on the topic, Subsets of Whole Numbers. It is important to further check and settle some difficulties of students if there are still any through additional exercises.

5. Practice and ApplicationIn this stage, students consolidate their learning through independent or guided practice and transfer their learning to new or different situations.

Background or purposeThis stage challenges the students to draw connection and apply what they learned to real life experiences.

StrategyConsider All Factors (CAF). A thinking tool that promotes consideration of all factors involved. This encourages students to think about the factors involved when thinking about something.

Materialssquare cutouts, manila paper/flip chart

Activity 5: Tiling a FloorDistribute 60 or more square cut outs to each group. Refer to Teacher Resource Sheet 6, page 35. Instruct them to use the cut outs to perform the tiling activity. Let them discuss the directions stated on Student Activity Sheet on page 36. You may guide them to do this.

Formative AssessmentA rubric for assessing the group performance and output may be used on this activity. Refer to the suggested rubric on page 38.




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RoundupStudents are hoped to have gained understanding on the practical application of the concept of odd and even numbers, prime and composite numbers, factors and multiples, and divisibility rules. Enrichment activity maybe given if it is needed.

6. ClosureThis 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 purposeIt is expected that the students have acquired the knowledge and deeper understanding of the whole topic. This stage checks what they learned about the concepts considered in the different activities. This time, they will complete the Agree and Disagree Chart by checking on the “AFTER” columns.

StrategyAgree Disagree (Restructured)- A Revisit. This strategy will be used to evaluate the knowledge just acquired. This will guide the teacher if the students have deeper understanding on the concepts discussed.

MaterialsAgree Disagree Chart used in Activity 1 and marker

Activity 6: Check Me NowLet the students go back to their grouping in Activating Prior Learning. Give them back the Agree Disagree chart they used in the first activity. Instruct them to finish filling in the chart by checking appropriately each statement on the AFTER columns. Then, let them post their work.

The teacher will check if there is any disagreement and discuss those statements that need clarification.

Formative AssessmentStudents' performance maybe assessed using the chart that they had accomplished.

A short discussion maybe done for any concepts they missed in the “AFTER” columns.

RoundupStudents are hoped to have gained the knowledge of the different lessons on the topic, Subsets of Whole Numbers. It is important that the students' misconceptions and difficulties will be checked by giving further enhancement activities.

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:




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Teacher Resource Sheet 1Agree or Disagree Chart (Restructured)

Statements

BEFORE AFTER

Agree Disagree Don't Know

Agree Disagree Don't Know

1) Each digit in a numeral has a specific place value.

2) The place value of 2 in 425 is hundreds.

3) Numbers can be written in symbols and in words.

4) 6,578 is a 5-digit numeral.

5) 385 is lesser than 299.

6) We can count numbers by 2's, 3's, 4's,5's, etc.

7) The Roman numeral for 10 is L.

8) First (1st), second (2nd), third (3rd), etc. are ordinal numbers.

9) Numbers that are added are called factors.

10) 5,400 — 1,742 = 3,658

11) 1 is a prime number.

12) The prime factors of 8 are 2 and 4.

13) Numbers that are not paired are odd numbers.

14) Numbers that end in 2, 4, 6, 8 and 0 are even numbers.

15) Numbers that are multiplied are called factors.

16) Numbers whose only factors are one and the number itself are prime.

17) A number is divisible by 9 if the sum of its digits is divisible by 3.

18) Even numbers are divisible by 2.

19) The multiples of 5 are 5, 10, 15, 20, 25, 30, etc.

20) The least common multiple(LCM) of 4 and 5 is 20.




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Teacher Resource Sheet 2Number Cards for Activity 2

Directions:

Below is a set of 20 number cards. Cut each card and give 1 set to each group.


1 53

28823

6 21 101



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103

15105

11 25

13

108106

182616



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Student Activity 3Numbers All

Task 1Odd or Even

Objective:

➢ Tell which numbers are odd and which are even.

Materials: a bag of pebbles and number cards

Directions: Discover the numbers which can be arranged in pairs and those which cannot. All members of the group should take turn in doing this.

1. Arrange yourselves to form a circle so that all the members will face

each other.

2. The first member will get a pebble or a number of pebbles from the

bag and count them.

3. After which, pair them or group them by two's.

4. Now, look at the table and find the number that corresponds to the number of pebbles you picked.

5. Opposite to it, write either “pair” if the pebbles can be completely paired or “not pair” if the number of pebbles can not be paired completely.

6. Then, return the pebbles in the bag.

7. The next member will do the same. But if he/she gets the same number of pebbles as the first member, he/she should return them and do another try. Then, he/she will do what the first member did by following steps 3 to 6.

8. Then, the next member will do the same.

9. Continue doing the steps until all the numbers from 1-20 in the activity sheet has been identified as either “pair” or “not pair”.

10.If you have difficulty in following the directions, you may request the help of your teacher.


A)



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Table 1 – Pair or Not Pair

Number of pebbles Pair or not pair Number of pebbles Pair or not pair

1 11

2 12

3 13

4 14

5 15

6 16

7 17

8 18

9 19

10 20

Now, write all the numbers which can not be paired starting from the least to the greatest inside box A below.

These numbers are odd numbers.

What are odd numbers? ____________________________________________

Give 10 more odd numbers after 20. Write them inside the box below.

Now, look at your table again. Write inside box B below those numbers which can be paired in ascending order.

These numbers are called even numbers.

What are even numbers? ___________________________________________

Give 10 more even numbers after 20. Write them inside the box below.


B - Paired:

A - Not paired:

B)



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Observe the digits in the unit or ones position in each group.

In what digits do even numbers end? ______________________________

What about the odd numbers? _______________________________

This time, you will be given 5 number cards.

Using these cards, form at least 5 odd and 5 even numbers. You may rearrange the digits the way you want to form different 5-digit numbers. See to it that each number has 5 digits. Write the numbers that you form appropriately in the table below.

Odd Numbers Even Numbers

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.


C)

D)



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Teacher Resource Sheet 3for Activity 3 Task 2

Square Cut outsDirections:

Below is a set of shapes to be used in Task 2. Cut each shape and give 1 set to each group.




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Student Activity 3Task 2

Prime and CompositeObjectives:

1. Find the factors of a number using the cutouts.

2. Identify the common factors of the given numbers.

3. Differentiate prime and composite numbers.

Materials: 10 pcs. square cutouts and activity sheet

Directions:

1. Form as many squares or rectangular shapes as you can using the cutouts. Start with 2 cutouts first.

2. Count the number of rows and columns. Write these in the appropriate columns in Table 1 of your activity sheet .A sample figure inside the box below is given.

3. Next, write a multiplication sentence in the next column of the table. Then, list down the factors in the last column.

4. Now, use 3 cutouts and do steps 1 to 3.

5. This time, use 4 cutouts. Repeat steps 1 to 3. Discover more shapes using the 4 cutouts.

6. Complete the table by using 5, 6, 7, 8, 9, and 10 cutouts. Try to discover other shapes using the same number of cutouts. Extra rows are provided in the table for additional shapes that you will form.

7. If you are done, post your work on the designated corner of the room. Using the Gallery Walk strategy, you will move around and compare each others' outputs.

Sample figure for 6 cutouts:

In this example, there are 2 rows and 3 columns. So, the multiplication sentence is 2 X 3 = 6. 3 and 2 are factors of 6.

Can you rearrange the 6 cutouts to form another square/rectangle? How many rows and columns will there be? What will be the other factors of 6?


1 2 3

1 2



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Table 2 - FactorsNumber of square cutouts used

Number of rows

Number of columns

Multiplication sentences

Factors

2

3

4

5

6

7

8

9

10

Observe the factors of numbers 2 to 10 on the last column of table 2.

There are numbers which have only 2 factors, 1 and the given numbers.

There are also numbers with other factors aside from 1 and itself.

Now, continue answering exercises A and B on the next sheet.




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A) Rewrite all the numbers with factors of 1 and itself on the first column of Table 3 below and those with other factors aside from 1 and itself on the second column.

Numbers with factors 1 and itself Numbers with other factors aside from 1 and itself

These numbers are PRIME. These numbers are COMPOSITE.

B) Now, describe:

Prime numbers ______________________________________________________________________________________________________________________________________

Composite numbers ______________________________________________________________________________________________________________________________________

C) Write 5 more examples of prime and composite numbers greater than 20 in the appropriate space below.


Table 3

Prime numbers Composite Numbers



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1. Enumerate all the factors of the numbers indicated in the first column of the table below. Write them in the second column.

2. Then, write all their prime factors on the third column.

3. Observe the factors in the second column. Then, on the last column, write all the factors that are found in both numbers that are specified. These are their common factors.

Numbers Factors Prime Factors Common Factors

10

12

10 and 12

20

24

20 and 24


D)



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Student Activity3Task 3

MultiplesObjectives:

Enumerate the multiples of the given numbers. Identify the least common multiple.

Directions:

A) Study the pictures below. Then, follow the indicated directions.

1. Find the number pattern. Then, identify which flowers in the figure below will the butterfly drop by before it can join the group of butterflies. Draw an arrow connecting these flowers.

2. Write inside the box the numbers that are found on the flowers where the butterfly dropped by.

3. Aside from the numbers you had just placed in the box above, list down 5 more multiples of 2. __________________________

Now, look at the figure below. Which flowers will the butterfly drop by before it can join the group of butterflies? Find the pattern. Draw an arrow connecting these flowers.

4. Write the numbers that are found on the flowers where the butterfly dropped by.


These numbers are multiples of 2.



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5. Aside from the numbers you had just placed in the box above, list down 5 more multiples of 3. __________________________________

6. Which flowers do both butterflies dropped by in the 2 pictures?

7. Starting from 20, list down 10 more multiples of 2 and 3. Then encircle their common multiples.

2: ______________________________________________________

3: ______________________________________________________

B) Give at least

10 multiples of 4. ___________________________________

10 multiples of 5. ____________________________________

Now, encircle the common multiples of 4 and 5. Then, cross out the least common multiple (LCM).


These numbers are multiples of 3.

These are the common multiples of 2 and 3.



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C) Follow the directions below for the next task.

Directions:

Find the least common multiple of each pair of numbers inside the box below. Then, connect the least common multiples of the given pairs of numbers to form a figure on the right. Start from number 1 up to 10.

Enhance your figure by putting additional parts. Then, name it!


1) 2 and 42) 3 and 23) 3 and 44) 12 and 8

5) 60 and 156) 8 and 32

7) 100 and 10 8) 5 and 4

9) 25 and 10 10) 25 and 5

Name of the figure



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Teacher Resource Sheet 4Task Cards

Directions:Below is a set of task cards. Cut each card and give 1 set to every group. Depending on the number of members in a group, one student or pair will work on 1 task card. Then, the group will collate their output by completing the Activity Sheet 3, task 4.


Divide the numbers below by 2

2÷ 2 =___ 8 ÷ 2= ____4 ÷ 2 = ___ 10 ÷ 2= ___

6 ÷ 2= ___ 12 ÷ 2 = ____What kind of numbers are 2, 4, 6, 8,10 and 12? _______What kind of numbers are divisible by 2?_____________

When is a number divisible by 2? _____________________________________________________________


123 ÷ 3 = ____ 126 ÷ 3 = ____ 339 ÷ 3 = ____

Add all the digits of each number. Example: For 123:1+2+3=6 Is the sum of all the digits divisible by 3? ________

When is a number divisible by 3? __________________________________________________________________



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12 ÷ 4 = ____ 416 ÷ 4 = ____ 312 ÷ 4 = ____ 324 ÷ 4 = ____

Examine the last 2 digits of the numbers. Are the last 2 digits divisible by 4? _____

When is a number divisible by 4?________________________________________________________


10 ÷ 5 = ____ 25 ÷ 5 = ____ 15 ÷ 5 = ____ 30 ÷ 5 = ____ 35 ÷ 5 = ____

Look at the last digit (unit position) of each number.When is a number divisible by 5? ___________

__________________________________________________________________________________________________



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Divide the numbers below by the indicated numbers

12 ÷ 2 =___ 12 ÷ 3=___ 18 ÷2=___18 ÷ 3 =___ 12 ÷ 6=___ 18 ÷ 6=___

Are the numbers divisible by 2 and 3also divisible by 6? ___

When is a number divisible by 6? ______________________________________________________________________________________________________________

Divide the numbers by 8(For greater numbers)

1,016 ÷ 8 = ____1,832 ÷ 8 = _____ 1,168 ÷ 8 = ____ 4,176 ÷ 8 = ____

Can you divide exactly the last 3 digits by 8? _______ When is a number divisible by 8? _________________

___________________________________________________



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Divide the numbers by 9

351 ÷ 9 =___ 9,180 ÷ 9 = __ 486 ÷ 9 = __ 1,728 ÷ 9 = ____

Add all the digits of each number. Example: in 351: 3 + 5 + 1 = 9

Is the sum of all the digits divisible by 9? ______When is a number divisible by 9? __________

_________________________________________________

Divide the numbers by 10

10 ÷ 10= ___ 1,000 ÷ 10 = ____ 20 ÷ 10 = ___ 1,520 ÷ 10 = _____

Look at the last digit of each number.Describe it.

When is a number divisible by 10? _____________________________________________________________



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Student Activity 3

Task 4

Divisibility Rules

Objective: Write the divisibility rule of a number.

Materials: task cards and activity sheets

Directions: After working on your individual task using the task cards, review and discuss each other's output. Finally, do the activity below as your group output.

Write the Divisibility Rule for each number.

A whole number is

divisible by:

(Please indicate the condition/s below.)

if:

2

3

4

5

6

8

9

10




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Student Activity 4Cross-Number Puzzle

Directions:

Solve the puzzle below by giving the correct number as described by each statement.


Down:1. The smallest even number which is divisible by 2 and 52. An even number between 35 and 45 that ends in zero3. A common multiple of 10 and 1004. The least 2-digit number divisible by 2, 3 and 6.5. A multiple of 10 which is less than 406. An odd number which is divisible by 77. An odd number divisible by 3 and 58. A prime number which is greater than 30 but less than 35.9. A number divisible by 2, 4, 5, 10 and 2010. A prime number divisible by 2

Across:1. 1 and ___ are factors of 18.2. The least common multiple of 8 and 103. The lowest 2-digit number which is a multiple of 34. The common factor of 10 and 205. An odd and composite number whose factors are 11 and 3.6. An even and prime number7. A two-digit prime number 8. The least common multiple of 3 and 10.9. The common factor of 25, 50 and 100.10. The prime factor of 4.



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Teacher Resource Sheet 5Cross-Number Puzzle

This is the completed puzzle for teacher reference .




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Teacher Resource Sheet 6for Activity 5

Floor TilesDirections:

Prepare cut outs of these squares. Provide 60 or more cutouts per group.

Instruct each group to use the cut outs in solving their problem situation stated on the activity sheet.

For better understanding, explain to the whole class how each group will do the activity.




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Student Activity 5Tile the Floor

Objective:

Solve problems.

Directions:

1. Discuss the situation among yourselves. Plan how to solve it using the cut outs as tiles and the flip chart as the toilet floor.

2. Paste the cutouts to form each floor plan as indicated in a to e below. Then, indicate the measure of each side by writing the number of cutouts.

Tile a floor whose:

a) sides are equal.

b) sides are even numbers.

c) one side is odd and the other is even.

d) both sides are divisible by 2, 3 and 6.

e) one side is a prime factor of 8 and the other side is the least common multiple of 3 and 4.


Situation: Hamman is a skillful carpenter in their barangay. He is always the choice of the residents to repair and build their houses. Recently, he was hired to construct a toilet for Mr.Samaludin's house. To decide the shape of the toilet floor, Hamman needs your help to do a trial tiling of the toilet floor plan. To do this, follow the instructions below.



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Student Individual Performance Checklist

Names Differentiates odd and even

numbers

Differentiates prime and composite numbers

Finds factors of the given numbers

Finds prime factors of the given numbers

Finds the least

common multiples

Applies divisibility

rules

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.




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Rubric for Assessing Group Performance and Output

Criteria Very Satisfactory

3

Satisfactory

2

Needs Improvement

1

Cooperation

Members consistently and actively work

towards group goals without being told.

Members work towards group goals without

being told.

Members work towards group goals

only when told.

ParticipationMembers willingly

accept and perform roles within the group

Members accept and perform individual role

within the group.

Some members need to be

reminded to participate.

Group output Group output is done correctly among

themselves without asking help from the

teacher.

Group output is done correctly among themselves while

asking help from the teacher.

Group attempts to produce their

output but gives up readily.

Total 6 4 2




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Attachment Even and Odd Numbers

Even numbers can be divided evenly into groups of two. Example, number four can be divided into two groups of two. There is no remainder. Even numbers are paired numbers.

Odd numbers can NOT be divided evenly into groups of two. Example, number five can be divided into two groups of two with a remainder of one. Odd numbers are not paired.

Prime and Composite

Prime numbers are whole numbers with only 2 factors, one and the number itself. Example, number 7 has only 2 factors, 1 and 7 (1 X 7)

Composite numbers are whole numbers with more than 2 factors. Example, number 8 has 4 factors, 1, 2, 4 and 8 (1 X 8 and 2 X 4)

One (1) is neither a prime nor composite number.

Two (2) is the only prime number that is even.

Factors and Multiples

Factors are numbers which when multiplied will give a certain number.

For example, if we want to find the factors for 32, 1 X 32 = 32, 2 x 16 = 32, 4 x 8 = 32, so 1, 32, 2, 16, 4 and 8 are factors of 32.

A common factor is a number that is a factor for two or more products.

Example:

Factors of 32: 1, 2, 4, 8, 16 and 32

Factors of 16: 1, 2, 4, 8 and 16.

The common factors of 32 and 16: 2, 4, 8 and 16. (1 is not included as the common factor because it is a factor for all numbers.)

Factors Factors when multiplied give a certain number

2 and 3 2 X 3 = 6

8 and 5 8 X 5 = 40

1 is always a factor of any number.

2 is a factor of all even numbers.

Any number is always a factor of itself




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The multiples of a whole number are found by taking the product of any counting number and that whole number. For example, to find the multiples of 3, multiply 3 by 1, 3 by 2, 3 by 3, and so on. To find the multiples of 5, multiply 5 by 1, 2, 3, and so on. The multiples are the products of these multiplications. Some examples of multiples can be found below. In this example, the counting numbers 1 through 10 are used. However, the list of multiples for a whole number is endless. The ... at the end of each list below means that the list really goes on forever.

Example Find the multiples of the whole number 4

multiplication 4X1 4X2 4X3 4X4 4X5 4X6 4X7 4X8 4X9 4X10

multiples of 4 4 8 12 16 20 24 28 32 36 40

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 40, ....

Divisibility

Divisibility means dividing a number without any remainder.

A number is divisible by another number if after dividing a greater number by the smaller number, the answer is exact.

A number maybe divisible by more than 1 number.

Sources: http://www.mathgoodies.com/lessons/vol3/htm


6 is divisible by 2, 3 and 6. 6 ÷ 2 = 3, 6 ÷ 3 = 2, 6 ÷ 6 = 1

http://www.bmcc.edu/virtual_docs/MathTutorials/Numbers/n-gcf.htm http://www.mathgoodies.com/lessons/vol3/lcm.htmlDiscovering Math for Global Learners Grade V and VI

http://www.mathgoodies.com/lessons/vol3/htm



http://www.bmcc.edu/virtual_docs/MathTutorials/Numbers/n-gcf.htm



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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

Total time for the Learning Guide Total number of lessons needed for this Learning Guide


beam lg gr.5 module 1 - mathematicsematics 5 subsets of whole numbers

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