Place Value

QCM 501: PLANNING AND PREPARING A MATHEMATICS LESSON

Numbers to 10 000 Place Value

Pre-requisite skills and knowledge required for this lesson Pupils should be able to:

1.

Count in ones, tens, hundreds and thousands, read and write their corresponding numbers and number words

2.

Recognise concrete representation of numbers to 10 000

*Acquired within Whole Numbers, Counting

Specific Instructional Objectives (SIOs) for this lesson: At the end of the lesson, pupils should be able to:

1.

State the difference between a digit and a number

2.

State the place and value of each digit in a number

3.

Write a 4-digit number in terms of thousands, hundreds, tens and ones

4.

Write a 4-digit number as the sum of the values of each digit in the number

Key Concept

Level

The digits in each number have their own place and value.

Primary 3 Resources

Class Size

1.

Place Value video (Appendix A)

30 Students

2.

Individual Student Math Journal

3.

My Pals Are Here Textbook 3A (Appendix B)

Class Ability

4.

My Pals are Here Workbook 3A Part 1 (Appendix B)

Mixed

5.

Diene’s Base-Ten Blocks (Appendix C)

6.

10-sided Dice (Appendix C)

Duration

7.

Roll and Show Activity Sheet (Appendix D)

2 Periods, 60 minutes

8.

Star Sickers, simple prizes for Roll and Show Game

9.

Individual whiteboards

10. Class Blog or Lino Wall (Appendix E) PAGE 1 OF 8

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Engage (5 minutes) Time

Activities

Notes

Resource

Have students sit in groups of 6. Post Key Concept and SIOs on the board. ๏ 2 mins

๏ To warm up for the lesson, Teacher leads students into a Place Value Song and Dance.

๏ 2 mins

๏ Maths Journal entry, “What is the difference between a digit and a number?”

Have students write down what they think in their individual Math Journals.

Allow students 1 to 2 minutes to write down their responses and then discuss as a class the meaning of digits and numbers.

๏ To tap into students’ prior knowledge of hundreds, tens and ones from their Primary 2 Maths Syllabus

๏ Video: Place Value

๏ Ensuring students understand the difference digits and numbers is important here as many students at Primary 5 and 6 continue to describe digits as numbers and disregard the difference

๏ Maths Journal

๏ Reiterate SIO 1.

Number: An arithmetical value represented using digits

Song and Dance

Vocabulary Digit: Any numeral from 0 to 9

Place Value: The value of the place of the digit, such as ones, tens, hundreds, etc.

Post the difference on the board for students to copy into their maths journals ๏Maths Journal entry, ๏ 1 min

“What is Place Value then?”

Have student’s journal their answers and then discuss as before.

Post the definition on the board for students to copy into their maths journals

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Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Explore (10 minutes) Time ๏ 5 mins

Activities ๏ Concrete exploration, Distribute boxes of Diene’s Base-Ten Blocks to each group, and place one 1000-cube, 100-flat, one 10-long, and one unit block on the visualizer and prompt student groups retrieve one each as demonstrated.

“What is the value of each of these blocks? How do you know?”

(1000, 100, 10 and 1) Have students explore the blocks and guide them to explain how they determined the value of each block, i.e. there is one block in a unit block, 10 blocks in a 10-long, hundred blocks in a 100-flat and 1000 blocks in a 1000-cube.

Have the students recognize unit blocks as ones, 10-longs as tens, 100-flats as hundreds and 1000-cubes as thousands through the understanding of each block’s value.

Notes ๏ Key purpose of the activity is to assimilate association between concrete representation and their values. ๏ Group work where students are encouraged to discover answers on their own with the aid of their friends, so as to encourage collaborative learning (Constructivism). ๏Students begin the lesson by revisiting the concrete representations of the base-ten value system as part of the Singapore Maths Curriculum’s Concrete-Pictorial-Abstract (CPA) approach.

Resource ๏ Diene’s Base-Ten Blocks Vocabulary

Unit blocks/ones

10-longs/tens

100-flats/hundreds

1000-cube/thousands

PAGE 3 OF 8

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Time ๏ 5 mins

Activities ๏ Concrete exploration, “Students, I need 2 thousands, 4 hundreds, 7 tens and 5 ones, can you use the unifixcubes to represent them to me?”

Notes

Resource

๏ Ensure groups are evenly distributed based on their abilities, ensure an even mix of highability, middle-ability and lower-ability students to ensure that students have suitable people to learn from and learn with.

๏ Diene’s Base-Ten Blocks

An example of a suitable sitting position is shown below:

ones

Terms

Have the students explore representing 2 thousands, 4 hundreds, 7 tens and 5 ones with the Diene’s Base-Ten Blocks. Facilitate each group and guide them to present the correct representation.

tens

Have a volunteer group present their answer on the visualizer and explain their representation (use a piece of white paper as backing) :

thousands

hundreds

HA:High Ability, MA: Middle Ability, LA: Lower-Ability

Ensure that HA students and LA students are not face or shoulder partners so as to maximise meaningful interaction (Constructivism, Vygotsky’s Zone of Proximal Development and interaction with more knowledgeable others)

Then proceed to draw a place value table over the representations with the labels ones, tens, hundreds and thousands:

PAGE 4 OF 8

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Explain (10 minutes) Time ๏ 5 mins

Activities ๏ Discussion and explanation, “How many ones are there?”

Notes ๏ Many students fail to understand the importance of the -s suffix when writing down the place of a digit.

“What digit should I put in the ones column?”

Have a student write the digit in the ones column.

Resource ๏ Diene’s Base-Ten Blocks ๏ Maths Journal Terms ones place tens place hundreds place thousands place * -s suffix

(Repeat for tens, hundreds and thousands) “In what place, is the digit 5 in?”

Have students volunteer answers and then post answer on the visualizer:

Have students try on their own for the digits 7, 4 and 2 and have them record their answers in their Math Journals. Allow students to share answers and affirm correct answers.

After writing “the digit 5 is in the one place”, prompt students to point out the error in the statement. Highlight the suffix -s and reiterate its difference to the words ones, tens, hundreds and thousands without the -s suffix.

PAGE 5 OF 8

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Time ๏ 5 mins

Activities

Notes

๏ Discussion and explanation, “What is the value of the digit 2? How do you know?”

๏ Highlight the two ways of representing the values of each digit, for example: the value of the digit 2 is 2 thousands or 2000.

Have students volunteer answers and then post answers on the visualizer:

๏ Students may write only the digit itself when asked for the value of the digit. For example, when given the number 2475 and asked for the value of the underlined digit, students may write just the digit “2” and not 2,000.

Emphasize to these students that the place of the digit determines its value.

“What does the number 2-4-7-5 represent then?”

๏ Remember to break up teaching into small steps. Even posting onto the board has to be in small steps to aid students observe the flow and accumulate simple to more complex concepts (Behaviourism, teaching is presented in small steps according to some hierarchy that proceeds from simple to complex so as to aid establishment/reinforcement of StimulusResponse bonds)

Have students volunteer answers and then post answer on the board:

๏ Reiterate SIO 2.

➜ Have students try on their own for the digits 4, 7 and 5 and have them record their answers in their Math Journals. Allow students to share answers and affirm correct answers.

Resource ๏ Maths Journal

Explain that the number 2-4-7-5 is therefore a sum of 2000, 400, 70 and 5, i.e. 2475 = 2000+400+70+5

PAGE 6 OF 8

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Elaborate (15 minutes) Time ๏ 15 mins

Activities

Notes

Resource

๏ Roll and Show Game (Adapted from My Pals Are Here Textbook 3A), Distribute the activity sheets (one per student) and a 10-sided die to each pair.

๏ Introducing a game-based activity helps to strengthen Stimuli-Response bonds through increasing stimulus (Cognitivism).

๏ Activity Sheet (one per student)

Divide each group into Rollies and Showies:

๏ Highlight the terms “stands for” and “value of” and explain their inter-changeability

๏ 10-sided die

๏Bring up any ‘0’ examples by the students and explain the digit ‘0’ and its role as a place holder. If no student managed to obtain a ‘0’, teacher will explain using own example.

๏ Diene’s Base-Ten Blocks

๏ Students are often confused with the value of ‘0’ in a number especially when the ‘0’ is not in the ones place. Provide examples and show that no matter what place the digit ‘0’ is in, its value is always zero.

๏ A simple prize for students who performed well (ensure enough prizes available)

The Rollies roll the dice four times. The Showies use the numbers to form a 4-digit number and represent the number using Diene’s Base-Ten Blocks and write the digits’ place value on the activity sheet in four forms (teacher to demonstrate an example), e.g. The digit 2 is in the hundreds place, the digit 2 stands for 2 hundreds, the value of the digit 2 is 200 and 1241 = 1000 + 200 + 40 + 1 (Refer to Appendix D)

๏Notice that students now engage in cooperative learning (students engage in pair work but do not require the assistance of the other to create knowledge, partner simply serves to aid individual learning) rather than collaborative learning as teacher shifts focus from group work to pair work and then finally individual work in the next segment of the lesson (Evaluate).

(one per group)

๏ Star stickers

Terms stands for value of placeholder

๏ Introduce rewards, given by both peers and the teacher, to enhance reinforcement (Behaviourism, reinforcement through positive rewards). Despite the physical rewards, do not forget intangible rewards such as praise and affirmation of good practices. ๏ Reiterate SIO 3 Each student gets 3 tries. Have the Rollies check the Showies’ work and grade their work with simple star stickers.

๏ Reiterate SIO 4

Swap the Rollies and Showies.

Reward students who performed well (based on overall performance of the students) with a simple prize each.

PAGE 7 OF 8

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Evaluate (15 minutes) Time ๏ 15 mins

Activities

Notes

Resource

๏ Textbook Assignment, Have students attempt My Pals Are Here Textbook 3A, pages 12, 14 and 15 individually. Give them approximately 15 minutes.

๏ Note the number of students that exhibit difficulty in answering the questions. Teacher may have to revisit topic if many students displayed difficulty in answering the questions,

Roam the class and observe the students, paying closer attention to students who exhibit difficulty in solving the questions.

๏ Adjust homework depending on student performance during textbook assignment

After students have completed the questions, have students volunteer their answers and explanations for their choice of answers.

๏ Evaluation here is on the individual and not the group as teacher seeks to evaluate the accumulation of the learning objectives within individual students, not in groups.

Have all students post their answers on individual whiteboards so as to avoid dipsticking and have a view on all individual students and their ability to answer the questions. Post answers on the board.

Assign homework: My Pals Are Here Workbook 3A Part 1, pages 9 to 12.

๏ My Pals Are Here Textbook 3A, pages 12, 14 and 15 ๏ My Pals Are Here Worbook 3A Part 1, pages 9 to 12 ๏ Individual whiteboard

๏ Evaluation here serves to act as Assessment for Learning instead of Assessment of Learning.

End (5 minutes) Time ๏ 5 mins

Activities ๏ Summary, Refer to the key concept. Reiterate key questions: “What’s the difference between digits and numbers?”

“What is place value?”

Have students volunteer 4-digit numbers and pose questions on the place value of the digits within the volunteered numbers.

“What place is the digit _ in?”

“What does the digit _ stand for?”

Notes

Resource

๏ Reiterate key concept ๏ Having the students pose questions on the Class Blog or Lino wall allows students to pose questions that they did not have a chance to pose during the lesson

๏ Class Blog or Lino wall

๏ Having the students pose questions on the Class Blog or Lino wall also allows the teacher to identify, again, any concepts the students may have failed to grasp or any misconcepts the students may have

“What is the value of the digit _?”

Have students answer the questions. Have students pose questions they may have on the Class Blog or create a Lino wall if they have any.

Lesson plan adapted from My Pals Are Here, Textbook 3A, Teacher’s Guide.

PAGE 8 OF 8

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Appendix A

“Place Value Song and Dance” video can be found in the CD. Soft copies of the lesson plan and appendices can also be found in the CD.

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Appendix C

Diene’s Base-Ten Blocks

10-sided dice

Prepared by: Lee Wei Loong

PRIMARY 3: WHOLE NUMBERS, Place Value

Appendix E

Example of Lino Wall Online site: http://linoit.com/users/leeweiloong/canvases/Place%20Value Students can post questions as “post-its” freely onto the Lino Wall.

All they need to do is click on a post-it on the top-right hand corner and type in their question.

Prepared by: Lee Wei Loong