Identify Place Value to 100's Place: Concrete Level

More Teaching Plans on this topic: Representational, Abstract

 Introduction Phase 1 Initial Acquisition of Skill Phase 2 Practice Strategies Phase 3 Evaluation Phase 4 Maintenance Videos

PHASE 1: Initial Acquisition of Skill

Teach Skill with Authentic Context

Description: A story situation involving a field trip to the zoo and choosing the number of buses needed for the children will be used to show relevance of place value. (See the story situation used in the teacher instruction strategy “Explicit Teacher Modeling.”)

Build Meaningful Student Connections

Purpose: to help students to build meaningful connections between what they know about grouping objects by ones, tens, and hundreds to where those groupings can be represented on a place value mat and how those groupings represent the place value of digits in one, two, and three digit numbers.

Learning Objective 1: Identify the essential features of a place value mat, represent groups of ones, tens, and hundreds on place value mats appropriately using concrete materials, and say what each group of base-ten materials means.

Materials:

Teacher -

• Place value mat
• Base-ten materials

Description:

1) L ink to students’ prior knowledge of grouping ones, tens, and hundreds.

For Example:

I have a group of cubes here. You have all learned how to group objects like these cubes into groups of ones, tens, and hundreds. Let’s do that now. (Take your students through this process using a group of cubes less than nine, a group of thirty, and a group of one-hundred. Count the total aloud and then group the cubes accordingly. Involve your students while completing this activity by prompting them and having them come up to group).

2) I dentify the skill students will learn.

For Example:

Today we are going to use what we know about grouping ones, tens, and hundreds to group ones, tens, and hundreds using a special tool called a place value mat. (Hold up a place value mat for students to see.) What are we going to do today? (Elicit the response, “we are going to group ones, tens, and hundreds using a place value mat.”) That’s right!

3) P rovide rationale/meaning for grouping ones, tens, and hundreds using a place value mat.

For Example:

Learning how to use a place value map to group ones, tens, and hundreds is really important because it will help you begin to better understand something special about numbers like “four,” “twenty-three,” and “one-hundred forty-two.” (Write/show the numbers as you say them.) Once you learn where groups of ones, tens, and hundreds can be placed on a place value mat, you will then be able to understand what is special about numbers like these.

Learning Objective 2: Represent one, two, and three digit numbers using base-ten materials/place value mats and say what the digits represent in concrete terms.

Materials:

Teacher -

• Place value mat
• Base-ten materials

For Example:

1) L ink to student’s prior knowledge of grouping by ones, tens, and hundreds on a place value mat.

For Example:

Yesterday, we learned about our place value mat and how to represent groups of ones, tens, and hundreds on it using one cubes, ten sticks, and hundred flats. We also learned another way to say what one cubes, tens sticks, and hundred flats represent on the place value mat.

2) I dentify the skill students will learn.

For Example:

Today we are going to use what we know about groups of ones, tens, and hundreds to find out what is special about individual digits in numbers that have one, two, and three digits in them (Show students an example of a one-digit number, a two-digit number, and a three-digit number. Point out each digit in each number). The special thing this place value mat is going to help us learn about is called “place value.” We are going to learn how to decide the place value digits have in one-digit numbers (Point to the one-digit number you previously displayed), two digit numbers (Point to the two-digit number you previously displayed), and three digit numbers (Point to the three-digit number you previously displayed).

“Let’s look at a number (write the number 45 on the board/chart paper/overhead projector). What individual numbers/digits are there in the whole number “forty-five?” (Elicit the response, “There is a four and a five.”) Great! There is something very special about the ‘four’ and the ‘five.’ What makes them special is where they are positioned. For example, what side is the four on when I point to the ‘five.’ (Elicit the response, “it’s beside it, or it is to the left of the five.) Good. Now, where is the five if I point to the four? (Elicit the response, “it’s on the other side, or it’s to the right.) Great job! That’s what I mean by position. Where the individual number/digit is makes it special. We call this special quality “place value.”

3) P rovide rationale/meaning for learning how to name the place value of digits in one, two, and three digit numbers.

For Example:

Learning how to name the place value of digits in numbers will help you understand better what numbers really mean. Later in the year and next year, you are going to start adding and subtracting larger numbers and knowing about place value will really help you with this.

Provide Explicit Teacher Modeling

Purpose: to provide students a clear, multi-sensory model of where groups of ‘ones,’ ‘tens,’ and ‘hundreds’ can be placed on place value mats, and how the place value of these groupings relates to the ‘ones,’ ‘tens,’ and ‘hundreds’ digits in one, two, & three digit numbers.

Learning Objective 1: Identify the essential features of a place value mat, represent groups of ones, tens, and hundreds on place value mats appropriately using concrete materials, and say what each group of base-ten materials means.

Materials:

• Place value mat with a one cube, a ten-stick, and/or a hundred flat placed at the top the corresponding place value columns
• Proportional (linked) base-ten materials (one cubes, ten sticks, hundred flats)

Description:

A. Break down the skill of identifying essential features of a place value mat and representing groups of ones, tens, and hundreds on a place value mats appropriately using concrete materials.

1) Introduce story context.

2) Identify the characteristics of a place value mat that represents ones, tens, and hundreds.

3) Place a one cube, ten stick, and hundred flat in the appropriate columns on a place value mat.

4) Place a group of ones (up to nine) in the appropriate column - relate to picture and language “ones.”

5) Place a group of tens (up to ninety) in the appropriate column - relate to the picture and language “tens.”

6) Place a group of hundreds (up to nine-hundred) in the appropriate column - relate to the picture and language “hundreds.”

Learning Objective 2: Represent one, two, and three digit numbers using base-ten materials/place value mats and say what the digits represent in concrete terms.

Materials:

• Place value mat with a one cube, a ten-stick, and/or a hundred flat placed at the top the corresponding place value columns
• Proportional (linked) base-ten materials (one cubes, ten sticks, hundred flats)

Description:

A. Break down the skill of representing one, two, and three digit numbers using base-ten materials/place value mats and saying what the digits represent in concrete terms.

1) Tell students there is something “special” about digits.

2) Represent two-digit numbers with concrete objects using a place value mat.

3) Write/position digits of two-digit number over the appropriate place value columns and the concrete materials that represent each digit.

4) Describe that the ones digit represents the group of one cubes and that the tens digit represents the group of ten sticks.

5) Relate place value of two-digit numbers to the authentic context/story situation.

6) Represent three-digit numbers with concrete objects using a place value mat.

7) Write/position digits of three-digit number over the appropriate place value columns and the concrete materials that represent each digit.

8) Describe that the ones digit represents the appropriate number of one cubes (‘ones’), that the tens digit represents the appropriate number of ten sticks (‘tens’), and the hundreds digit represents the appropriate number of hundred flats (‘hundreds’).

9) Relate place value of three-digit numbers to the authentic context/story situation.

Scaffold Instruction

Purpose: to provide students the opportunity to build their initial understanding of the skill and to provide you the opportunity to evaluate your students’ level of understanding after your initial modeling of the skill.

Learning Objective 1: Identify the essential features of a place value mat, represent groups of ones, tens, and hundreds on place value mats appropriately using concrete materials, and say what each group of base-ten materials means.

Materials:

Teacher -

• Place value mat with a one cube, a ten-stick, and/or a hundred flat placed at the top the corresponding place value columns
• Proportional (linked) base-ten materials (one cubes, ten sticks, hundred flats)

Students -

• Place value mat with a one cube, a ten-stick, and/or a hundred flat placed at the top the corresponding place value columns
• Proportional (linked) base-ten materials (one cubes, ten sticks, hundred flats)

Description:

1) Scaffold Using a High Level of Teacher Direction/Support

a. Choose one or two places in the problem-solving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction. (Examples of choices are shown in red.)

Introduce students to the scaffolding process.

“We’ve discovered how to place our base-ten materials on a place value mat and we’ve also learned how to say what the base-ten materials represent on the place value mat. We’re going to do some more now, except this time you are going to help me. As we begin, I want you to use you materials and place value mat to do what I do. Every so often, I’m going to ask you questions and ask you to move your base-ten materials on your own.

Prompt student thinking about the characteristics of a place value mat that represents ones, tens, and hundreds.

“Let’s all look at our place value mats. What are some special things we need to know about our place value mats? (Emphasize: columns are for placing base-ten materials; that concrete materials at top of place value columns represent which base-ten materials should be placed there; the language of ‘ones’, ‘tens’, and ‘hundreds’.)

Place a group of ones (up to nine) in the appropriate column and relate the group to the picture of a one cube, the phrase/language of ‘ones’ written at the top of the ones column, and saying how many ‘ones’ the group represents.

“I know some special things about my place value mat. Now, I need to know where to place my base-ten materials on it. Hmm, I have a group of five one cubes here. I remember I can use the special things on my place value mat to help me decide where to put my group of five one cubes. (Model pointing to the one cube and reading the word ‘ones’.) Where do I place this group of five one cubes? (Elicit the appropriate response.) How do I know this is the correct place to place my group of one cubes? (Elicit the appropriate response.) What does my group of one cubes represent? (Elicit the appropriate response.)”

Place a group of tens (up to ninety) in the appropriate column and relate the group to the ten stick at the top of the “tens” column, the phrase/language of ‘tens’ written at the top of the tens column, and saying how many ‘tens’ the group represents.
“Now, I have a group of four ten sticks. I need to decide where to place this group of four ten sticks. I know I used the one cube and the word written at the top of the column to help me with my group of five one cubes. I’ll do the same thing for my group of ten sticks. (Model pointing to the ten stick and reading the word ‘tens’.) I know I can put my group of four ten sticks here. (Place ten sticks in the appropriate column.) How do I know this is the correct place to place my group of ten sticks? (Elicit the appropriate response.) What does my group of ten sticks represent? (Elicit the appropriate response.)“

Place a group of hundreds (up to nine-hundred) in the appropriate column and relate the group to the hundred flat at the top of the “hundreds” column, the phrase/language of ‘hundreds’ written at the top of the hundreds column, and saying how many ‘hundreds’ the group represents.

“Ok, I have a group of two hundred flats. Just like my group of five one cubes and my group of four ten sticks, I need to decide where to place this group of two hundred flats. I’ll use the hundred flat at the top of the column and word cue to help me do this, just like I did with my groups of one cubes and tens sticks. (Model pointing to and the hundred flat and reading the word ‘tens’.) I know I can put my group of two hundred flats here. (Place hundred flats in the appropriate column.) How do I know this is the correct place to place my group of hundred flats? (Elicit the appropriate response.) What does my group of hundred flats represent? (Elicit the appropriate response.)”

Use language to describe what the concrete materials represent.

“Now that I have represented all my base-ten materials on the place value mat and I know what each group of materials represent, I need to say what the my groups of one cubes, ten sticks, and hundred flats mean altogether. I can do that by pointing to each group and saying what it represents. I’ll start with my group of hundred flats. It means ‘two hundreds’. Next I’ll point to my group of ten sticks and say what it represents. It means ‘four tens.’ Last, I’ll point to my group of one cubes and say what it represents. It means ‘five ones’. By saying what all three groups mean altogether, I can say what all my base-ten materials mean. I’ll do that now. I have ‘two hundreds’, ‘four tens’, and ‘five ones’. (Point to each group of materials as you say this.) Everybody, say with me what all my groups of materials mean altogether. (Elicit the appropriate response.)”

b. Maintain a high level of teacher direction/support for another example if students demonstrate misunderstanding/non-understanding; move to a medium level of teacher direction/support if students respond appropriately to the selected questions/prompts.

2) Scaffold Using a Medium Level of Teacher Direction/Support

a. Choose several more places in the problem-solving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction.

Prompt student thinking about the characteristics of a place value mat that represents ones, tens, and hundreds.

“Let’s all look at our place value mats. What are some special things we need to know about our place value mats? (Emphasize: columns are for placing base-ten materials; that concrete materials at top of place value columns represent which base-ten materials should be placed there; the language of ‘ones’, ‘tens’, and ‘hundreds’.)

Place a group of ones (up to nine) in the appropriate column and relate the group to the one cube at the top of the “ones” column, the phrase/language of ‘ones’ written at the top of the ones column, and saying how many ‘ones’ the group represents.

“Hmm, I have a group of threeone cubes here. What two things on my place value mat can help me (Elicit the appropriate response and then model pointing to the one cube and reading the word ‘ones’.) Where do I place this group of three one cubes? (Elicit the appropriate response.) How do I know this is the correct place to place my group of one cubes? (Elicit the appropriate response.) What does my group of one cubes represent? (Elicit the appropriate response.)”

Place a group of tens (up to ninety) in the appropriate column and relate the group to the ten stick at the top of the “tens” column, the phrase/language of ‘tens’ written at the top of the tens column, and saying how many ‘tens’ the group represents.

“Now, I have a group of six ten sticks. I need to decide where to place this group of four ten sticks. What two things on my place value mat can help me (Elicit the appropriate response and then model pointing to the ten stick and reading the word ‘tens’.) Where do I place this group of six ten sticks? (Elicit the appropriate response.) (Place ten sticks in the appropriate column.) How do I know this is the correct place to place my group of ten sticks? (Elicit the appropriate response.) What does my group of ten sticks represent? (Elicit the appropriate response.)”

Place a group of hundreds (up to nine-hundred) in the appropriate column and relate the group to the hundred flat at the top of the “hundreds” column, the phrase/language of ‘hundreds’ written at the top of the hundreds column, and saying how many ‘hundreds’ the group represents.

“Ok, I have a group of three hundred flats. Just like my group of five one cubes and my group of four ten sticks, I need to decide where to place this group of two hundred flats. What two things on my place value mat can help me (Elicit the appropriate response and then model pointing to and reading the hundred flat and the word ‘hundreds’.) Where do I place this group of three hundred flats? (Elicit the appropriate response.) (Model pointing to the hundred flat and reading the word ‘hundreds’.) I know I can put my group of three hundred flats here. (Place hundred flats in the appropriate column). How do I know this is the correct place to place my group of hundred flats? (Elicit the appropriate response.) What does my group of hundred flats represent? (Elicit the appropriate response.)”

Use language to describe what the concrete materials represent.

“Now that I have represented all my base-ten materials on the place value mat and I know what each group of materials represent, I need to say what my groups of one cubes, ten sticks, and hundred flats mean altogether. I can do that by pointing to each group and saying what it represents. I’ll start with my group of hundred flats. It means ‘three hundreds’. Next I’ll point to my group of ten sticks and say what it represents. It means ‘six tens.’ Last, I’ll point to my group of one cubes and say what it represents. It means ‘three ones’. By saying what all three groups mean altogether, I can say what all my base-ten materials mean. What do my groups mean altogether? (Point to each group and elicit the appropriate response.)”

b. Maintain a medium level of teacher direction/support for another example if students demonstrate misunderstanding/non-understanding; move to a low level of teacher direction/support if students respond appropriately to the selected questions/prompts.

3) Scaffold Using a Low Level of Teacher Direction/Support

a. When students demonstrate increased competence, do not model the process. Ask students questions and encourage them to provide all responses. Direct students to replicate the process at their desks as you work together.

Place a group of ones (up to nine) in the appropriate column and relate the group to the one cube at the top of the “ones” column, the phrase/language of ‘ones’ written at the top of the ones column, and saying how many ‘ones’ the group represents.

“Hmm, I have a group of seven one cubes here. What two things on my place value mat can help me? (Elicit the appropriate response.) Where do I place this group of seven one cubes? (Elicit the appropriate response.) (Place one cubes in the appropriate column.) How do I know this is the correct place to place my group of one cubes? (Elicit the appropriate response.) What does my group of one cubes represent? (Elicit the appropriate response.)”

Place a group of tens (up to ninety) in the appropriate column and relate the group to the ten stick at the top of the “tens” column, the phrase/language of ‘tens’ written at the top of the tens column, and saying how many ‘tens’ the group represents.

“I also have a group of one ten sticks. I need to decide where to place this group of one ten sticks. What two things on my place value mat can help me (Elicit the appropriate response.) Where do I place this group of one ten sticks? (Elicit the appropriate response.) (Place ten sticks in the appropriate column.) How do I know this is the correct place to place my group of ten sticks? (Elicit the appropriate response.) What does my group of ten sticks represent? (Elicit the appropriate response.)”

Place a group of hundreds (up to nine-hundred) in the appropriate column and relate the group to the hundred flat at the top of the “hundreds” column, the phrase/language of ‘hundreds’ written at the top of the hundreds column, and saying how many ‘hundreds’ the group represents.

“Ok, I have a group of four hundred flats. What two things on my place value mat can help me (Elicit the appropriate response.) Where do I place this group of four hundred flats? (Elicit the appropriate response.) (Place hundred flats in the appropriate column.) How do I know this is the correct place to place my group of hundred flats? (Elicit the appropriate response.) What does my group of hundred flats represent? (Elicit the appropriate response.)”

Use language to describe what the concrete materials represent.

“Now that I have represented all my base-ten materials on the place value mat and I know what each group of materials represent, I need to say what the my groups of one cubes, ten sticks, and hundred flats mean altogether. How can I do that? (Elicit the appropriate response.) I’ll point to each group and you say what each group means. (Point to each group and elicit the appropriate response.) By saying what all three groups mean altogether, I can say what all my base-ten materials mean. What do my groups mean altogether? (Elicit the appropriate response.)”

b. When you are confident students understand, ask individual students to direct the problem solving process or have the class direct you: Students ask questions and you and your students respond/perform the skill. Have students replicate this process at their desks with your prompts.

*The student practice strategies described below can be used for both skills taught during initial acquisition through Teacher Directed Instruction. A detailed description for providing practice for one of the skills is provided below.

Videos

Learning Objective 1: view  Clip 1, Clip 2
Identify the essential features of a place value mat, represent groups of ones, tens, and hundreds on place value mats appropriately using concrete materials, and say what each group of base-ten materials means.

Learning Objective 2: view  Clip 1, Clip 2, Clip 3
Represent one, two, and three digit numbers using base-ten materials/place value mats and say what the digits represent in concrete terms.