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Identify Place Value to 100's Place
Description:
Students will relate place value at the representational/drawing level during Explicit Teacher Modeling by investigating how many groups of ones and tens there are in the number of students in their class. For three-digit numbers, students can investigate how many groups of hundreds, tens, and ones there are in the number of students in their school.
Purpose: to assist students to build meaningful connections between what they know about using concrete materials to represent the place value of one, two, and three digit numbers and representing place value by drawing pictures.
Materials:
Teacher -
Place value mat
Base-ten materials
Format for display your writing so all students can see (e.g. dry-erase board/chalkboard, chart and chart paper, overhead projector).
Description:
1.) L ink to students’ prior knowledge of grouping ones, tens, and hundreds using place value mats and how those concrete representations identify the place value of digits in one, two, and three digit numbers.
For Example:
Ok guys, I have a place value mat here with some base-ten materials placed on it. (Show students the place value mat with base-ten materials representing ‘four tens’ and ‘three ones’.) What do these materials represent? (Elicit the response, ‘four tens and three ones.’) Yes, I have four tens and three ones. We’ve learned how to write numbers that represent groups of tens and ones. What number does four tens and three ones represent? (Elicit the response, ‘forty-three’.) That’s right. My four ten sticks and three one cubes represent the written number ‘forty-three’. (Write ‘’43’ or place the appropriate number cards above the appropriate columns on the place value mat.) The digit ‘3’ stands for three one cubes and the digit ‘4’ stands for four tens. (Point to each written number and then point to the appropriate base-ten materials as you say this.) We also learned a special name for what a number represents. For example, the digit ‘4’ in the number ‘forty-three’ represents ‘four tens’. We know it represents ‘four tens’ because we have four ten sticks in the tens column. (Point to the number ‘4’ and then to the four ten sticks in the tens column.) We also know that the digit ‘4’ represents ‘four tens’ because of its position or ‘place’ in the written number ‘43’. Its position is the ‘tens place’. We know this because when we determine its position, or place, we start with the digit in the ones place. The digit ‘3’ is in the ones place. (Point to the number ‘3’.) The digit next to it (‘standing in line behind it”), is in the tens place. Therefore the digit ‘4’ is in the tens place. Who remembers the special name we use for what the number represents based on its position? (Elicit the response, ‘place value’.) That’s right, the special name we use is place value. (Write the words ‘place value’ on the chalkboard/overhead/dry-erase board)
2.) I dentify to students that they will learn to draw pictures to represent the place value of one, two, and three digit numbers.
For Example:
You know how to find the place value of digits in one, two, and three digit numbers using base-ten materials. Today you are going to learn how to find place value by drawing pictures instead of using base-ten materials. (Provide a visual that represents the learning objective.) What are you going to do today? (Elicit the response, “we are going to learn how find place value by drawing pictures.”) That’s right!
3.) P rovide rationale/meaning for finding place value by drawing pictures.
For Example:
Learning how to draw pictures to find place value is important because it will allow you to find the place value of digits in one, two, and three digit numbers without base-ten materials. You will not always have base-ten materials to use, and drawing pictures is faster than using base-ten materials. This will really be important when you begin adding and subtracting larger numbers. There will be times you will need to know the place value of numbers in order to solve these type problems. Drawing will be something that can help you if you get stuck. Drawing pictures is also fun!!
Purpose: to provide students a clear, multi-sensory model of how to draw pictures that represent the place value of digits in one, two, and three digit numbers and to relate the place value of each digit to the drawings for each digit.
Learning Objective: Draw pictures on place value mats to represent place value of one, two, and three digit numbers.
Materials:
Teacher -
Place value mat with pictures of a one cube, a ten stick, and/or a hundred flat above the corresponding place value columns
Proportional (linked) base-ten materials
A format for writing/drawing as you model so all students can see (e.g. chart paper, dry-erase board/chalkboard, overhead projector)
Pen/marker/chalk for writing and drawing
Description:
A. Break down the skill of drawing pictures on place value mats to represent place value of one, two, and three digit numbers.
1.) Review/model representing one, two, and three digit numbers with concrete materials and place value mat.
2.) Introduce place value mat with pictures of one cube, ten stick, and hundred flat at top of place value columns.
3.) Read number.
4.) Find the digit that represents the ones place.
5.)Draw horizontal tally marks or dots to represent the value of the digit in the ones place.
6.) Find the digit that represents the tens place.
7.) Draw long vertical lines to represent the number of ‘tens’ represented by the digit in the tens place.
8.) Find the digit that represents the hundreds place (if appropriate).
9.) Draw squares to represent the number of ‘hundreds’ represented by the digit in the hundreds place.
10.) Write the number above the columns of the place value mat so that the digits are directly over the appropriate ones, tens, and hundreds columns.
11.) Say the place value of each digit by relating the drawings to each digit in the number.
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: Draw pictures on place value mats to represent place value of one, two, and three digit numbers.
Materials:
Teacher and Students -
Place value mats with pictures
Writing instruments
Description:
*Scaffolding at the representational/drawing level of instruction should occur using the same process as scaffolding instruction at the concrete level of instruction. The steps used during Explicit Teacher Modeling should be used as structure for scaffolding your instruction. Scaffolding should start with drawing pictures from concrete representations of a given number (e.g. begin with a concrete representation of a two or three digit number and then make drawings that represent the concrete materials). Drawing pictures from concrete objects during a High Level of Teacher Direction/Support and even a Medium Level of Support may be appropriate. The use of concrete objects can be faded to drawing pictures from the written number only (e.g. begin with a written two or three digit number and draw representations of that number without the use of concrete objects) during a Low Level of Teacher Direction/Support.
A. Scaffold instruction using a high level of teacher direction/support. Move to the next phase of scaffolding only when students demonstrate understanding and ability to respond accurately to your prompts.
B. Scaffold instruction using a medium level of teacher direction/support. Move to the next phase of scaffolding only when students demonstrate understanding and ability to respond accurately to your prompts.
C. Scaffold instruction using a low level of teacher direction/support. Move students to independent practice of the skill only after they demonstrate the ability to perform the skill with limited prompting from you.
Purpose: to provide students multiple opportunities to practice matching place value drawings to one, two, and three digit numbers and/or using place value language that describes those numbers.
Learning Objective: Draw pictures on place value mats to represent place value of one, two, and three digit numbers.
Self-Correcting Materials – Punch-hole cards
Materials:
Sets of punch-hole cards that have on the front a place value drawing with several choices of one, two, and three digit numbers; or, place value language that describes those numbers at the bottom and punch holes adjacent to each choice. On the back is written the correct response adjacent to the hole. Cards are numbered sequentially (e.g. 1-30)
A pencil
A response record sheet with the numbers 1-30 written.
Description:
Activity: Students read the picture on each card and then the choices at the bottom. Students put the tip of their pencil in the hole of their choice. Then students look at the back of the card to see if they responded correctly. Students put a check next to the number on their response record sheet that corresponds to the card’s number for those responses that are correct. The teacher monitors student work and reviews the response records of students to evaluate which drawings are giving students trouble.
Self-Correcting Material Steps:
1.) Introduce self-correcting material.
2.) Distribute materials.
3.) Provide directions for using the self-correcting material, and teach/review any behavioral expectations.
4.) Provide time for students to ask questions.
5.) Model performing the skill within the context of the self-correcting material.
6.) Provide time for students to ask questions about how to respond.
7.) Model how students can keep track of their responses using their response record sheet.
8.) Provide ample amounts of positive reinforcement as students use the self-correcting material.
9.) Provide specific corrective feedback/ re-model skill as needed.
10.) Review response record sheets of students and note particular card numbers where students have problems.
11.) Provide feedback to students as appropriate.
Purpose: to provide students the opportunity to describe what their pictures mean using place value language.
Learning Objective: Draw pictures on place value mats to represent place value of one, two, and three digit numbers.
Provide Structured Language Experiences/Structured Peer Tutoring
Materials:
Sets of cards with a one, two, or three digit number on one side and the appropriate place value language that describes that number on the back (e.g. “four hundreds, two tens, and three ones”)
Paper with place value mats copied on them, or individual dry-erase boards/chalk boards with place value mats written on them (*laminated tag board squares can also be used)
Pencils, dry-erase markers, or chalk.
Description:
Activity:
Students work in pairs. One student plays the coach and presents front side of card with number written on it. The player then reads the number, draws the place value of each digit, and then says the number using place value language. The coach reads the back of the card to evaluate the player’s response and to provide feedback. The coach shows the back of the card to the player to provide feedback. If the player responds incorrectly, the coach checks the drawing and provides feedback as appropriate or says the appropriate place value language written on the card. He then shows the “correct” response to the player. The coach then gives the player a second chance to respond to the same prompt. If the player responds correctly, then the coach still shows the player the back of the card to reinforce the player’s response. Points can be included by the coach recording two points for each correct response (first try) and one point for each correct response (second try). Tallies can be made by the coach to record points. Halfway through the practice period, students switch roles. The coach becomes the player and the player becomes the coach. The teacher monitors students as they work and provides corrective feedback and positive reinforcement. Point sheets can be reviewed by the teacher to evaluate the performance of individual students.
Structured Language Experiences/ Structured Peer Tutoring Steps:
1.) Select pair groups and assign each pair a place to practice (try to match students of varying achievement levels if possible).
2.) Review directions for completing structured language experiences/peer tutoring activity and relevant classroom rules. Practice specific peer tutoring procedures as needed (see step #4).
3.) Model how to perform the skill(s) within the context of the activity (using the cards and type of place value mat students will use) before students begin the activity. Model both how to draw place value of numbers using a place value mat and model how to describe the drawing and number using place value language.
4.) Divide the practice period into two equal segments of time. One student in each pair will be the “talker/describer-player” and will draw and then describe their place value drawing of the number. The other student will be the “listener/evaluator-coach” and will give the “player” feedback based on their description of their drawing using the back of the card that has the appropriate place value language written. The “listener/describer-coach” will also provide positive reinforcement, corrective feedback, and tally corrects and incorrects/mistakes based on the player’s responses.
5.) Provide time for student questions.
6.) Signal students to begin.
7.) Signal students when it is time to switch roles.
8.) Monitor students as they work in pairs. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate tutoring behaviors. Also provide corrective feedback and modeling as needed.
Purpose: to provide you with continuous data for evaluating student learning and whether your instruction is effective. It also provides students a way to visualize their learning/progress.
Materials:
Teacher –
Appropriate prompts if they will be oral prompts
Appropriate visual cues when prompting orally
Student –
Appropriate response sheet/curriculum slice/probe
Graph/chart
Description:
*You should continuously evaluate your students’ abilities to draw representations of base-ten materials on place value mats, saying what their drawings mean using place value language, and identify the place value of digits in one, two, and three digit numbers using their drawings. The following steps outline a process for doing this.
Steps for Conducting Continuous Monitoring and Charting of Student Performance:
1.) Choose whether students should be evaluated at the receptive/recognition level or the expressive level.
2.) Choose an appropriate criteria to indicate mastery.
Select 8 to 10 prompts to evaluate your students’ drawing abilities. Students should demonstrate 100% accuracy (e.g. 8 out of 8 for two to three consecutive days). This number of tasks allows you to complete the evaluation period within 3 to 5 minutes. *It is important that this evaluation strategy is time-efficient because it should be done every day or every other day and if it is not time-efficient, you will probably not implement this important evaluation strategy.
3.) Provide appropriate number of prompts in an appropriate format (receptive/recognition or expressive) so students can respond.
Based on the skill, your students’ learning characteristics, and your preference, the curriculum slice or probe could be written in nature (e.g. a sheet with appropriate prompts; index cards with appropriate prompts), or oral in nature with visual cues (e.g. display a card that has a number written on it and say, “draw the number ‘67’ using your place value mat and write each digit over the appropriate drawings.”) or a combination of written curriculum slices/probes and oral prompts with visual cues (e.g. students have a curriculum slice/probe that is numbered “1, 2, 3…” where each number has several one, two, and three digit numbers written – “23,” “146,” “673,” and students circle the correct response when teacher represents the correct number by drawing it using a place value mat.)
4.) Distribute to students the curriculum slice/probe/response sheet.
5.) Give directions.
6.) Conduct evaluation.
7.) Count corrects and incorrects/mistakes (you and/or students can do this depending on the type of curriculum slice/probe used – see step #3).
8.) You and/or students plot their scores on a suitable graph/chart. A goal line that represents the proficiency (for representational/drawing level skills, this should be 100% – 8 out of 8 corrects) should be visible on each students’ graph/chart.
9.) Discuss with children their progress as it relates to the goal line and their previous performance. Prompt them to self-evaluate.
10.) Evaluate whether student(s) is/are ready to move to the next level of understanding or has mastered the skill at the abstract level using the following guide:
Representational Level: demonstrates 100% accuracy drawing place value of written numbers (given 8-10 response tasks) over two to three consecutive days.
11.) Determine whether you need to alter or modify your instruction based on student performance.
Purpose: to provide students periodic opportunities to respond to previously mastered skills, thereby helping students to maintain their level of mastery.
Problem of the Day
Materials:
Teacher –
Chalkboard/overhead projector
Chalk/overhead pen
Student –
Appropriate concrete materials
Description:
Provide a problem of the day that focuses on drawing place value of numbers using a place value mat. Orally give the problem while students read the question/prompt written on the chalkboard. Ask students to discuss the strategy they used to get the answer. Students can share their drawings. Model the skill after this discussion, highlighting important ideas/features. Asking students to determine the number represented by drawings you make may also be a helpful activity. Encourage students to describe the drawings!
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