Identify Place Value to 100's Place: Representational Level

More Teaching Plans on this topic: Concrete, Abstract

PHASE 1: Initial Acquisition of Skill

Teach Skill with Authentic Context

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.

Build Meaningful Student Connections

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!!

Provide Explicit Teacher Modeling

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.

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: 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.

Videos

Learning Objective 1: view  Clip 1, Clip 2
Draw pictures on place value mats to represent place value of one, two, and three digit numbers.