Using Base-Ten Blocks to Represent Two-Digit Numbers

Objectives

In this unit, students represent two-digit numbers in various ways. Students will:

use base-ten blocks to represent a number.
explore a simple way to draw base-ten blocks.
match numbers and displays of base-ten blocks.

Essential Questions

How are relationships represented mathematically?

How can mathematics support effective communication?

How can recognizing repetition or regularity assist in solving problems more efficiently?

How is mathematics used to quantify, compare, represent, and model numbers?

What does it mean to estimate or analyze numerical quantities?

What makes a tool and/or strategy appropriate for a given task?

How is mathematics used to quantify, compare, represent, and model numbers?

Vocabulary

Digit: A number used to make a larger number. The digits we use to write numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Ones: The digit all the way on the right. In the number 35, the digit 5 is in the ones place.
Place Value: The value of the place of a digit in a number.
Tens: The place next to the ones place. In the number 35, the digit 3 is in the tens place.

Duration

45–60 minutes

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

I Have, Who Has Base Ten cards (M-1-1-2_I Have, Who Has Base Ten.pdf)
Number Cards (M-1-1-2_Number Cards.docx)
base-ten blocks, sets for each student
Place-Value Mat (M-1-1-2_Place-Value Mat.docx)
Base-Ten Matching Game (M-1-1_Base-Ten Matching Game.doc)
Base-Ten Matching Game with Three-Digit Numbers (M-1-1_Base-Ten Matching Game with Three-Digit Numbers.doc)
whiteboards
whiteboard markers
whiteboard erasers: felt or sock
Drawing Numbers with Base-Ten Blocks (M-1-1-2_Drawing Numbers with Base-Ten Blocks and KEY.docx)

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

Formative Assessment

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- Observe students as they complete the Drawing Numbers with Base-Ten Blocks worksheet (M-1-1-2_Drawing Numbers with Base-Ten Blocks and KEY.docx).
- Observe students as they play I Have, Who Has Base Ten (M-1-1-2_I Have, Who Has Base Ten.pdf).
- Observe student responses during the Instructional Procedures section.

Suggested Instructional Supports

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Scaffolding, Active Engagement, Modeling, Explicit Instruction

W:	Inform students that our system for writing numbers is called the base-ten system because it is based on grouping things by tens. Inform them that base-ten blocks can be helpful in representing numbers.
H:	Play I Have, Who Has Base Ten.
E:	Students will use base-ten blocks to represent two-digit numbers.
R:	The questions asked before, during, and after the lesson will enable students to reflect on their understanding of representing numbers using base-ten blocks.
E:	Use the Drawing Numbers with Base-Ten Blocks worksheet and the responses to questions throughout the lesson to determine understanding of expanded form.
T:	The lesson may be tailored using the suggestions in the Extension section.
O:	The lesson is intended to review the concept of using base-ten blocks to represent numbers. Students are asked to represent numbers using base-ten blocks and then draw a picture to represent that number.

Instructional Procedures

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Students stand in a circle. Distribute I Have, Who Has Base Ten cards (M-1-1-2_I Have, Who Has Base Ten.pdf) until all cards have been distributed. Some students may have more than one card. Have one student start by reading his/her card. Continue until all cards have been read.

“In the last lesson we used base-ten blocks to represent numbers. Base-ten blocks were displayed; you counted them and named the number the base-ten blocks represented. In today’s lesson I will display a two-digit number using numeral cards, and you will show that number using base-ten blocks.”

“Drawing pictures may be more efficient than using actual blocks. Pictures can also be used to explain and record a solution to a problem.” Show students how to draw a cube and a long. To save time, encourage students to draw a simple line for a long, and a dot or square for a cube.

Using the Place-Value Mat (M-1-1-2_Place-Value Mat.docx) and Number Cards (M-1-1-2_Number Cards.docx) display the number 63. “Use your base-ten blocks to display this number.” (Students should display six longs and three cubes.) Now have students draw the number on their whiteboards using pictures of longs and cubes.

Repeat with the following numbers:
- 54
- 72
- 20
- 8
- 49
Give each student a copy of the Drawing Numbers with Base-Ten Blocks worksheet (M-1-1-2_Drawing Numbers with Base-Ten Blocks and KEY.docx). Move around the room observing and asking clarifying questions, such as the ones listed below, to evaluate which students understand using base-ten blocks to represent two-digit numbers and which students need additional exploration.
- “Why did you decide to use the blocks that you have there?”
- “What would happen if you added or took away a long?”
- “What would happen if you added or took away a cube?”
Extension:
- Routine: Partners play Base-Ten Matching Game (M-1-1_Base-Ten Matching Game.doc). Links listed under Related Resources can also be used for ongoing learning and practice.
- Small Group: Using the Place-Value Mat (M-1-1-2_Place-Value Mat.docx) and Number Cards (M-1-1-2_Number Cards.docx), display the number 27. “Use your base-ten blocks to display this number.” (Students should display two longs and seven cubes.) Now have students draw base-ten blocks of 27 on their whiteboards.
Repeat with the following numbers:
- 52
- 7
- 40
- 81
- Expansion: Partners play Base-Ten Matching Game with Three-Digit Numbers (M-1-1_Base-Ten Matching Game with Three-Digit Numbers.doc).
Have students represent three-digit numbers using base-ten blocks and draw them. Links listed under Related Resources can also be used for Expansion activities.

Using Base-Ten Blocks to Represent Two-Digit Numbers