Representing Numerals with Base-Ten Blocks

Objectives

In this unit, students use base-ten blocks to compose and decompose numbers 11–20 to gain place-value understanding. Students will:

use base-ten blocks to represent a number in the number range 11–20.
match numbers and displays of base-ten blocks in the number range 11–20.
identify how many tens and ones are in number range 11–20.

Essential Questions

How can mathematics support effective communication?

How can patterns be used to describe relationships in mathematical situations?

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?

When is it is appropriate to estimate versus calculate?

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

Vocabulary

Digit: A symbol used to make a number. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the ten digits we use to write numbers.
Ones: The place first from the right in a number. In the number 15, the digit 5 is in the ones place.
Place Value: The value of the position of a digit in a number. In the number 13, the 1 is in the tens place and its value is 10.
Tens: The place second from the right in a number. In the number 15, the digit 1 is in the tens place.

Duration

45–60 minutes

Prerequisite Skills

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

Materials

number cards 11–20 (M-K-2-1_Number Cards 11-20.docx)
place-value mats (M-K-2-2_Place-Value Mat.docx)
Place-Value Worksheet (M-K-2-2_Place-Value Worksheet 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 during Lesson 2 activities and assess their understanding of representing numerals with base-ten blocks.
- Use the Place-Value Worksheet (M-K-2-2_Place-Value Worksheet and KEY.docx) to evaluate students’ understanding of place value.
- Observe students throughout the Extension activities to determine their knowledge of place value and the base-ten system.

Suggested Instructional Supports

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Scaffolding, Active Engagement, Modeling, Explicit Instruction

W:	Tell students that throughout this lesson they will be using base-ten blocks to represent numbers. Games and a worksheet will be used to gain understanding.
H:	The activities and games in this lesson will hook and hold students’ interest and enthusiasm.
E:	Students will represent numbers through activities and games. Activities and games will be introduced using the gradual release of responsibility from modeled, shared, and guided activities to independent/partner activities.
R:	Questions throughout the lesson allow students to reflect, revisit, revise, and rethink their mathematical understanding.
E:	Use the Formative Assessment ideas to evaluate students’ mathematical understanding of representing numbers.
T:	Routine, Small-Group, and Expansion activities can be found in the Extension part of the lesson.
O:	Instruction will move from modeled to shared to guided, and then to individual practice.

Instructional Procedures

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Begin the lesson by doing choral counting from 10 to prepare students for work with base-ten blocks. For example, “Count forward starting at 10 until I tell you to stop.” Stop students at 18. Have students count from 10 several times, having them stop at 16, 20, and 17.

Hold up a cube and a long. “These are called base-ten blocks.” Hold up a cube. “This is a base-ten cube. It represents one.” Hold up a long. “This is a long. It represents ten. Why do you think a long represents ten?” (It is made up of ten cubes.)

“Our system for writing numbers is called the base-ten system because it is based on grouping things by tens. Base-ten blocks can be used to help understand numbers and solve problems.”

Give each child a set of number cards (11–20) and a place-value mat (M-K-2-2_Place-Value Mat.docx). Display 1 long and 5 cubes on a place-value mat. “Show the number 15 by putting your cards on your place-value mat.” (Students show 15 by putting the card for 1 in the tens place and the card for 5 in the ones place.) “How many tens?” (1) “How many ones?” (5) “Read the number.” (Fifteen)

Repeat with other numbers in the range of 11–20. After a few examples, display the base-ten blocks at random without the mat. This will allow students to sort the blocks mentally into ones and ten.

Reverse the above procedure. Write numbers in the range of 11–20 on the board and ask the students to show the number by placing base-ten blocks on their place-value mats.

Continue with a series of procedures using base-ten blocks, number cards, written numbers, and spoken numbers. For example,

“Show the number 12 with base-ten blocks.” (1 long, 2 cubes)

“Use your number cards to show the number with a 3 in the ones place, and a 1 in the tens place.” (13)

“In 17, which digit is in the ones place? (7) “The tens place?” (1)

“Read the number on the board.” (Seventeen)

Give each student a copy of the Place-Value Worksheet (M-K-2-2_Place-Value Worksheet and KEY.docx). Move around the room observing and asking clarifying questions to evaluate which students understand place value and which need additional exploration.

Extension:
- Routine:Students draw a number card (M-K-2-1_Number Cards 11-20.docx) and use base-ten blocks to represent the number drawn.
  - Small Group: Use base-ten blocks and number cards (M-K-2-1_Number Cards 11-20.docx). Display a number. Students use base-ten blocks to represent the number. Students may need to use all cubes or exchange 10 cubes for a long at first if they have difficulty starting to count at 10.
  - Expansion: Use the activities in the links listed under Related Resources for additional practice and extension with larger numbers.

Representing Numerals with Base-Ten Blocks