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Lesson excerpt:

NC Mathematics Standard(s):                Understand place value.

NC.1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.

• Unitize by making a ten from a collection of ten ones.

• Model the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

• Demonstrate that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or

nine tens, with 0 ones.

Additional/Supporting Standards: Understand place value.

NC.1.NBT.3 Compare two two-digit numbers based on the value of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Standards for Mathematical Practice

2.   Reason abstractly and quantitatively.

3.      Construct viable arguments and critique the reasoning of others.

4.      Model with mathematics.

5.      Use appropriate tools strategically.

6.      Attend to precision.

7.      Look for make use of structure.

Student Outcomes:

·       I can understand the quantities to 99.

·       I understand that the two digits of a two-digit number represent amounts of tens and ones.

·       I can unitize a collection of 10 objects.

·       I can model the values of tens and ones for a given two digit number.

·       I can explain in words the values of two- digit numbers.

Materials:

·       Arrow cards

·       Place value materials (Unifix cubes, pop cubes, mini-ten frames)

·       White wipe-off boards

Advance Preparation:

·   This task would be done after many experiences with various place value materials.

·   Reproduce Arrow cards.

·   Arrow cards are a set of place value cards with an “arrow” on the right side. Students can organize the cards horizontally or vertically to represent numbers in expanded form

o  (27 = 20 + 7). The cards can overlap cards and line up the arrows to form multi-digit numbers.

·   Prepare a list of names for working pairs of students.

Directions:

1.      Assess students’ prior knowledge of place value by asking the questions below in the section, Questions: Before.

·          Show me 30.

·          Tell me what you know about the number 30. (If the student says 30 cubes you would want to ask follow-up questions so you will know if the student is counting by ones or recognizing the cubes as units of 10’s.)

2.      Ask students to show you the number 46. The students work with their partners to show the number with the Arrow cards, the place value materials (Unifix cubes, pop cubes, mini-ten frames) and write the numbers on their white wipe-off boards. (See questions below.)

3.      As students work, these are questions you may ask to monitor their learning: How many tens are there in this number and how do you know that? How many ones are there in this number and how do you know that? What is the value of each digit in both numbers?

4.      Next, ask students to show you the number 64. The students work with their partners to show the number with the Arrow cards, the place value materials (Unifix cubes, pop cubes, mini-ten frames) and write the numbers on their white wipe-off boards. (See questions below.)

5.      As students work, these are questions you may ask to monitor their learning: How many tens are there in this number and how do you know that? How many ones are there in this number and how do you know that? What is the value of each digit in both numbers?

6.      Also ask:

What do they notice about the numbers 46 and 64.

How are the two numbers similar and different and how do you know that?

7.      Continue this activity with different numbers such as 15 and 51.

Questions to Pose:

Before:

1.      Show me a train of 30.

2.      Tell me what you know about the number 30. (If the student says 30 cubes you would want to ask follow-up questions so you will know if the student is counting by ones or recognizing the cubes as units of 10’s.)

During:

1.      What is the quantity (value) of the number in the tens place?

2.      What is the quantity (value) of the number in the ones place?

3.      How are the two numbers similar and different and how do you know that?

4.      What is the value of each digit in both numbers?

5.      Look at a 2-digit number.  How do you know how many ones and tens there are in the number?

Possible Misconceptions/Suggestions:

Special Notes:

This task needs to be repeated often for students to develop place value understanding.

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