1. Thinking About Numbers Flexibly
Unit of Study: Counting and Modeling Numbers to 120
Global Concept Guide: 3 of 4

2. Content Development Common Misconceptions
“Students sometimes think that a number can only be made by showing its exact tens and ones. For example, 38 can only be represented by 3 tens and 8 ones. This representation is typical but numbers can be decomposed in different ways. 38 can also be recorded as 2 tens and 18 ones or even 38 ones. Students need to understand this concept in order to add and subtract later in first grade.”
Being able to decompose numbers is essential for students to understand so that they can regroup numbers to add and subtract.
The use of base ten blocks is necessary for students to build a concrete understanding of how to represent numbers flexibly.

3. Day 1
Essential Question: How can two different base ten models represent the same number?
Engage: Use the I Have You Have cards to begin the lesson. This task should take 5-10 minutes.
Use the Tens and Ones Match Up task to allow students the opportunity to discover the concept of flexible representation. (This activity takes prep work before class). Facilitate discussion about the similarities and differences amongst the representations.
Repeat this activity with different numbers so students can continue to build their concrete understanding of flexible representation.
Challenge students thinking by asking them to show a third representation of their number. Provide base ten blocks for students as needed.
Tens
Tens
Ones
Ones

4. Day 1 Continued…
Essential Question: How can two different base ten models represent the same number?
Closure: Present students with the number 49. Then have students journal a quick pic of 2 different representations of the number. (Students may use manipulatives to assist them in drawing a quick pic.)
By the end of Day 1, students should be able to represent two-digit numbers in two different ways.

5. Day 2
Essential Question: How can you show different ways to represent a two digit number using base ten?
Engage: Present the students with the number 47. Ask them to represent the number using base ten blocks. (Most students will show you 4-tens and 7-ones.) Share the models in the class. Now ask students to show a different way to represent the number 47. If a student creates a model other than 4-tens and 7-ones, and show 47, have the student share model with the class . Discuss how the models are represent the same number.
If necessary the teacher may need to directly model how to do this through trading a ten rod for 10 ones.
Building Conceptual Knowledge: Create an anchor chart of the different representations so students can begin recognizing patterns.
Probing questions to ask your students: What pattern do you notice in the tens and ones?; What is another representation of this number?; If the value stays the same, what happens when we exchange a ten?; How can we record the representation?

6. Day 2 Continued…..
Essential Question: How can you show different ways to represent a two digit number using base ten?
Independent Practice: Go Math Lesson 6.8, Share and Show p. 271 #s 4-6
Encourage students to draw base ten quick pics for each representation. If needed, students can still use the base ten blocks to show tens and ones.
Closure: Discuss #4 from the independent practice. Probe students for different representations of the number 59. Have students explain how their model represents the number. Ask students: Does the value change with this model?
By the end of Day 2, students should be able to communicate the tens and ones pattern when flexibly representing a number. Students should be able to explain the exchange of 10 ones for 1 ten and how the value does not change.

7. Day 3
Essential Question: How can you show all the ways to represent a two-digit number using base ten?
Engage/Building Conceptual Knowledge: Go Math Unlock the Problem p Give students time to discuss what is happening in the scenario and create a quick pic of the stickers. Use teacher guided questions on p. 269 in the TE manual.
These guiding questions walk students step by step through the problem solving process, so it is important to have students explore on their own or with a partner first.
Independent Practice: Different Ways Task
In this task, students will practice drawing quick pics for different representations of a number. Students are encourage to show all of the ways for each number.
If there are students who have difficulty with listing all of the different representations, pull a small group and provide remediation. An idea for the small group is to repeat the Day 2 investigation with exchanging tens and ones and notice the pattern between tens and ones. Use base ten blocks if students are having difficulty with the exchange of 1 ten and 10 ones.
By the end of Day 3, students should be able to show all of the different ways to represent a number.

8. Day 4
Essential Question: How can you use tens and ones to represent a number in more than one way?
Re-teach:
Give students the Different Ways to Show Numbers worksheet. The teacher should sit with these students in a small group and have students work through problems. You may need to provide base ten manipulatives for students. Make sure to ask students questions to challenge their thinking. Example: Is there another way to represent the number?; Can you prove your answer is correct?
Really 36?-This activity poses different representations where the students must determine if the representation show 36 or not.
Place Value -This website offers a number of place value worksheets. You can select what worksheet would best meet the needs of your students.
Core:
Base Ten Concentration Game: Students use the concentration game to match a number with a base ten representation. Students will record the number and the representation on the Base Ten Concentration Recording Mat. On the mat, students will draw a quick pic for a second representation.
Different Ways Concentration-Students will play a concentration game with the number in many different forms.
Enrich:
Give students the Different Ways to Show Numbers worksheet. This worksheet challenges students to solve place value scenarios.
Give students questions similar to the H.O.T. questions listed on the GCG.
By the end of Day 4, students should be able to flexibly represent numbers 0-99 independently. Students should be completing this task without manipulatives, encourage students to draw quick pics.

9. Literature Connection