“We have been using connecting cubes, counting jar materials, and base-ten blocks to represent numbers in many ways. Today we are only going to use base-ten blocks and continue working with numbers to 100.”
Read the book Meet the Base-Ten Blocks by ETA/Cuisenaire to your students as an introductory activity.
“Before we begin using our base-ten blocks, I would like to read a book to you. Let’s look at the cover. What do you think our book will be about?” [IS.3 - All Students]
Take student suggestions and predictions about the book.
“What can you tell me about base-ten blocks?” [IS.4 - All Students]
“The title of the book is Meet the Base-Ten Blocks.” If this book is not available, a summary of the story may be read to students or an alternative book may be used. See alternative book suggestions in the Related Resources at the end of this lesson. “The base-ten blocks are a family that has an adventure.”
Ask students questions about the book and the base-ten blocks in the book as you read. Sample questions could include: [IS.5 - Struggling Learners and ELL Students]
“What did you learn from the book?”
“How many different base-ten blocks did we read about?”
“What is the smallest base-ten block called?” Hold up a ten and a one and ask students to give their names.
“Why is this base-ten block a ten?”
Play Represent It
“Please put your dry-erase boards and markers in the top left-hand corner of your desk. I will be passing out a plastic bag to each of you filled with some ones and tens blocks. Please place those in the top right hand corner of your desk.”
“I am going to say a number between 0 and 100. After I say the number, I want you to show me the number in two different ways. You can use your dry-erase boards or the base-ten blocks on your desk. When you are finished representing the number, put your thumb up on your desk so I know you are ready to continue. Please show me the number 24.”
Students will be busy using their dry-erase boards and base-ten blocks. When all students have their thumbs up, ask students to share their representations. [IS.6 - All Students]
“You seem to have shown me 24 in different ways. Who would like to share their representations?”
Sample ways students might represent 24 include:
2 tens 4 units
20 and 4 units
10 and 14 units
Complete this activity with additional numbers between 0 and 100 to make sure students understand there is more than one way to represent each number. [IS.7 - Struggling Learners] Highlight the base-ten examples. Students need to see many examples of how a number can be represented in more than one way with base-ten blocks.
Play Build, Represent, and Count
“Everyone did a great job representing the numbers I gave you. I am now going to have you build with the base-ten blocks. You will be able to use as many of the base-ten blocks as you have on your desk. You don’t need to use them all. Use a few or a lot of base-ten blocks. It is up to you. However, you won’t have a lot of time to build with the base-ten blocks. I am only going to give you one minute to build. When I say ‘time’s up,’ you will need to stop building and count your base-ten blocks. Any questions?” [IS.8 - All Students]
“Ready, set, build!”
Give students one minute to build with the base-ten blocks. [IS.9 - Struggling Learners] After the time is up, ask students to share what they built and discuss what value the structure represents. [IS.10 - All Students] Select a few students to quickly share their ideas. The math goal in this activity is to look at different representations for the numbers using base-ten blocks.
Show students that 43 is the same as 4 tens and 3 ones. You might want to mention these various groupings. That 43 can also be 3 tens and 13 ones or 2 tens and 23 ones. [IS.11 - All Students] Some students will exchange ten ones for a ten to make it easier to count the base-ten blocks.
If an overhead is available, choose a few students to place their base-ten block structure on top of it so all students can see the tens and ones. Have selected students count their base-ten block tower or pile aloud.
If the same number is represented by two different students, have both students come to the overhead and display their base-ten blocks. Count both students’ blocks and ask, “How is the same number represented?” Walk students through this situation and let them see that both students can be correct. Clarify any misconceptions that students may have. Make a chart that will hang on the wall to show students that numbers can be represented in more than one way. [IS.12 - All Students]
The activity Build, Represent, and Count should be played multiple times. The more it is used, the more comfortable students will become at representing numbers in various ways.
You will have opportunities to assess students during the Represent It and Build, Represent, and Count activities, through discussions and questions. Listening to students’ responses, you can see which students will need to be pulled into small groups for further instruction, or you can clarify student understanding at another time.
Here are some additional numeration activities to use in your classroom to meet the needs of your students during the year.
Intervention: Hundreds Board and Base-Ten Blocks: Use the hundreds chart and base-ten blocks to help students see number relationships. Ask students to make the number ___ with base-ten blocks. Use numbers between 0 and 100. Discuss the different ways students represented the number. If students all represented the number the same way, ask them to show you another way to represent the number using base-ten blocks. [IS.14 - All Students]
Next, have students find the same number on the hundreds chart.
Then look at numbers in the same row or column on the hundreds chart. Discuss how the written number and the representation using base-10 blocks changes. Repeat several times.
Finally, indicate a number on the hundreds chart. Have students model the number with base-ten blocks. Ask, “What would you have to change in your model to make each of the neighboring numbers on the hundreds chart?” Students should represent this with base-ten blocks. Have students explain how they changed their model. It is left to the teacher’s discretion as to whether this should be modeled.
Number given: 43
Neighboring numbers: 53, 33, 42, and 44
Routine: Base-Ten Block Flash: Show some random displays of base-ten blocks on the overhead. Let students see the base-ten blocks on the overhead for about five seconds. Then turn off the overhead and have students write down the number on a dry-erase board. Students share their responses and explain their thinking. Turn the overhead back on and count the base-ten blocks. You can organize the tens and ones when you are ready to count the base-ten blocks or leave them on the overhead displayed randomly. Discuss with students which is easiest to count and why. Represent the number another way before giving students another problem. [IS.15 - All Students]
Intervention 2: Have students cut apart a hundreds chart into puzzle pieces; put them in a plastic bag and trade puzzles with a partner. Each partner puts together the puzzle pieces to create a complete hundreds chart.
Practice matching up numbers in different forms (use M-1-3-3_Base-Ten Match-Up Cards – 3 Digits in the Resources folder).
The discussion of the story Meet the Base-Ten Blocks at the beginning of the lesson introduces students to base-ten blocks. The main activity, Represent It, engages students in showing different representations for numbers. The goal is for students to become more comfortable with using multiple representations of numbers and to be able to transition smoothly between the different representations. Mastering the movement between different representations and placement on hundreds charts will help to improve students’ mathematical fluency.