During this unit, students will use base-ten blocks to add and subtract three-digit numbers. Students are going to: 
- figure out the sum, and join the base-ten blocks that represent each addend in the equation. 
- find the difference, represent the minuend with base-ten blocks and the subtrahend with base-ten blocks removed.

- What mathematical representations exist for relationships? 
- How does effective communication benefit from mathematics? 
- How can numbers be represented, compared, quantified, and modeled using mathematics? 
- What does it mean to evaluate or estimate a numerical quantity? 
- What qualifies a tool or strategy as suitable for a particular task?

- 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. 
- Hundreds: The place third from the right in a number. In the number 2, 435 the digit 4 is in the hundreds place. 
- Ones: The place first from the right in a number. In the number 2, 435 the digit 5 is in the ones place. 
- Place Value: The value of the position of a digit in a number. In the number 7,863, the 8 is in the hundreds place and its value is 800. 
- Tens: The place second from the right in a number. In the number 2, 435 the digit 3 is in the tens place.

- base-ten blocks
- mini-whiteboard for each student
- whiteboard marker for each student
- whiteboard eraser for each student
- Adding and Subtracting Using Base-Ten Blocks Worksheet (M-2-2-1_Adding and Subtracting Using Base-Ten Blocks Worksheet and KEY)
- Top-It directions (M-2-2-1_Top-It Directions)
- Beat the Calculator directions (M-2-2-1_Beat the Calculator Directions)
- number cards
- calculators
- paper
- pencils

- Watch the students as they work through the M-2-2-1_Adding and Subtracting Using Base-Ten Blocks Worksheet and KEY to see how they add and subtract.
- Throughout the Instructional Procedures, keep an eye on the student responses.
- While students play the games found in Related Resources, such as Beat the Calculator and Top-It, keep an eye on them.

Explicit instruction, modeling, scaffolding, and active engagement 
W: Explain to the students that because our system of writing numbers is based on grouping items by tens, it is also known as the base-ten system. Tell them that you can add and subtract three-digit numbers with base-ten blocks. 
H: Show the blocks that are base ten. Let students know that these resources will be used to aid in their addition and subtraction of three-digit numbers. 
E: Using base-ten blocks, students will add and subtract three-digit numbers. 
R: The pre-, during-, and post-lesson questions will prompt students to consider how well they grasp the concept of adding and subtracting three-digit numbers using base-ten blocks. 
E: Assess students' comprehension of adding and subtracting three-digit numbers using base-ten blocks by using the Adding and Subtracting Using Base-Ten Blocks Worksheet and their answers to the lesson's questions. 
T: You can modify the lesson by implementing the ideas mentioned in the Extension section. 
O: The purpose of the lesson was to improve the students' comprehension of adding and subtracting three-digit numbers. When adding and subtracting three-digit numbers, students transition from using base-ten blocks to pictures of base-ten blocks. 

"We're going to use base-ten blocks to add and subtract two- and three-digit numbers today."

Say, "This is a flat," and hold up a flat. "It stands for one hundred." Say, "This is a long," and hold up a long. "It stands for ten." Say "This is a cube" while holding up a cube. "It stands for 1."

Put the equation 231 + 146 = on the whiteboard.

"I'm going to demonstrate how I can calculate the sum of these two numbers using base-ten blocks. There are two hundreds, three tens, and one one in the number 231." Gather three longs, two flats, and one cube while you are speaking. "I have 146, which is one hundred, four tens, and six ones." Gather six cubes, four longs, and one flat while you are speaking. "To find the sum of 231 + 146, I can now join the base-ten blocks and count them." Put the cubes, longs, and flats together to create a model, and then count the base-ten blocks. Place the total after the equals symbol.

Teach students the base-ten block drawing technique. A dot symbolizes a cube, a square denotes a flat, and a vertical line denotes a long. Write this down on the board. Now, instead of using actual base-ten blocks, show students what the above problem would look like with pictures of base-ten blocks.

Give each student a set of base-ten blocks. On the board, write the equation 257 + 222 =. "Together, let's try one. We have 257 first. How many hundreds do we require? (2) How many tens do we need? (5) How many ones do we need? (7) We now have to create 222. How many hundreds do we need? (2) How many tens do we need? (2) How many ones do we need? (2) Please calculate the sum of these two numbers using your base-ten blocks." Help students figure out how much these two numbers add up to. A student can write the sum after the equal sign and demonstrate what they did for the class.

On the board, write the equation 458 + 123 =. Offer students to solve this equation using base-ten blocks. As students figure out the sum of these two numbers, assist them. Ask a student to present their work to the class, making sure to write the total after the equals symbol.

"Now, rather than using the actual base-ten blocks, please illustrate for me on your whiteboard how this addition problem would appear if you drew pictures of the blocks instead." Instead of using actual base-ten blocks, help students by drawing pictures of the blocks as they work out the sum. Ask a student to present what they accomplished on their whiteboard to the class.

"Base ten blocks are useful not only for finding the sum of two numbers but also for finding the difference between two numbers." Put 548 – 324 = on the board.

"I'm going to demonstrate how I can calculate the difference between these two numbers using base-ten blocks. I have a minuend of 548. Recall that a "minuend" is a number that is subtracted from another number. I have four tens, eight ones, and five hundred in 548." As you speak, gather five flats, four longs, and eight cubes. "Now, I have to deduct 324, which is the subtraction. There are two tens, four ones, and three hundreds in this number. I must thus remove three flats, two longs, and four cubes. To determine the difference, I will count the blocks that are left." After the equal sign, write the difference based on the number of blocks that remain.

Now, instead of using actual base-ten blocks, show students what the above problem would look like with pictures of base-ten blocks. Using images of base-ten blocks, draw 548. Then, count the number of blocks that remain after 324 have been crossed out.

On the board, write the equation 695 – 381 =."Please find the difference between these two numbers using your base-ten blocks. Use base ten blocks to represent the minuend first, then remove the base ten blocks that represent the subtraction and count the remaining base ten blocks to determine the difference." Assist students in determining the difference between these two figures. Ask a student to demonstrate to the class how they used base-ten blocks to determine the difference.

"Please illustrate for me on your whiteboard how this subtraction problem would appear if you used drawings of base-ten blocks instead of the actual base-ten blocks. Encourage students to find the difference by having them draw pictures of base-ten blocks to symbolize the subtrahend, cross off the base-ten blocks to symbolize the minuend, and count the base-ten blocks that are left over." Ask a student to present their work to the class using their whiteboard.

"You will now utilize base-ten blocks to assist you in solving addition and subtraction problems. You have eight tasks to complete. You will need to utilize the actual base-ten blocks to solve the puzzles for four of them. To solve the remaining four, you will need to sketch base-ten block images." Give a copy of the M-2-2-1_Adding and Subtracting Using Base-Ten Blocks Worksheet and Key to every student. Around the classroom, keep an eye on the students and probe with questions to get clarification on who can add and subtract three-digit numbers using base-ten blocks without regrouping and who needs more practice.

Extension:

Routine: Students use the calculator or play Top-It. (M-2-2-1_Beat the Calculator Directions and M-2-2-1_Top-It Directions). Students can practice computation by using base-ten blocks. Gamers can also enjoy the games found in the Related Resources section.

Small Group: Ask the following questions of students who require more in-depth investigation:

213 + 424 = 765 – 234 =
567 + 232 = 875 – 234 =
324 + 341 = 948 – 523 =
432 + 156 = 654 – 231 =

Help students solve the aforementioned problems using base-ten blocks. Encourage them to draw pictures as they solve the problems using base-ten blocks.

Expansion:

Using three-digit numbers, students write number stories that involve addition and subtraction.

M-2-2-1_Top-It Directions and M-2-2-1_Beat the Calculator Directions are the extensions that are recommended for students to play when playing Top-It and/or Beat the Calculator.

Students demonstrate their thought processes by adding four-digit numbers.