Students will explain why addition and subtraction strategies work using base-ten by creating concrete models, adding up to four two-digit numbers, and mentally adding or subtracting 10 or 100 from a given number within 1000.

In this lesson, students will create pictures using base ten blocks as models for numbers between 200 and 1000.

10 minutes

In this lesson students will apply various strategies, modeling, and drawings to find different ways to solve problems.* *

**Materials needed: ** Centimeter graph paper or base-10 patterns, scissors, glue, overhead or smart board

To begin this lesson, I asked the students to recall each base-ten block and their value. Then I write the following numbers on the board. (386, 295, and 521) I ask student volunteers to represent these numbers using base-tens. As students are working, I ask what number is in the ones/tens/and hundreds place.

When students are able to demonstrate each number correctly, I provide them with a sheet of centimeter paper. I ask them to trace the hundreds and tens blocks on the graph paper to be sure they are marking the correct amount of squares. *If time does not permit this, I may ask students to use base ten images instead.* At this point, I encourage students to label each traced figure with its value. After that, students cut out the blocks so they can use them to make animal pictures.

**Connecting the practices:**

**MP6- Attending to precision.**

**MP1-Make sense of problems & persevere in solving them.**

**MP4-Model with mathematics.**

25 minutes

In this portion of the lesson I want to use illustrations to help students gain a deeper understanding. I want to make sure students are able to reason with models or pictorial representations to solve problems, translate situations into symbols for solving problems, and convert situations into symbols to appropriately solve problems.

I ask students to move into their assigned groups. I explain that we are going to use what we know about base-tens/numbers sense/and place-value to create something different.

Once students have their supplies in place, I show them an animal picture (elephant) using the smart board or overhead.

I demonstrate how to use base-tens to recreate the elephant:

*I use two hundred blocks for the mid-section of the elephant, 1 hundred block for his head, 3 tens for legs, five ones for feet, four tens for his trunk.*

I ask students how many hundred/tens/and ones I used. ** Can I use place value to group these numbers?** (Yes!)

I give the students about ten-minutes or so to re-create the elephant with their pieces and determine the number of hundreds, tens, and ones used to make the picture. I remind students to turn and talk to their neighbor if they get stuck, or have a question. I circle the room as students are working to check for understanding. * Can you explain what you have done so far? *Students immediately begin to point out the base-tens they used to construct their picture.

•**What else is there to do?****•Why did you decide to use this method?****• Can you think of another method that might have worked?****• Is there a more efficient strategy?****•What did you notice?****•Why did you decide to organize your results like that?****• Do you think this may work with other numbers?****• Have you thought of all the possibilities?**

**MP2-Reason abstractly and quantitatively.**

Students seem to find their own ways to demonstrate their answers and they are able to explain the numbers and their place values with accuracy.

As students share their thoughts, I ask them come up to the board and circle the parts they added together to show how they organized each number to reach a total. I then asked how many other students came up with the same total and to share their pictures. At the same time this happens students are able to compare/contrast their work.

See: Student sample

15 minutes

To bring this lesson to a close, students place the animal picture they created in a basket located in the front of the room. Once all of their papers are collected, I disperse them back to different students so they can determine the value of that given picture and record it on a recording sheet. I then place a number line on the wall and have the students to place their picture where it would appear between 200 and 900. I continue to check for understanding as students display and explain their work.

**Questions:**

• What else is there to do?

• Why did you decide to use this method?

• Can you think of another method that might have worked?

• Is there a more efficient strategy?

• What did you notice?

• Why did you decide to organize your results like that?

• Do you think this may work with other numbers?

• Have you thought of all the possibilities?

Some students were able to explain their reasoning precisely, and other used words they already knew to explain.

**Examples: **

1) I found two three-digit numbers within my picture. The first number is 234 and the second number is 135. I notice that 4 and 5 are in the ones place, 3 and 3 are in the tens place, 2 and 1 are in the hundreds place. So, I decided I would add them up. I added the ones place first, then the tens and hundreds. So then, 234 + 135 = 369.

2) I circle the first number 214, and then I circle the second number 152. I added them up and got 366.

I point out that the first student explanation has visible mathematical terms, whereas, the second explanation does not. I remind students that we are working our way towards explaining precisely using math vocabulary.

See: Student sample work