Lesson and Assessments - Adding 3 Digit Numbers

Progression of Skills (outline)

Before the lesson:

• Students should have an understanding of place value (CCSS: 2.NBT.A) and be able to fluently add within 100 using strategies based on place value (Ex: compensation, decomposition, counting on/back) properties of operations, and/or the relationship between addition and subtraction (CCSS: 2.NBT.B.5)

During this toolkit lesson:

• Students will use concrete models to build an understanding of adding three-digit numbers. Specifically, like units should be added (hundreds and hundreds, tens and tens, ones and ones) and sometimes it is necessary to compose tens or hundreds. They will also practice using concrete models to accurately add within 1,000 and explore how concrete models relate to a written method.

After the lesson:

• Students should be able to use concrete models to accurately add within 1,000 and be able to relate a concrete model (Base-10 blocks) to a written method (partial sums).

Lesson Step 1 Concrete Modeling (30-45 minutes):

This step focuses on developing students’ ability to use a concrete model to accurately add within 1,000 without recording the numerical process.

Lesson Activity 1: Model (15 minutes)

Directions:

1. Provide students with Hundreds Place Value Charts and Base-10 Blocks. The facilitator will need a set of these materials as well.
   1. Ask: How would we build the number 234 using our blocks?
   2. Give students time to think and discuss their answers.
2. Build the number and have students build the number using 2 hundreds blocks, 3 tens blocks and 4 ones blocks on their place value chart.
   1. Ask: If we wanted to add the number 312 to the 234 we already built, what might that look like?
   2. Give students time to think and discuss their answers.
3. Model for students how to leave space on their place value charts before building the second number. Build the number 312 and have students do the same with their materials.
   1. Say: We have built two 3-digit numbers. If we wanted to find the total amount we built, what could we do?
   2. Give students time to think and discuss.
4. Model adding the blocks by place value to find the total number starting with the ones place.
   1. Talk through what you are doing aloud (do for each of the steps): First, I’m looking in the ones place and I see 4 ones plus 2 more ones. I know that there are 6 ones. Next, I’m looking in the tens place on my place value chart and I notice 3 tens in our first number and 1 more ten in our second number. That is a total of 4 tens. Finally, When I look in the hundreds place, I see a group of 2 hundreds and a group of 3 hundreds. I know 2 hundreds plus 3 hundreds is 5 hundreds. What is my total number? That’s right, 546!
   2. NOTE: The order above follows the traditional algorithmic order starting with the ones place, but that is not necessary. If your students started with the hundreds place, acknowledge their process and reinforce the need for the next question below.
   3. Ask: Did we have to regroup any of our ones or tens when we found a total? No, not this time!
   4. Have students clear their place value charts.
5. Say: We are going to try adding another set of 3-digit numbers. This time, let’s start by building the number 127.
   1. Allow students time to build the number; check student place value charts for accuracy before moving on.
6. Say: Let’s leave some space and build a second number, 453.
   1. Allow students time to build the second number and check student place value charts for accuracy before moving on.
7. Say: Let’s add the two numbers together to see what the total is.
   1. Watch as students find their totals for each place value; students should notice that 10 ones will need to be regrouped as a ten- assist them if they need help making this trade or model it if several students get stuck by counting 10 of the ones, removing them from the chart and replacing them with a 10 block in the tens column of the chart.
   2. Ask: What total did you get when you added this time? (127 + 453= 580) What was different this time? (discuss regrouping some of the ones to make 10).

Lesson Activity 2: Roll, Build, Add Game (15 minutes)

• Pair students.
• Provide each pair with:
  • 3 dice
  • Set of Base-10 blocks (physical, paper or digital )
  • Hundreds Place Value Chart
• Explain game play to students.
  • 1. One player will roll all three dice to create a 3-digit number. The same student will build their number using Base-10 blocks on the place value chart.
  • 2. The second player will then take a turn rolling all three dice to create a second 3-digit number and that same student will build their number using Base-10 blocks on the place value chart below the first player’s blocks.
  • 3. Beginning in the ones place, players will determine together how many total ones there are and whether regrouping is necessary. They will then determine how many tens and then how many hundreds there are, using regrouping as necessary until the final answer is determined.
  • 4. Have students repeat steps 1-3 to play more rounds as time allows.

Progress Monitoring:

Using Concrete Models Progress Check (15 minutes)

• The progress check will be used to evaluate students’ ability to use concrete models to accurately add within 1,000.

Directions:

1. Distribute a copy of the Progress Check to each student. The facilitator can read the directions to students if accommodation is needed.
2. Allow students time to work through the progress check independently. Make observations about the correct use of Base-10 Blocks to add as students work as well as the accuracy of students’ answers. The Progress Check should help the facilitator determine whether students need reteaching and/or additional practice before moving on to the next toolkit activity.

Lesson Step 2 Connecting a Concrete Model to a Written Method (45 minutes):

This step focuses on developing students’ ability to connect concrete representations to written methods of addition within 1,000.

Lesson Activity: Model (30 minutes)

Directions

1. Provide each student with Base-10 Blocks and a Hundreds Place Value Chart. The facilitator should have a set of these materials as well. Model the problem 403 + 154 with your Base-10 Blocks. Tell students you can also write to show that the two numbers are being added together to find a total. (It can help to show both left to right and right to left models work) Use paper and a pencil or whiteboard and dry erase surface to show students what this looks like alongside your physical model:

2. Ask students: What do you notice about the two different models?
3. Have students build 143 + 328 with their Base-10 Blocks. Check their work for accuracy and regrouping 10 ones into a ten. Guide students through writing the partial sums method for this problem.

4. Ask students: How are the two strategies different? How are the two strategies the same? Which method do you like better? Why?
5. Pair students to do the Partner Builds Activity and give the directions:
   1. Taking turns, one of you will be responsible for building with the Base-10 blocks and the other will write down the steps to show partial sums. Switch roles with each problem.
   2. Prompt the students to build and solve using the two methods while observing their work. Have students play for as many rounds as time allows:

• 513 + 341= 854 (no regrouping)
• 125 + 234 = 359 (no regrouping)
• 816 + 143 = 959 (no regrouping)
• 716 + 245 = 961 (regroup ones)
• 471 + 244 = 715 (regroup tens)
• 632 + 129= 761 (regroup ones)

Progress Monitoring (15 minutes)

Relating a Concrete Model to a Written Method Progress Check

1. The progress check will be used to evaluate students’ understanding of the relationship between concrete models and a written method when adding within 1,000.
2. The facilitator will use the progress check to identify if more practice should continue before moving on to Step 5 of the toolkit. Answers are included in the Progress Check.

Directions:

1. Print the activity for each student, cut out the cards and mix them up before presenting a set to each student.
2. Read the directions aloud, if needed.
3. Students will be asked to match the correct Base-10 model to the corresponding Partial Sums method.
4. Make note of students’ scores, which will determine mastery of the strategy or if there is a need to reteach the strategy.

Once students have mastered the skill in this toolkit, they can try out these relevant activities.

Other Models and Strategies for Adding

This toolkit demonstrates the use of Base-10 blocks and the partial sums strategy of addition. There are many other ways to represent multi-digit addition problems, including:

• Invented strategies: compensation, decomposition and counting on/counting back
• Bundling
• Number lines
• Place value discs
• Standard algorithm

Real World Applications

Addition is a fundamental mathematical concept that has numerous real-world applications. Here are some examples:

• Shopping & Budgeting: When shopping, individuals use addition to calculate the total cost of items in their cart so they expect how much they will need to pay. They also use addition to calculate weekly, monthly and yearly expenses in order to create budgets and savings plans. If we spend $126 on groceries this week and $147 on groceries next week, how much money will we spend on groceries?
• Travel Planning: When planning a trip, people use addition to calculate the total distance they'll be traveling and the total amount of time it will take. If we travel 582 miles the first day of our trip and 319 miles the second day, how many miles will we travel in all?
• Population: When thinking about situations about population (wildlife population, student population, residential population) addition can be used to find a total. If an elementary school has a population of 427 and a middle school has a population of 643, what is the total student population?

• Didax (Virtual Base-10 Blocks)
• EMBARC (EngageNY)
• Book: Teaching Student-Centered Mathematics, Vol. 1 PreK-2 , Van de Walle et. al