Adding two-digit numbers without regrouping - math grade 2 - lesson 34

TEACHER SAY: In our last math lesson, we learned how to decompose numbers. Today, we are going to decompose to solve some story problems. We will do one together and then you will solve some on your own. Raise your hand if you remember what it means to decompose numbers.

STUDENTS DO: Raise hands if they remember the meaning of decompose. Selected students share their thinking.

TEACHER DO: Confirm or correct students’ thinking.

TEACHER SAY: Here is our first story problem. Hassan bought 23 chocolate cookies from the bakery. He also bought 35 vanilla cookies. How many cookies does Hassan have in all? First, we will write the numbers in an addition sentence. Second, we will decompose the numbers in two ways. Third, we will add the numbers together.

TEACHER DO: Write the numbers in the addition sentence from the story problem on the board: 23 + 35 = ___.

TEACHER SAY: I wrote the addition sentence. Now we will decompose the two addends. Yesterday we learned two different ways to decompose our numbers. Let’s use the sticks and dots method first.

TEACHER DO: Model drawing 2 sticks for the Tens and 3 dots for the Ones for the number 23 and 3 sticks and 5 dots for the number 35 on the board. Ask students to help you.

STUDENTS DO: Help the teacher determine what to write in the place value chart.

2.TEACHER SAY: Now let’s solve the problem. To solve the problem using this method, we add the Tens sticks together and draw them all in the Tens place under the sum. Help me figure out what to draw.

TEACHER DO: If necessary, ask students questions to help them think through how to add the Tens sticks together and draw them on the chart. Encourage students to show you using their fingers. If possible, invite volunteers to the board to draw the Tens sticks.

STUDENTS DO: Help the teacher determine how many Tens sticks to draw. Selected students draw Tens sticks on the board.

TEACHER SAY: We have 5 Tens all together. Let’s do the same thing with the Ones.

TEACHER DO: Repeat the process with the Ones dots.

STUDENTS DO: Help the teacher determine how many Ones dots to draw. Selected students draw Ones dots on the board.

TEACHER SAY: Yes, there are 8 Ones all together. Our sum has 5 Tens and 8 Ones. Read the number aloud with me.

STUDENTS DO: Say together: 58.

TEACHER DO: Draw the Tens and Ones on the chart under the sum. The completed problem should look like this:

3.TEACHER SAY: We can also use our Tens and Ones boxes to help us decompose. Watch as I Model this strategy.

TEACHER DO: Model using the Tens and Ones boxes to decompose the numbers 23 and 35. Ask students to help you.

STUDENTS DO: Help the teacher determine what to write in the Tens and Ones boxes.

TEACHER DO: Write 20 + 30 on the board.

TEACHER SAY: When we add 20 and 30 together, we can count on by adding Tens. We start at 30 and count up two more Tens—40, 50. 20 plus 30 is 50.

TEACHER DO: Write 50 in the Tens box.

TEACHER SAY: We also have to add the Ones: 3 + 5. Show me on your hands what 3 + 5 is.

STUDENTS DO: Show the sum of 3 + 5 on their hands.

TEACHER SAY: Yes, 8. The answer has 5 Tens and 8 Ones. The sum is 58.

TEACHER DO: Complete the problem on the board. Completed problem should look like this:

4.TEACHER SAY: Hassan has 58 cookies all together. Wow. That was a lot of work. But you can see how decomposing the numbers into smaller numbers makes it easier to add the numbers together. If we did not decompose the numbers, we would have had to start at 35 (the bigger number) and count on 23, which would take a long time and we may make mistakes. Decomposing numbers is a great way to add large numbers together.

Now it is time for you to try this with your Shoulder Partner. Take out your student book and turn to page Lesson 34: Apply.

STUDENTS DO: Turn to page Lesson 34: Apply in the student books.

TEACHER SAY: In your student book, you will see the story problem we just solved and three more story problems. I will read each story problem aloud. For each problem, there is a Tens – Ones chart and Tens–Ones boxes. Work with your Shoulder Partner to decompose the problems both ways and find the sums. Be sure to show your work. Put your finger on the first story problem and read it aloud with me: Miryam found 68 seashells on the beach. Her sister found 21 seashells. How many seashells did they find in all?

TEACHER DO: Depending on your students, read only the first story problem or all three.

TEACHER SAY: First, write down the numbers from the problem. Th en you may begin decomposing and adding.

STUDENTS DO: Work with their Shoulder Partner to decompose the numbers and add them together in the student books.

TEACHER DO: Walk around the classroom to assist students as needed. Allow time for students to solve and check their work. Take note of students who may need additional instruction and support. If time allows, call a student to the front to share their work. Repeat with the other story problems in the student book.

TEACHER SAY: Th at was great work, class. I admire how hard you worked on those problems.