Cracking the Code: Understanding 'Carrying' in Addition!

Mathematics Grades 4th Grade 2:30 Video
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Lesson Description

Learn why carrying works in addition by expanding numbers and understanding place value. Let's explore the magic behind regrouping!

Video Resource

Adding: why carrying works | Addition and subtraction | Arithmetic | Khan Academy

Khan Academy

Duration: 2:30
Watch on YouTube

Key Concepts

  • Place Value (ones, tens, hundreds)
  • Expanded Form of Numbers
  • Regrouping (Carrying) in Addition

Learning Objectives

  • Students will be able to explain why carrying works in addition using expanded form.
  • Students will be able to decompose numbers based on place value.
  • Students will be able to correctly add numbers using the carrying method.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing place value (ones, tens, hundreds) with students. Ask: 'What does the digit 3 represent in the number 345?' Briefly discuss the standard addition method, prompting students to recall what 'carrying' means.
  • Video Viewing (7 mins)
    Play the Khan Academy video: 'Adding: why carrying works'. Instruct students to pay close attention to how the numbers are expanded and how the carrying process is explained.
  • Guided Practice (10 mins)
    Work through a similar addition problem on the board, expanding the numbers as shown in the video. For example: 287 + 145. Guide students through each step, emphasizing the regrouping process and connecting it to the expanded form. Encourage active participation and questions.
  • Independent Practice (10 mins)
    Provide students with 2-3 addition problems to solve independently, using the expanded form method. Circulate to provide support and answer questions. Examples: 456 + 278, 199 + 321.
  • Wrap-up and Discussion (3 mins)
    Review the key concepts of the lesson. Ask students to explain in their own words why carrying works in addition. Address any remaining questions or misconceptions.

Interactive Exercises

  • Place Value Chart Addition
    Use a place value chart (hundreds, tens, ones) and base-ten blocks to physically represent addition problems. Have students manipulate the blocks to understand the regrouping process. For example, adding 7 ones and 5 ones results in 12 ones. Exchange 10 ones for 1 ten, demonstrating the 'carrying' concept visually.
  • Group Expanded Form Challenge
    Divide students into groups. Give each group an addition problem. Each student in the group is responsible for expanding one or more of the numbers. Then the group works together to solve the problem, showing all the steps of regrouping

Discussion Questions

  • Why is it important to understand place value when adding numbers?
  • How does expanding numbers help us understand the carrying process?
  • What happens to the 'carried' digit? Where does it go, and why?

Skills Developed

  • Understanding Place Value
  • Addition with Regrouping
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

In the number 456, what place value does the digit 5 represent?

Correct Answer: Tens

Question 2:

When adding 27 + 35, you get 12 in the ones place. What do you do with the 1 in '12'?

Correct Answer: Carry it to the tens place

Question 3:

What does it mean to 'carry' in addition?

Correct Answer: To move a digit to the next place value column

Question 4:

Which of the following shows 345 in expanded form?

Correct Answer: 300 + 40 + 5

Question 5:

When you carry a '1' to the tens place, what does that '1' REALLY represent?

Correct Answer: 1 ten

Question 6:

In the number 829, what does the 8 represent?

Correct Answer: 8 hundreds

Question 7:

What is 10 + 30 + 90?

Correct Answer: 130

Question 8:

What is 100 + 500 + 300?

Correct Answer: 900

Question 9:

What does the number 14 equal?

Correct Answer: 10 + 4

Question 10:

When adding, do you start with the leftmost column or the rightmost column?

Correct Answer: Rightmost column

Fill in the Blank Questions

Question 1:

In the number 678, the 7 is in the ______ place.

Correct Answer: tens

Question 2:

When you add and the ones column equals 15, you write the 5 and ______ the 1.

Correct Answer: carry

Question 3:

400 + 20 + 7 is the ______ form of 427.

Correct Answer: expanded

Question 4:

When we carry a 1 to the hundreds place, it really represents ______.

Correct Answer: 100

Question 5:

Understanding ______ ______ helps us understand carrying in addition.

Correct Answer: place value

Question 6:

The first step to adding numbers is to add the numbers in the ______ place.

Correct Answer: ones

Question 7:

8 + 6 = ______

Correct Answer: 14

Question 8:

If you get a two digit number after adding the digits in a single column, you must ______ the digit in the tens place.

Correct Answer: carry

Question 9:

600 + 20 + 1 is the same as the number ______.

Correct Answer: 621

Question 10:

When adding numbers, always start with the column furthest to the ______.

Correct Answer: right

Educational Standards

4.N.1.2:Use place value to describe whole numbers between 1,000 and 1,000,000 in terms of millions, hundred thousands, ten thousands, thousands, hundreds, tens, and ones with written, standard, and expanded forms. 4.N.2.2:Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms. 4.N.2.4:Apply and analyze models to solve multi-step problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results.

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