📊Lesson 2.6 Outline- Subtracting Zeros with Constant Difference (For Teacher-Do Not Publish)

Standards: 

4.NBT.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Objectives: 

Math Objective:  I can subtract multi-digit whole numbers with zeros in the minuend using constant difference. 

Language Objective:  I can discuss different ways to subtract using the standard algorithm with other students. 

Vertical Alignment: 

3.NBT.2: Fluently add and subtract within 1,000 using strategies and algorithms vbased on place value, properties of operations, and/or the relaitionship between addtion and subtraction.

4.NBT.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm. 

5.NBT.7: Add,subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 

Common Misconceptions/notes: 

Subtraction is defined in different ways depending on the context. In kindergarten and first grade students are familiar with “taking from,” “taking apart,” and “comparing” problems. As students progress into second and third grades, they learn that subtraction means the difference or distance between two numbers. Constant difference is a subtraction strategy that was taught in third grade with numbers less than 1,000.

Lesson Outline: 

🚀Launch:

Students solve a constant difference problem including age. 

  • Explain that in subtraction, the numbers can be increased or decreased by any amount. As long as both numbers are changed by the same amount, the difference is constant.
  • In this situation, 12 was added to both ages but the difference is the same.
  • 2.6 launch explanation.PNG
  • Explain when you should use constant difference (see Advantage Math Outline for details)
  • Teacher should model (create video to make remote) on how to use constant difference. This could be done by using the fish problem from the previous lesson. 

🤔Explore:

  • Students practice constant difference through completing three subtraction problems using this strategy. 
  • Model constant difference as needed through these problems. 
  • Make sure students understand whatever you change on one number you must do to the other. 
  • Point out how you know the constant difference method is appropriate for a problem.

💬Discuss:

  • Students will explain to each other, what it means to use constant difference in subtraction. 
  • Teacher should choose the best responses and discuss as a class.
  • Teacher question: ask students why they do or do not like this method. 

✅Exit Ticket:

Students will complete one subtraction problem and one self reflection question.

Additional Resources: 

2.6 safe share.PNG

Constant Difference on a Number Line (Student Resource Video #1) Links to an external site.

2.6 safe share 2.PNG

Constant Difference Subtraction Strategy (Student Resource Video #2) Links to an external site.

Differentiation: 

Challenge: For students who need a challenge, or for a lesson extension, have students create a problem where it would be beneficial to add some to each number instead of subtract. For example, in the problem 365 − 199, the larger digits are in the subtrahend instead of the minuend. If 1 is added to each number, the subtrahend would then have smaller digits than the minuend, eliminating the need to regroup (366 − 200). See Student Resource video #1.

Struggling: For students who are struggling, the concept of constant difference can be explored in more detail by holding a piece of string that is a certain number of inches long and then showing on a yard stick how moving the string to different numbers doesn’t change the length of the string. For example, if the string is 5 inches long, then the distance from 6 to 11 is the same as the distance from 11 to 16, etc.