📊Lesson 3.2 Outline- Distributive Property (For Teacher- Do Not Publish)

Lesson 3.2

For full lesson outline please see  Advantage Math Lesson 3.2.

Standards:

4.NBT.5- Use strategies based on place value and the properties of operations to multiply a whole number of up to four digits by a one-digit whole number, and multiply two, two-digit numbers.

Objectives:

Math Objective: Students will be able to decompose factors and use the distributive property to multiply.

Language Objective: Students will be able to discuss with a partner how repeated addition relates to the distributive property.

Vertical Alignment:

3.OA.7.B- Know from memory all products of two one-digit numbers 

4.NBT.5- Use strategies based on place value and the properties of operations to multiply a whole number of up to four digits by a one-digit whole number, and multiply two, two-digit numbers.

5.NBT.5- Fluently multiply multi-digit whole numbers using the standard algorithm

Common Misconceptions:

It is important that when adding a column of numbers other than the ones, that student call the digits in those places by their values. For example, a 4 in the tens column is not 4, it’s 40.

Lesson Outline:

🚀Launch (in class or remote)

  • Students will need a whiteboard or a piece of paper. They are solving the problem 5 X 43 with what comes naturally to them. They may naturally add 5 X 43 using repeated addition which is fine. However, we want students to approach math with a natural approach so the challenge is to do it more than one way. Students will experience many new ways to multiply in the coming lessons and because of that there needs to be a level of comfort with trying new things and coping with the concept that there is more than one way to solve a problem. 
    • Questions you could ask:
      • How does it feel to solve a challenging math problem?
      • How does it feel to have to come up with two strategies to solve a challenging math problem?
    •  Vocabulary words: Decompose and Distributive Property of Multiplication

🤔Explore (in class or remote)

  • Students are exploring the commutative property and how it can relate to repeated addition. 
    • Insert a video explaining the commutative property. This can be a simple visual using base ten blocks or even cuisinare rods that show 5 X 2. The problem that is presented should be simple and comfortable for the students so the focus is on what the commutative property is and not understanding the numerals component. 
    • Questions you could ask:
      • How does the commutative property change how a problem looks visually?
      • What do repeated addition and multiplication have in common?
      • Do you think that the commutative property could be a helpful tool as you progress in math and solve more challenging problems. 

💬Discuss (in class or remote)

  • Questions to use in your discussion:

    • How has decomposing numbers helped you when solving multiplication problems?

    • When multiplying numbers, when do you think you would need to decide if a number is uncomfortable for you to try to multiply? Would decomposing that number or those types of numbers be a helpful strategy?

Additional Resources:

    • Ways to make remote:
      •  Have students watch the video and answer questions that you create based on the needs of your students. Stop throughout the video and challenge students with a similar problem, leaving the problem on the board so they can reference it for help if needed. 

 

  • Differentiation (in class or remote)
    • Challenge: Ask students to decompose the multiplier in other ways besides tens and ones. For example, with 27 × 4, the 27 could be decomposed into 25 + 2 because 25 is a benchmark number and easily multiplied by 4. Have the students list other examples.
      • Ways to make remote:
      • Students can do this challenge on their own and submit their work and thoughts. 
    • Struggling : Have the students who need to start with smaller numbers and have them draw the arrays on graph paper. Draw a line on the array to show the distributive property. For example, have students make a 3 × 15 array. Decompose the 15 into 10 and 5. Draw a vertical line between the 10 and 5. Show how the 3 is multiplied by the 10 to get 30 and the 5 to get 15. 10 and 15 must be added to get the total number of squares in the array.
      • Ways to make remote:
      • Have students join you in an online meeting format (Zoom or Teams) and do the exact same activity. They might not have the place value disks, but you can show them yours to discuss.

 

  • Lesson Extension (in class):
    • As an extension, have students create one-digit by two-digit multiplication problems. With the problems they create, have them solve each problem twice; see if the different ways they decompose a number result in the same answer.