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📊Lesson 3.6 Outline- Arrays (Two-Digit X Two-Digit) (For Teacher- Do Not Publish)

Lesson 3.6

For full lesson outline please see  Advantage Math Lesson 3.6.

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 represent multiplication using an array and draw the representation using the box-line-dot method.

Language Objective: Students will be able to discuss with a partner how to model a multiplication problem with an array.

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:

None noted in Advantage Math Lesson 3.6

Lesson Outline:

🚀Launch A(in class or remote)

  • The problem 6 X 13 is presented and the students are asked to solve using base-ten blocks or drawing base ten blocks. The option to use disks/circles is up to you as the teacher; this option might be more visually appealing to some students.   
    • Questions you could ask:
      • What did you struggle with today that surprised you?
      • What are the things you think you will need help with?
      • What do you think you did well?
    •  Vocabulary words: No new vocabulary words.

🤔 Download 🤔Explore A(in class or remote)

  •  Students are not solving this word problem. They are just exploring the setup of a two-digit X two-digit equation on the Array Bar Map. Students should recognize that both factors require expanded form to properly set up the equation. 
    • Questions you could ask:
      • Did you use expanded form for each factor?
      • Why is using expanded form important for the Array model?

💬Discuss A (in class or remote)

  • Question to use in your discussion:
    • If you did not use expanded form, what issues might arise?

🚀Launch B(in class or remote)

  • The problem  10 X 23 is presented and the students are asked to solve using base-ten blocks or drawing base ten blocks. The option to use disks/circles is up to you as the teacher; this option might be more visually appealing to some students.   
    • Questions you could ask:
      • Both factors are two-digits, what was different in your set up than previous equations that you have solved today?
      • What are the things you think you will need help with?
      • What do you think you did well?

🤔Explore B(in class or remote)

  •  Students are asked to solve a two-digit X tow-digit problem using the array model. 
    • Questions you could ask:
      • With each factor in expanded form, how many factors did you have in total to solve the problem?
      • What do you notice about the product of each equation?

💬Discuss B(in class or remote)

  • Questions to use in your discussion:
    • Why is it important to notice how many sections there would be for an equation in an array?

Additional Resources:

  • Differentiation (in class or remote)
    • Challenge: Have the students use a graph paper and solve the equations using the concept of area. Do their answers match the original answer?
      • Ways to make remote:
      • Students can do this challenge on their own and submit their work and thoughts. 
    • Struggling : Place them in a small group and start back with Lesson 3.3, making one-digit by two-digit arrays with base-ten blocks. Then work up to larger factors. The red lines discussed in the lesson as an option to separate groups may be something they should do first before filling in the array so they can understand the four sections.
      • 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):
    • Instead of chart paper or the array bar map students could use masking tape on the floor to create the array bars. Let students work in groups to create the arrays.