This lesson gives students an introduction to two-digit multiplication. Students will use their understanding of place value and single digit multiplication to begin multiplying two-digit numbers.

**Class:** 4th grade

**Duration:** 45 minutes

**Materials:**

- paper
- coloring pencils or crayons
- straight edge
- calculator

**Key Vocabulary:** two-digit numbers, tens, ones, multiply

**Objectives:** Students will multiply two two-digit numbers correctly. Students will use multiple strategies for multiplying two-digit numbers.

**Standards Met:** 4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

**Lesson Introduction:** Write 45 x 32 on the board or overhead. Ask students how they would begin to solve it. Several students may know the algorithm for two-digit multiplication. Complete the problem as students indicate. Ask if there are any volunteers who can explain why this algorithm works. Many students who have memorized this algorithm don't understand the underlying place value concepts.

**Step-by Step Procedure:**

- Tell students that the learning target for this lesson is to be able to multiply two-digit numbers together.
- As you model this problem for them, ask them to draw and write what you present. This can serve as a reference for them when completing problems later.
- Begin this process by asking students what the digits in our introductory problem represent. For example, "5" represents 5 ones. "2" represents 2 ones. "4" is 4 tens, and "3" is 3 tens. You can begin this problem by covering the numeral 3. If students believe that they are multiplying 45 x 2, it seems easier.
- Begin with the ones:

4**5**

x 3**2**

=**10**(5 x 2 = 10) - Then move on to the tens digit on the top number and the ones on the bottom number:

**4**5

x 3**2**

10 (5 x 2 = 10)

=**80**(40 x 2 = 80. This is a step where students naturally want to put down “8” as their answer if they aren’t considering the correct place value. Remind them that “4” is representing 40, not 4 ones.) - Now we need to uncover the numeral 3 and remind students that there is a 30 there to consider:

4**5**

x**3**2

10

80

=**150**(5 x 30 = 150) - And the last step:

**4**5

x**3**2

10

80

150

=**1200**(40 x 30 = 1200) - The important part of this lesson is to constantly guide students to remember what each digit represents. The most commonly made mistakes here are place value mistakes.
- Add the four parts of the problem to find the final answer. Ask students to check this answer using a calculator.
- Do one additional example using 27 x 18 together. During this problem, ask for volunteers to answer and record the four different parts of the problem:

27

x 18

= 56 (7 x 8 = 56)

=160 (20 x 8 = 160)

= 70 (7 x 10 = 70)

=200 (20 x 10 = 200)

**Homework/Assessment:** For homework, ask students to solve three additional problems. Give partial credit for the correct steps if students get the final answer wrong.

**Evaluation:** At the end of the mini-lesson, give students three examples to try on their own. Let them know that they can do these in any order; if they want to try the harder one (with larger numbers) first, they are welcome to do so. As students work on these examples, walk around the classroom to evaluate their skill level. You will probably find that several students have grasped the concept of multi-digit multiplication fairly quickly, and are proceeding to work on the problems without too much trouble. Other students are finding it easy to represent the problem, but make minor errors when adding to find the final answer. Other students are going to find this process difficult from beginning to end. Their place value and multiplication knowledge is not quite up to this task. Depending on the number of students who are struggling with this, plan to reteach this lesson to a small group or the larger class very soon.