##
* *Reflection: Developing a Conceptual Understanding
Multiplying 2-Digit Numbers by Multiples of Ten - Section 3: Group or Partner Activity

Using area models to find the products is an excellent way to give the students a visual concept. Sometimes when we us algorithms the students just follow the steps but do not have a clue about what they are actually doing. This is a practice that I want to incorporate more in my teaching.

*Area Model*

*Developing a Conceptual Understanding: Area Model*

# Multiplying 2-Digit Numbers by Multiples of Ten

Lesson 6 of 23

## Objective: SWBAT use grids and a short cut to multiply 2-digit numbers and multiples of 10.

#### Opener

*5 min*

I tell the students, *you have learned to estimate to find the product of numbers.* *You have also learned the distributive property.* * In today's lesson, you use both strategies to multiply a 2-digit number by multiples of 10. * I ask the students, "*Who can name a multiple of 10*?" All of the students' hands go up. I tell the students to call out the multiples of 10. The students yell 10, 20, 30, 40, etc.

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#### Direct Instruction

*15 min*

To begin the lesson, I call all of my students to the carpet. This gives all of them an opportunity to sit close and absorb all of the information from the lesson. We begin the lesson with a review.

Tonya counted 15 bikes on her street as she roller skated. As she passed the bikes, she noticed that they all had 40 spokes on their wheels. How many spokes are there in all?

Call on a few students to explain how to break about the 15.

We can break apart the 15 in many ways. Let’s break apart the 15 into 10 + 5.

(10 x 40) + (5 x 40)=

400 + 200=600

Underline the basic facts which is 1 x 4=4.

Next, count your zeros and add them behind the 4 which gives you 400. For the next problem, the basic facts are 5 x 4= 20. Add one zero behind the 20, which gives us 200. Last, add 400 + 200=600.

Because I want the students to use area models, I show a quick video before the students go to their seats.

Possible Misconception(s):

1. Not adding the zero when using the short cut to multiply by tens

In order to get students to understand that when they multiply by tens that there is always a zero in the ones place, I will use examples. In the problem above, the students multiply 10 x 40. I would explain to students that 1 x 4 = 4 but they are not multiplying by 4, they are multiplying by 40 - which is 4 - tens. 1 x 40 = 40 so 10 x 40 would be 40 ten times which equals 400. They can also draw a visual model to represent the problem.

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#### Group or Partner Activity

*20 min*

To give the students practice with the skill and to allow them to work with their classmates, I will allow the students to work in pairs. I let my students work in pairs because it is small enough for all of the stdents to be heard. The activity the students will work on will require the students to make a model of the distributive property **(4.NBT.5 **Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.) The pair can choose a problem to solve from a list of 2 digit multiplication problems. The activity is as follows:

1. The students will work together to break apart a problem into 2 simpler problems. **(MP2 -**Mathematically proficient students make sense of quantities and their relationships in problem situations.)

2. Cut out an area model of each simpler problem with grid paper** (MP4)**

3. Glue the model on the construction paper

4. Find the product

5. Explain how the model helped find the product.

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#### Independent Activity

*10 min*

To let me see how well each student understood this skill, the students will complete an independent assignment. The students will need paper and pencil to solve the problem. Have the problem displayed on the Smart board.

Problem:

20 people gave money to a charity. They each gave $25. How much did they give in all?

Directions:

1. Use the distributive property to solve.

2. Explain how the distributive property helped you find your answer.

As the students work on the independent activity, I walk around to observe their work. Any student that is having a difficult time finding the product is identified and will be put in a small group for further instruction.

From my observation, I noticed several students struggling with this skill. I am not surprised because multiplying a 2 digit number by 2 digit number has always started out difficult for a lot of the students. Even though we have worked on the distributive property in other lessons, it was with multiplying a 1 digit by 1 digit. The students seemed a bit confused by breaking apart the 2-digit number, multiplying, and then adding the two partial products. We will continue to work on the skill.

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- UNIT 1: Fractions
- UNIT 2: Skills Review
- UNIT 3: Algebra
- UNIT 4: Geometry
- UNIT 5: Patterns & Expressions
- UNIT 6: Problem-Solving Strategies
- UNIT 7: Decimals
- UNIT 8: Measurement and Data
- UNIT 9: Multiplication and Division Meanings
- UNIT 10: Place Value
- UNIT 11: Adding and Subtracting Whole Numbers
- UNIT 12: Multiplying and Dividing

- LESSON 1: Multiplying by Multiples of 10 and 100
- LESSON 2: Using Rounding to Estimate
- LESSON 3: Is Your Answer Reasonable?
- LESSON 4: Using Clues to Multiply or Divide
- LESSON 5: Using Mental Math to Multiply 2-Digit Numbers (Are You My Match?)
- LESSON 6: Multiplying 2-Digit Numbers by Multiples of Ten
- LESSON 7: Multiplying Greater Numbers
- LESSON 8: Modeling: Multiplying a 2-digit number by a 1-digit number
- LESSON 9: Multiplying 2-digit number by 1-digit number
- LESSON 10: Multiplying a 3-digit number by a 1-digit number
- LESSON 11: Estimating Products
- LESSON 12: Multiplying 2-Digit by 2-Digit Numbers
- LESSON 13: Multiplication: Arrays and an Expanded Algorithm
- LESSON 14: Multiplication Unit Assessment
- LESSON 15: Using Mental Math to Divide
- LESSON 16: Estimating Quotients
- LESSON 17: Dividing with Remainders
- LESSON 18: Dividing 2-Digit by 1-Digit Numbers
- LESSON 19: Dividing 3-Digit by 1-Digit Numbers
- LESSON 20: Deciding Where to Start Dividing
- LESSON 21: How Much Will They Get?
- LESSON 22: Factors
- LESSON 23: Prime and Composite Numbers