## Questions that create dialogue and critical thought - Section 1: Core Lesson: Extending What We Already Know About Estimation

*Questions that create dialogue and critical thought*

# Estimating Double Digit by Double Digit Multiplication

Lesson 15 of 19

## Objective: SWBAT estimate a double digit by double digit multiplication product.

## Big Idea: This is a straightforward lesson that begins by tapping into student's critical thinking and reasoning about why we estimate; therefore how would we go about this?

*35 minutes*

Students had been practicing almost on a daily basis in little opportunities using IXL.com for sample problems to work with. It was time to learn how to estimate double digit by double digit. Using a constructive approach, I developed a SB file that begins by encouraging students to think about estimation of these products by using what they understand about place value.

I opened up the lesson with the first page of the double digit multiplication estimation SB file. I asked students: "Why would we need to estimate double digit multiplication products in a real world situation?"

One student suggested that we might be figuring out an approximate measurement. I told him I was happy to hear his usage of the word "approximate." I quickly used that moment to review estimation vocabulary they had learned in the past and listed the words on my white board. They presented the words "about" and "around."

Another student suggested that we might be making large groups of something and would need to round it and multiply. I used this teaching moment to emphasize that yes, the same process of rounding the factors first occurs, just as it had in the past and complimented him on remember the process. I like to connect real world situations each time conceptual understanding is being built upon.

I worked through the SB file with my students page by page. When I got to the page that helps students questions and create dialogue and critical thought, they stumbled on the questioning that pushed them to think about how estimation of double digits are different than estimating double by one digit. One student explained that he realized that both numbers needed to be rounded. I am hoping this question helps them remember the process.

I asked why you would round both this time? They had a hard time understanding that rounding both would be easier to multiply. So I asked if they could multiply, using powers of ten and basic facts, 30 x 40 in their heads. They could do that! So, through that, they understood how rounding both is functional and helps with mental math.

We practiced the problems on each page of our math notebook. They worked through solving exact and estimated problems helping them to see if they were reasonable answers. I then led them into using the equation written horizontally and using their basic facts and powers of ten to help them transition into understanding how they will use mental math for quick estimation. I roved and checked progress as they practiced.

Thinking and Writing : The last page encouraged students to think about their learning by writing their thoughts in their notebook.

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When we finished practicing, I used a page from old math curriculum from many years ago, Scott Forsman published this worksheet, Multiplying with Double Digits Worksheet 6-5 Practice, , but it still is a nice quick sample of double digit problems they could use for practice. IXL.com is also a good resource for problems, but, students must show work for either resource. I expected them to do both exact and estimation work for the problems. They needed to discern if the problems were reasonable. Students who were struggling, I pulled aside and assigned fewer problems, but expected that they solve exact and estimates too.

#### Resources

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Pretesting The Multiplication Unit
- LESSON 2: Introduction to Area Models
- LESSON 3: Area Models: Extension of Understanding
- LESSON 4: Area Models: 4 Digit by 1 Digit Multiplication
- LESSON 5: Getting Ready to Quiz: The Greatest Product Game
- LESSON 6: Quiz 1 in Multiplication: Area Model fluency 1x2,1x3 & 1x4 digits
- LESSON 7: Estimation of Products Using 1 Digit up to 4 Digit Equations.
- LESSON 8: Multistep Word Problems, Algebraic Concepts & Equations: Strategy Toward Mastery!
- LESSON 9: Quiz 2 : Multiplication Word Multi-Step Problems: 1x2,1x3,1x4 digit and estimation
- LESSON 10: An 1870's Classrom Meets Common Core: Drilling Math Facts & a Game of What's Wrong with This Answer?
- LESSON 11: Double Digit Multiplication and the Area Model
- LESSON 12: Powers of Ten: Review and Practice and Writing Clear Explanations
- LESSON 13: Multi-step word problems: Review and Support to Mastery
- LESSON 14: Quiz 3: Double Digit Multiplication, Estimation and Solving Word Problems
- LESSON 15: Estimating Double Digit by Double Digit Multiplication
- LESSON 16: Reviewing for Multiplication Assessment: A student jigsaw presentation.
- LESSON 17: RTI: Making Solving One Step Word Problems a Piece of Cake!
- LESSON 18: Estimation Scenarios: Writing Estimation story problems.
- LESSON 19: Assessing Multiplication