Eureka Math

Module 2

Lesson 2

At the request of elementary teachers, a team of Bethel & Sumner educators met as a committee to create Eureka slideshow presentations. These presentations are not meant as a script, nor are they required to be used. Please customize as needed. Thank you to the many educators who contributed to this project!

Directions for customizing presentations are available on the next slide.

Presentation Project

Customize this Slideshow

Reflecting your Teaching Style and Learning Needs of Your Students

• When the Google Slides presentation is opened, it will look like Screen A.
• Click on the “pop-out” button in the upper right hand corner to change the view.
• The view now looks like Screen B.
• Within Google Slides (not Chrome), choose FILE.
• Choose MAKE A COPY and rename your presentation.
• Google Slides will open your renamed presentation.
• It is now editable & housed in MY DRIVE.

Screen A

“pop-out”

Screen B

This slideshow presentation is in VIEW ONLY. In order to edit the presentation and make it your own, you’ll need to MAKE A COPY.

Follow the directions on the slide to MAKE A COPY that will be housed in MY DRIVE and that you’ll be able to edit.

Icons

Learning Target

Think Pair Share

Individual

Partner

Whole Class

Small Group Time

Small Group

Personal White Board

Problem Set

Manipulatives Needed

Fluency

Suggested timing for each component of the lesson.

We recommend teaching each component. When you customize this lesson, you may need to adjust the timing and/or content of the components to align more closely with the Mid- and/or End-of-Module Assessments (Backward Planning), meet the needs of your students, or fit time constraints.

I can estimate multi-digit products by rounding factors to a basic fact using place value patterns.

Lesson learning objective stated as an “I can” statement. Teachers, feel free to customize this to fit your class needs, make more student-friendly, etc.

SPRINT

Multiply by 10, 100, and 1,000

(8 minutes)

Note: This review fluency activity helps preserve skills students learned and mastered in Module 1 and lays the groundwork for future concepts.

Round to Different Place Values

48,625

Between which two ten thousands is 48,625?

40,000

50,000

What’s the midpoint for 40,000 and 50,000?

45,000

Would 48,625 fall above or below 45,000?

48,625 ≈_______ What’s 48,625 rounded to the nearest ten thousand?

T: Say the number

S: 50,000

Round to Different Place Values

48,625

Between which two thousands is 48,625?

47,000

48,000

What’s the midpoint for 47,000 and 48,000?

47,500

Would 48,625 fall above or below 47,500?

48,625 ≈_______ What’s 48,625 rounded to the nearest thousand?

S: 48,000

Round to Different Place Values

48,625

Between which two hundreds is 48,625?

48,600

48,700

What’s the midpoint for 48,600 and 48,700?

47,650

Would 48,625 fall above or below 47,650?

48,625 ≈_______ What’s 48,625 rounded to the nearest hundred?

S: 48,600

Round to Different Place Values

48,625

Between which two tens is 48,625?

48,620

48,630

What’s the midpoint for 48,620 and 48,630?

47,625

Would 48,625 fall above or below 48,625?

48,625 ≈_______ What’s 48,625 rounded to the nearest ten?

S: 48,600

Multiply by Multiples of 10

31 x 10 = ______

310 x 2 = ______

310 x 20 = ______

Write 310 x 20 as a three-step multiplication sentence, taking out the ten.

Show your white board.

T: Say the multiplication sentence.

S: 31 x 10 = 310

T: Say the multiplication sentence.

S: 310 x 2 = 620

S: writes 310 x 10 x 2 = 620

Multiply by Multiples of 10

Solve using the same method…

23 x 40

32 x 30

Application Problem

Jonas practices guitar 1 hour a day for 2 years. Bradley practices the guitar 2 hours a day more than Jonas. How many more minutes does Bradley practice the guitar than Jonas over the course of 2 years?

NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: It may be helpful to offer a conversion table to students working below grade level and others, which includes the following: 1 hour = 60 minutes 1 year = 365 days

Note: The Application Problem is a multi-step word problem that asks students to convert units and multiply with multi-digit factors using their knowledge of the distributive and associative properties from Lesson 1. Allow students to share approaches with classmates.

Application Problem

This is one example of how to solve the problem.

Estimate multi-digit products

How many students do we have in class?

Do all of the classes have exactly 23 students?

There are 18 classes, but I’m not sure exactly how many students are in each class. What could I do to find a number that is close to the actual number of students in our school?

Great idea. What number could help me make an estimate for the number of students in each class?

Note: Use class, school, and building numbers for the following that would yield a two-digit estimation equation.

S: Estimate how many students are in each class.

S: You could use the number in our class of 23.

Estimate multi-digit products

True, but 23 is a little more difficult to multiply in my head. I’d like to use a number that I can multiply mentally. What could I round 23 students to so it is easier to multiply?

What could I round 18 classes to?

How would I estimate the total number of students?

What would my estimate be? Explain your thinking.

S: 20 students.

S: 20 classes.

S: Multiply 20 by 20.

S: 400. 2 times 2 is 4. Then you multiply 4 by 10 and 10.

Estimate multi-digit products

(4 × 10) × 10 = 40 × 10 = 4 × 100

About 400 students. Estimates can help us understand a reasonable size of a product when we multiply the original numbers.

Estimate multi-digit products

456 x 42 = _______

Suppose I don't need to know the exact product, just an estimate. How could I round the factors to estimate the product?

460 × 40 is still pretty hard for me to do in my head. Could I round 456 to a different place value to make the product easier to find?

500 × 40 does sound pretty easy! What would my estimate be? Can you give me the multiplication sentence in unit form?

(5 × 100) × (4 × 10) = 20 × 1,000 = 20,000 So, my product is about 20,000.

S: You could round to the nearest 10. You'd get 460 × 40.

S: You could round to the hundreds place. 500 × 40 is just like we did in the previous lesson!

S: 5 hundreds × 4 tens equals 20 thousands.

Estimate multi-digit products

1,320 x 88 = _______

Round the factors to estimate the product.

Now, before you estimate 13,205 × 880, compare this to the problem we just did. What do you notice is different?

What do you think that will do to our estimate?

Let’s test that prediction. Round and find the estimated product.

Was our prediction correct?

Note: Accept any reasonable estimates of the factors. The most important thinking is how the properties are used to arrive at a product. Ask students to justify their choice of place value for rounding.

S: I used 1,300 × 90, so I multiplied 13 × 9, then multiplied that by 1,000. This gave me 117,000. I used 1,000 × 90 and got 90,000.

S: The factors are greater. 13,205 is about 10 times as large as 1,320, and 880 is exactly 10 times as large as 88.

S: It should increase the product. The product should be about 100 times as large as the first one

NOTE: Accept any reasonable estimate of the factors. The important thinking is the properties and the comparison of the relative sizes of the products.

S: 13,205 → 10,000 and 880 → 900. So, 10,000 × 900 = (9 × 1) × 10,000 × 100 = 9,000,000.

S: Yes. 9 million is 100 times as large as 90,000.

Repeat the sequence for 3,120 × 880 and 31,200 × 880.

Estimate multi-digit products

Repeat the sequence for 3,120 × 880 and

31,200 × 880.

Problem Set

Consider assigning students Must Do problems and May Do problems. Problem sets can also be differentiated by assigning different problems to different students, depending on their understanding of the concept of the lesson.

Items in the problems set move from less complex to more complex, and mirror the homework for that lesson.

Debrief

Raise the idea of a different rounding strategy for Problem 1(c) using factors of 25 as “easy” mental factors. Ask students to consider the notion of rounding only one factor (e.g., 5,840 to 6,000). Multiply 6 × 25 = 150, and then multiply 150 × 1,000 to reach 150,000. What makes 25 an easy factor even though it is not a multiple of 10? Are there other numbers that students think of as easy like 25? Compare this to rounding both factors.

Lesson Objective: Estimate multi-digit products by rounding factors to a basic fact and using place value patterns. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. Any combination of the questions below may be used to lead the discussion.

Debrief

In Problem 6, there are many ways to estimate the solution. Discuss the precision of each one. Which is the closest estimate? Does it matter in the context of this problem?

Consider allowing students to generate other factors in Problem 4 that would round to produce the estimated product. Compare the problems to see how various powers of 10 multiplied by each other still yield a product in the thousands.

NOTES ON MULTIPLE MEANS OF REPRESENTATION: Depending on the needs of English language learners, consider allowing students to discuss their responses to the Student Debrief in their first language or providing sentence frames or starters such as: “I notice when I multiply 25 by any number that ….” “I chose to round to the ____ place because ….” “My estimate was close to the actual answer because ….”

Students may use any of these or may have other valid responses: Consider allowing students to generate other factors in Problem 4 that would round to produce the estimated product. Compare the problems to see how various powers of 10 multiplied by each other still yield a product in the thousands. Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help with assessing students’ understanding of the concepts that were presented in today’s lesson and planning more effectively for future lessons.

The questions may be read aloud to the students. 423 × 12 ≈ 400 × 10 = 4,000 4,000 × 4 = 16,000 423 × 48 ≈ 400 × 50 = 20,000 423 × 12 ≈ 423 × 10 = 4,230 4,230 × 4 ≈ 4,200 × 4 = 16,800 423 × 4 years ≈ 423 × 5 years ≈ 400 × 60 months = 24,000

Exit Ticket

Copy of 5.M.2 Lesson02_BSDSSD - Google Slides