Extend the use of place value disks to represent three- and four-digit by one-digit multiplication...

Extend the use of place value disks to represent three- and four-

digit by one-digit multiplication

Lesson 3.8:

Say the addition sentence with the answer in standard form.

200 + 30 + 4 3,000 + 500 + 60 + 8 400 + 7 + 90 8,000 + 400 + 2 7,000 + 30 + 1

Expanded Form Fluency

Write the expanded form. 572 572 = 500 + 70 + 2 8,463 9,075

Expanded Form Fluency

Andre bought a stamp to mail a letter that cost 46 cents. He also mailed a package that cost 5 times as much as a stamp. How much did it cost to mail the package and the letter?

Application Problem

Solution

Application Problem

Use your place value chart to represent the number 2 times 324.

What is the value of the ones? 2 × 4 ones = 8 ones = 8 What is the value of the tens? 2 × 2 tens = 4 tens = 40 What is the value of the hundreds? 2 × 3 hundreds = 6 hundreds = 600. Beneath your place value chart, as we did in

yesterday’s lesson, write an expression that shows the total value expressed in the chart.

Guided Instruction Concept Development: Problem 1

2 x 4 = 8 ones2 x 2 tens 4 tens = 40

2 x 3 hundreds = 6 hundreds = 600

Write 2 × 324 vertically on your board. Record the partial products for the ones, tens, and hundreds.

Add the values that you wrote in the equation. What is their sum?

648

2 x 4 = 8 ones2 x 2 tens 4 tens = 40

2 x 3 hundreds = 6 hundreds = 600

600 + 40 + 8 = 648


Work with a partner to solve 3 × 231. What is 3 x 1? What is 3 x 20? What is 3 x 200? What is the total?

231 x 3 3 (3 x 1) 90 (3 x 30) 600 (3 x 200) 691


4 × 605 Draw symbols to represent 4 × 605 on your place

value chart. Write 4 × 605 vertically on your board. Tell your partner the value of the digit in each

place.


The value of the ones is 4 × 5 ones = 20 ones. The value of the tens is 4 × 0 tens = 0 tens. The value of the hundreds is 4 × 6 hundreds = 24

hundreds. Do we need to regroup?

4 x 6 hundreds + 4 x 5 ones 24 hundreds + 20 ones


Yes. We can change 10 ones for 1 ten twice and 10 hundreds for 1 thousand twice.

What value is represented on the place value chart?

2,420

4 x 6 hundreds + 4 x 5 ones 24 hundreds + 20 ones

2 thousands, 4 hundreds, 2 tens, 0 ones


Multiply to complete the partial products method.


Multiply 5 x 464 What is 5 x 4? What is 5 x 60? What is 5 x 400? What is the total?

464 x 5 20 (5 x 4) 300 (5 x 60) 2000 (5 x 400) 2320


Write the equation 3 × 851. This time, rather than recording 3 groups of 851 to begin, let’s record the partial products as we multiply each unit.

3 × 1 one is? 3 times 5 tens? 3 times 8 hundreds? What is the total?

851 x 3 3 (3 x 1) 150 (3 x 50) 2400 (3 x 800) 2,553


3 × 763 3 × 3 ones is? 3 times 6 tens? 3 times 7 hundreds? What is the total?

763 x 3 9 (3 x 3) 180 (3 x 60) 2100 (3 x 700) 2,289


Write the equation 4 × 6,379. Let’s record the partial products as we multiply each unit.

4 x 9 ones is? 4 times 7 tens? 4 times 3 hundreds? 4 times 6 thousands? Can you see the four partial products? Find the total of the partial products both in your

equation. What is the total? 25,516

6,379 x 4 136 (4 x 9) 280 (4 x 70) 1,200 (4 x 300) 24,000 (4 x 6,000) 25,516


3 x 2,567 3 x 7 ones is? 3 times 6 tens? 3 times 5 hundreds? 3 times 1 thousands? Can you see the four partial products? Find the total of the partial products both in your

equation. What is the total?

Concept Development: Problem 4

2,567 x 3 21 (3 x 7) 180 (3 x 60) 1,500 (3 x 500) 6,000 (3 x 2,000) 7,701

Represent the following expressions with disks, regrouping as necessary. To the right, record the partial products vertically.

4 × 513

3 × 1,054

Exit Ticket

What pattern did you notice in the answers to Problems 1(a) and 1(b)?

Math Logs

Extend the use of place value disks to represent three- and four-digit by one-digit multiplication...

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