MLC: Introducing the Standard Multiplication Algorithm

 

 

 

 

 

 

 


 

Quantile®
 Resource
 Overview
 


  Resource
 Title:
 
 

Introducing
 the
 Standard
 Multiplication
 Algorithm
 


 
 

Quantile
 Skills
 
  • Multiply
 a
 multi-­‐digit
 whole
 numbers
 by
 a
 1-­‐digit
 whole
 
and
 Concepts:
 
 
number
 or
 a
 2-­‐digit
 multiple
 of
 10. (QSC165)
 

 
• F
  ind
 the
 value
 of
 an
 unknown
 in
 a
 number
 sentence.

  (QSC549)
 

 
Quantile
 Measure:
 
3

 
   30Q
 


 

Excerpted
 from:
 
 


 


 

 

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Set A5 Number and Operations: Multi-Digit Multiplication

Set A5 H Activity 5

activity

Introducing the Standard Multiplication Algorithm

Overview You’ll need
Students use the standard algorithm to multiply two- and H Roll Your Own Multiplication Problems (page A5.38,
three-digit by one-digit numbers.
run a class set)
Skills & Concepts
H multiply 2- and 3-digit by 1-digit numbers using the H dice numbered 1–6 (class set)

standard multiplication algorithm H dice numbered 4–9 (class set)

H estimate products to approximate solutions and H several blank transparencies
determine reasonableness of answers
H overhead pens

H Student Math Journals or 1 piece of lined or grid
paper per student

Instructions for Introducing the Standard Multiplication Algorithm

1. Write 8 × 28 on the board or overhead. Ask students to first pair-share estimates and then call on vol-
unteers to share their thinking with the class.

Students It’s kind of like 8 times 30. That would be 240 because 8 × 3 is 24.
We said 10 times 28 is 280, so it’s going to be less than that.
Eight times 20 is 160, but then you have to add on the 8 × 8.
It’s going to be more than 200 for sure.

2. Next, ask students to find the product using the computing method they practiced during the previous

activity. Encourage them to make sketches to support their thinking if that’s helpful to them. Then ask a

volunteer to make a labeled sketch that shows the partial products, and another volunteer to record the

computations at the board.

20 8 28

_x___8
8 x 20 = 160
8 160 64 8 x 8 = +__6_4_

224

3. Explain that many people use a method for solving problems like these that features some interesting
shortcuts. Before calculators were invented, this method helped people solve large multiplication prob-
lems. Then demonstrate the standard algorithm at the overhead or board. Talk your way through each
step as you do it. Ask students to watch and listen closely to see if they can make sense of what you’re
doing based on all the experiences they’ve had with multiplication.

© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A5.35

Set A5 Number and Operations: Multi-Digit Multiplication

Activity 5 Introducing the Standard Multiplication Algorithm (cont.)

Teacher This method starts with the ones instead of the tens. So first I multiply 8 × 8. That’s 64.
I write the 4 in the ones place and move the 6 tens from 64 over to the tens place. Then I multiply 8
times 20. That’s 160. If I add the 60 I carried over to the tens place, it’s 220, and 220 plus 4 is 224.

6
28
_×___8
224
4. When you have finished the demonstration, ask students to explain how this method works. Can they
see any connection between the algorithm and the area model? Does the strategy make sense to them?

Students My mom showed me how to do it that way last year.
I don’t get where the little 6 at the top came from.
It’s like carrying when you add.
I like that way of doing it. It seems faster and easier.
Why do they start with the ones instead of the tens? I like the other way better.

Ask your students to connect the algorithm you’ve modeled to the array. Where do they see 224 in the array?

20 8 6

28 28
_x__8_ _x__8_
8 x 20 = 160 224
8 160 64 8 x 8 = +__6__4

224

Students I don’t see 224 in the array at all.
But that’s what you get if you add 160 and 64 together because 160 and 60 makes 220, and then 4
more is 224, right?
It’s kind of like you just do everything at the same time instead of doing it in two steps.

5. Now give students a chance to try the standard algorithm for themselves. Write 6 × 26 on the white-
board and ask students to copy the problem into their journals and jot an estimate to the side. Then
work with class input to solve it together, using the standard algorithm. Work the following four prob-
lems together in a similar fashion.
• 36 × 4
• 48 × 5
• 144 × 6
• 345 × 5

6. Provide students with more practice using the standard algorithm. Depending on the needs and
strengths of your class, you may want to have some students solve additional problems with you, while
others work independently on the Roll Your Own Multiplication sheet. Students who are very comfort-
able with the algorithm can be assigned to solve the challenge problem at the bottom of the sheet.

A5.36 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center

Set A5 Number and Operations: Multi-Digit Multiplication

Activity 5 Introducing the Standard Multiplication Algorithm (cont.)

Set A5 Number and Operations: Multi-Digit Multiplication Blackline Run a class set. DATE
NAME

Roll Your Own Multiplication Problems

1 For problems e–g below:
• Choose a die numbered 1–6 or 4–9.
• Roll it as many times as you need to fill in each of the boxes below. You can

write each number you roll in any box on the sheet, but once all the boxes are
filled, you can’t change them.

• Use the method you just learned in class to solve your problems.
• When you’re finished, trade papers with a classmate and have him or her

check your answers.

a bc d

××××

ef g

×××

CHALLENGE

5 Use each of these digits just one time: 0 1 2 3 4 5 6 7 8 9

Write them in the spaces below to make each problem correct.

a6 b4 c d

4 82

××××

366 3 1 45 32

Note If some of your students are confused by the standard algorithm, you may want to share the strategy
shown below, in which the partial products are added, but computation starts with the ones instead of the tens.
This strategy may help ease some students’ transition into the standard algorithm.

2

47 47
_x___4 _x__4_
4 x 7 = 28 188
4 x 40 = +__16_0_
188

Independent Worksheet

Use Set A5 Independent Worksheet 4 to provide students with more practice using the standard algo-
rithm for multiplication for 2-digit by 1-digit multiplication.

© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A5.37

Set A5 Number and Operations: Multi-Digit Multiplication Blackline Run a class set. date

name

Roll Your Own Multiplication Problems

1 For problems e–g below:
• Choose a die numbered 1–6 or 4–9.
• Roll it as many times as you need to fill in each of the boxes below. You can

write each number you roll in any box on the sheet, but once all the boxes are
filled, you can’t change them.

• Use the method you just learned in class to solve your problems.
• When you’re finished, trade papers with a classmate and have him or her

check your answers.

a bc d

××××

ef g

×××

challenge

5 Use each of these digits just one time: 0 1 2 3 4 5 6 7 8 9

Write them in the spaces below to make each problem correct.

a6 b4 c d

4 82

××××

366 3 1 45 32

A5.38 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center

Roll
 Your
 Own
 Multiplication
 Problems
 Answer
 Key
 


 
1.)
 a
 –
 g
 
  Answers
 will
 vary.
 

 
5.)
 
  a.
 61
 ×
 6
 =
 366
 

  b.
 43
 ×
 7
 =
 301
 
 
 

  c.
 49
 ×
 5
 =
 245
 

  d.
 82
 ×
 4
 =
 328
 

Introducing
 the
 Standard
 Multiplication
 Algorithm
 -­‐
 KEY