Jossey-Bass Teacher - Math Wise Phần 6 potx

In the figure below, the students are checking the answer to the

problem 6,492 multiplied by 384. First, they added the digits in 6,492

and got 21, then they added the digits in 21 and got 3. They stopped

there, because 3 is a single digit number. Next they added the digits

in 384 and got 15, then added the digits in 15 and got 6. At this point

they multiplied 3 and 6 to get 18, then added the digits of 18 and finally

got 9. Last step was to add the digits in the answer 2,492,928 and they

computed 36, then added the digits in 36 and got 9. This result is the same

as the 9 they got previously; therefore their answer to the multiplication

problem is correct. (Note: Please read the tips for checking subtraction

and division in the Examples. Also, an error possibility is discussed in

Extension 3.)

Rapid Checking 207

Examples:

1. Remind students to add

digits to obtain single-digit

representative numbers as

they follow the rapid check￾ing of the problem below.

257

×43

771

1028

11051

5

×7

35

8

14

(Representative

Answers)

8

2. Now have students try the

same process with a column

addition problem.

6

21

(Representative

Answers)

6

14

18

10

15

312

567

482

777

+433

2571

6

9

5

3

+1

24

3. When rapidly checking a

division problem, students

may benefit from thinking

of the procedure in terms of

multiplication. The quotient

and divisor are multiplied

together to get the divi￾dend. Make sure students

include any remainders in

their answers.

Think:

9

12

35)423

350

73

70

3

6

×3

24

35

×12

OK

6

+3

9

4. Students are most readily

able to check subtraction

computations, such as the

one shown below, when

they think of them in terms

of addition. The difference

and the number being sub￾tracted are added to get the

number being subtracted

from.

Think:

7

7

9

+7

16

270

+52

322

–52

270 OK

Extensions:

1. Have students see if the rapid checking works for relatively easy

problems, such as 12 + 45 or 8 × 9.

2. Students may use the method to check decimal problems, such as

0.97 + 0.42 + 0.38 or 0.4321 + 0.5 + 0.892.

3. Be careful that students do not switch the digits around in their

original answers; if they should do so, the rapid check would

falsely confirm their answers. For instance, in the addition problem

shown in Example 2 above, although the true answer is 2,571, if

one mixes the digits to read 2,517, the representative outcome

would be 6 in either case. (Such errors happen infrequently. Thus

most answers rapidly checked will be correct.)

208 Computation Connections

Section Three

Investigations and

Problem Solving

Students cannot be prepared for every problem they

will encounter throughout life. However, they can and should

be exposed to a wide variety of situations warranting investi￾gation, and should be equipped with problem-solving strate￾gies. The activities in this section stem from a variety of

real-life situations and include both written and verbal word

problems; problem-solving plans; problems with multiple

answers; and investigations that incorporate spatial think￾ing, statistics and probability, measurement, and scheduling.

Because many of the tasks are hands-on and nearly all call

for direct participation, students will be highly engaged and

have fun with the learning process.

Activities from other parts of this book can be used to

help young learners develop problem-solving skills. Some

of these are Everyday Things Numberbooks (p. 7), Celebrate

100 Days (p. 27), and A Million or More (p. 62) from Section

One, Dot Paper Diagrams (p. 112) and Silent Math (p. 203) in

Section Two, and Problem Puzzlers (p. 392) and String Triangle

Geometry (p. 411) from Section Four.