Math 406 410 TG
Math 407, Lesson 11
Lesson 11
11
pp. 38-41 Lesson Preparation • ÷9
AND
L F LASH C ARDS
Drill • Do ÷9 AND L F LASH C ARDS . • Do Speed Drill 11 and mark the speed drill record.
Flash Cards ÷9 and Set L
Speed Drill 11, page 66
Multiplying Three-Digit Numbers by Three-Digit Numbers Follow the steps to multiply 738 by 426. Remember to keep all digits in the correct column. 2 4
738 426 4428
Step 1
Multiply 738 by 6 ones.
Step 2
Write a 0 to hold the ones place. Multiply by 2 tens.
Step 3
×
1 2 4
738 426 4428 14760
×
Write two zeros to hold both the ones and tens places. Multiply by 4 hundreds.
Step 4
Add to get the final answer. Remember to include the comma.
1 3 1 2 4
1 3 1 2 4
738 426 4428 14760 295200
×
738 426 4428 14760 +295200 3 1 4,3 8 8 ×
{
Solve. 2 3 4 5
1. a.
1 2 1
2 5 8 × 1 4 7 1
18 103 +2 5 8 3 7,9
0 2 0 2
b.
3 4 2 × 1 3 5
1
17 102 +3 4 2 4 6,1
6 0 0 6
7 3 4 2
1 6 0 7
0 0 0 0
c.
1 2
2 8 4 × 9 5 1
2 142 +2 5 5 6 2 7 0,0 1 1
8 0 0 8
4 0 0 4
7 0 3 × 5 1 7
d.
1
49 70 +3 5 1 5 3 6 3,4 1
2 3 0 5
1 0 0 1
38
Teaching the Lesson Multiplying Three-Digit Numbers by Three-Digit Numbers Stress that keeping numbers lined up and in their proper places becomes even more important when using three-digit numbers.
Board Work
593 ×641 ( 5 9 3) (2 3 7 2 0) ( 3 5 5 8 0 0) 38011 3
802 ×397 (5 6 1 4) (7 2 1 8 0 ) (2 4 0 6 0 0) 318394 122
Math 407, Lesson 11 Lesson 11
W e R emember
If students have problems with accuracy, encourage them to draw vertical lines to separate their columns as they work the multiplication problems.
Underline the correct word. 2. If Evangel is as tall as her friend Gertrude, and Gertrude is taller than her brother Peter, then Evangel is taller, shorter than Peter. Write the products. 11 3. × 3
11 × 7
11 × 2
11 × 6
11 ×10
11 × 4
11 × 9
11 × 5
11 × 11
11 × 8
33
77
22
66
11 0
44
99
55
121
88
Estimate. 4. Timmy enjoyed watching for giraffes as his family drove across South Africa. He knows that giraffes have big appetites. An adult giraffe can eat 75 pounds or 34 kilograms of leaves in a day. Estimate how many pounds of leaves a herd of 18 giraffes would eat in a day.
80
×
20
=
1,600
pounds
5. Estimate how many kilograms of leaves 18 giraffes would eat in one day.
30
×
20
=
600
kilograms
Complete the analogies. 6. Fast : slow : : tall :
short
b. 0.1 :
1 10
: : 0.6 :
6 10
Write = or ≠. 7. a. If a = 11, and b = 11, then a
= b.
b. If s = t, and t = u, then s =
u.
Round to the nearest ten. 8. a. 496
500
b. 3,594 3,590
Round to the nearest hundred. 9. a. 6,972 7,000
b. 495
500 39
Teacher Notes:
123
Tips for Struggling Students
Helpful Hints Stress the need to work accurately. This sort of problem has many steps and much potential for errors.
Math 407, Lesson 11 Lesson 11 My Work Space
10. Brother David often preaches in Pollsmoor Prison in South Africa. There are 45 prisoners, ranging in age from 13 to 22, in each cell. One section has 32 cells. How many prisoners are in that section of the prison?
1,440
1 1
45
× 32 90 +1350 1,440
prisoners
My Work Space
11. Brother David wrote a tract to give out to the men in prison. He made 200 copies of the tract. He has given out 125 copies. How many copies are left?
75
191
200
– 125 75
copies
My Work Space
12. What fraction of the tracts has been given out? Reduce the fraction to simplest form. 5 8
125 = 25 = 5 200 40 8
of the tracts have been given out.
Classify each angle as right, obtuse, or acute. 13. Angle C is a
right
angle.
B
14. Angle B is an
acute
angle.
15. Angle A is an
obtuse
angle.
A C
Use the graph on page iv. Underline the correct choice. 16. An elephant’s ears weigh less than 100 pounds, more than 400 pounds, more than 200 pounds. Write the first six multiples of 16. 17.
16
32
48
64
80
96
Write the ratio for 4 ostrich eggs to 6 chicken eggs. 18.
4:6
40
Teacher Notes:
124
No river runs straight for longer than 10 times its width. It always bends before that time.
Math 407, Lesson 11 Lesson 11
19. A building in Cape Town needs a fresh coat of paint. One side measures 50 feet by 27 feet. What is the area?
My Work Space
50
× 27
350 1000 1,350 Write number sentences to find the areas. Answer the question.
ft 2
1,350
20. A small storage shed nearby will be painted also. One side measures 9 feet by 9 feet. What is the area?
9 × 9 = 81 ft 2
21. On a farm just outside of town chickens scratch in the dirt in their triangle-shaped pen. The triangle has a base of 4 meters and a height of 3 meters. What is the area of the pen?
12 ÷ 2 = 6 m 2
4 × 3 = 12
4:3
22. What is the ratio of the base to the height?
-26-25-24-23-22-21-20-19-18-17-16-15-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Answer the question. 23. What is the temperature if it is –25° and rises 30°?
-
S kill B uilders +÷ x 2 4 4 7 1
24. a.
1
2 133 +740 8 7,6 1 25. a. –
9 2 0 1
Write remainders as fractions. Write fraction answers in simplest form. 5 1 4
3 2
1 4 8 × 5 9 2
6 0 0 6
8 8 7 8 1 8
b.
2 6 0 × 6 0 4
10 00 +1560 1 5 7,0
4 0 0 4
1 1 2
b.
5°
0 0 0 0
c.
18
3 7 1 × 8 2 6
1
22 1 1 7 4 +2968 3 0 6,4
2 2 0 4
9 10
6 0 0 6 91
245 × 24
101.06 c. – 4 2 . 0 8
980 4900 5,880
58.98
6 32
8
1
d. + 2 32
e. – 3
19
3
8 32
55
6
3
798 = 79 4
d. 8 ) 6 3 8
566 78 72 6
Teacher Notes:
125
7 5 4 5
1
244
e. 4 ) 9 7
86 17 16 1
41
Math 407, Lesson 12
Lesson 12 pp. 42-45
12
Lesson Preparation •B
AND
×0 F LASH C ARDS
Drill • Do B AND ×0 F LASH C ARDS . • Do Speed Drill 12 and mark the speed drill record.
Flash Cards, Set B and ×0
Speed Drill 12, page 66
Comparing Numbers Across Zero To compare numbers across zero you must picture where they belong on a number line. -8 -7 -6 -5 -4 -3 -2 -1
0 1
2
3
4
5
6
7
8
When comparing two numbers, the number to the left on the number line is always smaller than the one to the right. Compare -8 and -4. Find -8 on the number line. Now find -4. -8 is to the left of -4.
-8 < -4 because -8 is to the left of -4.
Compare 2 and -5. 2 > -5 because 2 is to the right of -5. Write < or >. -3
>
-9
b. -6
-25
d. -21
-21
d. 24
>
17
45
Teacher Notes:
129
Lesson 11
11
pp. 38-41 Lesson Preparation • ÷9
AND
L F LASH C ARDS
Drill • Do ÷9 AND L F LASH C ARDS . • Do Speed Drill 11 and mark the speed drill record.
Flash Cards ÷9 and Set L
Speed Drill 11, page 66
Multiplying Three-Digit Numbers by Three-Digit Numbers Follow the steps to multiply 738 by 426. Remember to keep all digits in the correct column. 2 4
738 426 4428
Step 1
Multiply 738 by 6 ones.
Step 2
Write a 0 to hold the ones place. Multiply by 2 tens.
Step 3
×
1 2 4
738 426 4428 14760
×
Write two zeros to hold both the ones and tens places. Multiply by 4 hundreds.
Step 4
Add to get the final answer. Remember to include the comma.
1 3 1 2 4
1 3 1 2 4
738 426 4428 14760 295200
×
738 426 4428 14760 +295200 3 1 4,3 8 8 ×
{
Solve. 2 3 4 5
1. a.
1 2 1
2 5 8 × 1 4 7 1
18 103 +2 5 8 3 7,9
0 2 0 2
b.
3 4 2 × 1 3 5
1
17 102 +3 4 2 4 6,1
6 0 0 6
7 3 4 2
1 6 0 7
0 0 0 0
c.
1 2
2 8 4 × 9 5 1
2 142 +2 5 5 6 2 7 0,0 1 1
8 0 0 8
4 0 0 4
7 0 3 × 5 1 7
d.
1
49 70 +3 5 1 5 3 6 3,4 1
2 3 0 5
1 0 0 1
38
Teaching the Lesson Multiplying Three-Digit Numbers by Three-Digit Numbers Stress that keeping numbers lined up and in their proper places becomes even more important when using three-digit numbers.
Board Work
593 ×641 ( 5 9 3) (2 3 7 2 0) ( 3 5 5 8 0 0) 38011 3
802 ×397 (5 6 1 4) (7 2 1 8 0 ) (2 4 0 6 0 0) 318394 122
Math 407, Lesson 11 Lesson 11
W e R emember
If students have problems with accuracy, encourage them to draw vertical lines to separate their columns as they work the multiplication problems.
Underline the correct word. 2. If Evangel is as tall as her friend Gertrude, and Gertrude is taller than her brother Peter, then Evangel is taller, shorter than Peter. Write the products. 11 3. × 3
11 × 7
11 × 2
11 × 6
11 ×10
11 × 4
11 × 9
11 × 5
11 × 11
11 × 8
33
77
22
66
11 0
44
99
55
121
88
Estimate. 4. Timmy enjoyed watching for giraffes as his family drove across South Africa. He knows that giraffes have big appetites. An adult giraffe can eat 75 pounds or 34 kilograms of leaves in a day. Estimate how many pounds of leaves a herd of 18 giraffes would eat in a day.
80
×
20
=
1,600
pounds
5. Estimate how many kilograms of leaves 18 giraffes would eat in one day.
30
×
20
=
600
kilograms
Complete the analogies. 6. Fast : slow : : tall :
short
b. 0.1 :
1 10
: : 0.6 :
6 10
Write = or ≠. 7. a. If a = 11, and b = 11, then a
= b.
b. If s = t, and t = u, then s =
u.
Round to the nearest ten. 8. a. 496
500
b. 3,594 3,590
Round to the nearest hundred. 9. a. 6,972 7,000
b. 495
500 39
Teacher Notes:
123
Tips for Struggling Students
Helpful Hints Stress the need to work accurately. This sort of problem has many steps and much potential for errors.
Math 407, Lesson 11 Lesson 11 My Work Space
10. Brother David often preaches in Pollsmoor Prison in South Africa. There are 45 prisoners, ranging in age from 13 to 22, in each cell. One section has 32 cells. How many prisoners are in that section of the prison?
1,440
1 1
45
× 32 90 +1350 1,440
prisoners
My Work Space
11. Brother David wrote a tract to give out to the men in prison. He made 200 copies of the tract. He has given out 125 copies. How many copies are left?
75
191
200
– 125 75
copies
My Work Space
12. What fraction of the tracts has been given out? Reduce the fraction to simplest form. 5 8
125 = 25 = 5 200 40 8
of the tracts have been given out.
Classify each angle as right, obtuse, or acute. 13. Angle C is a
right
angle.
B
14. Angle B is an
acute
angle.
15. Angle A is an
obtuse
angle.
A C
Use the graph on page iv. Underline the correct choice. 16. An elephant’s ears weigh less than 100 pounds, more than 400 pounds, more than 200 pounds. Write the first six multiples of 16. 17.
16
32
48
64
80
96
Write the ratio for 4 ostrich eggs to 6 chicken eggs. 18.
4:6
40
Teacher Notes:
124
No river runs straight for longer than 10 times its width. It always bends before that time.
Math 407, Lesson 11 Lesson 11
19. A building in Cape Town needs a fresh coat of paint. One side measures 50 feet by 27 feet. What is the area?
My Work Space
50
× 27
350 1000 1,350 Write number sentences to find the areas. Answer the question.
ft 2
1,350
20. A small storage shed nearby will be painted also. One side measures 9 feet by 9 feet. What is the area?
9 × 9 = 81 ft 2
21. On a farm just outside of town chickens scratch in the dirt in their triangle-shaped pen. The triangle has a base of 4 meters and a height of 3 meters. What is the area of the pen?
12 ÷ 2 = 6 m 2
4 × 3 = 12
4:3
22. What is the ratio of the base to the height?
-26-25-24-23-22-21-20-19-18-17-16-15-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Answer the question. 23. What is the temperature if it is –25° and rises 30°?
-
S kill B uilders +÷ x 2 4 4 7 1
24. a.
1
2 133 +740 8 7,6 1 25. a. –
9 2 0 1
Write remainders as fractions. Write fraction answers in simplest form. 5 1 4
3 2
1 4 8 × 5 9 2
6 0 0 6
8 8 7 8 1 8
b.
2 6 0 × 6 0 4
10 00 +1560 1 5 7,0
4 0 0 4
1 1 2
b.
5°
0 0 0 0
c.
18
3 7 1 × 8 2 6
1
22 1 1 7 4 +2968 3 0 6,4
2 2 0 4
9 10
6 0 0 6 91
245 × 24
101.06 c. – 4 2 . 0 8
980 4900 5,880
58.98
6 32
8
1
d. + 2 32
e. – 3
19
3
8 32
55
6
3
798 = 79 4
d. 8 ) 6 3 8
566 78 72 6
Teacher Notes:
125
7 5 4 5
1
244
e. 4 ) 9 7
86 17 16 1
41
Math 407, Lesson 12
Lesson 12 pp. 42-45
12
Lesson Preparation •B
AND
×0 F LASH C ARDS
Drill • Do B AND ×0 F LASH C ARDS . • Do Speed Drill 12 and mark the speed drill record.
Flash Cards, Set B and ×0
Speed Drill 12, page 66
Comparing Numbers Across Zero To compare numbers across zero you must picture where they belong on a number line. -8 -7 -6 -5 -4 -3 -2 -1
0 1
2
3
4
5
6
7
8
When comparing two numbers, the number to the left on the number line is always smaller than the one to the right. Compare -8 and -4. Find -8 on the number line. Now find -4. -8 is to the left of -4.
-8 < -4 because -8 is to the left of -4.
Compare 2 and -5. 2 > -5 because 2 is to the right of -5. Write < or >. -3
>
-9
b. -6
-25
d. -21
-21
d. 24
>
17
45
Teacher Notes:
129
