teaching • sequences • digits reference...

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Saxon Math Intermediate 5 1 Adaptations Lesson 1

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11 Teacher Notes:

• Introduce Hint #1 “Finding Patterns in Sequences” from the Teaching Guide.

• Refer students to “Multiplication Table” on page 5 in the Student Reference Guide.

• Sequences

• Digits

New ConceptNew Concept

• A sequence has a counting pattern or rule.

• Subtract to find the rule.

Example

3, 6, 9, 12, , , , … 12− 9 3

3− 6

3

Now we know to look at the 3s row in the multiplication table:

3, 6, 9, 12

3 3 3

3, 6, 9, 12, 15, 18, 21, …

Rule: Count up by 3s.

• Digits are the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

The number 26,348 has 5 digits. The last digit is 8.

Lesson Practice

Write the next three numbers in each sequence. Subtract to find the rule.

a. 6, 8, 10, , , , … b. 7, 14, 21, , , , …

Rule: Count by . Rule: Count by .

c. 4, 8, 12, , , , … d. 21, 18, 15, , , , …


• Sequences

Math Language

• A sequence is an ordered list of numbers.

It can go up or down.

1, 2, 3, 4, …

20, 15, 10, 5, …

• Digits

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SM_H5_AD_L001_FF.indd 1SM_H5_AD_L001_FF.indd 1 10/29/07 11:11:33 AM10/29/07 11:11:33 AM


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Lesson Practice, continued

e. 45, 40, 35, , , , … f. 12, 18, 24, , , , …


HOW MANY digits are in each of these numbers?

g. 36,756 h. 8002 i. 1,287,495

What is the LAST digit of each of these numbers?

j. 17 k. 3586 l. 654,321

Write a sequence using the rule “ count down by nines.”

m. 81, , , , ,

Written PracticeWritten Practicepage 10

1. Subtract to find the rule.

10, 15, 20, , …

2.

56, 49, 42, , …

3.

8, 16, 24, , …

4.

18, 27, 36, 45, , …



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onWritten Practice,Written Practice, continued continued

5.

24, 21, 18, , …

6.

32, 28, 24, 20, , …

7.

7, 14, , 28, 35, …

8.

40, , 30, 25, 20, …

9.

20, , 28, 32, 36, …

10.

24, 32, , 48, …

11.

, 36, 30, 24, …

12.

21, 28, , 42, …

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Written Practice,Written Practice, continued continued

13.

3, 6, 9, 12, , , , …

Rule: Count by .

Use work area.

14.

8, 16, 24, , , , …

Rule: Count by .

Use work area.

15.

6, 12, 18, , , , …

Rule: Count by .

Use work area.

16.

40, 35, 30, , , , …

Rule: Count by .

Use work area.

17.

18, 21, 24, , , , …

Rule: Count by .

Use work area.

18.

9, 18, 27, , , , …

Rule: Count by .

Use work area.

19. An ordered list of numbers is called

a s .

Use work area.

20. How many digits?

186,000

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21. 73,842 22. 30,004,091

23. What is the last digit?

26,348

24. 347

25. 9,675,420

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22 Teacher Note:

• Refer students to “Even/Odd” on page 13 in the Student Reference Guide.

• Even and Odd Numbers


• All whole numbers are either even or odd: Even numbers: 0, 2, 4, 6, 8, … Odd numbers: 1, 3, 5, 7, 9, …

• Look at the last digit: 3586 even 2345 odd

• Half of an even number is a whole number. Half of 6 = 3

• Half of an odd number is not a whole number. Half of 5 = 2 1 __

2

ActivityActivity page 13

Halves

Continue the list of counting numbers and their halves through 20.

Counting Number

8 9 10 11 12 13 14 15 16 17 18 19 20

Half of Number

4 4 1 __ 2 5 5 1 __

2

Math Language

0, 1, 2, 3, 4, 5, 6, …

• Whole numbers are the counting numbers and the number 0.

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Lesson PracticeIs each number odd or even?

a. 0 b. 1234

c. 20,001 d. 999

e. 3000 f. 391,048

g. All the students in the class separated into two groups. The same number of students were in each group.

Was the number of students in the class an odd number or an even number?

When you divide an number by 2, each group will have the

same number.

h. Tamayo has seven berries to share with Kasim. If Tamayo shares the berries equally, how many berries will each person have?

1. If a whole number is NOT even, then what is it?

2. Name the last digit.

47,286,560

Written PracticeWritten Practice page 14



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3. last digit

296,317

4. odd or even?

15

5. 196 6. 3567

7. Which of these numbers is even?

3716 2345 2223

8. Which of these numbers is odd?

45,678 56,789 67,890

9. Which of these numbers is NOT odd?

333,456 654,321 353,535

10. Which of these numbers is NOT even?

300 232 323

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15. 55, 50, 45, , , , …

16. 18, 27, 36, , , , …

17. 36, 33, 30, , , , …

18. 18, 24, 30, , , , …

13. 120, 110, 100, , ,

, …

14. 28, 24, 20, , , , …


9, 12, 15, , , , …

12. 16, 24, 32, , , , …

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19. 14, 21, 28, , , , …

20. 66, 60, 54, , , , …

21. 48, 44, 40, , , , …

22. 99, 90, 81, , , , …

23. 88, 80, 72, , , , …

24. 84, 77, 70, , , , …

25. If there were an equal number in each line, it could not be .

A 30 B 31 C 32 D 28

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30. Cost of 10 tickets?

Number of tickets 1 2 3 4 5 6 7 8 9 10

Cost $7 $14 $21 $28

26. half of 5

27. Which is a whole number (no fraction)?

Draw a picture to show your answer.

A half of 11 B half of 12 C half of 13 D half of 15

28. Number of Tickets 1 2 3 4

Cost $7 $14 $21 $28

Each ticket costs .

29. Rule: Number of tickets × .

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33

• Using Money to Illustrate Place Value


• The bills on the place-value template below show the expanded form of 312:

Place-Value Template

• The expanded form for 312 is:

3 hundreds + 1 ten + 2 ones

3 hundreds 300

1 ten 10

2 ones + 2 312

ActivityActivity Page 17

Place Value

• Use your textbook to complete this activity.

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Use money manipulatives.

a. Which digit in 365 shows the number of tens?

b. Use digits to write the number for “3 hundreds plus 5 tens.”

3 hundreds

5 tens

0 ones

c. How much money is one $100 bill plus ten $10 bills plus fifteen $1 bills? (Start with ones.)

3. tens

560

4. ones

365

5. ten $10 bills

1. 5 hundreds

7 tens

8 ones

2. 2 hundreds

5 tens

0 ones

Lesson Practice




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12. 54, 48, 42, , , , …

13. 8, 16, 24, , , , …

6. greatest

even

7. Which number is NOT even?

A 1234 B 2345

C 3456 D 4560

8. Which number is NOT odd?

A 365 B 653

C 536 D 477

9. Two teams have an equal number of players. The total number of players on both teams could not be

A 22 B 25

C 50 D 38

10. We can count to 12 by 2s or by 3s. We do not count to 12 when counting by

A 1s B 4s

C 5s D 6s


9, 12, 15, , , , …

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14. 80, 72, 64, , , , …

15. 16, 20, 24, , , , …

16. 40, 36, 32, , , , …

17. 27, 36, 45, , , , …

Rule: Count by .

Use work area.

18. 81, 72, 63, , , , …

Rule: Count by .

Use work area.

19. 10, 20, 30, , , , …

Rule: Count by .

Use work area.

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20. 33, 30, 27, , , , …

Rule: Count by .

Use work area.

21. What number equals four tens?

22. What number equals five hundreds? 23. two $100 bills

twelve $10 bills

fourteen $1 bills

24. The number 80 means “eight tens.”

The number 800 means eight what?


4, 8, 12, 16, 20, , , , , …

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29. Number of Tricycles 1 2 3 4

Number of Wheels 3 6 9 12

Hint: Number of wheels on one tricycle.

Rule: Number of wheels ÷ .

30. 27 ÷ 3 =

28. Is the greatest two-digit number odd or even?

is an odd number because the last digit is an number.

26. half of $10 27. half of $5

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44 Teacher Notes:

• Introduce Hint #3 “Comparing Numbers.”

• Refer students to “Comparison Symbols” on page 12 in the Student Reference Guide.

• Comparing WholeNumbers


• A number line shows numbers in order from least togreatest.

Example

60 7040 50

46 54 64

• The smaller end points to the smaller number.

3 < 4 Three is less than 4.

4 > 3 Four is greater than 3.

3 = 3 Three is equal to 3.

• To compare numbers, start at the greatest place value.

Example

373 382

Hundreds Tens Ones

3 3

2

7

83

1. Start at the hundreds. 373 382

The hundreds are the same.

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2. Look at the tens. 373 382

Seven is less than 8.

373 < 382

Three hundred seventy-three is less than three hundred eighty-two.

Lesson Practice

Start at the greatest place value.

a. Write the numbers in order from least to greatest.

324, 243, 423

, ,

least

Compare:

b. 36 632 c. 110 101

d. 90 90 e. 112 121

Write each comparison using digits:

f. Twenty is less than thirty.

g. Twelve is greater than eight.

New Concept,New Concept, continued continued



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1. Four is less than ten.

Use work area.

2. Fifteen is greater than twelve.

Use work area.

3. 97 101

Use work area.

4. 34 33

Use work area.

5. 3 hundreds

6 tens

5 ones

6. hundreds

675

7. ones

983

8. One $100 bill equals ten bills.

9. Odd or even?

36,275

10. 36,300



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11. 5,396,428 12. greatest

odd


A 1s B 4s

C 6s D 9s

14. Write 435, 354, and 543 in order from least to greatest.

Start at the greatest place value.

, ,

least


6, 12, 18, 24, , , ,

, , …

16. five $100 bills

thirteen $10 bills

ten $1 bills


20, 24, 28, ,

, , …

18.

106, 104, 102, ,

, , …

19.

0, 6, 12, ,

, , …

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20.

0, 7, 14, ,

, , …

21.

40, 32, 24, ,

, , …

22.

45, 36, 27, ,

, , …

23. What number equals nine tens?

24. What number equals eleven tens?


8, 16, 24, ,

, , …

26. Odd or even?

2, 4, 6, 8, , , , , , , , …

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28. The number is because the sum of an odd number and an

even number is an number.

Use work area.

29. Number of Ladybugs 1 2 3 4

Number of Legs 6 12 18 24

Hint: One ladybug has 6 legs.

Rule: Number of legs ÷ .

30. 54 ÷ 6 =

27. half of 9

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55 Teacher Notes:

• Introduce Hint #4 “Place Value (Digit Lines)” and Hint #5 “Writing Numbers.”

• Refer students to “Spelling Numbers” and “Place Value” on pages 12–13 in the Student Reference Guide.

• Display reference chart “Spelling Numbers.”

• Naming Whole Numbers and Money


0 zero 1 one 2 two 3 three 4 four 5 five 6 six 7 seven 8 eight 9 nine

10 ten 11 eleven 12 twelve 13 thirteen 14 fourteen 15 fifteen 16 sixteen 17 seventeen 18 eighteen 19 nineteen

20 twenty 30 thirty 40 forty 50 fifty 60 sixty 70 seventy 80 eighty 90 ninety 100 one hundred

• Use hyphens when writing the numbers 21–99 (except those numbers that end with zero).

80 eighty

81 eighty-one

108 one hundred eight

Example

Cameron County 906 square miles

Collingsworth County 919 square miles

Which has greater land area?Start at the greatest place value.

The hundreds are the same. 906 919

1 is greater than 0. 906 919

919 > 906

Collingsworth County has greater land area than Cameron County.

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• Use “and” between dollars and cents.

$324.56

three hundred twenty-four dollars and fifty-six cents

Lesson Practice a. Use words to name $563.45.

– dollars and – cents

b. Use words to name 101.

c. Use words to name 111.

d. Use digits to write two hundred forty-five.

e. Use digits to write four hundred twenty.

f. Use digits to write five hundred three dollars and fifty cents.

.

g. 1825 83 locks Start at the greatest place value.

1862 72 locks 83 72

In the year , the Erie Canal contained the greater number of locks.

h. Day

TotalSales

Monday $40

Tuesday $26

Wednesday $18

Thursday $25

Friday $11

Order from least to greatest.

least



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1. three hundred seventy-four dollars and twenty cents

2. $623.15

words:

dollars and

cents

Use work area.

3. two hundred five 4. 109

words:

Use work area.

5. one hundred fifty is greater than one hundred fifteen

Use work area.

6. 346 436

Use work area.

7. 5 hundreds

7 tens

9 ones



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8. Arrange these four numbers in order from least to greatest:

462 624 246 426

, , , least

9. tens

567

10. Count up by tens.

90,

11. odd or even?

363,636

12. odd or even?

36,363

13. odd or even?

2000

14. greatest

even

15. We can count to 20 by 2s or by 10s. We do not count to 20 when counting by .

A 1s B 3s

C 4s D 5s

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16. There are equal numbers of boys and girls in the room. Which could not be the number of students in the room?

A 12 B 29

C 30 D 44

17. six $100 bills

nine $10 bills

twelve $1 bills


0, 9, 18, , , , , …Use work area.

19. 25, 30, 35, , , , , …

Use work area.

20. 6, 12, 18, , , , , …

Use work area.

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21. 100, 90, 80, , , , , …

Rule: Count by .Use work area.

22. 90, 81, 72, , , , , …

Rule: Count by .Use work area.

23. 88, 80, 72, , , , , …

Rule: Count by .

Use work area.



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24. 7, 14, 21, , , , , …

Rule: Count by .

Use work area.

25. What is the ninth term in this sequence?

3, 6, 9, , , , , , …

26. odd or even?

1, 3, 5, 7, 9, , , , , , …

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29. 4 quarters in a dollar

Multiply the number of d

by .

30. $10 × =

27. greatest

odd or even?

28. half of $7.00

$7 ÷ 2 = with left over.

Half of is .


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66 Teacher Notes:

• Introduce Hint #6 “Column Addition (Sets of Ten).”

• Refer students to “Word Problem Keywords” on page 6 in the Student Reference Guide.

• Display reference chart “Word Problem Keywords.”

• Adding Whole Numbers


• Look for sets of ten.

Example

Sets of 10

9 + 1 = 10

8 + 2 = 10

7 + 3 = 10

6 + 4 = 10

5 + 5 = 10

7 . 4 3 .

+ 6 20

Properties of Operations

Commutative Property of Addition 5 + 6 = 11 6 + 5 = 11

Identity Property of Addition 2 + 0 = 2 37 + 0 = 37

• To add three-digit numbers, follow these steps:

First add ones.Then add tens.Then add hundreds.

11

$462$ 58$520

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Math Language

Addends are the numbers that are added.

2 addend+ 4 addend 6 sum

Sum is the answer to an addition problem.



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Find each sum. Show the sets of ten.

a. 8 + 6 + 2 = b. 4 + 7 + 3 + 6 = c. 9 + 6 + 4 =

d. 4 + 5 + 6 + 7 = e. 7 + 3 + 4 = f. 2 + 6 + 3 + 5 =

g. 6 + 7 + 5 = h. 8 + 7 + 5 + 3 =

i. The sum of 5 one-digit whole numbers is certain to be .

A greater than 4 B less than 50 C an odd number D an even number

Add.

j. $463

+

k. 674

+

l. $323

+

m. 543

+

n. $47

+


1. Use money manipulatives.

$5200000$ 86

2. $212.50

words:

dollars and cents

Use work area.

Lesson Practice



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3. hundreds

274

4. odd or even?

1234

5. 12,345 6. 1,234,567

7. five hundred eight dollars

8. 580

words:

Use work area.

9. Find each sum. sets of 10

1 + 6 + 9

10. 7 + 6 + 4 = 11. 8 + 3 + 1 + 7 = 12. 4 + 5 + 6 + 7 =

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10, 20, 30, , , , , , ...

19. 6, 12, 18, , , , , , ...

13. $436+ $527

14. 592+ 408

17. All the books were put into two piles. There was one more book in one pile than in the other pile. The total number of books in both piles could not be .

A 28 B 29 C 33 D 55

15. 963+ 79

16. $180+ $747

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20. 7, 14, 21, , , , , , ...

21. 8, 16, 24, , , , , , ...

24. 5 + 5 + 5 4 + 5 + 6

25. smallest

odd

22. nine hundred sixteen nine hundred sixty

23. Six hundred ninety is greater than six hundred nine.

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29. Number of Quarters 1 2 3 4

Number of Nickels 5 10 15 20

Rule: Number of nickels ÷ .

30. 50 ÷ 5 =

26. smallest

odd or even?

27. Is the 29th term odd or even?

2, 4, 6, 8, …

When counting by twos, all the

terms are .

28. half of 9

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77 Teacher Notes:

• Review Hint #5 “Writing Numbers.”

• Review “Place Value” and “Spelling Numbers” on page 12 in the Student Reference Guide.

• Review Reference Chart “Spelling Numbers.”

• Writing and Comparing Numbers Through Hundred Thousands

• Ordinal Numbers


,

(thousands family) (units family)

• Picture the numbers in groups of three.

Each group is a family (units family, thousands family).

The comma tells us the family name.

Each family has three members: ones, tens, and hundreds.

• Count from the right. Place a comma after every third digit: 54,321

Example

Use words to name 52370.

Insert a comma. 52370 52,370

Circle the families. 52 , 370

Write the families. fifty-two thousand, three hundred seventy

• Place a comma after the word thousand.

Example

Use digits to write:

“one hundred fifty thousand, two hundred thirty-four” 150,234

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• Writing and Comparing Numbers Through Hundred Thousands




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• The table shows two ways to write the first twelve ordinal numbers.

Ordinal Numbers for 1–12

1st first

2nd second

3rd third

4th fourth

5th fifth

6th sixth

7th seventh

8th eighth

9th ninth

10th tenth

11th eleventh

12th twelfth

Example

Tom was the fourth person in a line of ten people waiting for a movie. How many people were in front of Tom? How many people were behind Tom?

Tom Theater

6 Behind3 In front

Lesson PracticeUse words to name each number. (Hint: Add commas first.)

a. 36420

• Ordinal Numbers

Math Language

• Ordinal numbers name position (or order).


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200

8 S

axon


b. $12300 dollars

c. 4567

Use digits to write each number.

d. sixty-three thousand, one hundred seventeen ,

e. two hundred fifty-six thousand, seven hundred

,

f. fifty thousand, nine hundred twenty-four ,

g. seven hundred fifty thousand dollars ,

h. Christina was the sixth person in a line of ten people.

1st Christina

How many people were in front of Christina?

How many people were behind her?



0000$4620000$ 88

2. tens

567

3. seven hundred seven



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4. 29,035 feet

words:

Use work area.

5. Find the sum of 54 and 246.

246

Use work area.

6. $463+ $364

7. $286+ $414

8. 709+ 314


10, 20, 30, , , , , …

Use work area.

10. 5, 10, 15, , , , , …

Use work area.

11. 6, 12, 18, , , , , …

Use work area.

12. 7, 14, 21, , , , , …

Use work area.

13. 8, 16, 24, , , , , …

Use work area.

14. 9, 18, 27, , , , , …

Use work area.

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15. two hundred fifty two hundred fifteen

Use work area.

16. Compare without adding.

365 + 366 365 + 365

366 is one m than

365, so 366 + 365 is one

m than 365 + 365.Use work area.

17. sets of ten

$436$ 72

0000$ 54

18. 361 493 147

19. 506 79 434

20. Four hundred eight is less than four hundred eighty.

Use work area.

21. We can count to 24 by 2s or by 3s.

We do not count to 24 when counting by .

A 4s B 5s C 6s D 8s

22. odd or even?

1969

23. 1492 24. 1776

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25. smallest

odd

26. How many in front?

How many behind?

1st Rosario

in front behind

Use work area.

27. Is the twentieth (20th) term odd or even?

1, 3, 5, 7, …

28. half of 5

Could half of five birds fly away? Why?

. Half of 5 is , and birds c fly away.

Use work area.

29. Number of Dimes 1 2 3 4

Number of Pennies 10 20 30 40

Rule: number of dimes ×

Use work area.

30. 10 × 8 =

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88 Teacher Notes:

• Introduce Hint #7 “Addition/Subtraction Fact Families.”

• Review “Word Problem Keywords” on page 6 in the Student Reference Guide.

• Review Reference Chart “Word Problem Keywords.”

• Relationship Between Addition and Subtraction


• When you learn one fact family, you know four facts.

2 3

5 2

+ 35

3+ 2

5

5– 2

3

5– 3

2

• Addition and subtraction are inverse operations. One operation “undoes” the other.

5 + 3 – 3 = 5

Lesson Practice Subtract:

a. 17– 9

b. 12– 8

c. 15– 9

d. 11– 5

e. 17– 8

f. 16– 8

Write two addition facts and two subtraction facts for each fact family:

g.

7 8

15 7

+

8

+

15

–

15

–

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Math Language

The answer to a subtraction problem is called the difference.

5– 2 3 difference



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h.

5 7

12 5

+

7

+

12

–

12

–


1. thousands

3654

2. List the five odd, one-digit numbers.

, , , ,

Use work area.

3. When seven is subtracted from 15, what is the difference?

15 7

4. When 56 is added to 560, what is the sum?

560 56

5. Seven minus four

7 4

6. Sixty-four plus two hundred six

206 64



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7. $812,000

words:

dollars

Use work area.

8. eight hundred two

9.

odd

10. 4 hundreds

4 tens

4 ones +

words:

Use work area.


6, 12, 18, , , , , , , …

Rule: Count by .

Use work area.

12. 3, 6, 9, , , , , , , …

Rule: Count by .

Use work area.

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16. 15– 7

17. 12– 5

13.

4 8

12 4

+

8

+

12

–

12

–

Use work area.

14. odd

+ odd

sum

odd or even?

15. 18– 9

18. 11– 8

19. 14– 6

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20. 13– 9

21. sets of ten

$36 + $403 + $97 =

26. smallest

Circle one: odd even

Use work area.

22. 572

+

23. 47

+

24. $590

+

25. 364 287 428 273

greatest odd

smallest even +

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27. half of 18

28. House School

house to school and back 5 mi

house to school mi

29. Number of Weeks 1 2 3 4

Number of Days 7 14 21 28

Rule: number of days ÷

30. 56 ÷ 7 =

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99 Teacher Notes:

• Introduce Hint #8 “Regrouping Across Zeros.”

• Use money manipulatives to demonstrate concepts in this lesson.

• Practicing the SubtractionAlgorithm


• Subtraction algorithm:

Subtract ones. Borrow from 2 tens.

Subtract tens. Borrow from 5 hundreds.

$524− $ 58

1

$5 214− $ 518

6

4 11

$5 214− $ 5 8

$4 6 6

• Shortcut: Borrow across all zeros in one step.

5 96 010

− 1 2 34 7 7

5 9 96 0 011

− 1 2 3 44 7 6 7

Lesson PracticeSubtract.

a. $496− $157

b. 400− 136

c. $315− $264

d. $500− $ 63

e. 435− 76

f. 800− 406

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g. 86

−

h. $132

−

i. 203

−



$550

0000$ 75

2. List the five even, one-digit numbers.

, , , ,

3. tens

596

4. One hundred is equal to how many tens?Hint: One dollar is equal to how many dimes?



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5. When seven is subtracted from 15, what is the difference?

15

7

6.

7 8

15 7

+

8

+

15

−

15

−

Use work area.

7. What is the sum of one hundred ninety and one hundred nineteen?

190

8. Five hundred forty is greater than five hundred fourteen.

9. 761,266 acres

words:

Use work area.

10. less than 200

123

even

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11. $346− $178

12. 56− 38

13. $219− $ 73

14. 600− 321

15. 300− 124

16. $500− $246

17. 608− 314

18. 415− 378

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19. sets of ten

$787$156

+ $324

20. 57390

+ 438

21. $645$489

+ $ 65

22. 42985

+ 671


7, 14, 21, , , , , , , …

24. 9, 18, 27, , , , , , , …

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25. 8, 16, 24, , , , , , , …

26. odd or even?

All numbers that end in 0 are .

27. 31 − 12 31 − 15

28. half of 21

29. Number of Insects 1 2 3 4

Number of Legs 6 12 18 24

Rule: number of insects x

30. 7 × 6 =

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L E S S O N

Name


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1010 Teacher Notes:

• Introduce Hint #9 “Finding Missing Numbers.”

• Refer students to “Missing Numbers” on page 7 in the Student Reference Guide.

• Missing Addends


• To find a missing addend:

1. Add the other addends.

2. Subtract from the sum.

15 Check: 15 20 41 20

6+ w

55

55– 41

14 = w

6+ 14

55

Lesson PracticeFind each missing addend.

a. 35 + m = 67 b. n + 27 = 40

0067

35 m

67 0040

n 27

40

000035 000027

= m = n

c. 5 + 7 + 9 + f = 30 d. 15 + k + 10 + 25 = 70

00500700009

30

= f

00150010000025

70

= k

e. I can check my answer by adding all the a to find

the s .

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Math Language

An equation uses = to show that two amounts are equal.

15 – 8 = 7




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f. Yasmin had sixteen pebbles in her pocket. She gave some away. At the end of the day she had 6 pebbles.

Choose the correct equation.

A 16 – 6 = g B g – 16 = 6 C 16 – g = 6 D g – 6 = 16

pebbles



$467

0000$200

3. Six hundred thirteen is less than six hundred thirty.

2.

4 5

9

+ + − −

Use work area.



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4. greater than 500

odd

5. 34 + m = 61

000061

34 m

61

000034

m =

6. 510 7. hundreds

325,985


A 2s B 4s C 5s D 6s

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9. odd

+ even

sum odd or even?

10. 100 − 10 100 − 20

11. $363− $179

12. 400− 176

13. $570− $ 91

14. 504− 175

15. sets of ten

$367$ 48

+ $135

16. 179484

+ 201

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17. $305 $897

+ $725

18. 32 248

+ 165

19. $463

−

20. sets of ten

432

+

21. 18 + w = 42

000042000018

18 w

42

w =

22. 12 + r = 80

000080000012

12 r

80

r =


3, 6, 9, 12, , , ,

, …

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24. 4, 8, 12, 16, , , ,

, …

25. 6, 12, 18, 24, , , ,

, …



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26. How many 100s in 1000? 27.

11 in.

?

8 in. 12 8 in. 1

2

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28. Is half of 37,295 a whole number? Hint: Is 37,295 odd or even?

Why or why not?

Half of an even number a whole number.

Half of an odd number a whole number.

Use work area.

30. 28 ÷ =

29. Number of Dogs 1 2 3 4

Number of Paws 4 8 12 16

Rule: number of paws ÷


Saxon Math Intermediate 5 61 Adaptations Investigation 1

Name I N V E S T I G A T I O N 11©

200

8 S

axon

page 60

Focus onFocus on• Translating and Writing

Word Problems

• Combine Add.

Example

• Example of a story about combining:

a. The troop hiked 8 miles in the morning.

b. The troop hiked 7 miles in the afternoon.

c. Altogether, the troop hiked 15 miles.

Use an addition and subtraction facts triangle.

8 7

15

1. Formulate Write a question that asks for the number in a.

How many miles did the troop hike in ?

2. Formulate Write a question that asks for the number in b.

How many miles did the troop hike in ?

3. Formulate Write a question that asks for the number in c.

Altogether, how many miles ?

Teacher Notes:

• Introduce Hint #10 “Word Problem Cues, Part 1.”

• Review “Word Problem Keywords” on page 6 in the Student Reference Guide.

• Review Reference Chart “Word Problem Keywords.”

SM_H5_AD_Inv01_FF.indd 61SM_H5_AD_Inv01_FF.indd 61 10/29/07 11:09:43 AM10/29/07 11:09:43 AM


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I N V E S T I G A T I O N continued1

• Separate Subtract.

Example

• Example of a story about separating:

d. Jack went to the store with $28.

e. Jack spent $12 at the store.

f. Jack left the store with $16.


12 16

28

4. Formulate Write a question that asks for the number in d.

How much money did Jack have when he

?

5. Formulate Write a question that asks for the number in e.

How much money did Jack

?

6. Formulate Write a question that asks for the number in f.

How much money did Jack have when he

?



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• Equal groups Multiply or divide.

Number in each group × number of groups = total number in all groups.

Example

• Example of an equal groups story:

g. At Lincoln School there are 4 classes of fifth-grade students.

h. There are 30 students in each fifth-grade class.

i. Altogether, there are 120 fifth-grade students in Lincoln School.

Use a multiplication and division facts triangle.

4 30

120

7. Formulate Write a question that asks for the number in g.

How many classes of fifth-grade students are

there at ?

8. Formulate Write a question that asks for the number in h.

How many students are in each

?



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I N V E S T I G A T I O N continued1

9. Formulate Write a question that asks for the number in i.

Altogether, how many

?

• Compare Subtract.

Larger group – smaller group = difference.

Example

• Example of a story about comparing:

j. Abe is 5 years old.

k. Gabe is 11 years old.

l. Gabe is 6 years older than Abe.


5 6

11

10. Formulate Write a question that asks for the number in j.

How old is ?



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11. Formulate Write a question that asks for the number in k.

How old is ?

12. Formulate Write TWO questions that ask for the number in l.

Gabe is how much

?

Abe is how much

?

ActivityActivity page 63

Writing Word Problems

• This activity is optional.


teaching • sequences • digits reference...

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