name 8-1 add it up...find 517 + 238 by breaking apart numbers to make a ten. break 238 into 200 + 35...

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Enrichment

8-1Name

Add It UpFor Exercises 1 and 2, tell whether you use the Commutative (Order) Property, the Associative (Grouping) Property, or the Identity (Zero) Property. Explain your answer. Then solve.

1. ? + 14 = 14. You use the Property because

. The solution is .

2. (10 + 9) + 8 = ? + (9 + 8). You use the Property because

The solution is .

3. How can you write 9 + 13 using 9 and two other addends? Find the sum and explain your answer.

4. Use two different addends to write a problem that has the same sum as 9 + 13. Explain your answer.

E 8∙1


Enrichment

8-2Name

Code Breakers ClubAlan and Trudy love to solve puzzles and write coded messages. Together they created the following problems for others to solve. If you can solve all four problems, you can join their Code Breakers Club!

1. What are the next three letters in this pattern? Write them in the space provided.

ABC XYZ DEF UVW GHI

2. What are the next four numbers in this pattern? Fill in the diamond shapes.

3 5 8 12

3. What set of 3 shapes will complete this pattern? Draw or write your answer.

4. In the following message the numbers 1–26 have been substituted for the letters A–Z (e.g., 1 = A, 2 = B, etc.). What does the 4-word message say?

9 12-15-22-5 19-5-3-18-5-20 3-15-4-5-19!

E 8∙2


Enrichment

8-3Name

And the Answer Is?1. If 569 rounds to 570, what is the

rounding place?

2. When this 3-digit number is rounded to the nearest ten, the sum of its digits is 16. The hundreds digit of this number is 8 and the ones digit is 5. What is the number?

3. When this 3-digit number is rounded to the nearest ten, it rounds to 350. The number is less than 360 and greater than 350. The ones digit is an even number that you count after 2. What is the number?

4. When this 3-digit number is rounded to the nearest hundred, it rounds to 200. Rounded to the nearest ten, this number rounds to 200. The sum of the digits of this number is 19. What is the number?

5. When this 3-digit number is rounded to the nearest ten or hundred, the number rounds up. All of the digits in this number are the same. The sum of the digits is 15. What is the number?

6. When this 3-digit number is rounded to the nearest hundred, it rounds up to 500. The hundreds digit is less than 6. The digits in the tens and ones place add to a sum of 10 and they are the same. What is the number?

7. When this 3-digit number is rounded to the nearest hundred it rounds down to 600. The digit in the ones place is the third odd number that you count beginning with 1. The sum of the digits is 13. What is the number?

E 8∙3


Enrichment

8-4Name

Break It Up and Add1. Which choice helps the most to solve 243 + 18?

A Think of 18 as 9 + 9.

B Think of 243 as 244 − 1.

C Think of 18 as 20 − 2.

Explain.

243 + 18 =

2. Which choice helps the most to solve 357 + 239?

A Think of 357 as 353 + 4.

B Think of 239 as 240 − 1.

C Think of 239 as 235 + 4.

Explain.

357 + 239 =

3. Which choice does NOT help you solve 463 + 328 using mental math?

A Think of 463 as 460 + 3.

B Think of 328 as 330 − 2.

C Think of 328 as 325 + 3.

Explain.

463 + 328 =

E 8∙4


Enrichment

8-5Name

Find DifferencesUse mental math to subtract. Then write each number sentence in the correct box below.

162 − 49 =

162 − 152 =

343 − 311 =

562 − 247 =

462 − 248 =

243 − 130 =

562 − 541 =

643 − 622 =

843 − 528 =

762 − 730 =

943 − 729 =

243 − 233 =

− =

− =

− =

− =

− =

− =

− =

− =

− =

− =

− =

− =

Difference of 10

Difference of 113

Difference of 21

Difference of 214

Difference of 32

Difference of 315

Reason Write 6 different subtraction sentences that will fit in each of the boxes above. Use only 3-digit numbers.

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Vocabulary


Name Reteach to Build Understanding

8-1

1. The Commutative (Order) Property of Addition states that you can add numbers in any order and the sum will be the same.

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+

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=

TX POD Trans K-01cA

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TX POD Trans K-01cA

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TX POD Trans K-01cA

3 + 4 = 7

TX POD Trans K-01cA

TX POD Trans K-01cA

TX POD Trans K-01cA

TX POD Trans K-01cA

+

TX POD Trans K-01cA

TX POD Trans K-01cA

TX POD Trans K-01cA

=

TX POD Trans K-01cA

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+ =

2. The Associative (Grouping) Property of Addition states that you can group numbers in any way and the sum will be the same.

=

(4 + 2) + 1 = 4 + ( + )

3. The Identity (Zero) Property of Addition states that the sum of any number and zero equals that same number.

5 + =

4. Draw pictures to complete the model of the Commutative Property of Addition. Complete the equation.

+ = 5 + 3 = 8

+ =

3 + =

On the Back!

5. Draw a picture that shows the Associative Property of Addition. Use 9 objects, 6 objects, and 4 objects in your picture. Include equations for the picture.

R 8•1

Vocabulary



8-2

1. An even number can be shown as two equal groups or as doubles. Circle all the examples of even numbers.

6 + 7 8 + 8 24 107

2. An odd number cannot be shown as two equal groups or as doubles. Circle all the examples of odd numbers.

2 + 2 3 + 2 28 19

When you add even and odd numbers, you can see patterns.

3. An even number plus an even number has an even sum.

+ =

4. An number plus an number has an sum.

+ =

On the Back!

5. Describe a pattern shown by the sums that are shaded. Explain why the pattern is true.

+ 0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 10

2 2 3 4 5 6 7 8 9 10 11

3 3 4 5 6 7 8 9 10 11 12

4 4 5 6 7 8 9 10 11 12 13

5 5 6 7 8 9 10 11 12 13 14

R 8•2

Vocabulary



8-3

1. Place value is the value of the place a digit has in a number. Use the number 753. Write the digit in each place value.

7 is in the hundreds place. It has a value of 700.

is in the tens place. It has a value of 50.

is in the ones place. It has a value of .

2. When you round a number, you find another number that is close to your number. Look at the digit to the right of the place you are rounding. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the digit alone. Change digits to the right of the rounding place to 0.

Round 549 to the nearest ten and hundred.

is in the ones place. So, the tens digit rounds up to .

549 rounded to the nearest ten is .

is in the tens place. So, the hundreds digit stays the same.

549 rounded to the nearest hundred is .

You can use a number line and what you know about place value to help round numbers.

3. Round 487 to the nearest ten.

481 482 483 484 485480 490486 487 488 489

Between which two multiples of ten is 487 located? 480 and

Is 487 closer to 480 or to 490? 487 rounds to .

4. Round 487 to the nearest hundred.

420 430 440 450 460400 500470 480 490410

Between which two multiples of one hundred is 487 located? and

487 is closer to . 487 rounds to .

On the Back!

5. Draw number lines to round 445 to the nearest ten and to the nearest hundred.

R 8•3

Vocabulary



8-4

1. When you use mental math to find 24 + 17, you do not need paper and pencil. You can use place value to break apart the addends into tens and ones.

tens ones24 = 20 + 4

17 = +

Add the tens: 20 + 10 = Add the ones: 4 + 7 =

Add the sums of the tens and ones: + =

So, 24 + 17 = .

2. You can break apart numbers to make them easier to add mentally.

Find 336 + 142 by breaking apart the addends into hundreds, tens, and ones.

hundreds tens ones

336 = 300 + +

142 = + +

Add the hundreds: + =

Add the tens: + =

Add the ones: + =

Add the sums: + + =

3. Find 517 + 238 by breaking apart numbers to make a ten.

Break 238 into 200 + 35 + .

Add 3 to 517 to make a ten.

517 + 3 = Add 200 to 520. 520 + 200 = Add 35 to 720. 720 + 35 = So, 517 + 238 = .

On the Back!

4. Use mental math to find 129 + 436. Write the steps you used.

R 8•4

Vocabulary



8-5

1. The difference is the answer when subtracting two numbers.

Look at the problem 45 - 10 = 35.

The difference is .

2. Use mental math to find 356 - 128.

Make a simpler problem by changing each number in the same way. If you add the same amount to each number, it does not change the difference.

Look at the number being subtracted. Change 128 to 130 because it is easier to subtract 130. Add 2 to both 128 and 356.

356 + 2 =

128 + 2 =

Now subtract: 358 - 130 =

So, 356 - 128 = .

3. Find 453 - 196 using mental math.

It is easier to subtract 200.

453 - 200 =

If you subtract 200, you subtract 4 more than 196. You must add 4 to the answer.

253 + 4 =

So, 453 - 196 = .

On the Back!

4. Use mental math to find 651 - 328. Write the steps you used.

R 8•5

name 8-1 add it up...find 517 + 238 by breaking apart numbers to make a ten. break 238 into 200 + 35...

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