Whole Numbers

Adding & Subtracting Group #1 Copyright © Ed2Net Learning, Inc.

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Warm-up

 What is the next number in the pattern?

 3,7,11,15, 19  16 - 4 + 2 - 10 = 4  Insert <, >, or =  22 – 7 = 10 + 5  6 + 23 > 33 -5 Copyright © Ed2Net Learning, Inc.

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Notation and Place Value



Place Value

helps you better understand the Whole Numbers (0,1,2,3,4,5,6,7,8,9..)  To determine the

value

of each

digit

number, we need to look at its number.

place

in the in the Copyright © Ed2Net Learning, Inc.

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Notation and Place Value

 Here is the place value chart to the

billions

place.

  , , Fill in the number 34,567,129 , Which number is in the ten thousands place? 6 Notice the commas separating every three digit Copyright © Ed2Net Learning, Inc.

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Let’s look at the number 37,264,908

 Which number is in the

millions

place? 7  Which number is in the

hundreds

place? 9  Which number is in the

tens millions

place? 3  Which number is in the

thousands

place? 4 Copyright © Ed2Net Learning, Inc.

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Different ways to write numbers

 Standard Form: 423  Expanded Form: 400 + 20 + 3  Word Form: Four hundred twenty three Copyright © Ed2Net Learning, Inc.

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Let’s look at the number 1,734

 This number is written in standard form  Can you write this number for me in

word form

? One thousand seven hundreds thirty four  Can you write this number for me in

expanded form

? 1000 + 700 + 30 + 4 Copyright © Ed2Net Learning, Inc.

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Comparing & Ordering

  We compare numbers using

Place Value

When we compare two numbers, we start from left to right. It is necessary to find the first place where the digits are different.

  Step 1: Begin at the greatest place. Find where the digits are different.

Step 2: Compare the digits that are different. Write > or <.

 Example: Compare 3,567 and 3,576  Step 1: 3,5 6 7 Step 2: 3,5 7 6 3,5 6 7 3,5 7 6 Same Different 7 hundreds > 6 hundreds So, 3,576 > 3,567 Copyright © Ed2Net Learning, Inc.

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Comparing & Ordering

 Many times there are more than 2 numbers that we want to compare. We can

order

the numbers by placing them in an order from

least to greatest

or

greatest to least

 We must compare two at a time.

Copyright © Ed2Net Learning, Inc.

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Comparing & Ordering

 Let’s order these numbers from

Least to Greatest

3,670 3,607 3,076 3,706

Remember to start with 2 at a time

 Be careful when reading the instructions! Are they asking for the smallest or the biggest? Are they asking you to order the numbers from least to greatest or greatest to least?

Copyright © Ed2Net Learning, Inc.

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Estimate

 When we

estimate

, we find a number that is close to the exact number.

 Let us estimate the sum of 198 + 104  198 is close to 200  104 is close to 100  300 is an

estimate

of the sum Copyright © Ed2Net Learning, Inc.

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Try This!

 1.

Estimate each sum: 93 + 54 = 90 + 50 = 140 2.

487 + 519 = 500 + 500 = 1,000 3.

26 + 197 = 30 + 200 = 230 Copyright © Ed2Net Learning, Inc.

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Rounding



Rounding

is one of the ways we estimate  We can use place value to round  Let’s round 2,345 to the nearest thousands place.

 Step 1: We need to underline the thousands place. 2,345 Copyright © Ed2Net Learning, Inc.

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Rounding

 Step 2: We need to look at the digit just to the right of the underlined digit. 2,345   If that digit is 5 or more, we increase the underlined digit by 1.

If that digit is 4 or less, we do not change the underlined digit.

 Since this digit is 4, we do not change the the digit 2 Copyright © Ed2Net Learning, Inc.

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Rounding

 Step 3: We change all the digits to the right of the underline digit to 0.

 2,345 rounds to 2,000 Copyright © Ed2Net Learning, Inc.

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Try This!

1.

Round 2,456 to the nearest tens place. 2,460 2.

Round 836 to the nearest hundreds place. 800 3.

Round 34,185 to the nearest thousands place. 34,000 Copyright © Ed2Net Learning, Inc.

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Addition of Multi-Digit Numbers

    There are several properties of addition

Commutative Property

 We can change the order and the sum stays the same.

  4 + 6 = 10 6 + 4 = 10

Associative Property

 We can change the grouping and the sum stays the same.

  2 + (3 + 8) = 13 (2 + 3) + 8 = 13

Identity Property

 We can add zero and the sum stays the same.

 7 + 0 = 7 Copyright © Ed2Net Learning, Inc.

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Try This!

 Use the commutative property of addition to complete this problem  34 + 56 = 56 + 34  Use the associative property of addition to complete this problem  47 + (94 + 25) = (47 + 94) + 25 Copyright © Ed2Net Learning, Inc.

.

Where do you put the parentheses ?

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Try This!

 Use the identity property of addition to complete the problem.

 7,984 + 0 = 7,984 Copyright © Ed2Net Learning, Inc.

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Addition of Multi-Digit Numbers

 Step 1: We add numbers together by first lining up the digits  Step 2: Then we need to determine if we must regroup.

 1 197 +35 232 7 + 5 = 12 so we must regroup 12 ones as 1 ten and 2 ones Copyright © Ed2Net Learning, Inc.

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Try This!

 673 + 87 760  759 +682 1,441 Copyright © Ed2Net Learning, Inc.

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Subtraction of Multi-Digit Numbers

 13 – 0 =13  If we subtract zero from any number the difference is that number  57 – 57 = 0  If we subtract a number from itself, the difference is 0 Copyright © Ed2Net Learning, Inc.

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Subtraction

 Subtraction is similar to addition  We need to line up digits  Often we need to regroup Copyright © Ed2Net Learning, Inc.

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Subtraction

 Remember that subtraction begins from the top number and starts in the ones place.

 27 - 5 It’s 7 minus 5  If the problem is written horizontally 156 – 78  The top number is the number to the left of the subtraction sign Copyright © Ed2Net Learning, Inc.

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Subtraction

 We begin by subtracting the ones.

  If the top number is smaller than the bottom number, we have to regroup.

23 -17 1 23 13 - 17 6 Copyright © Ed2Net Learning, Inc.

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Try This!

 532 -278 254  3,254 - 367 2,887 Copyright © Ed2Net Learning, Inc.

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Assessment

1.

2.

3.

4.

5.

6.

7.

Write 23,654 in word form. Twenty three thousands, six hundreds fifty four Write the place value of the underlined digit; 546,981 500,000 Which number is smaller, 67,987,024 or 67,987,042 ? 67,987,024 What does the word “estimate” mean? Can you give me an example? 99 When we estimate we find a number that is close to the exact number; 100 is an estimate of Round 5,632 to the nearest hundreds place. 5,600 Round 1,287,583 to the nearest ten thousands place. 1,290,000 Order this set of data from least to greatest: 134 143 157 107 140 107, 134, 140, 143, 157 Copyright © Ed2Net Learning, Inc.

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Assessment

7.

8.

9.

10.

11.

Use the commutative property of addition to complete the problem 134 + 58 = 58 + 134 Use the associative property of addition to complete the problem 148 + (92 + 302) = (148 + 92) + 302 Find the sum 1,473 + 698 = 2,171 Find the difference 23,064 – 12,635 = 10,429 The town where Henry lives has a population of 3,782 people. During the last two years, 319 people have moved into town. About how many people lived in Henry’s town two years ago? The number 3,782 rounded to the nearest hundred is 3,800. The number 319 rounded to the nearest hundred is 300. The number sentence 3,800 – 300 = 3,500 shows about how many people lived in Henry’s town two years ago. The population of Henry’s town two years ago was about 3,500 people.

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You did a great job today!

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