UN I TWhole Numbers - Weebly

[Pages:52]U N I T Whole Numbers

Learning Goals

? recognize and read numbers from 1 to 999 999

? read and write numbers in standard form, expanded form, and written form

? compare and order numbers ? use place value to represent

numbers ? recall basic multiplication and

division facts ? count by 11s and 12s ? estimate sums, differences,

products, and quotients ? add, subtract, and multiply

numbers mentally ? add and subtract 4-digit numbers ? multiply a 2-digit number

by a 2-digit number ? divide a 4-digit number

by a 1-digit number ? pose and solve problems using

whole numbers ? solve problems with more than

one step

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Key Words

compensation dividend divisor quotient compatible numbers

? Hay is one part of a dairy cow's diet. 140 kg of hay feeds 2 cows for 2 weeks. About how much hay do 2 cows eat each week? Each day?

? The Colyns have 30 dairy cows on their farm. Each day, they collect 27 L of milk from 1 cow. Estimate the amount of milk produced by 30 cows.

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LESSON

Representing, Comparing, and Ordering Numbers

Here are some ways to represent the number 4027.

Standard Form 4027

Words four thousand twenty-seven

Base Ten Blocks

Expanded Form 4000 + 20 + 7

Place-Value Chart Thousands 4

Hundreds 0

Tens 2

Ones 7

The heat of chili peppers is measured in Scoville units. The greater the number of Scoville units, the hotter the pepper.

Danielle tested several types of peppers. Her results are shown in the table.

Which pepper is the hottest? The mildest? Order the peppers from mildest to hottest.

Pepper Cayenne Jalapeno Ancho Tabasco Habanero Chipotle

Scoville Units 47 400 4960 2358 43 340 103 050 91 880

Show and Share

Share your results with another pair of students. What strategies did you use to compare and order the numbers?

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LESSON FOCUS Represent, compare, and order numbers to 999 999.

The table shows the population of some Canadian cities in 2001.

City

St. John's, NL Halifax, NS Quebec, QC Winnipeg, MB Edmonton, AB Vancouver, BC

Population

99 182 359 111 169 076 619 544 666 104 545 671

Order the numbers from greatest to least. Use a place-value chart.

Thousands

Units

City

Hundred

Ten

One

Hundreds Tens

Thousands Thousands Thousands

St. John's, NL

9

9

Halifax, NS

3

5

9

Quebec, QC

1

6

9

Winnipeg, MB

6

1

9

Edmonton, AB

6

6

6

Vancouver, BC

5

4

5

1

8

1

1

0

7

5

4

1

0

6

7

Ones

2 1 6 4 4 1

666 104 has the most hundred thousands and ten thousands.

It is the greatest number.

99 182 has no hundred thousands.

It is the least number.

The order of the numbers from greatest to least is: 666 104, 619 544, 545 671, 359 111, 169 076, 99 182

When we write numbers with more than 4 digits in standard form, we put a space between the hundreds digit and the thousands digit.

Edmonton has a population of 666 104. We can write this in expanded form: 600 000 + 60 000 + 6000 + 100 + 4 and in words: six hundred sixty-six thousand one hundred four

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1. Write each number in standard form. a) 600 000 + 20 000 + 50 + 7 b) nine hundred fifty thousand six

2. Order the numbers from least to greatest. 421 035 406 583 423 004 40 795

3. Write each number in question 2 in expanded form and in words.

4. Copy and complete. Replace each with >, < , or =.

How did you decide which symbol to use?

a) 35 937 35 397

b) 272 456 227 456

c) 456 123 456 123

d) 975 346 985 346

5. Mariette wrote a 6-digit number. One digit was 0. The other digits were odd. No two digits were the same. The number was the greatest number she could write with these digits. What number did Mariette write? How do you know?

6. The digits in 234 567 are in order from least to greatest. Write 5 different 6-digit numbers with their digits in order from least to greatest.

7. Use the digits from 1 to 9. Use each digit only once.

a) Make a 6-digit number as close to 100 000 as possible.

b) Make a 6-digit number as close to 500 000 as possible.

c) Which number did you get closest to?

How do you know?

Numbers Every Day

Denis said 84 914 is greater than 311 902 because 8 is greater than 3. Is Denis correct? Use words and numbers to explain.

Number Strategies

Copy and complete each pattern. What is each pattern rule?

94, 86, 78, 70, 48, 56, 64, 72, 212, , 196, 188 89, , 105, 113

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ASSESSMENT FOCUS Question 7

LESSON

Using Mental Math to Add

Workers at the Portage Bicycle Factory make mountain bikes and racing bikes. Last week, they made 2343 mountain bikes and 1998 racing bikes.

About how many bikes were made altogether? Find the total number of bikes that were made. Record your estimate and your sum. How close was your estimate to the sum?

Show and Share

Share your work with a classmate. Describe and compare the strategies you used to estimate and to find the total number of bikes.

Estimate the sum: 3438 + 4279

Use front-end estimation. Add the first digits of the numbers. 3438 + 4279 is about 3000 + 4000, or 7000.

For a better estimate, round each number to the nearest hundred. 3438 rounded to the nearest hundred is 3400. 4279 rounded to the nearest hundred is 4300. 3400 + 4300 = 7700

3438 + 4279 is about 7700.

I estimate when I don't need an exact answer. There are many ways

to estimate.

LESSON FOCUS Use different mental math strategies to add whole numbers.

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 Use mental math to add: 2180 + 6432 Use compensation. 2180 + 20 = 2200 6432 ? 20 = 6412 The sum of 2200 + 6412 is equal to the sum of 2180 + 6432. 2200 + 6412 = 8612

2180 + 6432 = 8612

Use mental math to add: 2625 + 432 Use the strategy of adding on.

Start with the greater number, 2625. There are 4 hundreds to add. Count on by 100 four times:

2625 2725 2825 2925 3025

100 100 100 100

There are 3 tens to add. Count on by 10 three times:

3025 3035 3045 3055

10 10 10

Then add 2: 3055 + 2 = 3057

2625 + 432 = 3057

To compensate, I took 20 away from 6432 and added it to 2180.

2625 + 400 + 30 + 2

Use mental math.

1. Add. Use as many different strategies as you can.

a) 6145 + 3007 b) 3654 + 372

c) 500 + 2150

d) 1999 + 999

e) 4003 + 2968 f) 7741 + 685

2. Find the sums less than 10 000. a) 3099 + 5824 b) 6489 + 3201 d) 9997 + 8763 e) 5036 + 297

c) 4673 + 6595 f) 9539 + 470

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3. Natalie's school gave a concert last week. On Friday, 4560 people attended. On Saturday, 2995 people attended. How many people attended the concert in all?

4. Victoria shows her friends a number trick. She says: ? Pick any 4-digit number. Don't tell me what it is. ? Add 498 to the number. ? Subtract 202 from the sum. ? Add 204 to the difference. ? Tell me what number you have now. ? The number you picked is . Victoria subtracts 500 from the number she is told. This always gives her the original number.

Why does this trick work? Use words and numbers to explain.

5. A blueberry pie has 2285 calories. A cherry pie has 2465 calories. About how many calories are in both pies altogether?

6. Write an addition problem you can solve using mental math. Solve your problem. Which strategy did you use to solve your problem? Why?

Describe 2 different ways you could mentally add 4621 + 5393.

ASSESSMENT FOCUS Question 4

Numbers Every Day

Number Strategies Round each number to the nearest ten, the nearest hundred,

and the nearest thousand. ? 6493 ? 7989 ? 5091 ? 8996 ? 3003

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