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Grade 5 MathNumeracy: Text Chapter 2

Standard Form

All numbers with spaces between periods (groups of 3 starting at place value 1)Large whole numbers are arranged in groups of three digits

called periods.No commas used

i.e. 294 056 783

Word Form

A whole number might be spoken aloud, in its word form.

Starting from the ones place at the far right, each three-digit place value group makes up a period—ones, thousands, millions, billions, and so on

For example, the number 201 536 794 is read, “two hundred one million, five hundred thirty-six thousand, seven hundred ninety-four.”

Place Value Chart

The digits used to write a number in standard form take their proper positions in the number according to a system of writing numbers called the decimal (or base ten) system, wherein every position, or place has a corresponding and specific place value.

The number 679 935 500 and 0.00049 are shown as an example of how to fill in the place value chart with a specific whole number or decimal number.

Decimals

A Decimal Number (based on the number 10) contains a Decimal Point.

It is all about Place Value !

As we move right of the ones place value, each position is 10 times smaller. We can continue with smaller

and smaller values, from tenths, to

hundredths, and so on, like in this example:

Expanded Form

The expanded form of a number breaks it down and calls attention to its parts by presenting the number as the total of its digits’ values. For example, the expanded form of the number 63 279 can be figured out by:

6 ten-thousands + 3 thousands + 2 hundreds + 7 tens + 9 ones

to (6 x 10 000) + (3 x 1 000) + (2 x 100) + (7 x 10) + (9 x 1)

and finally to the simple form of 60 000 + 3 000 + 200 + 70 + 9

Base Ten Diagram

We can use models, diagrams, or sketches to represent a number. The Base Ten diagrams offer a simple way to represent numbers visually.

For example the number 46 213 can be modeled by: = 10 000

= 1 000

= 100

= 10 = 1

Small Group Activity

Come up with a group consensus on a number that represents the distance from Earth to the Moon in km.

Use the following numbers to make the largest number possible starting with 3, “3,0,4,4,8,0”.

Small Group Activity

Use the following numbers to make the largest number possible starting with 3, “3,0,4,4,8,0”.

It’s 384 400 km

Label this number in your notes in Standard Form, Word Form, and Expanded Form

Small Group Activity

Standard Form - 384 400 km

Label this number in your notes in Standard Form, Word Form, and Expanded Form

Word Form – Three hundred eighty four thousand, four hundred km

Expanded Form – 300 000 + 80 000 + 4 000 + 400 km

Small Group Activity

Work with your group to come up with four different ways to represent this Standard Form number: 892 851.

Be sure to Label and Record all Five ways in your own math notes. (the first way is Standard Form)

Group Discussion

How many $1000 bills are in 100 thousand dollars?

How many $100s in $100 000?

How many $10 in $100 000?

How many $1 in $100 000?

How is our system of money like base 10 blocks?

100

1 000

10 000

100 000

Our currency units gets bigger or smaller in multiples of ten.

Rounding Numbers

A rounded number has about the same value as the number you start with, but it is less exact.

For example, 341 rounded to the nearest hundred is 300. That is because 341 is closer in value to 300 than to 400. When rounding off to the nearest dollar, $1.89 becomes $2.00, because $1.89 is closer to $2.00 than to $1.00

Here's the general rule for rounding:• If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Example: 38 rounded to the nearest ten is 40• If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Example: 33 rounded to the nearest ten is 30

4 827 rounded to the nearest ten is 4 830 . . But . . 4 827 rounded to the nearest hundred is 4 800

1 951 rounded to the nearest thousand is 2 000 (watch the ripple effect when rounding numbers to 0)

Number Lines

You can use a number line to compare two numbers. This will allow you to tell if a number is larger or smaller than another number, based on their placement on the line.

Rounding Numbers

pg50 Population of Saskatoon, rounding, and number line.

NOTE: As of December 2014, it is the largest city in the province with an estimated population of 257 300 and an estimated metropolitan area population of 300 634.

Class Discussion

pg50 Population of Saskatoon, rounding, and number line.

NOTE: As of December 2014, it is the largest city in the province with an estimated population of 257 300 and an estimated metropolitan area population of 300 634.

Using Place Value to Compare Large Numbers

When comparing two or more numbers, it is important to consider place value.

Step one: Look at the place value. Identify the ones place in each number.

Step two: Arrange the numbers in vertical (that's one on top of the other) form. Line up the number by place values, starting with the one's place.

Step three: Begin at the greatest place value (furthest to the left). Find where the digits are different and compare the whole numbers using the greater than (>) or less than (<) sign.

OK, let's take an example step-by-step

Step one: ID your purpose –fill in blank with the correct sign: <, >, or =. 8 239 489 _____ 8 238 470

Step two: Arrange the numbers one on top of the other, lining them up by place values, starting with the one's place. (This one is easy because both numbers have 7 places.)

8 2 3 9 4 8 9

8 2 3 8 4 7 0

Step three: Begin at the greatest place value (furthest to the left). Find where the digits are different and compare.

Same, same, same, different. (Don’t need to look any further since you have already found the largest place that differs.

Step four: Compare the different digits (1000s place value). . . and since 9 > 8 (or really 9 000 > 8 000): 8 239 489 > 8 238 470

Odering Large Numbers

Sometimes it is important to put a list of numbers in descending (going down) or ascending (going up) order. But it is easy, because you can use the same rules that you used for comparing numbers!

Let's try one! Put the these numbers in order, from largest to smallest.

8 567 905 8 568 890 7 899 999

You can consider place value when vertically arranging numbers

Once the numbers are arranged you can think about >, <, or =. Make sure to write the numbers in the order that was asked for;

was it smallest to greatest or greatest to smallest?

Answer

So the correct order from largest to smallest is:

8 568 890 > 8 567 905 > 7 899 999

Practice and find out what you Know

Chapter 2 Text Questions:

pg42 #1,2b,3a,9,10;

pg46 #1,3,4,7b;

pg51 #1

Quiz on September ______, 2015

For more practice try the following website

http://www.thatquiz.org/tq/practice.html?placevalue

Change the level to 5 and practice Place Value Identification and Rounding.

Practice and Find out What you Know

Test Review pg54 #1-4; pg75 #1-4

All questions due __________________ . Be prepared to identify those questions giving you trouble so we can review as a class.

Test Date: ________________________________.