A Place Value Study Guide for Grade 5s

A Place Value Study Guide

Michael A Chan - CHAMP 7

MICHAEL CHAN BOOKS PUBLICATIONS

Getting to know the world

1

A Place Value Study Guide

MICHAEL CHAN BOOKS PUBLICATIONS

Michael A Chan - CHAMP 7

Getting To Know The World

Place Value Information

ii

© 2012 Michael Chan Books Publishing

This book is made for Grade 5s to understand place value.

In school, we are learning about place value. This is a study guide for students who need help with place value. Our summative assessment was to make a study guide so I am here to help you.

This math unit’s central idea is “Using place value to organize the counting, ordering and the interpretation of number helps us to understand relationships between quantities”.

Our lines of inquiry are:

Without a place value system numbers have no meaning (causation)

Understanding the base 10 place value system allows us to perform number operations (connection)

Numbers can be represented in different forms (change)

The number line goes on infinitely in both directions and can be used to show integers (function)

I hope this guide will help you to improve your knowledge in place value and get a good grade in Grade 6.

- Champ 7

Learning About Place Value - The First Math Unit in Grade 6

PLACE VALUE

3

CHAPTER 1

Thinking About

IntegersThis chapter will guide students about basic things

about integers.

Learning About Place Value

Integers

5

Here is a part of a mind map about integers. On the next 4 pages there will be more explanations about each topic shown on the left. I hope you learn some more information about integers!

This section of the mind map shows some information about what integers are. This section is mainly for beginners in this type of math.

Integers are whole numbers, no matter whether the number is positive or negative. They cannot be a fraction, a decimal or a percentage, which results in a fraction or decimal. 0 is also an integer. This is what integers are.

This section explains how integers are connected to out unit. Integers are obviously connected to place value, as they are whole numbers. Integers are the most basic type of number. All numbers without a decimal point or a fraction is an integer. Integers also help measuring the absolute value. Without integers, the place value system will have not much meaning.

Learning About Place Value

Integers

6

Here is an introduction to positive integers. All positive integers are whole numbers larger than the number 0. Positive integers are automatically the absolute value. There is an infinite number of positive integers. You can go on and on and on and it’ll never stop.

Here is an introduction to negative integers. All negative integers are whole numbers smaller than the number 0. The negative integers’s absolute value, unlike positive integers, is the number but without the minus sign. The negative

integers, just like the positive integers have an infinite amount.

Learning About Place Value

Integers

7

We are now going more deeply into integers. Why do we need to learn them? What does the central idea mean? How do these relate to the lines of inquiry? Well, first we’re going to look at real situations when you need to use your math skills with integers. Time is an especially good one, when you need to make sure you answer math questions right in school and meet the time limit.

Sometimes, money can be important to as you have to count how much money you’ve spent and measure how much money you still have in the bank. Moving on, we’re going to talk about absolute value. The absolute

value of a positive number is just the number. The absolute value of a negative number is the numeral without the sign. It’s just really how far away one number is away from zero.

Learning About Place Value

Integers

8

I am now going to explain some fascinating facts about integers that you should know for the future. This includes: Every positive integer has a corresponding negative integer, there is an infinite quantity of integers, subtracting a negative integer is the same as adding a positive integer, two positive integers or two negative integers multiplied together always result in a positive integer.

At the bottom, there are some common rules that you should always need to know when using negative numbers and positive numbers in the same equation. These are - plus a - equals a +, + plus a - or - plus a + equals a -, + plus a + equals +, etc. If you see this equation (-5) + (-9) = ?, just ignore the brackets and you’ll get the answer.

Learning About Place Value

Integers

9

Chapter 2

Going Deeper Into Place Value

This chapter will clearly explain what place value is and some vocabulary.

About Place Value: Before, numbers never meant anything at all. Only when the “Base 10 Place Value System” was invented in India, numbers were then understood and can be used. This relates to 2 lines of inquiry - Without a place value system numbers have no meaning (causation) and understanding the base 10 place value system allows us to perform number operations (connection).

We all know what place value is - how much a digit is worth depending on where the digit is in the number. Since all of you should know what place value is anyways, we can now know how to perform number operations (addition, subtraction, multiplication and division).

Learning More About Place Value

Place Value

11

This section teaches students parts of the number. The numbers can go on infinitely in both directions but these are the more basic ones that you should know. Be sure to remember these!!!

Learning About Place Value

Place Value

12

Here are some links that go to websites to play games about place value. Hope you enjoy!

http://mrnussbaum.com/placevaluepirates1/ (recommended)

http://education.jlab.org/placevalue/

http://www.free-training-tutorial.com/place-value-games.html (recommended)

http://www.math-play.com/Middle-School-Math-Games.html (recommended)

http://www.toonuniversity.com/flash.asp?err=503&engine=15

http://www.funbrain.com/ofm/index.html

http://www.learningbox.com/Base10/BaseTen.html

http://www.dositey.com/2008/addsub/Mystery10.htm

http://www.quia.com/rr/32598.html

http://www.learningbox.com/Base10/CatchTen.html (recommended)

Learning About Place Value

Place Value Games

13

Chapter 3

Negative Numbers

This chapter will guide children on how to perform operations with negative numbers.

Here are the two signs that determine the operation. When you read the rules again that you have read in Chapter 1, you will understand it better. Here they are: - plus a - equals a +, + plus a - or - plus a + equals a -, + plus a + equals +.

So, if we follow the example on the left, the two operations that determine the operation are both minus signs, which according to the rules above, mean plus. So, we can simplify the operation like this= 3+5. This is a really easy question as the answer is really positive 8. These rules are really important

to know so you can understand how to do the operations addition and subtraction clearly. Please remember that this is only for the operations addition and subtraction!

Learning About Place Value

What do you mean by two plus signs or two minus signs?

15

Here is an explanation of how to use negative numbers in operations with multiplication and division. First for multiplication, you have to see the signs of both the operations. These come in affect with the common rules for multiplication. If you have two negative numbers like in the example, you take them both away and do 3 x 5 which is positive 15 and that’s your answer. But if you have one positive and one negative, it goes backwards on the number line, decreasing the value of the number. So if you had -6 x 4, the answer would be -24. So basically it is the two numerals multiplied together with a negative sign. If you had two positives - you know this already - it would end up as a positive number. So the rules are positive multiplied by positive equals a positive, negative multiplied by a positive equals a negative and a negative multiplied by a negative is a positive. The rules for multiplying negative numbers are the same as dividing negative numbers, you just change the sign. So if you look at the example on the left, the answer would be 5 because the two number are negatives and negatives divided by another negative

equals a positive and 25 ÷ 5= 5. P.S. You need to know your multiplication tables well in order to do this.

Learning About Place Value

The Next Operations

16

P + P= P

P + N= P/N (It depends how big each number is)

N + P= P/N (It depends how big each number is)

N + N= N

P - P= P/0/N (It depends how big each number is)

P - N= P

N - P= N

N - N= N/P (It depends how big each number is)

P x N= N

P x P= P

N x N= P

N x P= N

P ÷ N= N

P ÷ P= P

N ÷ N= P

N ÷ P= N

Learning About Place Value

If you still don’t understand the rules...

17

Legend: P = Positive

N = Negative

Here are some questions that you should answer to exercise your brain on negative numbers.

1) -8 x 9=

2) (-2) + (-6)=

3) (-17) - (-135)=

4) (-3) + 6=

5) (-100) ÷ (-50)=

6) 47 x -974=

7) (-14) + (+2738904)=

8) 4162889 - (-8941)=

9) (-531) - (-512)=

10) (-129) + (169)=

11) 167 - (-1672)=

12) (-189) + (-716)=

13) (-45) ÷ (-5)=

14) (-12) ÷ (+6) =

Learning About Place Value

Challenging Your Brain

18

If you can do these quickly and accurately, you’ve met the Grade 6 requirement in

negative numbers.

Check your answers!

1) -8 x 9= -72

2) (-2) + (-6)= -8

3) (-17) - (-135)= 118

4) (-3) + 6= 3

5) (-100) ÷ (-50)= 2

6) -47 x -974= 45778

7) (-14) + (+2738904)= 2738890

8) 4162889 - (-8941)= 4171830

9) (-531) - (-512)= -19

10) (-129) + (169)= 40

11) 167 - (-1672)= 1839

12) (-189) + (-716)= -905

13) (-45) ÷ (-5)= 9

14) (-12) ÷ (+6) = -2

Learning About Place Value

Answers

19

Below is a list of people who use negatives in regular life, this is why you should know negatives so that you can be successful in not only tests but in your job when you grow up.

- Weather Channels

- Stock Markets

- Temperature Checkers

- Teachers

- Students

- Engineers

- Authors

- Computer Programmers

- Mathematicians

- People with Jobs and

- More...

Learning About Place Value

Who Uses Negatives?

20

Chapter 4

A Math Glossary

This chapter allows you to know some words that you must know to learn math about place value.

Learning About Place Value

Understanding Important Words

22

Absolute Value- The absolute value of a number is just the numeral, the distance of the number from zero.

Addition- Joining two numbers/quantities together.

Algebra- A part of math where numbers are expressed by letters.

Base Ten System- An Indian number system based on ten.

Counting- Finding the number of something.

Counting Number- A whole number from a range of 1 to infinity.

Decimal- An object that separates the whole number from the fraction of the whole number.

Difference- The difference between numbers. You use subtraction to find answer.

Division- Dividing numbers into groups.

Exponents- Small numbers placed at the top right corner of the number to tell you how many times that number is multiplied by itself.

Hundred- Ten tens is a hundred.

Hundredths- Hundredths is the second digit past the decimal point.

Infinite- Will go on forever, unlimited.

Integer- A number that is not a decimal number or a fraction.

Interpret- To guess the answer of something, similar to estimate.

Learning About Place Value

Understanding Important Words

23

Millions- Ten hundred thousands.

Millionths- The sixth digit after the decimal point.

Multiplication- Multiplying numbers.

Negative Number- Any number that is below zero. It is shown as it has a minus sign before the number.

Number Line- The line with numbers to help with operations with numbers.

Numbers- Figures that show you how many of something there is, etc.

Ordering- An arrangement according to size.

Operations- Addition, Subtraction, Multiplication and Division

Percentages- The number presented if it was out of 100.

Place Value- The value of a digit which depends where it is in the number.

Positive Number- A number more than zero.

Product- The result after doing multiplication.

Quantity- The amount of something.

Quotient- The result after doing division.

Relationship- How two numbers are related.

Subtraction- To take away a quantity from a number.

Learning About Place Value

Understanding Important Words

24

Sum- The result of two numbers being added together.

Ten- Ten units/ones together.

Tenths- The number right after the decimal point.

Thousands- Thousands is ten hundreds.

Thousandths- The thousandths is the third digit after the decimal point.

Value- How much something is worth or the amount of something.

I hope you’ve learnt some new words regarding

place value.

Chapter 5

Bibliography

This chapter sites sources where I got information from.

This book gives credit to:

A Maths Dictionary

Google Images

Mr. MacPherson

Champ 15

Champ 7

Learning About Place Value

Credits

26

Learning About Place Value

Funny Picture

27