4. Learning About Place Value - The First Math Unit in Grade 6
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
3
5. CHAPTER 1
Thinking
About
Integers
This chapter will guide students about basic things
about integers.
6. Learning About Place Value
Integers
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!
5
7. Learning About Place Value
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.
6
8. Learning About Place Value
Integers
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.
7
9. Learning About Place Value
Integers
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.
8
10. Learning About Place Value
Integers
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.
9
11. Chapter 2
Going
Deeper Into
Place Value
This chapter will clearly explain what place value is
and some vocabulary.
12. Learning More About Place Value
Place Value
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).
11
13. Learning About Place Value
Place Value
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!!!
12
14. Learning About Place Value
Place Value Games
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)
13
15. Chapter 3
Negative
Numbers
This chapter will guide children on how to perform
operations with negative numbers.
16. Learning About Place Value
What do you mean by two plus signs or two minus signs?
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!
15
17. Learning About Place Value
The Next Operations
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.
16
18. Learning About Place Value
If you still don’t understand the rules...
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)
Legend: P = Positive
P - N= P
N = Negative
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
17
N ÷ P= N
19. Learning About Place Value
Challenging Your Brain
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= If you can do these quickly
5) (-100) ÷ (-50)= and accurately, you’ve met
6) 47 x -974=
the Grade 6 requirement in
7) (-14) + (+2738904)=
negative numbers.
8) 4162889 - (-8941)=
9) (-531) - (-512)=
10) (-129) + (169)=
11) 167 - (-1672)=
12) (-189) + (-716)=
13) (-45) ÷ (-5)=
14) (-12) ÷ (+6) = 18
21. Learning About Place Value
Who Uses Negatives?
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...
20
22. Chapter 4
A Math
Glossary
This chapter allows you to know some words that
you must know to learn math about place value.
23. Learning About Place Value
Understanding Important Words
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.
22
24. Learning About Place Value
Understanding Important Words
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.
23
Subtraction- To take away a quantity from a number.
25. Learning About Place Value
Understanding Important Words
Sum- The result of two numbers being added together.
Ten- Ten units/ones together.
I hope you’ve
Tenths- The number right after the decimal point.
learnt some new
Thousands- Thousands is ten hundreds. words regarding
place value.
Thousandths- The thousandths is the third digit after the decimal point.
Value- How much something is worth or the amount of something.
24
