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Prime Numbers and
Factors
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An integer (greater than one) is prime if the only whole numbers it
can be divided by (without a remainder) are itself and one. All
other integers are composite. In other words, a prime number has
only two positive factors. Composite numbers have more. For example,
seven is a prime number because its only positive factors are one
and seven. Fifteen is composite because it has four: one, three,
five, and fifteen.
Eratosthenes' Prime Number Sieve
Eratosthenes was a Greek mathematician who figured
out that to find all the prime numbers between two and some large
number, you need to remove all the multiples of each number between
two and your large number.
Dr. Math: Prime Numbers
"A prime number is a positive integer that has
exactly two positive integer factors, 1 and itself. For example, if
we list the factors of 28, we have 1, 2, 4, 7, 14, and 28. That's
six factors. If we list the factors of 29, we only have 1 and 29.
That's 2. So we say that 29 is a prime number, but 28 isn't." Dr.
Math presents an excellent introduction to prime numbers, the Sieve
of Eratosthenes, and links to other prime number sites.
Fact Monster: Prime Numbers
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Data Analysis
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Metric Measurement
All
About Place Value
Place Value Games
Rounding Practice
Can You Say Really Big Numbers?
Think of a
number, type it in and say it out loud, then find out how to write the
number. The game does not allow you to use decimal points.
Place Value Activity
Type in a number, click "Solve!," and
learn the place value of each digit. For example, if you type in the
number 25, you'll learn that the 2 is in the tens place and the 5 is
in the ones place.
Place Value Random Number Chart
This site can be used for whole
group instruction to review the place values of numbers and practice
reading large numbers.
Place Value Puzzler
Practice finding the
value of digits in a given number; has different levels of difficulty.
Finding the Values self-checking quiz This
activity asks for the value a digit has in different numbers.
Place Value- Mystery Numbers Solve the
riddles with your place value knowledge.
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Place Value Worksheet I
This activity focuses on the place value of hundreds
and has students arrange the numbers to create large and small
numbers. Click on "Change" for a new set of numbers.
Place Value Worksheet 2
This activity focuses on the place value of thousands and has students
arrange the numbers to create large and small numbers. Click on
"Change" for a new set of numbers.
Place Value Worksheet 3
This
activity focuses on the place value of ten thousands and has students
arrange the numbers to create large and small numbers. Click on
"Change" for a new set of numbers.
Place Value Worksheet 4
This activity focuses
on the place value of hundred thousands and has students arrange the
numbers to create large and small numbers. Click on "Change" for a new
set of numbers.
Write the Number that Fits the Words
self-checking quiz
Place Value Game
Try to outwit the program by
placing random digits to make the largest number possible.
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Unit 2, Using Numbers and Organizing Data
Subtraction Trade First Method
| Closest to the traditional
standard is a method that Everyday Mathematics calls "trade
first". It is the Everyday Math focus algorithm for
subtraction. It is a two stage process, first working right
to left to do all the borrowing (recording the intermediate
results above the top number) and then a second pass, in any
order, doing the subtractions. The intermediate results are
two-digit numbers, so one needs to use wide columns, and it
is recommended to separate the columns with clear vertical
lines. In the example at right, 325 - 58, we first recognize
that the ones column needs borrowing, so we replace 2*10+5
by 1*10+15. Then we recognize that the tens column also
needs borrowing, so we replace 3*100+1*10 by 2*100+11*10.
Then we do the subtraction in each column. |
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2|11|
| 1|15
3| 2| 5
- | 5| 8
--|--|--
2| 6| 7
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Partial Sums Method
| The Partial Sums method (the
Everyday Math focus algorithm for addition) is a two-stage
process. In the first stage one looks at each column
(working left to right) and adds up the place-values
represented by the digits in that column. In the second
stage those partial sums are added together. In the first
example at right the process is applied to 148 + 67 +
266. The Everyday Mathematics student reference does
not recommend a specific algorithm for the addition problem
in the second stage. Frequently the second stage problem
will be "easy" in that it can be done one column at a time
without any carries, as is the case in the first example.
Perhaps the pupil is expected to iterate the Partial Sums
method in cases where the second stage addition problem
involves carrying.
The reader may want to explore the Partial Sums algorithm
in a case where the second stage and even the logical third
stage involve carrying. Try 148 + 855 or, for
an example that is a bit harder for mental arithmetic, see
the second problem at right, 678 + 67 + 266.
The mathematically inclined reader will note that the
Partial Sums method (iterated so long as carrying is
required) terminates, because every application of the basic
step will reduce, from the right, the range of columns for
which carrying is required. |
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148 678
+ 67 + 67
+ 266 + 266
--- ---
-> 300 -> 800
+ 160 + 190
+ 21 + 21
--- ---
481 -> 900
+ 110
+ 1
----
-> etc
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Partial Sums and Column Addition Algorithm
Another site that explains.
White House Tour
Place Value
SmartBoard Interactive Place value exercises
Place Value Worksheet I
This activity focuses on the place value of hundreds
and has students arrange the numbers to create large and small
numbers. Click on "Change" for a new set of numbers.
Place Value Worksheet 2
This activity focuses on the place value of thousands and has students
arrange the numbers to create large and small numbers. Click on
"Change" for a new set of numbers.
Place Value Worksheet 3 This
activity focuses on the place value of ten thousands and has students
arrange the numbers to create large and small numbers. Click on
"Change" for a new set of numbers.
Place Value Worksheet 4 This activity
focuses
on the place value of hundred thousands and has students arrange the
numbers to create large and small numbers. Click on "Change" for a new
set of numbers.
Finding the Values self-checking quiz This
activity asks for the value a digit has in different numbers.
Write the Number that Fits the Words
self-checking quiz
Place Value- Mystery Numbers Solve the
riddles with your place value knowledge.
Place Value Random Number Chart
This site can be used for whole
group instruction to review the place values of numbers and practice
reading large numbers.
Place Value Puzzler Practice finding the
value of digits in a given number; has different levels of difficulty.
Place Value Game Try to outwit the program by
placing random digits to make the largest number possible.
All
About Place Value
Place Value Games
Wise-Up, Our Number System Explains place
value in a fun way and then tests for understanding.
Base 10 Blocks
manipulative applet
Base 10 Blocks interactive blocks
Data Analysis
What DO you do when someone asks you to
find the range, mean, median and mode
of a set of numbers?
BrainPOP range, mean, median and mode
New
Analyze Data and Graphs Unit from EdHelper.com
Math Goodies lessons on "range"
Worksheet
on range, median, mean and mode
Data Collection Projects
Right or Left-handed data collection project
Create a Graph
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Unit 3 Multiplying, Dividing, Number Sentences and Algebra
Unit 5 Big Numbers, Estimation, and
Computation
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EM Games
Learn how to play
"Multiplication Wrestling" and play at home!
Partial Products Method
| The Partial Products
Method is the Everyday Math focus algorithm for
multiplication. In the Partial Products Method one
takes the base-ten decomposition of each factor and
forms the products of all pairs of terms. Then these
partial products are added together. The student
text does not recommend any particular addition
algorithm for this second stage. In the example at
right I've assumed traditional addition with carries
done mentally, but an Everyday Mathematics pupil may
well do that addition problem by the Partial Sums or
the Column Addition method.
Observe that the number of terms in the addition
problem is the product of the numbers of digits in
the factors. The reader may want to explore Partial
Products on the example 121 * 121 and
compare with the traditional method, or try
128 * 128 for an example that is less skewed
towards the traditional method. |
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83
27
----
80*20 -> 1600
80* 7 -> 560
3*20 -> 60
3* 7 -> 21
----
2241 |
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Learning Goals for Unit 5
The student will be able to:
* Use exponential notation to represent powers of 10.
* Know extended multiplication facts.
* Gain proficiency in using the partial-product multiplication
algorithm
* Make magnitude estimates for products of multi-digit numbers.
* Solve multi-digit multiplication problems.
* Round whole numbers to a given place.
* Read and write numbers to billions; name the values of digits in
numerals to billions.
* Compare large numbers.
* Estimate sums.
Rounding Practice
The Million Dollar
Mission Go here to see very large amounts of
pennies pictured!
Information about exponents and scientific notation:
InfoPlease
Exponents for the "brainy ones"
Interactive Multiplication Table Go here to
practice those basic facts!
Sum Sense Multiplication Try this one for
a little different slant on multiplication practice!
100 Chart with Calculator
The
ArithmAttack
Take a timed test for
multiplication.
Black Dog's Multiplication Quizzes Have
some fun learning the multiplication tables with these fun games.
Math Mastery Cyber Challenge
Have some challenges on timed tests for all four operations!
Tic Tac Toe Play
Multiplication against the computer and see who wins the tic tac toe
game.
Multiplication Matho
Click on the correct answer before the timer runs out.
Can You Say Really Big Numbers? Think of a
number, type it in and say it out loud, then find out how to write the
number. The game does not allow you to use decimal points.
Big
Numbers Try these problem-solvers out to see if
you can find the answers!
Place Value- Mystery Numbers Solve the
riddles with your place value knowledge.
Country
Reports
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Unit 6 Division; Map Reference Frames;
Measures of Angles
Watch a demo of partial quotients--Click
here
The Partial Quotients Method,
the Everyday Mathematics focus algorithm for division, might
be described as successive approximation. It is suggested
that a pupil will find it helpful to prepare first a table
of some easy multiples of the divisor;
10 * 6 = 60
20 * 6 = 120
50 * 6 = 300
100*6 = 600...and so forth.Then we work up towards the answer from
below. In the example at right, 1220 divided by 6, we may
have made a note first that 100*6=600 and 3*6=18. Then we
work up towards 1220. |
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6 ) 1220 |
- 600 |100
---- |
620 |
- 600 |100
--- |
20 |
- 18 | 3
--- | ---
2 |103 R 2
- 0 |
-- |
2 |
answer: 103 R 2
Or, 103 1/6 as a mixed fraction. |
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Learning Goals for Unit 6
The student will be able to:
*identify locations on Earth for which latitude and longitude are
given; find latitude and longitude for given locations
*solve whole-number division problems
*express the remainder of a whole-number division problem as a
fraction and the answer as a mixed number
*interpret the remainder in division problems
*name and locate points specified by ordered pairs on a coordinate
grid
*identify acute, right, obtuse, straight, and reflex angles
*make turns and fractions of turns; relate turns and angles
*use a circular protractor and a half-circle protractor to measure and
draw angles
*write and solve multiplication and division number stories
Division Practice
Math Mayhem (6.1, 6.2, 6.3, 6.4) Go here and
just practice division, please. Great timed drill site.
Race
Car Math (6.1, 6.2, 6.3, 6.4) Race Car Math
for one player. Choose the division option. A row is highlighted with
a group of problems. The student chooses the problem with the highest
answer. They advance their race car that many spaces. The computer
will then choose and compete against the student.
TicTacToe (6.1, 6,2, 6.3, 6.4) Tic Tac Toe
with basic math facts. Use the division options, please.
Math Baseball for Two (6.1, 6.2, 6.3, 6.4)
Math baseball for two players. Allows to use problems that have
pre-algebra skills (What's My Rule)
Math
Baseball for One (6.1, 6.2, 6.3, 6.4) Math baseball
for one player. Allows to use problems that have pre-algebra skills
(What's My Rule) It has basic multiplication and division. It also has
addition and subtractions for remediation.
Latitude and Longitude
Latitude and Longitude Tutorial (6.5, 6.9, 6.10)
Latitude and longitude tutorial with great graphics and simple
explanations.
Latitude and Longitude
Quiz Go here to check your understanding.
Find Your Longitude (6.5, 6.9, 6.10) Latitude
and longitude game from NOVA.
What's
the Point? (6.5, 6.9, 6.10) Challenges
coordinate graphing skills and map grid skills.
Coordinate Geometry Find the points on the
grid. Excellent site that will introduce the concept, give you
practice with applying the skills, then a quiz to help you check for
your understanding. You must go to this site! It is great!
Practice Locating Coordinates Pick
the point on the graph based on the points.
Planet Hoppers Practice
coordinates by playing this space game.
The XY Encounter a performance task using elements of geometrical
figures and coordinates
Quarks
Play this coordinate game with a partner. It is
played very much like Battleship.
Coordinates II
Identify the
coordinates based on the point on the graph.
Feed Billy Bug Some Grub
Move Billy Bug to the feeding place with given
coordinates.
Angles
Angle Measurement with Protractors
Using the Protractor
Angles and angle terms Go here for all sorts
of information about angles.
Dr. Ufigure's What is an Angle? Excellent
site to visit to learn about the types of angles.
Label Angles and Triangles Go here to find a
print out sheet to label.
Classifying Angles Really great site that
will take you through introduction of angles, explain them thoroughly,
then have you apply the information, then give you a quiz to check for
your understanding. You must check this site out!
Angles-Create a polygon
Angle Investigations
Country
Reports
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Time Zones
