Number, Number
Sense and Operations 
(Based on the State
of Ohio Standards) 
(Based on the State of Ohio Standards)
1. Decompose and recompose
whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x
2 = 2^{5} ), and explain why “squared” means “second power”
and “cubed” means “third power.”


Math Dictionary animation for kids This is an outstanding
website allowing you to explore a comprehensive view of math with many
examples 4 Star

Math Glossary
Click on this link to illustrate and teach. This link will present
a
Visual
illustration. 4 star

You want to be a Math Millionaire.
All students will enjoy this site as well as teachers. It is fun
to do and see if you can make it to the Millionaire spot.
This
is an outstanding website.

Spy Guys Interactive  Ratio
 Click Skip Intro, then select Lessons,
and then click on Lesson

Exponents
This web site teaches about simplifying exponents and then has an
interactive quiz to test what was learned

Lesson
on Exponents
This is an online lesson that students can read through with good
examples and explanations of exponents, rules about them, and terms such
as factor, base, exponent, squared, and cubed. It finishes with an
interactive quiz the student can take right on the web page to see if
they understand the material.

Factorize 2 Learn
about factors through building rectangular arrays on a grid.

Exponents This
web site uses pictures and clear explanations to teach about exponential
form, expanded form, and standard form, and how to convert between them.
When done with the lesson, students can take an interactive quiz over
what they learned.

Gizmos are fun, easy to use, and flexible enough to support many
different teaching styles and contexts.
You will present to your students a visual animated manipulative
allowing for an easier and faster teaching pedagogy.
You will discover this tool strategically located throughout the
website.



2. Find and use the prime
factorization of composite numbers. For example:
a. Use the prime factorization to recognize the greatest common factor (GCF).
b. Use the prime factorization to recognize the least common multiple
(LCM).
c. Apply the prime factorization to solve problems and explain
solutions. 

Amby's Math Instruction
The
section titled "Properties of Numbers" has lessons on prime
factorization and using it to find GCF and LCM. After each lesson, there
are exercises for the student to try online.

Spy Guys Interactive  Ratio
 Click Skip Intro, then select Lessons,
and then click on Lesson 3

3. Explain why a number is
referred to as being “rational,” and recognize that the expression a/b
can mean ‘a’ parts of size 1/b each, a divided by b, or the ratio of a
to b. 
 One line
explanation This is a valued website
that will explain various concepts of rational, national numbers and
Integers plus more

4. Describe what it means to find
a specific percent of a number, using reallife examples. 

Spy Guys Interactive  Ratio
 Click Skip Intro, then select Lessons,
and then click on Lesson

5. Use models and pictures to
relate concepts of ratio, proportion and percent, including percents
less than 1 and greater than 100. 

All
About Ratios This site has many pictoral examples of ratios as well as exercises for
students to try.

6. Use the order of operations,
including the use of exponents, decimals and rational numbers, to
simplify numerical expressions. 

Order of Operations
This web site teaches
about simplifying expressions using order of operations, and then has an
interactive quiz to test what was learned.

Lesson on
Order of Operations This
is a collection of online lesson that students can read through with
good examples and explanations of order of operations. Each finishes
with an interactive quiz the student can take right on the web page to
see if they understand the material.

Effects of Parentheses This is an Excel spreadsheet
activity for a whole class or individual students.
There is an equation set in cell B3.
(=3*5+5*4+282*6/8*2)
The user inputs a parentheses, and then alters it to see how many
different answers can be generated.
Great for order of
operations.

Rational Numbers Triangle
–
Explore a
triangular array that contains every positive rational number exactly
once.

Spy Guys Interactive  Ratio
 Click Skip Intro, then select Lessons,
and then click on Lesson

7. Use simple expressions
involving integers to represent and solve problems; e.g., if a running
back loses 15 yards on the first carry but gains 8 yards on the second
carry, what is the net gain/loss? 

Mrs. Glosser's Math Goodies  Lesson on Introduction to Integers
This online lesson
explains what integers are, gives examples in real life, and offers
exercises for the student to do and get immediate feedback.

8. Represent multiplication and
division situations involving fractions and decimals with models and
visual representations; e.g., show with pattern blocks what it means to
take 2 2/3 ÷ 1/6. 

Visual Fractions
This site covers many
operations with fractions by showing visual representations and having
students do exercises with them.

Visual Fractions This is a virtual Manipulative site that will
allow the student's to create their own graphics.

Fractions Adding
Illustrates what it means to find a common
denominator and combine.

Fractions  Rectangle Multiplication
Visualize and practice multiplying fractions using an area
representation.


9. Give examples of how ratios
are used to represent comparisons; e.g., parttopart, parttowhole,
wholetopart. 

Fibonacci Sequence – Explore
the Fibonacci sequence and the golden ratio.

10.Recognize that a quotient may
be larger than the dividend when the divisor is a fraction; e.g., 6 ÷
1/2 = 12. 

Lessons in Division This site has video
and sounds Covers division in detail and does a nice job. At
the bottom left of the screen make sure you hit lessons.

11. Perform fraction and decimal
computations and justify their solutions; e.g., using manipulatives,
diagrams, mathematical reasoning. 

Virtual Manipulate
for determining percents. You will find
this extremely helpful for students.
4 Star

AAA Math  Fractions
This site has lessons
and exercises on many topics concerning fractions

AAA Math  Decimals
This site has lessons
and exercises for many decimal topics.

Fishy
Fractions  Adding and Subtracting Fractions
In this collection of games you
help Ulani the pelican catch fish by adding and subtracting fractions
and mixed numbers, with common and unlike denominators. Simply choose
the game you want to play.

Virtual Base Blocks  Adding and Subtracting Decimals This
online virtual manipulative lets the student use base blocks to add and
subtract decimals, by splitting and combining blocks. This is also a
great way to visualize the concepts of decimal place value

Virtual Manipulative  Adding Fractions This interactive web site helps
students learn to add fractions. Two randomly generated fractions are
shown along with a visual representation, which can be manipulated by
the student. They have to rename the fractions to have the same
denominator and then add them.

Spy Guys Interactive  Ratio
 Click Skip Intro, then select Lessons,
and then click on Lesson

12. Develop and analyze
algorithms for computing with fractions and decimals, and demonstrate
fluency in their use. 

Website for fractions has both a video and
also an interactive website. Click on Fractions at the top.
You will notice this website will work for quite a few various math
concepts.

13. Estimate reasonable solutions
to problem situations involving fractions and decimals; e.g., 7/8 +
12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25. 

On Line Quiz Estimation Created by:
Larry
Solomon

14. Use proportional reasoning,
ratios and percents to represent problem situations and determine the
reasonableness of solutions. 

How
Percentage works This is basic stuff with some
great examples explaining how percentage works.
Very nicely done.

15. Determine the percent of a
number and solve related problems; e.g., find the percent markdown if
the original price was $140, and the sale price is $100. 

ReviseWise  Percents This
web site uses colorful animation and great explanations to teach about
percents, visualizing percents, and percent of a number. After the
instruction, the students can take an online quiz to assess their
understanding. The only drawback is the use of English pounds instead of
American dollars.

Measurement 
1. Understand and describe the
difference between surface area and volume. 

Surface Area and Volume In
this online activity students manipulate dimensions of rectangular or
triangular prisms, and watch how the surface area and volume change

2. Use strategies to develop
formulas for finding circumference and area of circles, and to determine
the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/4
circle. 

Exploring Pi
This
is an Excel spreadsheet activity for the whole class. As students report
measurements on circumference and diameter of objects, the spreadsheet
calculates their ratio and averages them together to approximate pi.

Area
of a Circle Know and apply measurement formulas to solve
realworld problems that include area of squares, rectangles, triangles
parallelograms, and circles; and area of twodimensional composite
figures of circles, squares, rectangles and triangles.
SB

Circumference
Discover the
relationship between circumference and diameter (pi), and use it to
calculate unknown measurements of any circle. SB

Plotting to
find the area
This is a smart board
lesson SB

3. Estimate perimeter or
circumference and area for circles, triangles and quadrilaterals, and
surface area and volume for prisms and cylinders by:
a. estimating lengths using string or links, areas using tiles or grid,
and volumes using cubes;
b. measuring attributes (diameter, side lengths, or heights) and using
established formulas for circles, triangles, rectangles, parallelograms
and rectangular prisms. 

Mrs. Glosser's Math Goodies  Lesson on Circumference of a Circle
This online lesson explains the
different parts of a circle and how to find the circumference. Several
examples are given and exercises are provided for the students to do
online and get immediate feedback

Mrs.
Glosser's Math Goodies  Lesson on Area of a Circle
This online lesson explains
the different parts of a circle and how to find the area. Several
examples are given and exercises are provided for the students to do
online and get immediate feedback.

Exploring Pi
This
is an Excel spreadsheet activity for the whole class. As students report
measurements on circumference and diameter of objects, the spreadsheet
calculates their ratio and averages them together to approximate pi.

Estimator This
online activity has the student estimate length, quantity, or area. They
can control how close they need to be to the true answer, how difficult
the problem is, and if a grid is given to help with the estimate.

Triangle Explorer In this online activity students
learn about areas of triangles and about the Cartesian coordinate system
through experimenting with triangles drawn on a grid.

Area
of a Circle Know and apply measurement formulas to solve
realworld problems that include area of squares, rectangles, triangles
parallelograms, and circles; and area of twodimensional composite
figures of circles, squares, rectangles and triangles.
SB

Area
of a Triangle know and apply measurement formulas to solve
realworld problems that include area of squares, rectangles, triangles
parallelograms, and circles; and area of twodimensional composite
figures of circles, squares, rectangles and triangles.
SB

Determining Areas of shapes
You will find a
smart board lesson to help you in this area of learning
SB

Determining Areas
You
will find a smart board lesson to help you in this area of learning
ou will find a smart board lesson to help you in this area of learning
SB

Determining area of a triangle.
This Lesson will give
you an outstanding presentation of using Smart Board to determine area
ou will find a smart board lesson to help you in this area of learning
SB

Volume
Calculate the volume of various
shapes.
SB

The
area of a trapezoid
Learn the formula for finding the
area of a trapezoid, and practice, using examples created for visual and
kinesthetic learners
SB

Area of a parallelogram
Learn the formula
for finding the area of a parallelogram, and practice, using examples
created for visual and kinesthetic learners.
SB

Area
of a Square Learn the formula for finding
the area of a square, and practice, using examples created for visual
and kinesthetic learners
SB

4. Determine which measure
(perimeter, area, surface area, volume) matches the context for a
problem situation; e.g., perimeter is the context for fencing a garden,
surface area is the context for painting a room. 

The website. This website will
allow you to explore perimeter, area and surface area. Visually
scroll down the screen and look for area and perimeter.

How High?
– Try your hand at the classic Piagetian conservation of volume
test.

Virtual Manipulative Converting Units of different areas

Geoboard – Use geoboards to illustrate area, perimeter, and
rational number concepts.

Geoboard  Circular – Use circular geoboards to illustrate
angles and degrees.

Great Circle – Use a 3D globe to visualize and measure the
shortest path between cities.

How High? – Try your hand at the classic Piagetian conservation
of volume test.

5. Understand the difference
between perimeter and area, and demonstrate that two shapes may have the
same perimeter, but different areas or may have the same area, but
different perimeters. 

Shape Explorer
In
this online activity students are shown shapes on a grid and asked to
calculate areas and perimeters of the shapes.

6. Describe what happens to the
perimeter and area of a twodimensional shape when the measurements of
the shape are changed; e.g. length of sides are doubled. 

The website. This website will
allow you to explore perimeter, area and surface area. Visually
scroll down the screen and look for area and perimeter.

Determining Angles of a triangle You will find a lesson
allowing you to learn about angles.
You will find a smart board lesson
to help you in this area of learning
SB

Geometry and Spatial Sense 
1. Classify and describe
twodimensional and threedimensional geometric figures and objects by
using their properties; e.g., interior angle measures,
perpendicular/parallel sides, congruent angles/sides. 

Platonic Solids  Virtual Manipulative
This
online activity allows you to experiment with five platonic solids,
counting their faces, edges, and vertices.

Shapes
This website will allow your students to learn all about shapes and have
fun at the same time.

2. Use standard language to
define geometric vocabulary: vertex, face, altitude, diagonal,
isosceles, equilateral, acute, obtuse and other vocabulary as
appropriate. 

Sorting Triangles
This
interactive website begins with an animated review of scalene,
isosceles, and equilateral triangles. Then students get to sort the
triangles using Venn diagrams based upon single and multiple
characteristics.
Very good

3. Use multiple classification
criteria to classify triangles; e.g., right scalene triangle. 

Sorting Triangles This
interactive website begins with an animated review of scalene,
isosceles, and equilateral triangles. Then students get to sort the
triangles using Venn diagrams based upon single and multiple
characteristics.
Very good

4. Identify and define
relationships between planes; i.e., parallel, perpendicular and
intersecting. 
 Super
Maths World This is a highly visual game. Students
will be totally engaged. 4 Star

5. Predict and describe sizes,
positions and orientations of twodimensional shapes after
transformations such as reflections, rotations, translations and
dilations. 

Dam Jammer Game
 Flips and Turns
In
this online game you help Bucky the Beaver to plug holes in the dam by
flipping and rotating basic shapes, and then placing them on the
congruent holes in the dam.
Great Game!!

Translation Transformation  Virtual Manipulative
This online activity allows
you to place pattern blocks on a grid and apply a translation to them.
You can do this on your own, or go through three premade activities.

Rotation Transformation  Virtual Manipulative
This online activity allows you
to place pattern blocks on a grid and apply a rotation to them. You can
do this on your own, or go through three premade activities.

Reflection Transformation 
Virtual Manipulative
This
online activity allows you to place pattern blocks on a grid and apply a
reflection to them. You can do this on your own, or go through three
premade activities.

Dilation Transformation  Virtual Manipulative
This online activity allows you
to place pattern blocks on a grid and apply a dilation to them. You can
do this on your own, or go through two premade activities.

TransmoGrapher
Students
explore the world of translations, reflections, and rotations in the
Cartesian coordinate system by transforming squares, triangles and
parallelograms. Parameters: Shape, x or y translation, x or y
reflection, angle of rotation.

6. Draw similar figures that
model proportional relationships; e.g., model similar figures with a 1
to 2 relationship by sketching two of the same figure, one with
corresponding sides twice the length of the other. 

7. Build threedimensional
objects with cubes, and sketch the twodimensional representations of
each side; i.e., projection sets. 

Geoboard  Isometric
–
Use geoboard to illustrate threedimensional shapes.

Patterns, Functions and Algebra 
1. Represent and analyze
patterns, rules and functions, using physical materials, tables and
graphs. 

Algebraic
Reasoning
Learn how to think algebraically with these clever weighing scales. Levels
1 and 2 contain two scales. Level 3 is more difficult and has three
scales. Your goal is to determine the weight of one or more of the objects
4 Star

Algebra
Puzzle
Find the value of each of the
three objects presented in the puzzle. The numbers given represent the
sum of the objects in each row or column. Sometimes, only one object
will appear in a row or column. That makes the puzzle easier to solve.
Other times, you will have to look for relationships among the objects.
4
Star

Weigh the
Wangdoodles
Your
job is to find the weight of each Wangdoodle using the information
provided by the scales. To be successful, you will have to make sure
that the weight you assign to each Wangdoodle works on each scale. This
activity is a fun but challenging introduction to multiple algebraic
equations.
4
Star

Function Machine This
online tool has you put in a number, and then it spits out a result.
Your goal is to determine what the function machine is doing to the
number. You can choose the type of function it uses or let it be random.
Very good

Mystery Functions This is an
Excel
spreadsheet activity for the whole class or individual student use.
There are 20 different mystery formulas in this spreadsheet. For each
one the student enters several numbers for the "Input" and examines what
comes out for the "Result", trying to determine each function by looking
for patterns.

Whole Number Cruncher
Similar to the original
"Function Machine" but lists input and output in a table and will not
let the user attempt to guess the rule on without at least having two
data points.

Make
a Table This
web site uses pictures and clear explanations to teach about solving a
problem by making a table. When done with the lesson, students can take
an interactive quiz over what they learned.

Smart Board Algebra Lesson This
lesson has examples and videos.
Smart board manipulative SB


Algebra Tiles
–
Visualize multiplying and factoring algebraic expressions
using tiles. 

Algebraic Tiles  This website will allow you
to show students how this works.





Student Resources for Algebra
 Outstanding web
site for teachers and students.

2. Use words and symbols to
describe numerical and geometric patterns, rules and functions. 

Function Machine Students
investigate very simple functions by trying to guess the algebraic form
from inputs and outputs.

Mystery Functions This is an
Excel
spreadsheet activity for the whole class or individual student use.
There are 20 different mystery formulas in this spreadsheet. For each
one the student enters several numbers for the "Input" and examines what
comes out for the "Result", trying to determine each function by looking
for patterns.

Whole Number Cruncher
Similar to the original
"Function Machine" but lists input and output in a table and will not
let the user attempt to guess the rule on without at least having two
data points.

3. Recognize and generate
equivalent forms of algebraic expressions, and explain how the
commutative, associative and distributive properties can be used to
generate equivalent forms; e.g., perimeter as 2(l + w) or 2l + 2w. 

Simplifying Using Distribution This
web site teaches about using the distributive property to simplify
algebraic expressions, and then has an interactive quiz to test what was
learned.

Distributive problem
flashcards Interactive
flashcards to practice the distributive property

4. Solve simple linear equations
and inequalities using physical models, paper and pencil, tables and
graphs. 

Equations This
web site teaches about solving simple equations and then has an
interactive quiz to test what was learned.

5. Produce and interpret graphs
that represent the relationship between two variables. 

6. Evaluate simple expressions by
replacing variables with given values, and use formulas in
problemsolving situations. 

Using algebraic methods to solve systems of equations
Power
Point
Interactive, power point like notes that show the steps of solving an
equation. Interesting and easy to understand.

7. Identify and describe
situations with constant or varying rates of change, and compare them. 

8. Use technology to analyze
change; e.g., use computer applications or graphing calculators to
display and interpret rate of change. 

Slope Slider This
activity allows the manipulation of a linear function of the form f(x)=mx+b
and encourages the user to explore the relationship between slope and
intercept in the cartesian coordinate system.

Data Analysis and Probability 
1. Read, construct and interpret
line graphs, circle graphs and histograms. 

Pie Chart (8 items) This
is an Excel spreadsheet activity for the whole class or individual
students. A generic 8 item pie chart can be dynamically altered with
custom data and labels.

Pie Chart  Virtual Manipulative This online manipulative allows
the user to create a colorful pie chart with up to eight different
categories. Suggested activities are included on the site.

Box Plot and Histogram  Virtual Manipulative
This online interactive activity
generates a box plot and a histogram for data provided. You can choose
from several premade sets of topical data, or you can enter new data or
change the data there. Several measures of the data are given as well.

Histograms
This
web site uses clear explanations and diagrams to explain how to read and
create histograms. After the review, the student can take an interactive
quiz over the material.

Histograms Interactive example

Histograms The purpose of a histogram (Chambers)
is to graphically summarize the distribution of a univariate data set.

Circle Graphs This web site uses clear
explanations and diagrams to teach how to read and create circle graphs.
After the review, students can take an interactive quiz on the material.

Line Graphs
This web site uses clear
explanations and diagrams to teach how to read and create line graphs.
After the review, students can take an interactive quiz on the material.

Using Line Graphs This
web site explains the advantages and disadvantages of line graphs, and
provides an interactive quiz.

2. Select, create and use
graphical representations that are appropriate for the type of data
collected. 

3. Compare representations of the
same data in different types of graphs, such as a bar graph and circle
graph. 

Comparing Graphs  Excel Activity
This is an Excel spreadsheet
activity. In it three different sets of data (earnings, votes, heights)
are shown with three different types of graphs (line, bar, circle). The
student is to compare the different graphs to determine which is the
best representation

4. Understand the different
information provided by measures of center (mean, mode and median) and
measures of spread (range). 

Lessons on
Statistics
This
site has a collection of lessons on stats including range, mean, median,
and mode. Each lesson also has an interactive quiz.

ReviseWise  Mode, median, mean
This
web site uses colorful animation and great explanations to teach about
mean, median, and mode. After the instruction, the students can take an
online quiz to assess their understanding.

Comparing Data  Excel
Activity
This is
an Excel spreadsheet activity in which the student enters data and then
the spreadsheet generates several measures of that data such as
mean, median,
mode, quartiles,
and range. The student can then investigate the measures to compare the
different sets of data.

5. Describe the frequency
distribution of a set of data, as shown in a histogram or frequency
table, by general appearance or shape; e.g., number of modes, middle of
data, level of symmetry, outliers. 

6. Make logical inferences from
statistical data. 

7. Design an experiment to test a
theoretical probability and explain how the results may vary. 

Box Model  Virtual Manipulative
This online activity models a
probability experiment of pulling numbers from a box. First, the user
decides which numbers, and how many of each, are in a box. Then the
computer begins randomly drawing numbers and keeping totals.
Superimposed can be a graph of the expected theoretical probabilities.
This is excellent to show real v. theoretical probability, and the
effect of the number of trials on the results.






