3rd GradeMathCRCTStudyGuide2010

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3rd Grade Comprehensive CRCT Math Study GuideContent Weights: Number Operations-55%, Measurement-23%, Geometry-10%, Algebra-7%, Data Analysis & Probability-5%

Number and Operations: 55% = 33 questions

Number and Operations: Students will use decimal fractions and common fractions to represent parts of a

whole. They will also understand the four arithmetic operations for whole numbers and use them in basic

calculations, and apply them in problem solving situations.

M3N1 Students will further develop their understanding of whole numbers and decimals and ways of

representing them.

a. Identify place values from tenths through ten thousands.

b. Understand the relative sizes of digits in place value notation (10 times, 100 times, 1/10 of a single

digit whole number) and always to represent them including word name, standard form and

expanded form.

Place Value through the ten thousands.

Thousands Ones

tens ones hundreds tens ones

2 7 , 5 6 9Each group of 3 digits separated by a comma in a number is called aperiod.

vocabulary definition exampledigit Any one of the ten number

symbols

0,1,2,3,4,5,6,7,8, or 9

place value The value of a digit determined

by its place in a number

The value of the 2 in the number 27,569 is 20,000

standard form The usual, or common, way of

writing a number, using digits

27,569

expanded form A way of writing a number as

the sum of the values of the

digits

20,000 + 7,000 + 500 + 60 + 9

word form A way of writing a number

using words

Twenty-seven thousand, five hundred sixty-nine(and is only used when there is a decimal point)

Whole numbers Decimals

Ten

thousands

thousands hundreds tens ones

1.0

Tenths

1

10

or

0.1

Hundredths

1

100

or

0.017 1 , 3 8 2 . 2 1

Standard form 71, 382.21

Expanded form 70,000+1,000+300+80+2+ .2+ .01

Word form seventy-one thousand, three hundred eighty-two and twenty-one

hundredths

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M3N2 Students will further develop their skills of addition and subtraction and apply them in problem

solving.

a. Use the properties of addition and subtraction to compute and verify the results of computation.

b. Use mental math and estimation strategies to add and subtract.

c. Solve problems requiring addition and subtraction.

d. Model addition and subtraction by counting back change using the fewest number of coins.

Properties of Addition

Commutative property: When two numbers are added, the sum is the same regardless of the order of the

addends. For example 4 + 2 = 2 + 4

Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of

the addends. For example (2 + 3) + 4 = 2 + (3 + 4)

Identity Property: The sum of any number and zero is the original number. For example 5 + 0 = 5.

There is an inverse relationship between addition and subtraction .

Example: Since 3 + 7 = 10 then the following are also true:

10 - 3 = 7

10 - 7 = 3

Similar relationships exist for subtraction.Example: Since 10 - 3 = 7 then the following are also true:

3 + 7 = 10 7 + 3 = 10

An equation is balanced or the same on either side of the equals (=) sign. If exactly the same thing is done to bothsides of the equation, it will still be balanced or equal.

In the example above we start with the equation 3 + 7 = 10:

Subtract the same number from both sides

3 + 7 - 3 = 10 - 3

On the left side the 3 and -3 produce 0 which leaves7 = 10 - 3

Turning the equation around to be in more normal form

10 - 3 = 7

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M3N3 Students will further develop their understanding of multiplication of whole numbers and develop

the ability to apply it in problem solving.

a. Describe the relationship between addition and multiplication, i.e., multiplication is defined as

repeated addition.

For example, 3 x 7 = 21, instead you may consider it as 3 x 7 = 7 + 7 + 7 = 14 + 7 = 21. This particular method isa bit challenging in terms of addition for a child, but it lucidly shows the relationship between multiplication and

addition.Accordingly, you may also calculate 9 x 7 = 10 x 7 - 7 = 63 or 6 x 7 = 3 x 7 + 3 x 7 = 21 + 21 = 42. It is

also a creative method to learn the multiplication table, which explains you the exact working of math.

b. Know the multiplication facts with understanding and fluency to 10x10.

1 2 3 4 5 6 7 8 9 10 11 12

11 2 3 4 5 6 7 8 9 10 11 12

22 4 6 8 10 12 14 16 18 20 22 24

33 6 9 12 15 18 21 24 27 30 33 36

44 8 12 16 20 24 28 32 36 40 44 48

55 10 15 20 25 30 35 40 45 50 55 60

66 12 18 24 30 36 42 48 54 60 66 72

77 14 21 28 35 42 49 56 63 70 77 84

88 16 24 32 40 48 56 64 72 80 88 96

99 18 27 36 45 54 63 72 81 90 99 108

1010 20 30 40 50 60 70 80 90 100 110 120

1111 22 33 44 55 66 77 88 99 110 121 132

12 12 24 36 48 60 72 84 96 108 120 132 144

Multiplication by a single digit

2 3

x 4

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23 is 2 tens and 3 ones.

3 ones multiplied by 4 gives 12 ones and

2 tens multiplied by 4 gives 8 tens (that is 80).

80 and 12 are added to give the final product 92.

The 3 ones are first multiplied by 4 giving the product 12, which is 1 ten and 2 ones. 2 is written in the ones

column and the 1 is recorded in the tens column. Now the 2 tens are multiplied by 4 to give 8 tens. The 1 ten

recorded before is added on, so the product has 9 tens.

M3N3

c. Use arrays and area models to develop understanding of the distributive property and to determine

partial products for multiplication of 2- or 3- digit number.

Multiplication can be defined in terms of repeated addition. For example, 3 6 can be viewed as 6 + 6 + 6. More generally,

for any positive integern, n b can be represented as n b = b + b + + b

where the sum on the right consists ofn addends.

A rectangular array provides a visual model for multiplication. For example, the product 3 6 can be represented as

By displaying 18 dots as 3 rows with 6 dots in each row, this array provides a visual representation of 3 6 as 6 + 6 + 6.

An equivalent area model can be made in which the dots of the array are replaced by unit squares.

Besides representing 3 6 as an array of 18 unit squares, this model also shows that the area of a rectangle with a height of

3 units and a base of 6 units is 3 6 square units, or 18 square units.

Given a pair of numbers a and b called factors, multiplication assigns them a value a b = c, called their product.

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The Commutative Property of Multiplication states that changing the order in which two numbers are multiplied does not

change the product. That is, for all numbers a and b, a b = b a.

The array model can be used to make this plausible. For example, because 3 6 = 6 3, an array with 3 rows and 6 dots in

each row has the same number of dots as an array with 6 rows and 3 dots in each row.

Another important property of multiplication is the Identity Property of Multiplication. It states that the product of any

number and 1 is that number. That is, for all numbers a, a 1 = 1 a = a.

The Zero Property of Multiplication states that when a number is multiplied by zero, the product is zero. That is, for all

numbers a, a 0 = 0 a = 0.

M3N3

d. Understand the effect on the product when multiplying by multiples of 10.

8x1=8

8x10=808x100=800

8x1000=8,000

8x2=16

8x2=1608x200=1600

8x2000=16,00

e. Apply the identity and commutative and associative properties of multiplication and verify the

results.Multiplication Property definition Example

Commutative Property When you change the order of the

factors, the product stays the same.

5 x 4 = 4 x 5

Associative Property When you group factors in different

ways, the product stays the same. The

parentheses tell you which numbers to

multiply first.

(6 x 7) x 9 = 6 x (7 x 9)

Distributive Property When two addends are multiplied by a

factor, the product is the same wheneach addend is multiplied by the factor

and those products are added.

(3 + 5) x 2 = (3 x 2) + (5 x 2)

Property of One When you multiply any number by 1,

the product is equal to that number.

12 x 1 = 12

Zero Property When you multiply any number by 0,the product is 0.

178 x 0 = 0

Factorthe number used in a multiplication problem: 6 x 5 = 30 6 and 5 are factors

Product-the answer in a multiplication problem: 6 x 5 = 30 30 is the product

Addend-the number to be added in an addition problem: (3+5) x 2 3 and 5 are addends

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f. Use mental math and estimation strategies to multiply.

g. Solve problems requiring multiplication.

M3N4 Students will understand the meaning of division and develop the ability to apply it in problem

solving.

a. Understand the relationship between division and multiplication and between division and

subtraction.

b. Recognize that division may be two situations: the first is determining how many equal parts of agiven size or amount may be taken away from the whole as in repeated subtraction, and the second

is determining the size of the parts when the whole is separated into a given number of equal parts

as in a sharing model

c. Recognize problem-solving situations in which division may be applied and write corresponding

mathematical expressions.

When you divide to find the number of objects in each group, the division is called fair sharing or partitioning. For example:

A farmer is filling baskets of apples. The farmer has 24 apples and 4 baskets. If she divides them equally, how many apples

will she put in each basket?

When you divide to find the number of groups, the division is called measuring or repeated subtraction. It is easy to see that

you can keep subtracting 4 from 24 until you reach zero. Each 4 you subtract is a group or basket.

A farmer has 24 apples. She wants to sell them at 4 apples for $1.00. How many baskets of 4 can she fill?

Manipulatives and visual aids are important when teaching multiplication and division. Students have used arrays to illustrate

the multiplication process. Arrays can also illustrate division.

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Since division is the inverse, or opposite, of multiplication, you can use arrays to help students understand how multiplication

and division are related. If in multiplication we find the product of two factors, in division we find the missing factor if the other

factor and the product are known.

In the multiplication model below, you multiply to find the number of counters in all. In the division model you divide to find

the number of counters in each group. The same three numbers are used. The model shows that division undoesmultiplication and multiplication undoes division. So when multiplying or dividing, students can use a fact from the inverse

operation. For example, since you know that 4 x 5 = 20, you also know the related division fact 20 4 = 5 or20 5 = 4.

Students can also check their work by using the inverse operation.

Notice that the numbers in multiplication and division sentences have special names. In multiplication the numbers you

multiply are called factors; the answer is called the product. In division the number being divided is the dividend, thenumber that divides it is the divisor, and the answer is the quotient. Discuss the relationship of these numbers as you

explain how multiplication and division are related.

There are other models your students can use to explore the relationship between multiplication and division. Expose your

students to the different models and let each student choose which model is most helpful to him or her. Here is an example

using counters to multiply and divide.

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factor

4

number of

groups

x

factor

3

counters in

each group

=

product

12

total number of

counters

dividend

12

total number

of counters

divisor

4

number of

groups

=

quotient

3

counters in

each group

Here is an example using a number line.

factor

4x

factor

5=

product

20

dividend

20

divisor

5=

quotient

4

Another strategy your students may find helpful is using a related multiplication fact to divide. The lesson Relating

Multiplication and Division focuses on this strategy. Here is an example.

18 6 = ?

Think: 6 x ? = 18 Six times what number is 18?

6 x 3 = 18,

so 18 6 = 3.

When students understand the concept of division, they can proceed to explore the rules for dividing with 0 and 1. Lead

students to discover the rules themselves by having them use counters to model the division. A few examples follow.

Divide 4 counters into 4 groups.

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4 4 = 1


2 2 = 1

When any number except 0 is divided by itself, the quotient is 1.

Put 3 counters in 1 group. Put 5 counters in 1 group.

3 1 = 3 5 1 = 5

When any number is divided by 1, the quotient is that number.


0 2 = 0


0 4 = 0

When 0 is divided by any number except 0, the quotient is 0.

Divide 6 counters into 0 groups. Divide 1 counter into 0 groups.

You cannot divide a number by 0.

Encourage students to think about the relationship between multiplication and division when they solve problems. For

example, they can use a related multiplication fact to find the unit cost of an itemfor example the cost of one baseball cap

priced at 3 for $18.

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$18 3 = $6

Think: 3 x ? = $18

3 x $6 = $18

So $18 3 = ?

The cost is $6 for one baseball cap.

Dividing by Repeated SubtractionsThe result of division is to separate a group of objects into several equal smaller groups. The starting group

is called the dividend. The number of groups that are separated out is called the divisor. The number of objectsin each smaller group is called the quotient.

ex: 24 divided by 6 (24 / 6 = 4)24 is the Dividend

6 is the divisorand the quotient is 4

Which means 24 can be divided into 4 equal parts of 6 each.

The results of division can be obtained by repeated subtraction. If we are separating 24 objects into 4 equalgroups of six, we would take (or subtract) six objects at a time from the large group and place them in 4 equal

groups. In mathematical terms this would be: 24-6-6-6-6.M3N4

d. Explain the meaning of a remainder in division in different circumstances.

e. Divide a 2- and 3- digit number by a 1- digit divisor.

f. Solve problems requiring division.

g. Use mental math strategies to divide.

If you divide 13 bananas evenly betweenJoe and Sally, how much does each oneget?

13 2 = ?

We say that Joe and Sally both get 6 bananas and one is left over. The leftover banana iscalled the remainder. Or, if we don't want leftovers or remainders, both would get 6 1/2bananas.

13 2 = 6, remainder 1.

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14 bananas divided between 3 peoplegives 4 bananas to each and 2 bananasthat cannot be divided.

14 3 = 4,

remainder 2

8 scissors divided between 5 peoplegives 1 scissors to each and 3 scissorsthat cannot be divided.

8 5= 1,remainder 3

Division Steps

There are five steps of dividing to remember.

1. Divide. Long Division

2. Multiply.

3. Subtract.

4. Compare.

5. Bring down the next number.

1. Divide 84 6 is the problem. Look at the first number only in the dividend so theproblem is 8 6. The answer is 1. Write it above the 8.

2. Multiply. 1 x 6 = 6. Write the number 6 under the 8.

4 -- QuotientDivisor -- 3 |12 -- Dividend

16 |84

1

6 |84

6

1

6|84

- 6

2

14

6 |84

-

-

6

24240

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3. Subtract. 8 - 6. The answer is 2. Write it down under the 6

4. Compare what is left over after subtracting with the divisor. It must be less than

the divisor, if not, then go back to step 1 and choose a larger number to multiple.

5. Bring down the 4. Then go through steps 1 through 4 again. 24 6 = 4. Multiple.

Subtract. Compare. There is not another number to bring down. The final answer is 14. 84 6 = 14.

M3N5 Students will understand the meaning of decimal fractions and common fractions in simple cases

and apply them in problem-solving situations.

a. Identify fractions that are decimal fractions and/or common fractions.

b. Understand that a common fraction (i.e., 3/10) can be written as a decimal (i.e. 0.3)

8 =810

One decimal digit; one 0 in thedenominator.

.08 =8

100Two decimal digits; two 0's in the

denominator.

.

008

=

8

1000

Three decimal digits; three 0's in thedenominator

c. Understand the fraction a/b represents an equal sized parts of a whole that is divided into b equal

sized parts.

d. Know and use decimal fractions and common fractions to represent the size of parts created by

equal divisions of a whole.

To show half, draw 2 equal boxes to represent the total number of equal parts and shade 1 part out of the

2 equal parts.

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1

5

+

2

5

=

3

5

Example:

Find7

-3

8 8

Both fractions have the same denominator of 8, so we can simply subtract the numerators:

7-

3=

4=

1

8 8 8 2

NOTE that the result was simplified (the numerator and the denominator divided by 4).

7

8-

3

8=

4

8

=

1

2

Measurement: 23% =14 questionsStudents will understand and measure time and length. They will also model and calculate perimeter and

area of simple geometric figures.

M3M1 Students will further develop their understanding of the concept of time by determining elapsed

time of a full, half and quarter-hour.

Start Time End Time Elapsed Time?

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0:00

Start Time End Time

Elapsed Time?

1:30

Start Time End Time

Elapsed Time?

1:00

Start Time End Time

Elapsed Time?

4:30

Start Time End Time

Elapsed Time?

1:00

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Start Time End Time

Elapsed Time?

2:15

Start Time End Time

Elapsed Time?

2:15

Start TimeEnd Time

Elapsed Time?

2:30

Start Time End Time

Elapsed Time?

2:00

Start Time End Time Elapsed Time?

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4:00

Start Time End Time

Elapsed Time?

0:00

Start Time End Time

Elapsed Time?

2:00

M3M2 Students will measure length choosing appropriate units and tools.

a. Use the units, kilometer (km) and mile (mi.) to discuss the measure of long distances.

b. Measure to the nearest inch, inch and millimeter (mm) in addition to the previouslylearned inch, foot, yard, centimeter, and meter.

c. Estimate length and represent it using appropriate units.

d. Compare one unit to another within a single system of measurement.

Units of Length

When measuring length in the customary system the common units used are inches, feet, yards, and miles. Units of length measure height, width,

length, depth, and distance.

People use "feet" to measure their height. Construction worker and architects use feet to measure walls, f loors, and ceilings. It is also used to determine

one point to another.

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The end of your thumb to your first joint is about 1 inch long.

An egg carton is about a foot long.

A standard doorway is about a yard in width. A man six-feet tall is 2 yards high.

Distances between cities are measured in miles

From smallest to greatest length measurements are compared as:

Inches Feet Yards Miles

Reading a Ruler

When reading a ruler, you want to find out how far the i tem is from zero. When reading a ruler, you must locate the zero marking, this may vary

depending on the ruler. On some rulers, the zeros start at the end, but on others it starts about 1/4 of an inch from the end. If you do not check your rule

beforehand you will not be getting an accurate measurement.

Point A is 1 1/4 inches or 1 1/4 inches away from zero.

Point B is 3 3/4 inches or 3 3/4 inches away from zero.

Point C is 4 1/8 inches or 4 1/8 inches away from zero.

stomary

Metric

gthinch - in foot - ft yard - yd mile - mi

1 ft = 12 in1 yd = 36 in1 yd = 3 ft

1 mi=63,360 in1 mi = 5280 ft

1 mi=1760 yd

centimeter-cm

decimeter -dm

meter - m kilometer

1 cm=10 mm 1 dm=100

mm1 dm=10 cm

1 m= 1000

mm1 m=100 cm1 m=10dm

1 km=1,00

mm1 km=100,01 km=10,0

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The distancebetween theknuckles onyour indexfinger is

approximately1 inch.

Your notebookis

approximately1 foot tall.

A baseball batis

approximately1 yard long.

Long distancesare measured in

miles. Thedistance a

vehicle travels ismeasured in

miles.

1 km=100

A paperclip isapproximately1 centimeter

wide.

A crayon isapproximately1 decimeter

long.

The distancefrom the floorto the door

knob isapproximately

1 meter.

The length oblocks

approxima

kilometer

ght

ounce - oz pound - lb ton - T

1 lb = 16 oz1 T = 32,000 oz1 T = 2000 lb

A slice abreadweighsabout 1ounce.

A loaf of bread weighsabout 1 pound.

A car weighs about 1 ton.

gram kilogram

1 kilogram = 1000 grams

A packet of sugarweighs about 1

gram. A book weighs about 1kilogram.

A car weigh

1000 kilog

acity

cups - c pint - pt quarts - qt gallon - gal

1 pt = 2 c1 qt = 4 c1 qt = 2 pt

1 gal = 16 c1 gal = 8 pt1 gal = 4 qt

A small cup ofcoffee holds

approximately1 cup.

A tall glass oflemonade or abowl of soup

holdsapproximately

1 pint.

Oil comes in aquart-sizedcontainer.

A largecontainer of

milk comes in a1 gallon

container.

milliliter - ml liter - l

1 liter =

1000 milliliters

Ten drops from a medicinedropper is approximately 1

milliliter.

A bottle of cola is one l iter. large bottle holds 3 lite

When converting any unit of measurements if you want:

To change to a larger unit, divide.

To change to a smaller unit, multiply.

M3M3 Students will understand and measure the perimeter of geometric figures.

a. Understand the meaning of linear unit and measurement in perimeter.

b. Understand the concept of perimeter as being the length of the boundary of a geometric figure.

c. Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.

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M3M4 Students will understand and measure the area of simple geometric figures (squares and rectangles)

a. Understand the meaning of the square unit and measurement in area.

b. Model (by tiling) the area of a simple geometric figure using square units (square inch, square foot,

etc.)

c. Determine the area of squares and rectangles by counting, addition, and multiplication with models.

\Surface Area and Perimeter of a Rectangle

The area of other squares can be found by counting squares or by multiplying the length of the sides.

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The perimeter of a square is the total length of the four sides.

Area of a Square

Iflis the side-length of a square, the area of the square is l2 or l l.

What is the area of a square having side-length 3.4?The area is the square of the side-length, which is 3.4 3.4 = 11.56.

Area of a Rectangle

The area of a rectangle is the product of its width and length.

What is the area of a rectangle having a length of 6 and a width of 2.2?The area is the product of these two side-lengths, which is 6 2.2 = 13

Geometry: 10% =6 questions

Students will further develop their understanding of characteristics of previously studied geometric figures.

M3G1 Students will further develop their understanding of geometric figures by drawing them. They will

also state and explain their properties.

M3G1a Draw and classify previously learned fundamental geometric figures and scalene, isosceles, andequilateral triangles.

There are three special names given to triangles that tell how many sides (or angles) are equal.

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Equilateral Triangle

Three equal sides

Three equal angles, always60

Isosceles Triangle

Two equal sidesTwo equal angles

Scalene Triangle

No equal sides

No equal angles

Triangles can also have names that tell you what type of angle is inside:

Acute Triangle

All angles are less than 90

Right Triangle

Has a right angle (90)

Obtuse Triangle

Has an angle more than 90

M3G1b. Identify and compare the properties of fundamental geometric figures

c. Examine and compare angles of fundamental geometric figures

The Rectangle

means "right angle"

and show equal sides

A rectangle is a four-sided shape where every angle is a right angle (90). Also opposite sides are

parallel and of equal length.

The Rhombus

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A rhombus is a four-sided shape where all sides have equal length. Also opposite sides are parallel andopposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) of

a rhombus bisect each other at right angles

The Square

means "right angle"

show equal sides

A square has equal sides and every angle is a right angle (90). Also opposite sides are parallel. A square

also fits the definition of a rectangle (all angles are 90), and a rhombus (all sides are equal length).

The Parallelogram

Opposite sides are parallel and equal in length, and opposite angles are

equal (angles "a" are the same, and angles "b" are the same)

The Trapezoid

A trapezoid has one pair of opposite sides parallel.

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Acute Angles

An acute angle is one which is less than 90

Right Angles

A right angle is an internal angle which is equal to 90

Obtuse Angles

An obtuse angle is one which is more than 90 but less than 180

Straight Angle

A straight angle is 180 degrees

M3G1d. Identify the center, diameter, and radius of a circle

A circle is easy to make:

Draw a curve that is "radius" away

from a central point.

And so:

All points are the same distance

from the center.

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Radius and Diameter

The Radius is the distance from the center to the edge.

The Diameter starts at one side of the circle, goes through thecenter and ends on the other side.

So the Diameter is twice the Radius:

Diameter = 2 Radius

M3M3c. Determine the perimeter of a geometric figure by measuring and summing/adding the lengths of

the sides.

Perimeter

The distance around a two-dimensional shape.

Example: the perimeter of this rectangle is

a+b+a+b = 2(a+b)

The perimeter of a circle is called the

circumference.

See: Circumference

Algebra: 7% = 4 questionsStudents will understand how to express relationships as mathematical expressions.

M3G1.Students will use mathematical expressions to represent relationships between quantities and

interpret given expressions.

a. Describe and extend numeric and geometric patterns.

b. Describe and explain a quantitative relationship represented by a formula (such as perimeter

of a geometric figure).

c. Use a symbol, such as and , to represent an unknown in a number sentence.

60 x = 120

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= 2

60 x 2 = 120

Evaluate 5n when n=12

Step 1 Step 2 Step 3Write the expression

5n

Replace n with 12

5 x 12

Solve

5 x 12 = 60

Data Analysis and Probability: 5% = 3 questionsStudents will gather, organize, and display data and interpret graphs.

M3D1.Students will gather, organize and display data and interpret graphs.

a. Solve problems by organizing and displaying data in charts, tables and graphs.

b. Construct and interpret line plot graphs, pictographs, Venn diagrams, and bar graphs using scale

increments of 1,2,5 and 10.

Graph definedLine plot A diagram that organizes data using a number line.Line graph A graph that uses lines to show changes in data over time.

Bar graph A graph in which information is shown by means of rectangular bars.

Pictograph A graph in which information is shown by means of pictures or symbols.

Circle graph A graph that represents data as part of a circle.

Venn diagram Two or more overlapping circles that show the relationship between sets(similarity/differences).

Line Plot

Suppose thirty people live in an apartment building. These are the

following ages:

58, 30, 37, 36, 34, 49, 35, 40, 47, 47, 39, 54, 47, 48, 54, 50, 35, 40, 38, 47,

48, 34, 40, 46, 49, 47, 35, 48, 47, 46

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Your first step should be: placing the values in numerical order.

30, 34, 34, 35, 35, 35, 36, 37, 38, 39, 40, 40, 40, 46, 46, 47, 47, 47, 47, 47,

47, 48, 48, 48, 49, 49, 50, 54, 54, 58

Now create your graph.

This graph shows all the ages of the people who live in the apartment building. It showsthe youngest person is 30, and the oldest is 58. Most people in the building areover 46 years of age. The most common age is 47.

Line plots allow several features of the data to become more obvious.For example, outliers, clusters, and gaps are apparent.

Outliers are data points whose values are significantly larger or smaller than othervalues, such as the ages of 30, and 58.

Clusters are isolated groups of points, such as the ages of 46 through 50.

Gaps are large spaces between points, such as 41 and 45.

Line Graphs

A line graph is a way to summarize how two pieces of information are related and how they vary

depending on one another. The numbers along a side of the line graph are called the scale.

Example 1:

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Circle Graph

The circle graph below shows the ingredients used to make a sausage and mushroom pizza. The fraction of each

ingredient by weight shown in the pie chart below is now given as a percent. Again, we see that half of the pizza's

weight, 50%, comes from the crust. Note that the sum of the percent sizes of each slice is equal to 100%.

Graphically, the same information is given, but the data labels are different. Always be aware of how any chart orgraph is labeled.

Venn Diagram

An example of a three-part Venn diagram follows:

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References (websites)

Math Worksheet Center

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AA Math

Math Is FunHoughton Mifflin Math

Math Slice

Learning NCJennifer Nord

Revise Soft

Homeschool Math

Model MethodJamit

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3rd GradeMathCRCTStudyGuide2010

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