6.1 Identify relationships of a given percent and describe orally and in writing the
equivalence relationship between fraction, decimals, and percents.
Enabling Objective:
a. Use manipulative to show the meaning of equivalence
b. Explain that percent means ―out of one hundred‖
c. Review parts of a whole is a fractional part. (SOL 3.5 first mention of fractions)
d. Review SOL 4.2 relating fractions to decimals
e. Convert decimals to fractions by counting the number of places behind the decimal
point and using that number to determine the number of zeros in the denominator
proceeded by a 1 and writing the decimal as the numerator without the decimal point
and then reducing the fraction to lowest terms.
Example: .25 = 25/100 = ¼
f. The student will be able to explain orally and in writing the procedure for converting
decimals to fractions. (e. from above)
g. Convert fractions with denominators of 10, 100, or 1000 to decimals by recognizing
the correct number of placeholders behind the decimal point (same as the number of
zeros in the denominator) and place the numerator in the correct place either before or
after the decimal pint. Example: 3/100=.03
h. The student will be able to explain orally and in writing the procedure to convert
fractions with denominators of 10, 100, and 1000 to decimals. (g from above)
i. Convert decimals to percents by moving the decimal point 2 places to the right and
writing the percent symbol. Example .5==50%. Hint: Move the decimal point
towards the percent symbol two places.
j. The student will be able to explain orally and in writing the procedure to convert
decimals to percents (c from above)
k. Convert decimals to percents by moving the decimal point 2 places to the left and
removing the percent symbol. Example: 25% = .25 Hint: * move the decimal 2
places away from the percent symbol. * the decimal point is ―hiding‖ behind the last
number if it is not written elsewhere.
l. The student will be able to explain orally and in writing the procedure to convert
percents to decimals. (k from above)
m. Convert percents to fractions. Hint: Write whole number percent as the numerator,
dropping the percent symbol and 100 as the denominator.
Example: 25% = 25/100
n. The student will be able to explain orally and in writing the procedure to convert
percents to fractions (m from above)
o. Convert fractions to percents by setting up a proportion with the second term being
x/100 and finding the missing term. (use cross products). The missing term is the
equivalent percent for the fractions. Example: 2/5 = x/100, x=40, therefore 2/5 is
40% (optional)
p. The student will be able to explain orally and in writing the procedure to convert
fractions to percents. (o from above)
q. The student will be able to convert a fraction to a percent that does not have a
denominator of 10, 100, and 1000 to a decimal by using division. Example: 2/5 =.4
and then converting the decimal to a percent. Hint: Remind student that this works
even when the denominator is 10,1 00, or 1000.
r. The student will be able to explain orally and in writing the procedure to convert a
fraction to a percent that does not have a denominator of 10, 100, or 1000. (q from
above)
s. Students will be able to convert decimals to percents or fractions, percents to
decimals or fractions, and fractions to decimals or percents using a calculator.
t. Students will be able to explain orally and in writing the calculator procedure for
fractions, decimal and percent conversion using a calculator.
u. Review the meaning and the symbols for greater than, less than, and equal to. (SOL
4.1)
v. Students will need to review the concept of reducing fractions (SOL 5.7)
w. Compare fractions, decimals, and percents.
x. Solve word problems involving fractions, decimals, and percents.
y. Comprehend the terminology: model, equivalence, fraction, decimal, and percent.
z. Students will need to know the most common percents used in everyday life and their
fraction and decimal equivalents. (25%, 33 1/3%, 50% 66 2/3%, 75%, 100%)
Manipulative:
Base ten blocks
Relational attribute blocks
Fraction, Decimal and Percent Towers
Chart and grid paper
6.2 Describe/compare two sets of data using rations and will use appropriate notations
(a/b, a to b, a:b)
** this SOL should follow 6.4
Enabling Objectives:
a. Review terms numerator and denominator (SOL 3.5)
HINT: D is Down under for Denominator
b. Using pictures/manipulative write fractions for several examples (SOL 3.5)
HINT: use candy/food (M&M’s, Skittles, Fruit Loops, etc.) to compare the
differences
c. Write definition of a ratio and relate it to proportion and fractions
d. Use appropriate notation to compare two sets of data (a/b, a to b, a:b)
HINT: remind students that order is important. Example: 3:4 is not the same as 4:3
e. Use real life application problems. Examples: ratios in cooking – sugar to flour, 2
cycle engines – gas to oil, matchbox cars to real cars, plastic figure people to real
people.
f. Convert proportions to the other forms. Example: if the student is given one form of
a ration (2/5) then they will be able to write the ratio in the other two forms (2:5, 2 to
5).
g. Compare two ratios using equivalence and reducing. Compare ratios by using cross
products. Example: Is 3:7 the same as 6:14? Hint: when reducing ratios, remember
not to change improper ratios to mixed numbers.
6.3 Explain orally and in writing the concepts of prime and composite numbers.
Enabling Objectives:
a. Review SOL 3.9
b. Review multiplication facts and understand that the numbers used are factors.
Example: Factors product
5 x 2 = 10
10 x 1 = 10
c. List the factors of any number. Hint: students can play ―Name Those Factors‖. Have
number cards from 2 –100, students bid, ―I can name 3 factors‖, etc. If a student
overbids they loose points.
d. Define the set of whole numbers
e. Define prime numbers (a whole number that only has exactly 2 factors – 1 and itself)
Hint: * Prime is Poor because it only has 2
* ―Rule Breakers‖ 0 and 1 are neither prime nor composite
* 2 is the only even prime number
* using a number board (100) students can cross out all the multiples to see all
the prime numbers less than 100.
f. Define composite numbers (a whole number that has no more than two factors)
Manipulatives:
Cuisenaire rods
Number Grids
6.4 Compare and order whole numbers, fractions, and decimals, using concrete materials,
drawings or pictures, and mathematical symbols.
Enabling objectives:
a. Review the use of symbols and their meanings (>, <, =, , ) for comparisons.
(SOL 4.1, 3.3, 2.2)
b. Review ordering whole numbers from smallest to largest and largest to smallest.
(SOL 2.2, 3.3, 4.1)
c. Use the correct symbol to compare two whole numbers.
d. Review place value of decimals.
e. Review comparing decimals. (SOL 5.2) Hint: remind students that even though a
decimal may have a lot of numbers behind the decimal point it does not mean that the
number is larger. Example: .6 is greater the .546901
f. Order decimals from largest to smallest and smallest to largest. Hint: Rewrite the
numbers vertically and line up the decimal filling in the empty spaces with zeros then
compare.
g. Determine the LCM to find the least common denominator to compare fractions.
Hint: Remind students that it is easier to compare/order fractions after they have
found the common denominator. At that point they will only need to compare the
numerators. Cross products can also be used to compare fractions.
h. Review how to convert fractions to decimals and decimals to fractions. Hint: remind
students to change the fractions or decimals so that they are comparing all fractions r
all decimals to whole numbers. Example: ½, 33.33%, ¾, 4/5) or all decimals, (.5,
.333, .75, .8) and then order the numbers.
Hint: Stress place value.
Activity: When given a number like 1,283,487 to remove the two. What number will
you have to subtract? (2 is in the hundred thousands place so we must subtract 200,
000)
Manipulatives:
Fraction towers
Fraction bars
Base 10 blocks
Graph paper
Cuisinaire rods
Circle charts
6.5 Identify and represent integers on a number line.
Enabling Objectives:
a. Define integers as being a set of whole numbers and their opposites including zero.
Hint: explain that 5 and – are opposites and when they are given an integer they will
be able to give the opposite.
b. Give real life examples of integers including but not limited to temperature, loss and
gains in football, money, and an elevator, above and below sea level. Have students
step off numbers by moving forward for positive integers and moving backward for
the negative numbers.
c. Review SOL 4.2; construct a horizontal and vertical number line including positive
and negative numbers. Hint: this is a good time to point out that 2 and –2 are the
same distance from zero, introducing absolute value.
d. Given a number line with the appropriate intervals and missing integers, the student
will fill in the missing numbers. Example:
-6 A -4 -3 -2 b 0 1 C D 4 5 E
Hint: remind students that the number line does not have to include zero, and that the
interval is very important.
e. Given an integer the students will construct an appropriate number line to identify the
number give. Example: -4
-4 -3 -2 -1 0
Hint: Remind students that a dot is used to show the location of the integer.
Manipulatives:
A class number line on the wall
Number lines on the student desks
Glencoe CD
Overhead thermometer
Two color counters
6.6 Solve problems that involve addition, subtractions, and/or multiplication with
fractions and mixed numbers, with and without regrouping, that include like and
unlike denominators 12 (answers in simplest form); and find the quotient, given a
dividend and divisor expressed as a decimal through thousandths with exactly one
non-zero digit. For divisors with more than one non-zero digit, estimation and
calculators will be used.
This SOL should be introduced without the use of calculator: however, students should
be taught how to use the calculator to find the correct answer and check.
Enabling objectives:
a. Review multiplication facts.
b. Review types of fractions. (mixed numbers, improper fractions, and proper fractions)
c. Review terminology. (LCM, GCF, LCD, reduce, simplest form and lowest terms_
d. Review parts of a fraction (denominator and numerator). Hint: D for Down.
e. Reduce fraction to lowest terms or simplest form when the denominator is 12. Hint
Whatever you do to the top you must do to the bottom *greatest common factor
f. Add fractions with like denominators with no regrouping. Hint: remind students do
NOT add the denominators.
g. Add fractions with like denominators with regrouping.
h. Review changing improper fractions to mixed numbers.
i. Add mixed numbers with like denominators with no regroups.
j. Add fractions with unlike denominators with no regrouping. Hint: remind students to
find LCM to find the LCD for unlike denominators.
k. Add mixed numbers with unlike denominators with no regrouping.
l. Add mixed numbers with unlike denominators with no regrouping.
m. Add fractions with unlike denominators with regrouping
n. Add mixed numbers with unlike denominators with regrouping.
o. Subtract fractions with like denominators with no regrouping.
p. Subtract fractions with like denominators with regrouping. Hint: Remind students
that nay number over itself is equal to one (1/1, 2/2, etc), and when they borrow for
subtraction it would be easier to chose the fraction that has the same denominator that
s used in the problem. Example: 5 – 1 ½ The first step would be to borrow from the
5 and change it to 4 2/2 then subtract. Review SOL 5.7
q. Subtract mixed numbers with like denominators with no regrouping.
r. Subtract mixed numbers with like denominators with regrouping.
s. Subtract fractions with unlike denominators with no regrouping.
t. Subtract mixed number with unlike denominators with no regrouping.
u. Subtract mixed numbers with unlike denominators with regrouping.
v. Convert mixed numbers to improper fractions. Hint: Students can change the mixed
numbers to improper fractions by multiplying the denominator times the whole
number and adding that product to the numerator to find the numerator of the
improper fraction, keep the same denominator. Start at the bottom and go clock wise,
multiply then add. Example 2 ¼
w. Change mixed numbers to improper fractions prior to multiplying.
x. Multiply fractions with no regrouping.
y. Multiply fractions with regrouping.
z. Multiply mixed numbers with no regrouping.
aa. Multiply mixed numbers with regrouping.
bb. Identify the quotient, dividend, and divisor. Hint: the dividend is in and the divisor
waits at the door.
cc. Review division of whole numbers (SOL 5.5) and setting up division problems.
dd. Divide whole numbers and place a decimal point in the quotient. Hint: remind
student that the smaller number does NOT always go on the outside.
ee. Divide with a decimal point in the dividend. (move the decimal point straight up)
ff. Divide with a decimal point in the divisor and in the dividend. Move the decimal
point in the divisor so that it becomes a whole number and move the decimal point in
the dividend the same number of spaces. Hint: Move the decimal in the divisor over
to ring the doorbell of the house. Move the decimal in the divisor over to get out of
the rain. Whatever you do outside the house you must do inside the house.
gg. Review key words that are used in word problems that tell the reader to add, subtract,
multiply, or divide.
hh. Estimate the correct answer and solve
Manipulatives:
Fraction Towers
Fraction Factory
Fraction Bars
Graph paper
ISSUE: DIVISION OF FRACTIONS!!! WHERE ARE THEY?
6.7 Use estimation strategies to solve multi-step practical problems involving whole
numbers, decimals, and fractions.
Enabling Objectives:
a. Review estimation strategies (rounding, front-end estimation, compatible numbers,
etc)
b. Use a problem of the day (POTD) to incorporate this SOL everyday.
c. Review key words for different operations. Example: difference means to subtract.
d. Practice multiplying and dividing multiples of ten stressing inverse operations.
e. Use estimation for measuring. Examples: ―how many inches across is your desk?‖,
―how many steps from your desk to the door?‖, and ―How high is the ceiling?‖
f. Estimate fractions rounding to the nearest half, or whole
6.8 Solve multi-step consumer application problems involving fractions and decimals
and present data and conclusions in paragraphs, tables, or graphs.
Enabling Objectives:
a. Review decimal and fraction operations (SOL 6.6, 6.7)
b. Review the construction of bar, line, circle graphs, stem-and-leaf plots, and box-
whisker plots. (SOL 6.18)
c. Review a problem solving plan (4 step)
d. Consumer problems. Example: Give each student a grocery store circular, and
instruct him or her to spend $100. They must purchase at least 2 meats, 3 breads, and
5 fruits/vegetables. They are to create a meal plan, figure out the cost of meals and
make a presentation. Incorporate fractions with weights like ½ lb. of grapes.
e. Summarize information that is presented in chart form.
ISSUE: CONSUMER APPLICATION
---BUDGET? —PERCENT OF A NUMBER? —
6.9 Compare/convert units of measure for length, weight/mass, and volume within the
US customary system and within the metric system and estimate conversions
between units in each system. Length: part of an inch to 1/8 inch, inches, feet, yards,
miles, millimeters, centimeters, meters, kilometers. Weight/mass: ounces, pounds,
tons, grams, and kilograms. Volume: cups, pints, quarts, gallons, milliliters, and
liters. Area: square units. The intent is to make ―ballpark‖ comparisons and NOT to
memorize conversion factors
Enabling Objectives:
a. Review SOL 3.14, $.11, 4.12, 4.13, 5.11 – measurement
b. Practice measuring to the nearest eighth of an inch.
c. Introduce conversions, this can be done by practicing to convert money i.e. nickels to
dimes, dimes to dollars, quarters to dollars, etc.
d. Chart units of measure from smallest to largest. Hint: This can be completed in the
form of a ladder. When the smallest unit is on the bottom and the largest unit is on
the top, the rule: ―when you go up you divide, and when you go down you multiply,‖
can be applied.
e. Locate products of different weight and volume measurements.
f. Convert inches to feet (divide by 12)
g. Convert feet to inches (multiply by 12)
h. Convert fee to yards (divide by 3)
i. Convert yards to feet (multiply by 3)
j. Know the number of feet in 1 mile (5,280 ft = 1 mile)
k. Introduce the metric system. Hint * There are three basic units (meter, liter, gram) *
prefixes are used to distinguish size (kilo-, hecto-, deka-, root, deci-, cent-, milli-)
*based on ten * this concept can be taught b jumping the decimal forward and
backward, representing multiplying and dividing by multiples of ten.
l. Students will make a conversion chart to use to solve conversion problems:
Convert mm to cm (divide by 10)
Convert cm to mm (multiply by 10)
Convert cm to m (divide by 100)
Convert m to cm (multiple by 100)
Convert m to km (divide by 1000)
Convert km to m (multiply by 1000)
Convert ounces to pounds (divide by 16)
Convert pounds to ounces (Multiply by 16)
Convert pounds to tons (divide by 2,000)
Convert tons to pounds (multiply by 2,000)
Convert g to kg (divide by 1000)
Convert kg to g (multiply by 1000)
Convert cups to pints (divide by 2)
Convert pints to cups (multiply by 2)
Convert quarts to pints (multiply by 2)
Convert quarts to gallons (divide by 4)
Convert gallons to quarts (multiply by 4)
Convert ml to L (divide by 1,000)
Convert L to ml (multiply by 1,000)
m. Area is measured in square units. Hint: Key word is cover; use grid paper to
determine square units for area. (solve for floor covering)-Attribute Blocks.
Students will relate measurements to items in everyday life. Example
LENGTH:
A millimeter is about the thickness of a sheet of paper
A centimeter is about the width of your thumb
An inch is as long as the top of your thumb to the first knuckle (about 2.5
centimeters)
A meter and a yard are almost the same, a meter is 3 inches longer, and they are both
as long as your arm.
A baseball bat is about a meter long
WEIGHT/MASS:
A kilogram is about twice as heavy as a pound
A quart and liter are very close, but a liter is a little bit larger that a quart
A kilometer and a mile compare (a kilometer is about 6/10ths of a mile)
A gram weighs about the same as a paper clip
Two loaves of bread have a mass of about 1-kilogram
A raisin has a mass of about 1-gram
A few grains of salt have a mass of about 1-milligram
VOLUME:
A liter is a little bit more than a quart
Capacity of a paint bucket is 1 gallon
Capacity of a cereal bowl is a cup
Freezing Point: 0 degrees Celsius and 32 degrees Fahrenheit
Boiling Point: 100 degrees Celsius and 212 degrees Fahrenheit
Body temperature: 37 degrees Celsius and 98.6 degrees Fahrenheit
6.10Estimate and then determine length, weight/mass, area, and liquid volume/capacity
using both standard and non-standard units of measure.
Enabling Objectives:
a. Review measurement (SOL 4.11, 4.12, 4.13, 5.11)
b. Create a color coded ruler to help students to measure length
c. Define mass
Differentiate mass and weight
d. Use a triple beam balance and other types of scales to determine mass/weight.
e. Define volume/capacity
f. Use graduated cylinder to determine volume (use displacement methods to determine
volume)
g. Practical application problems. Example: length- decorate a bulletin board and each
student must determine how much space they have to decorate, weight/mass- If I
purchase a pound of fudge, how much would each student get? How much does a
gallon of water weigh?
h. Compare the actual measurement, and estimated measurement of things so that
students will get a rough idea of which unit is more or less than another. Example:
volume of popcorn or cereal in a specific container – how much to fill one cup?
i. Review the comparisons in 6.6
Manipulatives:
Triple beam balance
Rulers
Centimeter cubes
6.11Determine if a problem situation involving polygons of < 4 sides represents the
application of perimeter or area and apply the appropriate formula.
Enabling Objectives:
a. Define polygon
b. Review the concept of perimeter: the distance around (SOL 2.12, 2.13, 4.14, 5.8)
Hint: pe-RIM-eter and RIM is the outside edge of something
c. Review the concept of area: The space inside a flat shape Hint: key word cover.
d. Review finding the perimeter of a 3 or 4 sided object (SOL 5.8) p-2l + 2w
Hint: add up all the sides and formulas for square and rectangle.
e.
Review height of a triangle, bass of a triangle, and finding the area of 3 and f sided
objects:
Triangle = bh/2 or (1/2)bh
Rectangle = lw
Square = s2
f. Review the key words used for area and perimeter (SOL 5.10) Example: area- cover,
perimeter- around
g. When given particular real life situations, determine if a real or perimeter is
appropriate (SOL 5.10) Example: I am going to tile the floor in my kitchen, or I want
to put a border around my bathroom..
h. When given a real life situation involving 3 and 4 sided objects determine which is
appropriate area or perimeter and then solve the problem. Example:
3 ft.
10 ft.
a. If I wanted to carpet this room, how much would I need?
b. If I wanted to put a border around this room, how much would I need?
Manipulatives:
Graph paper
Relational Attributes Blocks
Tangrams
Geoboards
6.12Create/solve problems by finding the circumference and/or area of a circle when
given the diameter or radius. Using concrete materials or computer models, derive
approximations for pi from measurements for circumference and diameter.
Enabling Objectives:
a. Review terminology from 5.9
b. Given the diameter, find the radius by dividing the diameter by 2 (r = d/2)
c. Given the radius, find the diameter by multiply the radius by 2 (d=2r)
d. Use a ruler, measure the diameter and radius on various circles
e. Find the circumference by using string or yarn
f. Students will differentiate between circumference and area by drawing pictures
(CIRCumference is the CIRCle and the area COVERS the circle)
g. Given the formula A=D, the student will be able to solve for circumference when
given either the diameter or the radius
h. Given the formula A=R, the student will be able to solve for area when given either
the diameter or the radius.
i. Through measuring diameters and circumferences, the student will make comparisons
and determine that pi is approximately 3. Create a chart to determine pi. Example:
Circumference Diameter C + D C – D C x D C / D
j. Include non-traditional problems
k. The approximation for pi that is used most often is 3.14
l. The exact measure for pi is 22/7 (this should be used when the measurements are
given in fractions)
m. Use the calculator and the memory function to solve and create problems
**** 3-14 (March 14th) is considered pi day
6.13Estimate angle measure using 45 degrees, 90 degrees, and 180 degrees as referents
and use the appropriate tools to measure the given angles.
Enabling Objectives:
a. Review SOL 5.14 (measure angles)
b. Identify angles that measure 45 degrees, 90 degrees, and 180 degrees
c. Understand that if an angle is smaller than the 45 degree angle then the measurement
must be from 1 – 44 degrees
d. Understand that if an angle is larger than 45 degrees, but smaller than 90 degrees then
the measurement of that angle will be between 46-89 degrees
e. Understand that if an angle is larger than 90 degrees but smaller than 180 degrees
then the measurement of that angle will be between 91 and 179 degrees
f. Using 45 degree, 90 degrees, and 180 degrees and their knowledge of angle students
will be able to estimate the size of any angle. Remember that the smaller the opening
the smaller the angle measures in degrees.
g. Use appropriate tools, i.e. protractor, to measure all types of angles.
h. Identify angles in everyday life to use as reference angles, such as, the corner of a
piece of paper is usually 90 degrees
i. Angles come from a circle. A circle measures 360 degrees.
6.14Identify, classify, and describe the characteristics of plane figures, including
similarities and differences.
Enabling Objectives:
a. Review definition of a plane figure (SOL 3.18)
b. Review vocabulary including: point, ray, line, and line segment
c. Review different plane figures known by students (SOL 5.18)
d. Review definition of right angles (SOL 5.13)
e. Describe orally and in writing the characteristics of plane figures by giving examples
of triangles, squares, rectangles, quadrilaterals, pentagon (including the number of
sides and the types of angles)
Hint: give examples of what a shape is and what it is not and have the students develop
their own definition and create a chart-example.
Name of figure # of sides # of angles Types of angles
6.15 Determine congruence of segments, angles, and polygons by direct comparison,
given their attributes. Examples of non-congruent and congruent figures will be
included.
Enabling Objectives:
a. Review-Identify and define a segment
b. Review-Identify and define an angle.
c. Review-Identify and define a polygon.
d. Define congruence, parallel, perpendicular, regular polygons, and intersecting
e. Construct congruent segments with a compass and straight edge.
f. Construct congruent angles with a compass and straight edge.
g. Construct congruent polygons wit a compass and straight edge.
h. Identify given segments, angles, and polygons as being congruent or non-congruent
Hint: Straight pretzels, toothpicks, marshmallows can be used to model angels.
6.16The student will construct the perpendicular bisector of a line segment and an angle
bisector, using a compass and straightedge
** Not Tested **
Enabling Objectives:
a. Review definition of perpendicular, line segment, arc, and angle. (SOL 4.16, 4.17)
b. Define bisector.
c. Demonstrate to students how to construct a perpendicular bisector of a line segment
using a compass and a straight edge.
d. Students will construct perpendicular bisectors using a compass and a straight edge.
e. Demonstrate to students how to construct an angle bisector using a protractor,
compass, and a straight edge.
f. Students will construct and angle bisector using a protractor, compass, and a straight
edge.
6.17Sketch, construct models, and classify rectangular prisms, cones, cylinders, and
pyramids.
Enabling objectives:
a. Explain the characteristics of rectangular prisms, cones, cylinders, and pyramids.
Hint: give examples and non-examples and have students identify them and come up
with their own definitions.
b. Break down rectangular prism, cone, cylinder, and pyramid into shapes within each
object. Example: a rectangular prism is made up of rectangles, etc… A great activity
for this is to cut up cereal boxes for rectangular prisms and paper towel holders for
cylinders.
c. Using pre-made nets, the students will construct different objects.
d. When given a net, the student will be able to identify the object without actually
constructing the object.
e. Using a straight edge or pattern block (rectangle, circle, triangles, square, etc.) the
students will create his or her own nets.
f. Using a straight edge and dot paper the student will sketch each shape.
Idea: Students can create these figures using gumdrops/marshmallows and toothpicks.
6.18Given a problem situation, collect/analyze/interpret data in line, bar, and circle
graphs and stem-and-leaf plots and box-and-whisker plots. Circle graphs will be
limited to halves, fourths, and eighths.
Enabling Objectives:
a. Collect data Examples: High temperature each day for the week, number of class
members who watch TV, number of hours it takes to complete a task, etc.
b. Analyze data (are there any trends, what is high and what is low)
c. Review vocabulary: polls, survey, frequency tables, tally sheets, spreadsheets, etc.
Determine which graph is appropriate for each situation (line-change over time or
dates stem-and-leaf/ box-and-whiskers – temperature, ages and grades work well).
d. Display appropriate data in a line graph.
e. Display appropriate data in a bar graph.
f. Display appropriate data in a circle graph using only 1/2s, 1/4s, and 1/8s
g. Display appropriate data in a stem-and-leaf plot
h. Display appropriate data in a whisker-and-box plot
i. Interpret data in a line graph
j. Interpret data in a bar graph
k. Interpret appropriate data in a circle graph using only 1/2s, 1/4s, and 1/8s
l. Interpret appropriate data in a stem-and-leaf plot
m. Interpret appropriate data in a whisker-and-box plot
n. Interpret and orally describe the clustering of data. Example: the temperature highs
for the week are mostly in the 70’s
o. Compare the different graphs and their uses. Example: Circle graph is good to show
percents or parts of a whole; the complete circle represents the whole, or 100%
6.19Describe the mean, median, and mode as measure of central tendency and determine
their meaning for a set of data
Enabling Objectives:
a. Review 6.4 compare and order whole numbers
b. When finding the mean, median, or mode of a set of numbers the numbers should be
ordered first.
c. Define mode- the number that occurs the most often.
d. Given different sets of data, students will identify the mode, modes, or ―No Mode‖
e. Define mean- average; add up all the numbers and divide their sum by the total of
numbers added. Example: add: 2+3+4+7 = 16
Count: 1 2 3 4
16 divided by 4 = 4
Mean is 4
f. Given different sets of data, students will find the mean for each group (grades,
points scored in a basketball game, etc)
g. Define median: the number in the middle (do not forget to order the numbers first)
Hint: the median strip in the highway is in the middle of the road.
h. Given different sets of data, students will identify the median for each set. If the data
has an even number of items without a middle number, show method of averaging the
two middle numbers
i. Given different sets of data, students will find mode, mean, and media for each set.
Example: Using sport statistics, when is the mean used? – Batting average. When is
the mode use? Golf par. When is the median used? – handicap in bowling.
j. When given median, mod, mean, and a partial set of data the student will use the
information to complete the set of data. Example: 40, 41, __, __, 54
Mode is 4
Median is 47
The two blanks must be 47 and 47
6.20Determine and interpret the probability of an event occurring from a given sample
space.
Enabling Objectives:
a. Review 6.2 (compare data using ratio), 5.7, 6.6 (express fractions in simplest terms)
b. Review and introduce terms: probability of a given event, probable – likely, trials,
outcomes, data, sample space – the set of all possible, multiply, favorable outcomes,
independent, and compound events.
c. View concrete items and write selection probabilities as ratio Example: when given
pictures of footballs, baseballs, soccer balls, basketball the student will write ratios of
footballs to baseballs, or basketballs to all balls, etc.
d. View a drawing of items and write selection probabilities by counting and setting up a
ratio.
e. Experimenting. Example: In a group each student will label a checker with their
name on a piece of masking tape. Place the checkers in a bag. Students take turns
drawing one checker (trial) out of the bag. Each student keeps a tally chart and
completes ten trials. Tally sheet would look like this:
My Checker Not My Checker
Drawing one’s own checker would be a favorable outcome. Write the result as a
ration: Total # of my checkers 4: Total # of checkers drawn 10 ( 4:10 )
More experiment ideas: Tossing a number cube to get an even number or a particular
number, coin toss – independent evens – toss 2 times, favorable outcome equal 2
heads etc…, spinner color probability, coin toss or cube list all possible combinations
compound event
f. Construct tree diagram Example: outfit combinations using 3 shirts and three pants
g. Counting principle Example: m choice for 1st decision and n choice for 2nd decision
then m * n =3 shirts * 3 pants = 9 different combinations
h. Given an independent event, student writes probability of the expected outcome.
i. Given a compound event, student writes probability of some particular outcome.
j. Given a chart, student will write probability.
k. Given a picture of a spinner, student will write probability.
l. Given a word problem, student will be able to interpret information and determine the
probability Example: The Virginia Lottery has a pick three and pick four – what is the
probability of winning? 10 * 10 * 10 or 10 * 10 * 10 * 10
m. Given a tree diagram, the student will orally and in writing give the probability of a
specific event. When given this tree diagram of tossing a coin twice the student will
be able to answer questions:
H (h, h) A. How many possible outcomes are there?
H 4
T (h, t) B. What is the probability of tossing heads,
T H (t, t) heads? P(h,h)=1/4
T (t, h)
6.21Recognize/describe/extend a variety of numerical and geometric patterns.
Enabling Objectives:
a. Review SOL 5.19 (patterns)
b. Recognize a numerical pattern. Example: even numbers, odd numbers, prime
numbers, counting by tens, etc
c. Recognize a geometric pattern. Example: increase/decrease the number of sides of a
regular polygon
d. Describe a numerical pattern. Example: the same number being
added/subtracted/multiplied/divided each time (3,9,27,72----times 3 each time)
e. Describe a geometric pattern
f. Extending a numerical pattern
g. Extending a geometric pattern
h. Use codes to show an example of a pattern. Example a=z b=y etc. or a=1 b=2 etc.
Students can develop their own codes
Manipulatives:
Relation Attribute Blocks.
6.22 Investigate and describe concepts of exponents, perfect squares, and square roots,
using calculators to develop exponential patterns. Patterns will include zero and
negative exponents. Investigations will include the binary number system as an
application of exponents and patterns
Enabling Objectives:
a. Review SOL 4.8, 5.19
b. Define exponents, power, and factor
52 means 5 x 5 = 25 base- big number on the bottom exponent-bug in the air
Hint: any number to zero power is always one (50 = 1), and any number to the first
power is always the number (51 = 5)
c. Practice using expanded form (5 x 5 x 5), numerical form (the answer 125), and
exponential form (53) including variables. Example: b3 = bbb
d. Practice reading powers. Hint: to the second power = squared, and to the third power
= cubed
e. Define square root
f. Identify the sign
g. Using the calculator and the square root chart, give the square root of a number.
h. Know the squares up to 152
i. Define perfect square.
Use a number chart up to 100 to identify all the perfect squares.
Use tiles to demonstrate how number can be a perfect square.
Hint: They actually make a perfect square
j. Practice using expanded form, numerical form, and exponential form including
variables with negative exponents. Example: 3-2 = 1/3 x 1/3 = 1/9
k. Create a chart to show the patterns in exponents. Hint: a positive exponent numeric
answer gets larger with negative exponents the numeric answer gets smaller.
l. To teach the binary number system- begin by stressing how the base 10 system
works- only 10 digits then we start over- place value ones, tens, hundreds. Base 2
place value is ones, twos, fours. Any base 2 number can be put into a place value
chart to determine its base ten value. Example: 64 32 16 8 4 2 1 to go
from base
1 1 0 1 1 0 1 10 to base 2 you
must add up the
place values.
6.23Model/solve algebraic equations, using concrete materials, and solve one-step linear
equations in one variable, involving whole number coefficients and positive rational
solutions.
Enabling Objectives:
a. Review definition and concept of a variable (5.20)
b. Review writing open sentences given real world situations (5.20, 5.21) Example:
model by saying ―I’m thinking of a number that is 5 more than 7, what is it?‖ or ―I’m
thinking of a number that if you add 2 to it, you will have 9, what is it?‖ or ―If you
multiply my number by 3 you get 21, what is it?‖
c. Define inverse operation (subtraction/addition and multiplication/division) Hint: One
―un-does‖ the other
d. Use concrete materials such as ―Hands On Equations‖ or ―Easter Egg Algebra‖ to
solve one step linear equations Hint: Keep equations balanced
e. Students will communicate orally and in writing an explanation of how the solution
of a one step linear equation was found. Examples of one-step linear equations as
define here:
m + 10 = 15
j – 6 = 12
10p = 50
x/3 = 4