practice hints & notes disks in a bag. what is the … review...reduce all ratios!!! 20 d....

Grade 6 SOL Review Packet 1

SOL 6.1

The students will describe and compare data, using ratios, and will use appropriate notations, such as a/b, a to b, and a:b.

HINTS & NOTES

** Make sure that you write the ratio in the order that is asked** Reduce all ratios!!!

PRACTICE 1. There are 20 green disks and 100 purple

disks in a bag. What is the ratio of purple disks to green disks?

A. 20

100

B. 100

20

C. 20

120

D. 100

80

2. What is the ratio of squares to total circles?

F. 4:5 G. 5:4 H. 4:9 J. 5:9

3. What is the ratio of the number of gray circles to black circles.

A. 2 to 5 B. 5 to 4 C. 4 to 2 D. 4 to 5

Skills Checklist I can…

Describe a relationship within a set by comparing part of the set to the entire set. Describe a relationship between two sets by comparing part of one set to a corresponding part of the

other set. Describe a relationship between two sets by comparing all of one set to all of the other set. Describe a relationship within a set by comparing one part of the set to another part of the same set.

Represent a relationship in words that makes a comparison by using the notations a

b

, a:b, and a to b.

Create a relationship in words for a given ratio expressed symbolically.


SOL 6.2 The students will

a) investigate and describe fractions, decimals, and percents as ratios; b) identify a given fraction, decimal or percent from a representation; c) demonstrate equivalent relationships among fractions, decimals, and percents; and d) compare and order fractions, decimals, and percents.

HINTS & NOTES

Percent – a percent is a ratio in which the first term is compared to 100. To write a visual as a percent – Count!: first write as a fraction, then convert to a decimal. Convert the decimal to a percent. Remember – think of percent as per hundred. To change a decimal to a percent → move the decimal to the right (→) two places. Example: .234 = 23.4% To change a fraction to a percent → divide the numerator (top number) by the denominator (bottom number). Move the decimal to the right (→) two places.

Example: 8

3=.375 = 37.5%

To change a fraction to a decimal → divide the numerator (top number) by the denominator (bottom number).

Example: 8

3=.375

PRACTICE 1. What percent of this grid is shaded?

A. 40% C. 50% B. 60% D. 70%

2. Of the kids in Ms. Bond’s class, 40% are boys. Which

is the decimal for the part of the class that are boys? F. 40 H. 4 G. 0.4 J. 0.04

3. Of the students in Mr. Wright’s sixth grade class, 75%

are in art. What fraction of the class is in art?

A. 9

7 C.

4

3

B. 10

7 D.

7

5

4. Which shows these numbers in order from least to greatest? 42.62 46.2 42.8 45.48

A. 45.48, 46.2, 42.8, 42.62 B. 42.62, 42.8, 46.2, 45.48 C. 42.62, 42.8, 45.48, 46.2 D. 46.2, 45.48, 42.8, 42.62


HINTS & NOTES Steps for ordering numbers: 1. Change all fractions to decimals. 2. Line up the decimals. 3. Add on zeros until the numbers are the same length. (same number of digits) 4. Ignore the decimals and put them in order. **Remember to look for the order that the questions asks. (Least →Greatest or Greatest→Least) = is equal to < is less than > is greater than ≠ is not equal to

MORE PRACTICE

5. Which statement is true?

F. 5

1 >

4

1 H.

3

2 >

7

6

G. 4

3 >

12

7 J.

8

3 >

11

6

6. Which symbol makes this statement true?

4

3

6

5

A. > B. < C. = D. None of the

7. Which ratio is equivalent to 4.5?

F. H.

G. J.

8. Which would be located between the two decimals on the number line?

0.6 0.8

A. 0.860 B. 0.481 C. 0.062 D. 0.731


Identify the decimal and percent equivalents for numbers written in fraction form including repeating

decimals. Represent fractions, decimals, and percents on a number line. Describe orally and in writing the equivalent relationships among decimals, percents, and fractions

that have denominators that are factors of 100. Represent, by shading a grid, a fraction, decimal, and percent. Represent in fraction, decimal, and percent form a given shaded region of a grid. Compare two decimals through thousandths using manipulatives, pictorial representations, number

lines, and symbols (<,≤,≥, >, =). Compare two fractions with denominators of 12 or less using manipulatives, pictorial representations,

number lines, and symbols (<,≤,≥, >, =). Compare two percents using pictorial representations and symbols (<,≤,≥, >, =). Order no more than 3 fractions, decimals, and percents (decimals through thousandths, fractions with

denominators of 12 or less), in ascending or descending order.



a) identify and represent integers; b) order and compare integers; and c) identify and describe absolute value of integers.

HINTS & NOTES

Remember – integers include positive whole numbers, negative whole numbers, and zero. It can be helpful to graph the integers on a number line. The point furthest to the left would have the least value and the point furthest to the right would be the greatest value. Absolute value- the distance of a number from zero on the number line. Absolute value is represented as |−6| = 6.

PRACTICE


A. -82 > 85 B. 4,117 < -2,654 C. -601 > -456 D. -72,643 > -81,249

2. Which integer is less than -7?

F. -9 G. -6 H. 0 J. 8

3. The temperatures this week were recorded in the chart

below.

On which day was the temperature the warmest?

A. Monday B. Tuesday C. Wednesday D. Friday

4. Circle all of the integers below.

Day Temperature

Monday -6

Tuesday -11

Wednesday -3

Thursday -9

Friday -4

-4 23 -0.3

2.2


HINTS & NOTES cont. **Remember**

PRACTICE cont. 5. Which list of integers is ordered from greatest to least?

A. -17, -16, -15 B. -15, -16, -17 C. -17, -15, -5 D. -16, -17, -15

6. Write an integer to represent each situation:

a) 10 degrees above zero b) a loss of 16 dollars c) a gain of 5 points d) 8 steps backward

7. Which expression has the smallest value?

A. |-19| B. |-34| C. |11| D. |47|


F. -17 < -19 G. -13 > -20 H. -11 > -9 J. -6 < -8

9. |-5| + |2| =

A. -7 B. -3 C. 3 D. 7

10. Which of the following is not an integer?

F. 9 G. 0 H. 0.1 J. -2


Identify an integer represented by a point on a number line. Represent integers on a number line. Order and compare integers using a number line. Compare integers, using mathematical symbols (<, >, =). Identify and describe the absolute value of an integer.


SOL 6.4 The students will demonstrate multiple representations of multiplication and division of fractions.

HINTS & NOTES

Demonstrate multiplication and division of fractions using representations.

PRACTICE

1. Look at the model.

The model represents which product?

A. 3 5

7 6 C.

3 2

7 7

B.

3 6

5 7 D.

5 7

3 6

2. Which model represents a product equivalent to ?

F.

G.

H.

J.


Demonstrate multiplication and division of fractions using multiple representations. Model algorithms for multiplying and dividing with fractions using appropriate representations.


SOL 6.5 The students will investigate and describe concepts of positive exponents and perfect squares.

HINTS & NOTES

Perfect square –the number that results from multiplying any whole number by itself. Example: 36 = 6 × 6 = 62

Perfect square numbers: 1, 4, 9, 16, 25, 36, 49, 64,.. Any real number other than zero raised to the zero power is 1. Zero to the zero power (0) is undefined. Ex: 20 = 1, 50 = 1, 30 = 1 Exponent – shows how many times a base is used as a factor. Ex: 53 = 5 x 5 x 5 (5 is the base, 3 is the exponent)

PRACTICE

1. A pattern of increasing perfect squares is

shown below.

36, 49, 64, ___, 100

What number needs to be squared to fill the blank for the missing term?

A. 6 B. 7 C. 8 D. 9

2. Based on the geometric pattern shown,

what is the value of 55? 51 = 5 52 = 25 53 = 225 54 = 625

F. 10 G. 25 H. 3,125 J. 15,625

3. Which is a perfect square between 64 and 100?

A. 81 B. 99 C. 68 D. 74

4. 24 =

F. 6 G. 16 H. 8 J. 32


Recognize and describe patterns with exponents that are natural numbers, by using a calculator.

Recognize and describe patterns of perfect squares not to exceed 220 , by using grid paper, square

tiles, tables, and calculators.

Recognize powers of ten by examining patterns in a place value chart:

,

,

4

3

2

1

0

10 10 000

10 1 000

10 100

10 10

10 1



a) multiple and divide fractions and mixed numbers; and b) estimate solutions and then solve single-step and multi-step practical problems involving

addition, subtraction, multiplication, and division of fractions.

HINTS & NOTES ** Change all mixed numbers to improper fractions before performing an operation** ** To add or subtract fractions – you MUST have a common denominator. ** When multiplying fractions – multiply the numerators and then multiply the denominators. Make sure to reduce!

Example:3

1 x

5

4 =

15

4

**When dividing fractions – change the division sign to multiplication and flip (write the reciprocal) of the fraction that follows the sign. Then multiply and reduce. KEEP – CHANGE - FLIP

Example: 3

1 ÷

5

4 =

3

1 x

4

5 =

12

5

**Remember** Sum means the result when numbers are added. Product means the result when numbers are multiplied. Quotient means the result when numbers are divided.

PRACTICE

1. Lindsay bought 24

3 meters of rope. She used

3

1

of it for a tire swing. How much rope did she use for the tire swing?

A. 212

5 meters C.

12

5 meters

B. 17

5 meters D.

12

11 meters

2. 6

1 +

4

3 =

F. 10

4 H.

12

11

G. 12

7 J. 1

12

1

3. Beth walked 4

1mile yesterday and

12

5mile today.

What was the total distance walked by Beth the last two days?

A. 8

3 miles B.

3

2miles

C. 12

5 miles D.

12

7 miles

4. 1 215 3 =

5. Look at the circle.

The shaded part is equivalent to %.


PRACTICE cont.

6. 2

3is equivalent to

F. 0.6666…. G. 0.6 H. 0.5 J. 0.66

7. Which set of numbers are equivalent?

A. 0.02 = 2% =

B. 60% = 0.06 =

C. = 0.25 = 25%

D. = 0.78 = 78%

8. Ryan used 2

1 a can of oil that had

88

7pints in it to fill his car. About how

much oil did he use? Choose the best estimate.

F. 4 pints

G. 42

1 pints

H. 8 pints

J. 82

1 pints

9. Maria cut a piece of ribbon 6

5foot long. She cuts

4

3foot off of the piece of ribbon. What is the length

of the remaining piece of ribbon?

A. 12

1foot

B. 8

1foot

C. 6

1foot

D. 4

1foot

10. Grandma’s cookie recipe calls for 24

3 cups of

sugar. If grandma wants to triple the recipe, how

much sugar will she need?

A. 84

3 cups C. 6

4

3 cups

B. 84

1 cups D. 6

4

1 cups


Multiply and divide with fractions and mixed numbers. Answers are expressed in simplest form. Solve single-step and multistep practical problems that involve addition and subtraction with fractions

and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

Solve single-step and multistep practical problems that involve multiplication and division with fractions and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.


SOL 6.7 The students will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of decimals.

HINTS & NOTES

** When estimating an answer – pick the answer choice that is closest to the answer that you came up with (round). Rounding – If the digit to the right of the place to which you are rounding is: 5 or greater – round up Less than 5 – round down Watch out for the backwards problems- the problems that give you the answer and want you to find the problem. To solve these – PLUG IN the answer choices to find the best fit. When using your calculator, watch your screen to be sure you have entered numbers correctly.

PRACTICE

1. Tom’s neighbor paid him $15.75 for mowing the lawn. Tom then buys a t-shirt for $10.43. How much money does he have left? A. $5.00 B. $26.18 C. $25.00 D. $5.32

2. The cost of dinner for three is $20.25. Which is the best estimate for the price per person of a meal?

F. $2.50 G. $5.50 H. $7.00 J. $10.25

3. The table shows the prices for CDs at different stores.

Which store has the lowest price per CD? A. Budget Buy B. CD City C. Music Mall D. Shop Smart


Solve single-step and multistep practical problems involving addition, subtraction, multiplication and division with decimals expressed to thousandths with no more than two operations.


SOL 6.8 The student will evaluate whole number numerical expressions, using order of operations.

HINTS & NOTES

The Order of Operations is as follows: First- complete all operations inside of the grouping symbols. ( ), [ ], { } Second-Solve all exponents Third-Multiply or Divide in order from left to right. Fourth- Add or subtract in order from left to right. The power of a number represents repeated multiplication of the number 83= 8 · 8 · 8. Any number, except 0, raised to the zero power is 1. 20 = 1, 50 = 1, 30 = 1

PRACTICE

1. Simplify: 42 + (8 + 2) ÷ 2

A. 13

B. 21

C. 9

D. 14

2. Simplify:

23 1

2

F. 2

G. 5

2

H. 6

J. 4

3. Evaluate:

A. 1

B. 9

C.

D.

4. Which step would be done first to simplify

the expression? 3 x 72 + 18 ÷ 2

F. 18 ÷ 2

G. 72

H. 3 x 72

J. 72 + 18

SOL 6.9


Simplify expressions by using the order of operations in a demonstrated step-by-step approach. The expressions should be limited to positive values and not include braces { } or absolute value | |.

Find the value of numerical expressions, using order of operations, mental mathematics, and appropriate tools. Exponents are limited to positive values.


The student will make ballpark comparisons between U.S Customary System of measurement and measurements in the metric system.

HINTS & NOTES

Length – 12 inches = 1 foot 3 feet = 1 yard 5280 feet = 1 mile 1760 yards = 1 mile 10 millimeters = 1 centimeter 100 centimeters = 1 meter 1000 meters = 1 kilometer Weight/mass – 16 ounces = 1 pound 2000 pounds = 1 ton 1000 grams = 1 kilogram Liquid volume – 2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon 1000 milliliters = 1 liter Conversions 1 inch ~ 2.5 cm 1 meter ~ 1 yard , meter > yard 1 mile ~ 1.5 kilometer 1 nickel ~ 5 grams 1 kilogram ~ 2 pounds 1 quart ~ 1 liter 0°C ~ 32°F water freezes 100°C ~ 212°F water boils 20°C ~ 70°F room temperature 37°C ~ 98°F body temperature Area – 100 square millimeters = 1 square centimeter 10000 square centimeters = 1 square meter

PRACTICE

1. Which measurement represents the least volume?

A. 9 quarts B. 35 cups C. 2 gallons D. 17 pints

2. Sam bought 324 inches of yarn. How many yards of yarn

did she buy?

F. 108 yards G. 27 yards H. 18 yards J. 9 yards

3. The factory worker filled 6 one-pint jars with jelly. He had

1 cup of jelly left over. How many cups of jelly did he have to start in all?

A.4 cups C. 7 cups B. 13 cups D. 25 cups

4. Kase bought 4.3 kilograms of peanuts. How many grams

did he buy? F. 0.43 grams G. 43 grams H. 430 grams J. 4,300 grams

5. The glasses shown each hold 10 fluid ounces when full. The shaded portions show how much water is in the glasses.

Which is closest to the amount of water in the glasses?

A. 34 fluid ounces B. 28 fluid ounces C. 22 fluid ounces D. 18 fluid ounces

SOL 6.10


Estimate the conversion of units of length, weight/mass, volume, and temperature between the U.S. Customary system and the metric system by using ballpark comparisons. Ex: 1 L ≈ 1qt. Ex: 4L ≈ 4 qts.

Estimate measurements by comparing the object to be measured against a benchmark.


The students will a) define pi (π) as the ratio of the circumference of a circle to its diameter; b) solve practical problems involving circumference and area of a circle, given the diameter or

radius; c) solve practical problems involving area and perimeter; and d) describe and determine the volume and surface area of a rectangular prism.

HINTS & NOTES

The radius of a circle is half the length of the diameter. pi (π) ≈ 3.14 Circumference of a circle C= 2πr or C = πd Area of a circle A = πr2 If the question is asking for the distance around something, it is asking for perimeter. If the question is asking for the amount needed to cover or the amount of space something takes, it is asking for area. Formulas: Perimeter – sum of all sides Area of triangle –

A = 2

1base x height

Area of rectangle – A = length x width Area of square – A = side x side *Use a piece of paper or ruler to help you measure length*

PRACTICE 1. If the diameter of a circle is 9 inches, which is

closest to the circumference?

A. 14.13 in. C. 28.26 in. B. 63.59 in. D. 254.34 in.

2. Bob is trying to grow grass on the circular section

of yard below. If the diameter of the circle is 6 yards, how much seed will he need to cover the entire area?

F. 18.84 yds.2 H. 28.26 yds.2 G. 113.04 yds.2 J. 254.34 yds.2

3. What is closest to the area of a circle if the radius

is equal to 2.5 centimeters? A. 7.85 sq. cm. C. 15.7 sq. cm. B. 19.63 sq. cm. D. 78.5 sq. cm.

4. Which situation would you use to gather data in order to derive pi (π)?

F. Measuring a string to wrap around a polygon. G. Measuring the Circumference and diameter of several circles. H. Determining how many one-inch cubes fit into a container. J. Determining the number of tiles needed to cover a surface.

5. What is the area of the large rectangle shown if each small square is 4 inches wide and 4 inches

long?

A. 30 sq. in. C. 80 sq. in.

B.120 sq. in. D. 480 sq. in

6 yds.


Rectangular prism – think cardboard box! All faces and bases are rectangles. Surface Area of a rectangular prism is the sum of the areas of all six faces SA = 2lw + 2lh + 2wh

Volume of a rectangular prism- V= lwh Dimensions – length x width of something

PRACTICE cont 6. How many square inches of fabric does Kendall need for a triangular flag with a base of 20 inches and a height of 40 inches?

F. 800 in.2 H. 400 in.2 G. 120 in.2 J. 100 in.2

7. Robin needs to paint this entire box for her school project.

How much surface will he need to paint?

A. 22 cm2 C. 44 cm2 B. 304 cm2 D. 320 cm

8. A rectangular prism-shaped box is pictured below. How much sand will it hold?

F. 4,096 mm3 H. 1,101 mm3 G. 2,048 mm3 J. 5,028 mm3

9. Greg walked around a football field 45 ft long and 15 ft wide. What was the total distance that Greg walked?

F. 60 ft H. 120 ft G. 600 ft J. 675 ft


Practice Cont.

10. The area of Pam’s garden is between 1,500 and 2,000 square inches. Which of these choices could be the dimensions of her garden?

A. 18 in. x 32 in. B. 40 in. x 30 in. C. 30 in. x 60 in. D. 36 in. x 72 in.

11. What is the area of a triangle with a length of 20.7 cm and a width of 18 cm?

Area =

12. Candy is covering a rectangular prism-shaped

box with cloth.

What is the minimum amount of cloth Carl needs to cover the box?

A. 272 sq. in.

B. 192 sq. in.

C. 136 sq. in.

D. 96 sq. in.


Derive an approximation for pi (3.14 or 22/7 ) by gathering data and comparing the circumference to the diameter of various circles, using concrete materials or computer models.

Find the circumference of a circle by substituting a value for the diameter or the radius into the formula C = πd or C = 2πr.

Find the area of a circle by using the formula A = πr 2. Apply formulas to solve practical problems involving area and perimeter of triangles and rectangles. Create and solve problems that involve finding the circumference and area of a circle when given the

diameter or radius. Solve problems that require finding the surface area of a rectangular prism, given a diagram of the

prism with the necessary dimensions labeled. Solve problems that require finding the volume of a rectangular prism given a diagram of the prism with the necessary dimensions labeled.



a) identify the coordinates of a point in a coordinate plane; and b) graph ordered pairs in a coordinate plane.

HINTS & NOTES Quadrants are named in counterclockwise order.

signs on the ordered pairs are: quadrant I (+,+) quadrant II, (–,+) quadrant III, (–, –) quadrant IV, (+,–) Origin-is the point at the intersection of the x-axis and the y-axis. For all points on the x-axis, the y-coordinate is 0. For all points on the y-axis, the x-coordinate is 0.

PRACTICE

1. Six points are shown on the grid.

Which three points can be connected in the order shown to form a right triangle?

A. Points N, P, and S. B. Points N, R, and T. C. Points M, N, and R. D. Points M, S, and P.

2. Which point is located in Quadrant I?

F. (-1, 3) G. (2, 1) H. (-5, -2) J. (4, -4)

3. Mary graphed the following two points on a grid

A (3, 11) and C (9, 11)

What is the length of ?

4. Using the numbers below, what two numbers could be moved below to make an ordered pair found on the x-axis. Name as many ordered pairs as you can find that are found on the x-axis.


Identify and label the axes of a coordinate plane. Identify and label the quadrants of a coordinate plane. Identify the quadrant or the axis on which a point is positioned by examining the coordinates (ordered

pair) of the point. Graph ordered pairs in the four quadrants and on the axes of a coordinate plane. Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate

plane. Relate the coordinate of a point to the distance from each axis and relate the coordinates of a single

point to another point on the same horizontal or vertical line.†


SOL 6.12 The student will determine congruence of segments, angles, and polygons.

HINTS & NOTES Congruent polygons – same shape and size Congruent segments – have the exact same length Congruent angles – have the exact same degree measure **You can always trace a figure, line, or angle and lay it on top of a second figure, line, or angle to see if they are congruent**

PRACTICE

1. Which shapes are congruent? A. B. C. D. 2.

3. Circle all the shapes that appear to be congruent.


Characterize polygons as congruent and noncongruent according to the measures of their sides and angles.

Determine the congruence of segments, angles, and polygons given their attributes. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the

length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving practical and mathematical problems.


SOL 6.13 The student will describe and identify properties of quadrilaterals. HINTS & NOTES

Quadrilaterals Trapezoid – figure has exactly one pair of parallel sides. Parallel sides are called bases. Non-parallel sides are called legs. If the legs are congruent then it is an isosceles trapezoid. Parallelogram – opposite sides are congruent and parallel Rectangle – parallelogram with four right angles. Diagonals bisect each other into two equal parts. Rhombus – parallelogram with four congruent sides Square – parallelogram with four right angles and four congruent sides Kite- quadrilateral with two pairs of adjacent congruent sides. One pair of opposite angles is congruent.

*sum of the measures of the interior angles of a quadrilateral = 360o Quadrilaterals can be classified by their sides (are they parallel? congruent?), by the measure of their angles (any right angles?)

PRACTICE 1. What is the sum of the measures of all the

interior angles of any quadrilateral?

A. 540o C. 360o B. 180o D. 90o

2. Which two figures always have four right angles?

F. parallelogram and rectangle G. square and equilateral triangle H. square and rhombus J. rectangle and square

3. Which shape is not a quadrilateral?

A. Trapezoid C. pentagon B. parallelogram D. square

4. Which set of angles could be the angle measures of a

quadrilateral?

F.

G.

H.

J.

5. What is the best name for all of the figures?

A. Parallelogram C. Rhombus B. Square D. Rectangle

6. Find the measure of the missing angle.

x = __________


Sort and classify polygons as quadrilaterals, parallelograms, rectangles, trapezoids, kites, rhombi, and squares based on their properties. Properties include number of parallel sides, angle measures and number of congruent sides.

Identify the sum of the measures of the angles of a quadrilateral as 360°.


SOL 6.14 The students, given a problem situation, will a) construct circle graphs; b) draw conclusions and make predictions, using circle graphs; and c) compare and contrast graphs that present information from the same data set.

HINTS & NOTES

Circle graph – compares parts to a whole – think of a pizza! All of the sections of a circle graph add up to 100% Read any title, labels, key, or categories of a graph. Graphs from previous years may also show up. Line graph – shows change over time Stem-and-leaf plot – displays data items in order. A leaf is the item’s last digit. Bar graph – displays items in bars and is used to compare amounts

PRACTICE 1. Which circle graph shows the data in the table below?

2. Which two items together make up more than half of Karen’s budget?

F. meat and vegetables G. vegetables and dairy H. bakery and meat J. dairy and fruits


PRACTICE cont.

3. A circle graph often gives what kind of information?

A. comparisons B. pictures C. percents D. rows

4. Which three sections of the circle graph make up 50% of the sports that students enjoy?

Favorite Sports of Middle

School Students

1.___________________ 2.___________________ 3.___________________

5. According to these two circle graphs, which statement is

correct?

A. The same number of boys and girls play the flute. B. The flute is played by more girls than boys. C. The number of boys playing either the tuba or the clarinet is

the same as the number of girls playing the tuba or clarinet. D. Fifty girls play the trumpet or trombone.

6. The students in Mr. Smith’s play a game using a fair spinner. After Spinning, they record the following results:

Which spinner was Mr. Smith’s class probably using?

F.

H.

H.

J.


Collect, organize and display data in circle graphs by depicting information as fractional. Draw conclusions and make predictions about data presented in a circle graph. Compare and contrast data presented in a circle graph with the same data represented in other

graphical forms.



a) describe the mean as balance point; and b) describe which measure of center is appropriate for a given purpose.

HINTS and NOTES

Mean =

Mean as Balance Point-The mean can also be defined as the point on a numb er line where the data distribution is balanced. The sum of all the distances from the mean of all points above the mean is equal to the sum of all the distances from the mean of all data below the mean. Median – middle number in a set of ordered data Mode – the item that occurs most often Measures of Center- When should I use mean, median, or mode? Mean- works well for data with no very high or very low numbers. Median-Use when data sets have a couple of values that are much higher or much lower than the other numbers. Mode-Use when you have identical values or when data is in a yes or no survey.

PRACTICE 1. For which data set is the mean the best measure of central

tendency?

A. 94, 96, 98, 100. 97 B. 54, 60, 58, 3, 64 C. 26, 29, 71, 28, 71 D. 5, 5, 5, 301, 5

2. School Enrollment

What is the median for the number of students in each grade attending this school? F. 72 G. 92 H. 91 J. 86

3. What is the balance point for the following data?

13, 13, 14, 18, 17, 18, 19 balance point =

4. Match each set of data on the left to the correct mode on the right. Draw a line to connect them.

1, 2, 6, 7, 9, 1, 3, 4, 12, 52 no mode 12, 13, 6, 8, 9 mode of 1 and 4 1, 3, 4, 1, 1, 4, 4 mode of 1

Grade # of Students

1st Grade 92

2nd Grade 91

3rd Grade 72

4th Grade 86

5th Grade 93


Find the mean for a set of data. Describe the three measures of center and a situation in which each would best represent a set of

data. Identify and draw a number line that demonstrates the concept of mean as balance point for a set

of data.



a) compare and contrast dependent and independent events; and b) determine probabilities for dependent and independent events.

HINTS & NOTES

Independent Event- the outcome of one event has no effect on the outcome of the other. Dependent Event-the outcome of one event is influenced by the outcome of the other. The probability of an event occurring is a ratio between 0 and 1. A probability of 0 means the event will never occur. A probability of 1 means the event will always occur. Always write probability as a fraction

first ( ), then

change it to a decimal or percent if needed

PRACTICE 1. Gerald has a fair number cube numbered one through six.

What is the probability that he will roll a 4 on his first roll?

A 1

6 C

1

4

B 4

6 D

5

6

2. Gretchen has a bag of candy of candy. In the bag, there are 2 green candies 4 red candies 3 yellow candies. If Gretchen draws a piece of candy from her bag and does not replace it, what is the probability that she will draw a red candy followed by a green candy?

F H

G

J 8

81

3. Choosing a marble from a bag, replacing it, and then choosing another marble is an example of which type of event?

A independent event B dependent event C complementary event D sequential event

4. Four of 9 kittens in a litter are gray and 5 kittens are black.

What is the probability that the first and second kittens to open their eyes will be the gray kittens?

F 1

6 G

2

9 H

4

9 J

Practice Cont.


5. A bag contains 10 yellow counting chips and 10 red counting chips. What is the probability that Sara will pick a yellow chip, keep it, and then draw a red chip on her second draw?

A 1

10 C

5

19

B 11

21 D

5

38

6. Madeline made a spinner with equal sections.

What is the probability of Madeline not landing on white when the spinner is spun?

F 0%

G 12.5%

H 50%

J 87.5 %

7. What is the probability of spinning a 6 on the first spin and a 5 on the second spin, if the spinner is spun twice?

A

B

C

D

8. The following cards are placed in a bag and drawn at

random without replacement. What is the probability of drawing an A, and then drawing a M?

A. B. C. D.

I T Y M A T H E M A T I C S


Determine whether two events are dependent or independent. Compare and contrast dependent and independent events. Determine the probability of two dependent events. Determine the probability of two independent events.


SOL 6.17 The students will identify and extend geometric and arithmetic sequences.

HINTS & NOTES

Arithmetic Sequence – A sequence where you add the same number to each term to get the next term. **The number added is called the common difference (d).**

If the numbers are getting bigger, the common difference is a positive number. If the numbers are getting smaller, the common difference is a negative number. Geometric Sequence – A sequence where you multiply the same number times each term to get the next term. **The number multiplied is called the common ratio (r).

PRACTICE 1.The first four figures in a pattern are shown.

If the pattern continues to double the number of dots, what will be the total number of dots in the 7th figure in the pattern?

A. 256 B. 128 C. 64 D. 32

2. Kendall wrote the number pattern shown

1, 2, 4, 7, 11, …

She noticed another pattern when she found that the differences between the numbers increased by 1 as shown below.

If the differences continue to increase by 1, what will be the 8th term in Kendall’s original pattern? F. 16 G. 22 H. 28 J. 29


PRACTICE cont.

3. Which sequence has a common

ratio of 4?

A. 4, 40, 400, 4000, …….

B. 8, 40, 200, 1000, ……

C. 4, 8, 16, 32, ……..

D. 3, 12, 48, 192, …..

4. Which sequence has a common

difference of 5?

F. 0, 5, 15, 30, 50, …..

G. 3, 8, 13, 18, …..

H. 55, 45, 35, 25, ……

J. 25, 35, 55, 75, ……

5. Match each sequence on the left with the correct answer

from below.

6. Match each sequence on the left with the correct answer

from below.


Investigate and apply strategies to recognize and describe the change between terms in arithmetic patterns.

Investigate and apply strategies to recognize and describe geometric patterns. Describe verbally and in writing the relationships between consecutive terms in an arithmetic or

geometric sequence. Extend and apply arithmetic and geometric sequences to similar situations. Extend arithmetic and geometric sequences in a table by using a given rule or mathematical

relationship. Compare and contrast arithmetic and geometric sequences. Identify the common difference for a given arithmetic sequence. Identify the common ratio for a given geometric sequence.


SOL 6.18 The student will solve one-step linear equations in one variable involving whole number coefficients and positive rational solutions.

HINTS & NOTES

Plug it in! Plug it in! For any problem involving solving an equation, plug in all of the answer choices until you find the one that works. Remember* To undo addition – subtract To undo subtraction – add To undo multiplication – divide To undo division – multiply Always do the exact same things to both sides of an equation!!! Variable – a letter or symbol that represents a number Coefficient – the number in front of a variable. In the term 7y, 7 is the coefficient. Term – part of an expression separated by a + or -. In the expression 4x + 5, both 4x and 5 are terms of the expression Equation - a statement in which two expressions are shown to be equal.

PRACTICE 1. Which represents the variable in the

following number sentence?

4 + 3h = 27

A. 4 B. h C. 3 D. 3h

2. Which method could be used to solve the number

sentence shown?

x + 9 = 12 F. Add 9 to both sides of the equation

G. Subtract 9 from both sides of the equation H. Multiply both sides of the equation by 9 J. Subtract 12 from both sides of the equation

3. What value of y makes the number sentence shown true?

4y = 20

A. 4 B. 5 C. 16 D. 80

4. Look at the equation mat.

What is the value of x? F. 2 G. 3 H. 6 J. 7


PRACTICE cont

5. Which is an equation?

A. x + 4

3= 16

B. x

C. x + 4

3

D. 4x < 6

6. How many terms are in the expression 3x + 2y + 4?

F. 2 G. 3 H. 4 J. 9

7. Circle all the terms of this problem.

8. Solve for w, write answer in box.

9. Solve for k, write answer in box.

13k = 39

10.

Using the representations above, which model best represents the following? 2r = 18


Represent and solve a one-step equation, using a variety of concrete materials such as colored chips, algebra tiles, or weights on a balance scale.

Solve a one-step equation by demonstrating the steps algebraically. Identify and use the following algebraic terms appropriately: equation, variable, expression, term,

and coefficient.


SOL 6.19 The students will investigate and recognize

a) the properties for addition and multiplication; b) the multiplicative property of zero; and c) the inverse property of multiplication.

HINTS & NOTES

Multiplicative property of zero-the product of any real number and zero equals zero. Additive Identity Property-the sum of any real number and zero is equal to the given real number. 5 + 0 = 5 Multiplicative Identity Property- the product of any real number and one is

equal to the given number.

Multiplicative Inverse Property- the product of a number and its multiplicative inverse (reciprocal) always

equals one.

PRACTICE 1. Three students wrote their work on a white board.

Lisa Doug Tricia Anna

6 + 1 = 7

6 + 0 = 6

6 ● 0 = 0

6● 1 = 6

Which student used the additive identity property?

A. Lisa B. Doug C. Tricia D. Anna

2. Which is not an example of the multiplicative property

of zero? F. 5 + (-5) = 0 G. 5 ● 0 = 0 H. 0 ● 1 = 0 J. 0(-5) = 0

3. Which property is shown in the following number

sentence?

A. Multiplicative Identity B. Multiplicative Inverse C. Additive Identity D. Additive inverse

4. Which property was used in the following number sentence? 6 ● 1 = 6 F. Multiplicative Inverse G. Additive Inverse H. Multiplicative Identity J. Additive Identity


Identify a real number equation that represents each property of operations with real numbers, when given several real number equations.

Test the validity of properties by using examples of the properties of operations on real numbers. Identify the property of operations with real numbers that is illustrated by a real number equation.

NOTE: The commutative, associative and distributive properties are taught in previous grades.


SOL 6.20 The students will graph inequalities on a number line.

HINTS & NOTES Inequalities – To graph < or > on a number line, use an open circle on the number line and a shaded line covering the solution. To graph ≤ or ≥ on a number line, use a closed circle on the number line and a shaded line covering the solution. The solution set to an inequality is the set of all numbers that make the inequality true. These inequalities are equivalent x > -6 and -6 < x Answers should have the variable on the left of the inequality sign. To flip the inequality, switch the two sides and change the inequality sign.

PRACTICE

1. Graph the following inequalities.

x ≥ 5

-3 < x

2. Look at the graph below.

Which inequality describes the graph? A. n < 4 B. n > 4 C. n ≤ 4 D. n ≥ 4

3. Which graph represents 50 > m?

F.

G.

H.

J.

Skills Checklist

I can… Given a simple inequality with integers, graph the relationship on a number line.

Given the graph of a simple inequality with integers, represent the inequality two different ways

using inequality symbols (<, >, <, >).

practice hints & notes disks in a bag. what is the … review...reduce all ratios!!! 20 d....

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