SECOND CHANCE POINTS



SECOND CHANCE POINTS

Second chance points can raise your grade to an ‘A’ for a particular assignment, quiz, or test if you follow the following steps.

SECOND CHANCE POINTS – Assignments, Quizzes, Tests

1. Second chance points are earned for a particular assignment on the day assigned (only after the assignment is graded) during the tutoring period and lunch.

2. Second chance points may be earned only on the parts of the assignment that were completely attempted but no correct,

3. Second Chance points must be done in the classroom. No second chance points will be earned if papers or manual are taken out of the classroom.

4. Follow directions on assignment unless stated otherwise below.

5. Second chance points will be written on a separate sheet of paper.

6. Each missed question or problem will have the following:

a. Missed question written out.

b. Write out complete answer or show completed problem steps with correct answer.

c. Write where you found the information that helped you solve the question or problem. This includes the lab manual or text, reading guide, etc., page number, where on the page (section) it is found.

7. Staple second chance points to the back of the assignment/exam.

8. Have teacher check off with signature before grading

9. Grade second chance answers in red ink and write additional points on the top of the front page of the second chance sheet of paper.

10. On the top of the assignment/quiz/exam, next to the original score write the additional points then add and circle the new total all written in red ink.

11. Place stapled packet in teacher’s basket.

SECOND CHANCE POINTS - LAB MANUALS

1. Make all corrections with color pencil or green ink pen in the Lab Manual on correct page.

2. Must have all corrections checked by teacher and placed in basket.

3. Must be completed by the end of the lunch period.

Determining Combinations

1. Count all the dots.

2. Start with the number one and divide the total by all numbers between the one and the total including the total number.

3. Numbers that divide into the total equally are multiples/factors.

4. Examples:

Determining Equivalencies

As an example let’s use the combination 3 groups of 4 dots. Each combination has three equivalencies.

|Combination |Equivalencies |

| |1 w = ___ g |

|[pic] |1 w = ___ d |

| |1 g = ___ d |

The first equivalence - the whole has how many groups? - 1 w = ___ g

Look at the domino above. How many groups (circles) are there? Place that number in the blank.

1 w = _3_ g

The second equivalence – the whole has how many dots? - 1 w = ___ d

Look at the domino above. How many dots (smaller circles) are there? Place that number in the blank. 1 w = _12_ d

The third equivalence – the group has how many dots? - 1 g = ___ d

Look at the domino above. How many dots (smaller dots) inside the larger circle? Place that number in the blank. 1 g = _4_ d

Converting Equivalencies To Conversion Factors

1. Using the equivalence 1g = 2d you can place a slash in place of the equal sign.

2. 1g = 2d - The 1g is the numerator and the 2d is the denominator.

3. The fraction looks like this . Now flip the fraction to get the reciprocal . The conversion factor looks like or .

4. To select the correct conversion factor you want the unit that is going to be the answer unit in the numerator and the unit we want to cross cancel in the denominator.

Dimensional Analysis Notes

1. Determine the combination.

2. Write out the equivalencies.

3. Determine the units from the conversion (problem).

4. Write out the conversion factors.

5. Write the given in the first rung of the ladder.

6. Determine the correct conversion fraction.

a. Cross cancel – same unit in the numerator of one fraction and denominator in the other.

b. Answer unit – unit in the numerator.

7. Place conversion fraction in the second rung of the ladder.

8. Cross Cancel units.

9. Multiply

10. Divide

11. Box answer (quantity)

GRAPHING STEPS

|Remember the multiples we want to use are 3, 4, or 5. |[pic] |

|Determine the number of squares on the ‘x’ axis. Write that number of squares in the blank for the x-axis (Determine the factors for | |

|that number.) and in the x-house. | |

|Determine the number of squares on the ‘y’ axis. Write that number of squares in the blank for the y-axis (Determine the factors for | |

|that number.)and in the y-house. | |

|Now determine the highest value for the independent variable in the data table. Divide the multiples for the ‘x’ axis into that number| |

|until one of them divides into it evenly. If they do not round the maximum value up until one of the multiples do divide into it | |

|evenly. Place that number in the value-house. | |

1. Now determine the highest value for the dependent variable in the data table. Divide the multiples for the ‘y’ axis into that number until one of them divides into it evenly. If they do not round the maximum value up until one of the multiples do divide into it evenly. Place that number in the value-house. Write these values at the end of the respective ‘x’ and ‘y’ axis.

2. The multiple that divides evenly into the maximum value determines the number of intervals and the value increase for each interval.

3. The other multiple will be the scale (number of squares between each interval).

4. Now that you have the maximum value for each axis divide that number by the number of squares. The answer will give you the value of each square on that axis. These quantities will help you be more accurate plotting data.

5. Now use the scale on each axis and plot your ordered pairs. Remember, you place the data point where the imaginary horizontal and vertical lines intersect.

6. Once all the ordered pairs have been plotted draw the best-fit-line. Keep in mind; the best-fit-line is the medium of the data points.

7. First determine the flow of the data points. Once the flow has been determined, align the best-fit-line so there are an equal number of data points on each side.

BEST FIT LINE The best fit line is the average (mean) of all the data points.

Align the straight edge along the data points to see if all the data points are in alignment. If so sketch the best fit line. If not follow the steps below.

1. Find the flow of the data points – set the straight edges at the same angle and same distance apart at the ends of each straight edge.

2. Move the straight edges toward one another alternating each straight edge one dot at a time. Continue doing this until they can’t move any closer to one another.

3. Remove one of the straight edges while holding the other in place. Then sketch the best fit line along the straight edge.

CALCULATING Y-INTERCEPT

1. Find where the best fit line crosses the y-axis.

2. Set up a ladder (dimensional analysis).

3. Count the number of squares up to the y-intercept. This is placed in the first rung of the ladder.

4. Write the value for every square in the second rung of the ladder.

5. Multiply to get the product fraction.

GAPHING SHAPES

|Graph shape |Written relationship |Modification required to linearize |Mathematical model |

| | |graph | |

|[pic] | | | |

|Horizontal Line |As x increases, y remains the same. There|None |y = b or y is constant |

| |is no relationship between the variables. | | |

|[pic] | | | |

|Positive Linear Line |As x increases, y increases |None |y = mx +b |

| |proportionally. | | |

| |Y is directly proportional to x. | | |

|[pic] | | | |

|Hyperbola |As x increases, y decreases. Y is |Graph y vs , or |y = m+ b |

| |inversely proportional to x. |y vs x-1 | |

|[pic] | | | |

|Parabola |Y is proportional to the square of x. |Graph y vs x2 |y = mx2 + b |

|[pic] | | | |

|Side Opening Parabola |The square of y is proportional to x. |Graph y2 vs x |y2 = mx + b |

TRIANGLE SET-UP

Placing the variables in the triangle.

1. First we start with the graph.

| [pic] |• The "y" on the graph represents the y-axis the dependent variable. |

| | |

| |• The "x" on the graph represents the x-axis the independent variable. |

| | |

| |• The "m" on the graph represents the slope. |

| | |

| |• The "b" on the graph represents the y-intercept. |

2. The math model for a linear line matches up with the different parts of the graph.

|[pic] |• The "y" in the math model, is the same as the dependent variable on the y-axis. |

| |• The "m" in the math model, is the same variable that the slope represents. |

| |• The "x" in the math model is the same independent variable on the x-axis. |

| |• The "b" in the math model is the y-intercept on the graph. |

3. Arranging the symbols for the different variables in the triangle.

|[pic] |• "y" the dependent variable is placed on the top. |

| |• "m" the variable for slope is placed in the lower left. |

| |• "x" the independent variable is placed in the lower right. |

Using the triangle.

• The unknown variable is written down with an equal sign after it.

• Place your index finger over the symbol of the unknown and write out the remainder of the equation.

• If "y" is what we are solving, place index finger over the "y". m•x occurs. So our equation is y = mx

• If "m" is being solved for, then place the index finger on the "m" and a fraction occurs. So our equation is m = .

• If "x" is being solved for then place the index finger on the "x" and the fraction occurs. So our equation is x = .

DETERMINING MATRIX DATA

1. Find two intersections along the best fit line and circle them both. An intersection is where the horizontal line, the vertical line, and the best fit line all go through the same point.

2. Number the intersection closest to the origin #1 and the intersection furthest away from the origin #2.

3. Start counting from the origin.

4. Count the number of squares to the right along the x-axis, to the intersection (#1).

5. Multiply the number of squares by the value for each square for the x-axis.

6. Place that calculation/quantity in the matrix at x1 position.

7. Count the number of squares up the y-axis to intersection (#1).

8. Multiply the number of squares by the value for every square for the y-axis.

9. Place that calculation/quantity in the matrix at the y1 position.

10. Repeat numbers 1 – 7 for the second intersection.

| | |

| | |

|[pic] | |

| | |

|[pic] | |

CALCULATING SLOPE

1. Write out the slope equation. m =

2. Substitute the x and y values from the matrix into the slope equation.

3. Complete the calculation in the numerator position of the equation (remember units).

4. Complete the calculation in the denominator position (remember units).

5. Complete the division calculation, cross out units if they are similar.

6. Box answer, check unit.

SLOPE DIAGRAM

1. The symbol for the independent variable is a square.

2. The symbol for the dependent variable is a dot.

3. The rules for placing the dots are on page 5.

4. The explanation for the slope diagram is ‘for every x number of unit of independent variable there are (number y) of unit of dependent variable.

5. Slope Diagram, Diagram Explanation and Written Relationship EXAMPLE!

|Slope Diagram |Diagram Explanation: |Written Relationship: |

| | | |

|[pic] |For every 1 cm of diameter there are 3 cm of |As diameter increases, circumference increases proportionally, |

| |circumference. |circumference is proportional to diameter. |

WRITTEN RELATIONSHIP AND MATHEMATICAL MODEL

The shape of the slope determines the written relationship. Match the slope shape on the graph with shapes in the first column in the table. The second column contains the written relationship. Replace the ‘x’ and ‘y’ with the independent and dependent variables when writing the written relationship. The fourth column contains the mathematical model. Again, find the graph shape that represents the slope in the graph and move to the right to the math model. Substitute the symbols for the independent, dependent value, and slope into the math model. Now we have the slope equation.

5% RULE FOR TESTING THE ORIGIN OR ANY Y-INTERCEPT (B-VALUE)

|Purpose: |Test your y-intercept to see if you can accept the value that you get from your slope (best-fit line). The y-intercept value |

| |will either be significant (value must be kept as part of the math model and is usually due to errors in measurement) or |

| |insignificant (value will be dropped from the math model). |

| | |

|Formula: |x 100 |

| | |

|Interpretation of results: | |

|1. |If the percent is less than or equal to ±5% the value is insignificant and dropped from the math model. |

|2. |If the percent is greater than ±5% the value is significant and remains in the math model. |

ESTIMATING

Estimating - to give an approximation as to the value of an object.

If measuring an object that is larger than a whole but less than two wholes, there is a certain number of one. To gain more information, an estimate must be made. If you cannot tell whether the edge is closer to one line or the other, it is best to report the reading at 1.5.

If the edge is closer to the line on the left, you should report the reading as 1.2 or 1.3. Either way, you will not be off by more that plus or minus 0.2. Similarly, if you decide that the edge is closer to the line on the right, report the reading as 1.7 or 1.8. Again, you will not be off by more that plus or minus 0.2. Had you read the scale as either line, you might have been off by as much as plus or minus 0.5.

Suppose that, as far as you can tell, the edge falls on a line. Then you should report the reading with a 1.0. This will give information that would have been lost if the uncertain number had not been included.

|The numbers 1, 4, 6, and 9 are not used when making estimations. |[pic] |

RULES FOR THE METER STICK

1. Hold the meter stick with the right hand in the middle with the arm at a 90° angle.

2. Never bounce the meter stick on the ground.

3. The measuring tool is always placed on a flat surface, when not in use.

4. Put absolutely no marks on the meter stick.

5. The meter stick makes no noise!

MEASURING

1. From an aerial view, align zero of the measuring tool on the left edge of the object being measured.

2. Hold the measuring tool and object in place.

3. If the object is smaller than the prefix being used in the measurement write a zero with a decimal (0._).

4. If the object is larger than the prefix being used in the measurement write the value and a decimal (2._).

5. Now get an aerial view over the part of the object that is being measured.

6. Now count the number of the next smaller prefix and write that number.

7. Repeat number seven until all prefixes have been accounted for.

8. Next image the scale and determine the uncertain number and write it down.

a. Is the end of the object greater or smaller than half?

b. If the object is larger than half is the end of the object closer to the 0.5 or closer to the 1.0? You have a choice of 0.6, 0.7, 0.8, or 0.9.

c. If the is object smaller than half is the end of the object closer to the 0.0 or closer to the 0.5? You have a choice of 0.1, 0.2, 0.3, or 0.4.

9. The unit and prefix written next completes the measurement.

Significants Figures

Using the arrow method to determine significant figures. First, determine if the number has a decimal (Row A) or no decimal (Row B). In case of a decimal the arrow always goes from left to right. For numbers with no decimal the arrow goes from right o left.

| |Row A |Sig Figs | |Row B |Sig Figs | |

| |0.12 | | | 124 | | |

| |0.12 |2 | |124 |3 | |

| |0.03 | | | 110 | | |

| |0.03 |1 | |110 |2 | |

| |0.0301 | | | 1 000 | | |

| |0.0301 |3 | |1 000 |1 | |

| |1.00 | | |12 010 | | |

| |1.00 |3 | |12 010 |4 | |

| |2.0001 | | | | | |

| |2.0001 |5 | | | | |

The arrow always passes through any zero and stops at the first whole number of significant figures.

RULES FOR ADDITION AND SUBTRACTION WITH SIGNIFICANT FIGURES

1. Change the units of all measurements, if necessary, so that all measurements are expressed in the same units (meters, kilograms, degrees Celsius, etc.).

2. The sum or difference of measurements may have no more decimal places than the least number of places in any measurement.

RULES FOR MULTIPLICATION AND DIVISION WITH SIGNIFICANT FIGURES

1. Students typically make one of two mistakes: either they keep too few figures by rounding off too much and lose information, or they keep too many figures by writing down whatever the calculator displays. Use of significant figure rules helps us express values with a reasonable amount degree of precision.

2. When multiplying or dividing, the number of significant figures retained may not exceed the least number of digits in either of the factors.

-----------------------

given

1

given conversion

1 fraction

given conversion product

1 fraction fraction

X

given conversion product quotient

1 fraction fraction fraction

given conversion product quotient

1 fraction fraction fraction

=

Step 3

Step 3

Step 2

#7

Step 5

Step 4

#7

#6

#6

Step 8

Step 8

Step 2

Step 3

Step 2

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