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Unit 1Understanding Numeric Values, Variability, and Change

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Lesson 1Rational and Irrational Numbers

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Vocabulary (Logs)0Real Numbers

0 Any number (point) on the number line0Rational Numbers

0 a number that can be written as a simple fraction 0 a/b where b ≠ 00 Terminating or repeating decimals

0 Irrational Numbers0 A number that cannot be written as a simple fraction0 √2 or π

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Vocabulary (Logs)

0 Integers0 zero, counting numbers, & negative of counting numbers

{…, -1, 0, 1, …}0Whole Numbers

0 Starts at 0 {0, 1, 2, 3, …}0Natural Numbers

0 Also counting numbers {1, 2, 3, …}

5Real Numbers Venn Diagram Draw in learning logs.

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0Flow charts are graphical representations of a process0Steps are shown in individual shapes and flow is indicated

with arrows connecting the symbols

Can the number

written as a fraction?

Irrational

RationalYES

NO

Can the fraction

be divided evenly?

NO

YES

Integer

Is the number

negative?

YES

NOWhole

Is the number

zero?Natural

NO

YES

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Examples

0 Identify the following numbers as Irrational, Rational, Whole Natural, and/or Integers:0 9

0Rational, integer, whole, natural0 3.666666666

0 rational0 -5

0Rational, Integer0 4.75

0 rational0 7.154976352118568763215489736

0 irrational

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Worksheet

0Complete Worksheet in Groups0 Complete Part I then stop0 Complete Part II then stop0 Complete Part III then stop

0 Review Time!!

0 Complete Page 1-12 for Homework

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Lesson 2Numeracy Review

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Order of Operations

• When evaluating arithmetic expressions, the order of operations is:• Simplify all operations inside parentheses. • Perform all multiplications and divisions, working from

left to right. • Perform all additions and subtractions, working from

left to right.

• If a problem includes a fraction bar, perform all calculations above and below the fraction bar before dividing the numerator by the denominator

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Vocabulary (Logs)

0 Whole Positive Exponents

0 Negative Exponents0 Negative is the opposite of positive0 Divide is the inverse (opposite) of multiply0 Negative exponents means how many times to we divide by that number

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Exact vs. Approximate

0 Exact number0 1. Any number obtained by a counting process.

Example: 60 students in a class — 60 is an exact number0 2. Any number given by definition. Example: One hour

equals 60 minutes — 60 is an exact number0 Approximate Number

0 1. Any number obtained by a process of measurement0 Example: The distance between two cities is 60 miles —

60 is an approximate number.0 The distance may be a little more or a little less than 60

miles

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Significant Digits0digits that have meaning relative to the measuring process

1. Nonzero digits are always significant2. Zeros that are preceded and followed by significant

digits are always significant.3. Final Zeros to the right of a decimal point are significant4. Final zeros on a whole number are not significant (unless

further information indicates otherwise).5. If no digits left of the decimal point, zeros between the

decimal point and the first digit are not significant

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Examples

014.24 has four significant digits (Rule 1)0 .0036 has two significant digits (Rule 1 & 5)014.0024 has six significant digits (Rule 3)07001 has four significant digits (Rule 2)08.9000 has five significant digits (Rule 3)00.03600 has four significant digits (Rule 1 & 5)

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Accurate to …0 If you need to express your answer as being "accurate

to" a certain place, here's how the language works with the above examples:0 0.00035 is accurate to the hundred-thousandths place0 0.000350 is accurate to the millionths place (note the

extra zero)0 1006 is accurate to the units place0 560 is accurate to the tens place0 560. is accurate to the units place (note the decimal

point)0 560.0 is accurate to the tenths place

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Worksheets

0Complete Review Worksheets0 Adding, Subtracting, Multiplying, & Dividing Integers0 Order of Operations0 Adding, Subtracting, &Multiplying Decimals0 Adding, Subtracting, Multiplying, & Dividing Fractions

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Lesson 3Scatter Plots

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Vocabulary (Logs)0Cartesian Coordinate

System0 formed by a horizontal axis

and a vertical axis0Domain

0 set of values of the independent variable for which a function or relation is defined; x-values

0Range0 set of values assumed by a

function or relation over all permitted values of the independent variables; y-values

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Vocabulary (Logs)

0 Independent Variable0 value freely chosen without considering values of any

other variable0Dependent Variable

0 depends on one or more other variables0Ordered Pairs

0 pair of numbers giving the location of a point (x, y)

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Scatter Plots0 Scatter plots are similar to line graphs

0 horizontal and vertical axes to plot data points0 show how much one variable is affected by another. 0 The relationship between two variables is called their correlation .

0 Scatter plots usually consist of a large body of data. 0 The closer the points come to making a straight line, the

higher/stronger the correlation between the two variables0 If the line going from the origin out to high x- and y-values, then

positive correlation0 If the line goes from a high-value on the y-axis down to a high-value

on the x-axis, then a negative correlation . 0 Remember when making a scatter plot, DO NOT connect the

dots

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Scatter Plots

0Positive0 y increases as x

increases0Negative

0 Y decreases as x increases

0No Correlation0 No relationship

between x and y

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Line of Best Fit0A straight line that best represents the data on a

scatter plot.

0May pass through some of the points, none of the points, or all of the points.

0Also called linear regression equation

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Slope

0Rate of Change-for each change in the independent variable, the dependent variable will change by m

0Negative slope defines negative correlation. Positive slope defines positive correlation.

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Activity

0At your tables:0 Use ruler to measure the length of each student’s foot

0 Inches0Centimeters

0 Use measuring tape to measure each student’s height0 Inches0Centimeters

0 Record data on chart at front of room and graph on scatter plot

0 Answer questions on worksheet

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Lesson 4Exponential Growth & Decay

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Exponential Functions

Decay Growth

The variable is the exponent, not the base. y = 3x

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Activities

0Complete the Exponential Growth & Decay Activity

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Lesson 5Putting it all Together

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0Complete the Linear or Non-Linear Activity and turn in your posters when you are finished

OR0Create scatter plots

based on the free throw and field goal percentages and answer questions that follow.

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Review

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Vocabulary

0Real Numbers0Rational Numbers0 Irrational Numbers0 Integers0Whole Numbers0Natural Numbers0Flow Charts0Exponent

0Cartesian Coordinate0Domain0Range0 Independent Variable0Dependent Variable0Ordered Pairs0Line of Best Fit0Slope

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Learning Log Checklist

0Vocabulary0Real Numbers Venn

Diagram0Real Numbers Flow

Chart

0Scatter Plots Rules0Order of Operations

Rules0Exact vs. Approximate0Significant Figures Rules

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Assessments & Review2-3 days

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Test Question 1

0 Cary’s Bakery sells cupcakes for $1.00 each. Cary is not making any profit, so she needs to raise the price. She wants to make the increase gradually to $1.80.0 Plan A: Raise the price by $0.05 per week0 Plan B: Raise the price by 5% per week0 Plan C: Raise the amount by the same amount over 8 weeks

0 Make a table for each plan and determine how many weeks each plan will take and the increase amount each week.

0 Create one graph displaying all three plans simultaneously.0 Answer the following questions:

0 Are the graphs linear?0 In your opinion, which plan should Cary implement? Give reasons for

your choice.

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Test Question 2

0Table listing rental prices for a car including mileage charges0 Explain what the data in the table means0 Determine rental cost before any miles are driven0 Graph0 Create a regression equation0 Calculate cost for 100 miles0 How far can you go on $60

0Extension: Compare cost for two different pricing schemes

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Test Questions

0Classify Numbers0Graph a linear and non-linear set of data and analyze0Perform operations on integers, decimals, fractions,

exponents0Order of Operations0Significant Figures0Find Slope