# Unit 1 Understanding Numeric Values, Variability, and Change 1.

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Unit 1 Understanding Numeric Values, Variability, and Change 1

Lesson 1 Rational and Irrational Numbers 2

Vocabulary (Logs) 0 Real Numbers 0 Any number (point) on the number line 0 Rational Numbers 0 a number that can be written as a simple fraction 0 a/b where b ≠ 0 0 Terminating or repeating decimals 0 Irrational Numbers 0 A number that cannot be written as a simple fraction 0 √2 or π 3

Vocabulary (Logs) 0 Integers 0 zero, counting numbers, & negative of counting numbers {…, -1, 0, 1, …} 0 Whole Numbers 0 Starts at 0 {0, 1, 2, 3, …} 0 Natural Numbers 0 Also counting numbers {1, 2, 3, …} 4

Real Numbers Venn Diagram Draw in learning logs. 5

0 Flow charts are graphical representations of a process 0 Steps are shown in individual shapes and flow is indicated with arrows connecting the symbols Can the number written as a fraction? Irrational Rational YES NO Can the fraction be divided evenly? NO YES Integer Is the number negative? YES NO Whole Is the number zero? Natural NO YES 6

Examples 0 Identify the following numbers as Irrational, Rational, Whole Natural, and/or Integers: 0909 0 Rational, integer, whole, natural 0 3.666666666 0 rational 0 -5 0 Rational, Integer 0 4.75 0 rational 0 7.154976352118568763215489736 0 irrational 7

Worksheet 0 Complete Worksheet in Groups 0 Complete Part I then stop 0 Complete Part II then stop 0 Complete Part III then stop 0 Review Time!! 0 Complete Page 1-12 for Homework 8

Lesson 2 Numeracy Review 9

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 10

Vocabulary (Logs) 0 Whole Positive Exponents 0 Negative Exponents 0 Negative is the opposite of positive 0 Divide is the inverse (opposite) of multiply 0 Negative exponents means how many times to we divide by that number 11

Exact vs. Approximate 0 Exact number 0 1. Any number obtained by a counting process. Example: 60 students in a class — 60 is an exact number 0 2. Any number given by definition. Example: One hour equals 60 minutes — 60 is an exact number 0 Approximate Number 0 1. Any number obtained by a process of measurement 0 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 12

Significant Digits 0 digits that have meaning relative to the measuring process 1. Nonzero digits are always significant 2. Zeros that are preceded and followed by significant digits are always significant. 3. Final Zeros to the right of a decimal point are significant 4. 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 13

Examples 0 14.24 has four significant digits (Rule 1) 0.0036 has two significant digits (Rule 1 & 5) 0 14.0024 has six significant digits (Rule 3) 0 7001 has four significant digits (Rule 2) 0 8.9000 has five significant digits (Rule 3) 0 0.03600 has four significant digits (Rule 1 & 5) 14

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 place 0 0.000350 is accurate to the millionths place (note the extra zero) 0 1006 is accurate to the units place 0 560 is accurate to the tens place 0 560. is accurate to the units place (note the decimal point) 0 560.0 is accurate to the tenths place 15

Worksheets 0 Complete Review Worksheets 0 Adding, Subtracting, Multiplying, & Dividing Integers 0 Order of Operations 0 Adding, Subtracting, &Multiplying Decimals 0 Adding, Subtracting, Multiplying, & Dividing Fractions 16

Lesson 3 Scatter Plots 17

Vocabulary (Logs) 0 Cartesian Coordinate System 0 formed by a horizontal axis and a vertical axis 0 Domain 0 set of values of the independent variable for which a function or relation is defined; x-values 0 Range 0 set of values assumed by a function or relation over all permitted values of the independent variables; y-values 18

Vocabulary (Logs) 0 Independent Variable 0 value freely chosen without considering values of any other variable 0 Dependent Variable 0 depends on one or more other variables 0 Ordered Pairs 0 pair of numbers giving the location of a point (x, y) 19

Scatter Plots 0 Scatter plots are similar to line graphs 0 horizontal and vertical axes to plot data points 0 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 variables 0 If the line going from the origin out to high x- and y-values, then positive correlation 0 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 20

Scatter Plots 0 Positive 0 y increases as x increases 0 Negative 0 Y decreases as x increases 0 No Correlation 0 No relationship between x and y 21

Line of Best Fit 0 A straight line that best represents the data on a scatter plot. 0 May pass through some of the points, none of the points, or all of the points. 0 Also called linear regression equation 22

Slope 0 Rate of Change-for each change in the independent variable, the dependent variable will change by m 0 Negative slope defines negative correlation. Positive slope defines positive correlation. 23

Activity 0 At your tables: 0 Use ruler to measure the length of each student’s foot 0 Inches 0 Centimeters 0 Use measuring tape to measure each student’s height 0 Inches 0 Centimeters 0 Record data on chart at front of room and graph on scatter plot 0 Answer questions on worksheet 24

Lesson 4 Exponential Growth & Decay 25

Exponential Functions Decay Growth The variable is the exponent, not the base. y = 3 x 26

Activities 0 Complete the Exponential Growth & Decay Activity 27

Lesson 5 Putting it all Together 28

29 0 Complete the Linear or Non-Linear Activity and turn in your posters when you are finished OR 0 Create scatter plots based on the free throw and field goal percentages and answer questions that follow.

Review 30

Vocabulary 31 0 Real Numbers 0 Rational Numbers 0 Irrational Numbers 0 Integers 0 Whole Numbers 0 Natural Numbers 0 Flow Charts 0 Exponent 0 Cartesian Coordinate 0 Domain 0 Range 0 Independent Variable 0 Dependent Variable 0 Ordered Pairs 0 Line of Best Fit 0 Slope

Learning Log Checklist 32 0 Vocabulary 0 Real Numbers Venn Diagram 0 Real Numbers Flow Chart 0 Scatter Plots Rules 0 Order of Operations Rules 0 Exact vs. Approximate 0 Significant Figures Rules

Assessments & Review 2-3 days 33

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 week 0 Plan B: Raise the price by 5% per week 0 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. 34

Test Question 2 0 Table listing rental prices for a car including mileage charges 0 Explain what the data in the table means 0 Determine rental cost before any miles are driven 0 Graph 0 Create a regression equation 0 Calculate cost for 100 miles 0 How far can you go on \$60 0 Extension: Compare cost for two different pricing schemes 35

Test Questions 0 Classify Numbers 0 Graph a linear and non-linear set of data and analyze 0 Perform operations on integers, decimals, fractions, exponents 0 Order of Operations 0 Significant Figures 0 Find Slope 36

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