Category 1 Numbers, Operations, and Reasoning (1) The student represents and uses numbers in a variety of equivalent forms. The student is expected to: (A) compare and order integers and positive rational numbers. Useful Vocabulary Rational numbers are numbers that can be written as the ratio of two integers where zero is not the denominator. A ratio can be expressed as a fraction. How Do You Compare and Order Rational Numbers? A number line can help you compare. Positive numbers are to the right of 0, and negative numbers are to the left YOUR TURN Step 2. Write each number with Step 1. Write all the numbers as decimals. 1/2 = 0.50 1/4 = 0.25 1/8 = 0.125 the same decimal place. 0.500 0.250 0.125 0.750 3/4 = 0.75 Step 3. List the numbers in order form greatest to least and change to the original form. Decimal form in order then Original form in order 0.750, 0.500, 0.250, 0.125 75%, 50%, 25 %, 12.5% (2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to: use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals. Vocabulary justify prove reasonableness of answer operations -the most common are +, -, x, and. YOUR TURN DeAndre bought 15 party hats priced at 3 for $0.65 and 56 noisemakers priced at 7 for $1.25. What was the total cost of the hats and noisemakers, not including tax?. Step 1. Determine Number of packages needed for each item. 15 hats 3 = 5 packages 56 noisemakers 7 = 8 packages. Step 2. Multiply the number of packages needed by the prices given for each item. 5 hat packages x $0.65 = $3.25 8 noisemaker packages x $1.25 = $10.00 Step 3. Add the two dollar amounts together. $3.25 + $10.00 = $13.25 The total cost of the hats and noisemakers not including tax is $13.25
Category 2 Patterns, Relationships and Algebraic Reasoning (3) The student solves problems involving direct proportional relationships. The student is expected to: (A/B) estimate and find solutions to application problems involving percent's and other proportional relationships such as similarity and rates. Useful Vocabulary A Ratio is a comparison of two quantities. A proportion is a statement that two ratios are equal and is solved by setting the cross products equal to each other. Your Turn Kim knows that 2 out of every 3 of her relatives lives in Wylie. If Kim has 48 relatives, how may live in Wylie? Step 1. Identify the ratios to be compared. Compare them in the same order. Kim s relatives in Wylie Total relatives Step 2. Write a proportion using the two ratios. Step 3. Solve the proportion. 2 x 48 = 3n so n =32. Kim has 32 relatives that live in Wylie. This process can be used to solve proportions with percents. Your Turn If 65% of adults said that Dallas was the best city and there were 320 people asked, then how many voted for Dallas? Step 1. Identify the ratios to be compared. 65% = and number who voted for Dallas = Step 2. Write a proportion using the two ratios. Step 3. Solve so n = 208 people (5) The student uses equations to solve problems. The student is expected to (B) formulate problem situations when given a simple equation and formulate an equations when given a problem situation. How do you compare different representations of a relationship? Vocabulary- variable unknown number Example: The following multiple choice question shows an equation that matches one of the verbal descriptions below. Which problem situation matches the equation below? x - 4.72 = 5.28 A. Sergio s lunch cost $4.72. He received $5.28 in change when he paid the bill. What is x, the amount of money he gave the cashier? In this verbal description, x represents the unknown amount that Sergio paid the cashier. Subtracting 4.72 from the unknown amount represents Sergio paying for his lunch and receiving the exact change of $5.28. This matches the equation given above. (x-4.72=5.28) B. Yvette cycled 4.72 kilometers in a race. The winning cyclist s time was 5.28 seconds faster than Yvette s. What is x, the time in seconds it took Yvette to finish the race? In this verbal description x represents the time it took Yvette to finish the race and 4.72 is the distance Yvette cycled. The information provided in this verbal description does not match the information in the equation above because there is not enough information to solve for the missing value. Right equation for this verbal description : (x + 5.28 =? ) C. Janice and Maura measured the wingspans of butterflies in science class. Janice s butterfly had a wingspan of 4.72 centimeters, and Maura s butterfly had a wingspan of 5.28 centimeters. What is x, the average length of a butterfly s wingspan? To find the average of two numbers you would have to find their sum and divide by 2. The information provided in this verbal description does not match the equation. Right equation for this verbal description: (4.72 + 5.28)/2 = x D. Mrs. Castro paid $4.72 for a jar of iced-tea mix that was originally priced at $5.28. What is x, the amount of money that Mrs. Castro saved altogether? In this verbal description the two numbers should be subtracted to find x the amount saved. This does not match the equation given above. Right equation for this verbal description: (5.28 4.72 = x) Step 1 Read each verbal situation to see which operation (+, -, x, ) matches up with X 4.72 = 5.28 translates to starting with an unknown amount and subtracting 4.72 from that amount and ending up with 5.28 Step 2 READ EVERY ANSWER CHOICE EVEN IF YOU THINK/KNOW THE FIRST ANSWER CHOICE IS CORRECT. Write an equation for each verbal description to correctly match each form and eliminate other answers. Answer choice A is the verbal situation that matches the equation above.
Category 3 Geometry and Spatial Reasoning (7) Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane. The student is expected to: (A) locate and name points on a coordinate plane using ordered pairs of integers (B) graph reflections across the horizontal or vertical axis and graph translations on a coordinate Useful Vocabulary Coordinate grid- A grid with an x axis and y axis and four regions or quadrants. Reflection In Math it means to flip a figure/point over a line of symmetry. Usually reflected over the x or y axis. Translation in Math it means to move each point of a figure on a coordinate plane the same distance and in the same directions S R What are the coordinates of Point R? Step 1. Start from the origin (0,0) Step 2. For letter R, the x-coordinate is a positive value and 2 units East (+) from the horizontal origin. The y-coordinate is a negative value and 4 units south (-) of the vertical origin Step 3. R is found at (2, -4) Can you name the coordinates of point S? Hint: Just start from the origin. Your Turn Triangle JKL is reflected over the x axis forming the new triangle J K L. What are the coordinates of the J K L Step 1. Name/Locate the points of each vertex of the triangle: J (2,4) K (8,1) L(2,1) Step 2. Locate the line of symmetry (x axis) and reflect (flip) each point of the triangle across the axis. Step 3. Locate/name the new points of the reflected triangle The new coordinates are J (2, -4), K (8,-1), and L (2, -1). J J L L J K K Translation example: Which of the following describes the transformation from ABC to A B C? A. 4 units right, 6 units down B. 6 units left, 4 units up C. 6 units right 4 units down D. 4 units left, 6 units up Step 1. Compare one old and one new corresponding coordinate of the two triangles Step2. Vertex A of the pre-image (original) is located at (-2,3). Vertex A of the image (new figure) is (4, -1) Point A was translated 6 units right and 4 units down to become point A. The answer is C because each vertex of triangle ABC was translated 6 units right and 4 units down to form triangle A B C.
Category 4 Measurement (9) Measurement. The student solves application problems involving estimation and measurement. The student is expected to (A) estimate measurements and solve application problems involving length (including perimeter and circumference) and area of polygons and other shapes; Useful Vocabulary Area the number of square units a figure encloses Circumference The distance around a circle Triangle Circle Volume for a 3-dimensioanl figure is a measure of the space it occupies. A math formula chart will be helpful in solving area and perimeter/ circumference problems. Your Turn Mark is buying a set of drums. He wants a cover for the drum head shown. He wants to know how much material will be needed to make the cover. The Dimensions are given in the diagram. What is the smallest area the cover could be in square inches? Step 1. Identify the shape and look for the formula on the chart provided The drumhead is the shape of a circle. The formula for area of a circle is A = πr 2 Step 2. Write the formula and evaluate (plug) in each value given The diameter shown is 14 inches so that means the radius is 7 inches A = πr 2 π= 3.14 r = 7 inches Step 3. Follow the order of operations (PEMDAS) and multiply all the numbers together 3.14 7 2 or 3.14 7 7 = 153.86 The smallest the cover could be is 153.86 in 2 (C) estimate measurements and solve application problems involving volume of prisms (rectangular and triangular) and cylinders. Your Turn with volume A cylindrical container with a 2-inch radius is filled with juice to a height of 12 inches. How much juice can the cylinder hold? Step 1. Identify the shape and decide what areas or formulas will be used to find the volume. Step 2. Step 3. Find the area of B or the base. Look on the formula chart for the area of a circle. It is πr 2 or 3.14 x 3 2 = 28.26 sq. in. Step 4. If V = Bh then multiply the area of the base times the height of the cylinder or 28.26 x 12 = 339.12 in 3
Measurement Continued: (B) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units. Useful Vocabulary What is a Proportional Relationship? In math, a proportional relationship exists when two shapes are similar but the lengths of the corre- Your turn A film negative is approximately 24 millimeters tall by 36 millimeters wide. The negative will be used to make a print that is proportional is size. If the picture print will be 25 centimeters wide, how tall must the picture be to the neatest centimeter. Step 1. Identify what side are corresponding on these similar figures. The width and the height. Step 2. Let h represent the height of the picture that is not known. Step 3. set up a ratio and solve. The print will be about 17 centimeters tall. Try it on your own. An architect built a model of a house to show a family. The length of the model was 12.5 inches and the width was 7.75 inches. If the actual house was going to be 64 feet long, how wide will the house be to the nearest foot? Tip.draw a picture if you need to. 7.75 in Set up your ratio and solve. 12.5 in. Answer? Letter B How did you do?
Math 7 Readiness Skills STAAR Review Category 5 Probabilities and Statistics (12) Probability and statistics. The student uses measures of central tendency and range to describe a set of data. The student is expected to (B) choose among mean, median, mode, or range to describe a set of data and justify the choice Connie rides her bicycle everyday. In the table below, she recorded the number of miles she rode every day for a week. Which of the following does not describe the number of miles Connie rides on typical day? A. Mean B. Median C. Mode D. Range Mean: (Average of the # s) - 30.57 (35 + 32 + 22 + 24 + 41 +22 + 38) 7 Median: (Middle number when listed in order)- 32 22 22 24 32 35 38 41 Mode : Number that occurs most often 22 22 22 24 32 35 38 41 Range: Difference of the lowest and highest value 19 41 22= 19 Step 1. Find the mean, median mode, and range of the data set so you can make an informed decision. Step 2. Compare the central tendency values to the original data set. Look for any values that are not close to the original set of data. The range is 19, it is lower than the other numbers in the original data set. The range does not describe the number of miles Connie rides on a typical day. (11) Probability and statistics. The student understands that they way a set of data is displayed influences its interpretation. The student is expected to: (B) make inferences and convincing arguments based on an analysis of given or collected data There are many types of graphs that are used to represent data. Scatterplot Histogram - which shows the number of data points that fall within specific intervals. Circle graphs which compares out of the total or % s. Venn diagram which shows how many pieces of data are common. Sometimes we have to look at a graph or data and determine if the conclusion about the data or graph is valid or is it correct. Look at the units on the graph, does the conclusion make sense? Use logic to help you decide. Your turn Jose has a part time job. The graph shows how he spends his money. If Jose earned $265 dollars last month, does the graph say that he spent a little more the $90 on lunches and entertainment? Step 1. Find how much he spent on lunches and entertainment. 13% and 21%. Add them. That is 34% of his total income. Step 2. Find what 34% of the total or 265 is. That is.34 x 265. Step 3. Solve..34 x 256 = 90.10$ Step 4. Evaluate! Does the data support the statement that Jose spend more than $90 on lunches. YES! Try It Last week, Janis surveyed people as they left Food Superstore. Of the 500 people surveyed, 447 said that Food Superstore was their favorite store. From these survey results, Janice concluded the Food superstore was the favorite store among all the people in her town. Which is the best explanation for why her conclusion might not be valid? A The sample may not have been representative of all the people in town. B She should have asked every 5th customer instead of all. C The survey did not has how old customer were. D The sample size was too small. Correct answer A