Scholar Zone Summer Math | Grade 7 Student Handbook

Student Handbook

Contents

WEEK 1

DAY 1 PR1ME: Algebraic Equations ........................................5 Math magazine: Hunt Like a Chameleon ...............7 Practice: Express Yourself .............................................9 Practice: A Capital Idea ............................................... 10 DAY 2 PR1ME: Using the Guess-and-Check Method to Solve Algebraic Equations .................................... 11 Math magazine: The Hunt on a Graph ................. 13 Math magazine: Graphing a Line ........................... 14 Math magazine: Exit Slips ......................................... 15 Practice: Onion Cooking Contest ............................ 16 Practice: A Very Cold Day ........................................... 17

DAY 3 PR1ME: Practice 2 .......................................................... 18 Math magazine: Mapping a Meltdown ................. 20 Practice: Watch Your Step .......................................... 24 Practice: Time for Fun ................................................. 25 DAY 4 PR1ME: Practice 2 .......................................................... 26 Math magazine: Glacier Percentages ................... 28 Math magazine: From Fractions to Percents .....29 Math magazine: Exit Slips ......................................... 30 Practice: X Marks the Spot! ....................................... 31 Practice: Iced Tea, Please ........................................... 32 DAY 3 PR1ME: Problem Solving ............................................ 50 Math magazine: Angles in Orbit ............................. 51 Math magazine: Angle Relationships ................... 52 Math magazine: Exit Slips ......................................... 53 Practice: Balancing Act ............................................... 54 Practice: A Sticky Situation ....................................... 55 DAY 4 PR1ME: Learn . ................................................................. 56 Practice: Give Y a Try! .................................................. 57 Math magazine: What’s for Lunch? ........................ 58 Practice: A Big Group ................................................... 60 DAY 3 PR1ME: Practice 4 .......................................................... 74 Math magazine: The Secret Lives of Parrots .....76 Practice: Uncle Sam ...................................................... 80 Practice: It’s a Gusher! ................................................. 81 DAY 4 PR1ME: Ratio and Fraction ........................................ 82 Math magazine: Who’s Visiting the Clay Walls? ................................................................. 84 Math magazine: Dynamic Data ............................... 85 Math magazine: Exit Slips ......................................... 86 Practice: Fractions Beyond Compare .................... 87 Practice: Alive and Well .............................................. 88

WEEK 2

DAY 1 PR1ME: Using the Balance Method to

Solve Algebraic Equations .......................................... 34 Practice: Expressions Everywhere . ........................ 37 Math magazine: The Science of Softball ............. 38 Math magazine: Home Run Review ....................... 40 Math magazine: Analyzing Word Problems .......41 Math magazine: Exit Slips ......................................... 42 Practice: Watch Your Step .......................................... 43 DAY 2 PR1ME: Practice 3 .......................................................... 44 Math magazine: Moon Math ..................................... 46 Practice: A Famous Author ........................................ 48 Practice: Home Sweet Home .................................... 49

WEEK 3

DAY 1 PR1ME: Learn . ................................................................. 62 Math magazine: Instagram: Beyond the Square ........................................................ 63 Practice: What’s the Inequality? .............................. 65 Practice: Exploring Underground ........................... 66 DAY 2 PR1ME: Practice 4 .......................................................... 67 Math magazine: Aspect Ratios Around Us ......... 69 Math magazine: Proportional Measures ............. 70 Math magazine: Exit Slips ......................................... 71 Practice: Equation Expert .......................................... 72 Practice: Born on the Fourth of July ...................... 73

2 Scholar Zone Summer: Math

WEEK 4

DAY 1 PR1ME: Practice 1 .......................................................... 90 Math magazine: A Towering Tradition .................. 92 Math magazine: What’s the Expression? ............. 94 Math magazine: Writing One-Variable Equations ....95 Math magazine: Exit Slips ......................................... 96 Practice: 6-A ..................................................................... 97 Practice: A Ticklish Tip Problem .............................. 98 DAY 2 PR1ME: Finding the Number of Times One Quantity is as Large as Another Given their Ratio ............100 Math magazine: Teeming with Life .....................102 Practice: 6-B ...................................................................104 Practice: The Bad Art Burglary ..............................105

DAY 3 PR1ME: Practice 2 ........................................................107 Math magazine: Reef Areas ....................................109 Math magazine: Areas of Shaded Regions .......110 Math magazine: Exit Slips .......................................111 Practice: 7-A ...................................................................112 Practice: Celebrity (pause) Seating .....................113 DAY 4 PR1ME: Solving Word Problems ............................115 Math magazine: Numbers in the News ..............116 Practice: 7-B ...................................................................118 Practice: In a Pickle .....................................................119 DAY 3 PR1ME: Ratio and Proportion . ...............................137 Practice: 9-A ...................................................................139 Math magazine: On the Brink ................................140 Practice: Mascot Mischief .........................................144 DAY 4 PR1ME: Practice 5 ........................................................146 Math magazine: Releasing Ferrets ......................149 Math magazine: Writing Percent Equations ....150 Math magazine: Exit Slips .......................................151 Practice: 9-B ...................................................................152 Practice: The Sweet Tooth Robberies .................153 DAY 3 PR1ME: Practice 6 ........................................................174 Math magazine: Horsey Histograms ...................176 Math magazine: Graphing Histograms ..............177 Math magazine: Exit Slips .......................................178 Practice: 11-A ................................................................179 Practice: Carlotta’s Coins ..........................................180 DAY 4 PR1ME: Practice 6 ........................................................181 Math magazine: Numbers in the News ..............182 Practice: 11-B ................................................................184 Practice: Under Particular Conditions ................185

WEEK 5

DAY 1 PR1ME: Learn and Practice 3 ..................................122 Math magazine: Bringing Math into the Fold .......... 124 Practice: 8-A ...................................................................126 Practice: A Case from Space . ..................................127 DAY 2 PR1ME: Learn and Practice 4 ..................................129 Math magazine: Calculating Crease Patterns ......132 Math magazine: The Triangulation Method .....133 Math magazine: Exit Slips .......................................134 Practice: 8-B ...................................................................135 Practice: Grappling over Grades ...........................136

WEEK 6

DAY 1 PR1ME: Word Problems ............................................156 Math magazine: Real-Life Heroes ........................160 Math magazine: Area Adventures ........................162 Math magazine: Dividing Fractions .....................163 Math magazine: Exit Slips .......................................164 Practice: 10-A ................................................................165 Practice: A View From Above ..................................166 DAY 2 PR1ME: Practice 6 ........................................................168 Math magazine: The Big Pony Swim ...................170 Practice: 10-B ................................................................172 Practice: A Brief Reply ...............................................173

Student Handbook 3

PR1ME WEEK 2 I DAY 1

Using the balance method to solve algebraic equations Learn a) Solve x + 6 = 10.

1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

The scale is balanced.

x + 6

To find the value of x , remove the same number of cubes from both sides until only x is left on one side.

1 1 1 1 1 1

1 1 1 1

x + 6 – 6

10 – 6

The scale stays balanced as the same number of cubes have been removed from both sides.

1 1 1 1

x = 4 is a solution of x + 6 = 10.

Check: When x = 4 , x + 6 = 4 + 6 = 10

✓

34 Scholar Zone Summer: Math

ISBN 978-981-09-0495-1

b) Solve 3 x + 4 = 10.

1 1 1 1

1 1 1 1 1 1 1 1 1 1

3 4 x

x x x

3 x + 4

The scale is balanced.

First, remove the same number of unit cubes from both sides. The scale stays balanced.

1 1 1 1

1 1 1 1 1 1

x x x

1 1 1 1 1 1

x x x

3 x + 4 – 4

10 – 4

3 x

1 1

x x x

Then, divide each side by 3 to find the value of x .

3 x ÷ 3

6 ÷ 3

1 1

The scale remains balanced.

x = 2 is a solution of 3 x + 4 = 10.

Check: When x = 2 , 3 x + 4 = 3 × 2 + 4 = 6 + 4 = 10 ✓

ISBN 978-981-09-0495-1 Student Handbook 35

PR1ME (cont.) WEEK 2 I DAY 1

1 2

c) Solve

q – 5 = 10.

I can carry out the same operations on both sides until only q is left on one side.

1 2 q – 5 + 5 = 10 + 5

Add 5 to both sides

1 2

q = 15

1 2

q × 2 = 15 × 2

Multiply by 2 on both sides

1 2

q × 2 =

× 2 × q

= q 1

q = 30

q = 30 is a solution of 1 2

q – 5 = 10.

Check: When q = 30 ,

1 2

× 30 – 5

q – 5 =

= 15 – 5 = 10

✓

Practice s 3 1. Use the balance method to solve these equations. Fill in each with +, –, × or ÷. a) j – 14 = 18 Practice 3

j – 14 + 14 = 18 +

j =

3 f – 19 = 17

= 17

3 f – 19

3 f =

3 f

f =

36 Scholar Zone Summer: Math

ISBN 978-981-09-0495-1

Practice WEEK 2 I DAY 1

Evaluating Expressions

Name

Date

Expressions Everywhere

Complete each set of problems below. 1. Evaluate each expression for n = 4.

3 + n ______________________

5.5 n ______________________

7 − n ______________________

2 n + 6 ______________________

n ___ 4 ______________________

n 2 − 5 ______________________

n 2 + n + 7.5 ______________________

3 n – 8 ______________________

15 – 2.5 n ______________________

n (3 x 0) ______________________

2. Evaluate each expression for a = 0.75 and b = 2.06.

a + b + 8 ______________________

2( a + b ) ______________________

a + b – 2.2 ______________________

3 a + 2 b ______________________

(2 a + b ) ÷ 4 _____________________ _

a + 4.55 – b ______________________

Student Handbook 37

Math magazine WEEK 2 I DAY 1

Since the 1960s, softball has been mainly played by women.

B ack in 1937, baseball legend Babe Ruth went to bat against a pitcher named John “Cannonball” Baker. But instead of hurling baseballs at the batter, Baker used a larger softball. After swinging and missing several times, Ruth finally told the catcher to switch places with him. “If you’re catching those, you might as well catch them in front of the plate because I can’t hit them,” he said. Why is it so hard for baseball players to hit a softball pitch? The secret is in how the ball is thrown. While baseball pitchers throw the ball overhand, softball pitchers throw underhand. When pitched underhand, a ball moves differently, making it almost impossible to hit without years of practice. Softball was invented in the 1880s as a form of indoor baseball to be played in winter. But people liked the game so SOFTBALL BASEBALL

much, they started playing it outdoors too. Softball has been a spring and summer sport ever since. At first, it was played by both men and women, but because girls weren’t allowed to play baseball, softball was important for female athletes. A softball is larger than a baseball, so it can’t be thrown as quickly. But the distance between the pitcher and batter is shorter, so the ball doesn’t have to travel as far ( see Softball vs. Baseball, below ). As a result, a 70 mph softball pitch reaches home plate in less than 0.4 seconds. That’s slightly faster than a 100 mph pitch reaches a batter in baseball! Throwing the ball underhand also allows softball pitchers to do things that baseball pitchers can’t, such as making the ball curve up at the end.

This is called a “rise ball.” When a ball is thrown overhand, the ball starts high, moving downward on its path to home plate. But with underhand throwing, the ball starts low and travels upward. Experienced softball batters often have a hard time hitting rise balls. So it isn’t surprising that baseball players— even Hall of Famers like Babe Ruth— would struggle. Expecting them to hit home runs would be like expecting a violinist to play the guitar just because both of the instruments have strings. Today there are many places to see softball played at a high level. It’s also a popular high school and college sport. Next year, softball—along with baseball—will return to the Summer Olympics! —Erica Westly

Ball Circumference

There are some important differences between the two sports. Here’s how they compare.

Distance Between Pitcher and Home Plate

Top Pitching Speed

Innings per Game

38 Scholar Zone Summer: Math

MIXED SKILLS

Use the information in the article and the “Softball vs. Baseball” chart to answer these mixed-skill questions.

1 A combined 25 million Americans play baseball and softball, according to a recent report by the Sports & Fitness Industry Association. With the U.S. population at roughly 325 million, what percent of Americans play softball or baseball, rounded to the nearest percent?

4 The fastest softball players can run from home plate to first base in about 2.5 seconds. Assuming a player kept up that speed, how many seconds would it take them to run from home around all the bases—first, second, and third—and back home again? 5 The path of a softball after it’s hit by a batter can be described by the function f ( x ) = -0.011 x 2 + 1.23 x + 5.5, where x is the softball’s horizontal position in feet and f ( x ), or y , is its vertical height in feet. Could a player standing 80 feet away catch the ball?

2 The formula for the surface area for a sphere is 4 π r 2 . How much larger is the surface area of a softball than a baseball’s, rounded to the nearest hundredth? Use 3.14 for pi. ( Hint: C = 2 π r )

3 In baseball, the distance between the pitcher and home plate is about 60 feet, and the distance between bases is 90 feet. In softball, the field

SOFTBALL FIELD

is smaller, but the ratio of pitching distance to home plate and the distance

between bases is the same: 2:3. Use information from the chart at left and this ratio to label

SOFTBALL BASEBALL 12 inches 9 inches 40 feet 60 feet 70-80 mph 95-105 mph 7 9

the pitcher’s distance to home plate and the distance between bases on the diagram to the right.

Student Handbook 39

Math magazine (cont.) WEEK 2 I DAY 1

Where Math Gets Real

Home Run Review In “The Science of Softball,” you answered mixed skill questions to learn about softball and baseball. Use what you learned to answer five more questions.

1. A softball game has 7 innings, compared with 9 innings in a baseball game. If each inning in both games lasts an average of 20 minutes, how much longer would a baseball game be than a softball game?

4. Softball was first included as an Olympic sport in 1996. It was a part of the Olympics until 2008 and returned to the Olympics in 2020. If you picked a Summer Olympics between 1996 and 2020 at random, what is the probability that it will include softball? ( Hint: The Summer Olympics are held once every 4 years. )

2. There are 124 countries in the International Softball Federation. Of those countries, 14.5% are located in Africa. How many countries in the International Softball Federation are in Africa?

5. An adult softball bat has a length of 34 inches and a diameter of 2.25 inches. An adult baseball bat has a length of 33 inches and a diameter of 2.5 inches. Using a cylinder as an approximation, which bat has the greater volume, and by how much? Round your answer to the nearest hundredth. Use 3.14 for pi. ( Hint: V = π r 2 h )

3. The longest softball games ever played had the following number of total innings in overtime: 28, 31, 25, 24, 21, 21, 20, 19, 19, 20. What is the mean, median, and mode of this data set?

The Science of Softball > MIXED SKILLS

40 Scholar Zone Summer: Math

Analyzing Word Problems Before solving a word problem, you need to analyze the information to understand what you are solving for. You can use the four-step process below to help you analyze and solve word problems. Where Math Gets Real

YOUR TURN ✎

HOW TO ANALYZE A WORD PROBLEM 1 UNDERSTAND: Identify what you are trying to find. What is it asking me to solve for? 2 PLAN: Organize the important information and identify the operations needed. What important information is in the problem? How will I find my answer? What operation(s) can I use? 3 SOLVE: List your strategy and steps to solve, then follow through with your plan. How many steps does the problem require? What equations will help me find the answer? 4 LOOK BACK: Validate your answer by checking all work. Does my answer make sense?

Analyze each word problem below. Then use the boxes to plan out your

strategies and solve. Round your answers to the nearest whole number.

1. During spring training, a softball team scored the following number of runs per game: 9, 3, 5, 10, 8, 10, 12, 3, 6, 5, 8, 8. What is the average number of runs scored?

UNDERSTAND

PLAN

SOLVE

LOOK BACK

2. To score in baseball and softball, the player has to touch each base and return to home plate. In baseball, the total distance traveled by the player is 360 feet. In softball, it’s 240 feet. If both a baseball and a softball team score 7 runs in a game, how much farther will the baseball team have traveled than the softball team?

UNDERSTAND

PLAN

SOLVE

LOOK BACK

3. Clayton Kershaw is a pitcher for the Los Angeles Dodgers, a Major League Baseball team. In 2017, he earned $33 million. In 2018, he earned $33.8 million. What was the percent change in Kershaw’s salary from 2017 to 2018?

UNDERSTAND

PLAN

SOLVE

LOOK BACK

The Science of Softball > OPERATIONS

Student Handbook 41

Math magazine (cont.) WEEK 2 I DAY 1

EXIT SLIP A

The Science of Softball > MIXED SKILLS

Where Math Gets Real

1. The World Series is the championship series for Major League Baseball. It was first held in 1903. It is a best- of-seven tournament, which means the lowest number of games played per World Series is 4 and the greatest is 7. Write an inequality to express the range for the number of games played as part of any World Series, using g as the variable. 2. In softball, the pitcher stands in the pitcher’s circle, which is marked on the field in chalk. The radius of the pitcher’s circle is 8 feet. What is the area of the pitcher’s circle? Use 3.14 for pi. ( Hint: Area = π r 2 )

CHECK YOUR UNDERSTANDING:

❑ Want help

❑ Need practice

❑ Almost there

❑ Got it!

EXIT SLIP B

The Science of Softball > MIXED SKILLS

Where Math Gets Real

1. A player’s batting average is found by dividing their number of base hits (hits that let the player advance to a base) by the number of times they were at bat. In the 1991-1992 season, Stacy Cowen had a 0.530 batting average. She was at bat 302 times. How many base hits did she make that season?

2. The shortstop is the softball fielding position between second and third base. The distance between second and third base on a softball field is 60 feet. If the shortstop fields a ball that is directly 12 feet behind third base, what is the diagonal distance the ball will travel from the shortstop to a player standing at second base? Round your answer to the nearest hundredth. ( Hint: Use a 2 + b 2 = c 2 )

CHECK YOUR UNDERSTANDING:

❑ Want help

❑ Need practice

❑ Almost there

❑ Got it!

42 Scholar Zone Summer: Math

Practice WEEK 2 I DAY 1

Name

Date

Watch Your Step

Evaluating Expressions

With a drop of 3,212 feet, this waterfall is the highest in the world. What is the name of this waterfall, and in which country is it located?

To answer the question, evaluate each expression for n = 3, t = 5, and y = 7. Then write the letter of the expression in the space above its answer. (Some letters will be used more than once. Some letters will not be used.) The first one has been done for you.

41203026 8 42 4 8 8 56

13 2612026 12 18 26 8 4

U. 6 × n

R. t + y + 4

B. ( n + t ) ÷ 4

A. 14 − ( n + y )

L. 24 ÷ n

T. t × 4 − n

W. (18 ÷ n ) ÷ 2

F. 2 × ( n × y )

N. 10 × ( y + t )

S. 8 × y

H. 75 ÷ ( n × t )

V. (70 ÷ y ) + n

E. ( t × n ) + ( y + 4)

G. 45 − ( n × t )

J. ( y + 8) − ( t − 4)

Z. 24 ÷ ( y − t )

Student Handbook 43

Check: When q = 30 ,

1 2

× 30 – 5

q – 5 =

PR1ME WEEK 2 I DAY 2

= 15 – 5 = 10

✓

c) Solve Practice s 3 1. Use the balance method to solve these equations. Fill in each with +, –, × or ÷. a) j – 14 = 18 1 2 q – 5 = 10. 1 2 q – 5 + 5 = 10 + 5 q = 15 Add 5 to both sides Practice 3

I can carry out the same operations on both sides until only q is left on one side.

1 2

q × 2 = 15 × 2

Multiply by 2 on both sides

j – 14 + 14 = 18 +

j =

1 2

q × 2 =

× 2 × q

= q 1

3 f – 19 = 17

q = 30 3 f – 19

= 17

q = 30 is a solution of 1 2

q – 5 = 10.

3 f =

3 f

Check: When q = 30 ,

1 2

× 30 – 5

q – 5 =

f =

= 15 – 5 = 10

✓

1 4

g + 11 = 16

1 4

= 16

g + 11

Practice s 3 1. Use the balance method to solve these equations. Fill in each with +, –, × or ÷. a) j – 14 = 18 Practice 3 1 4 g = 1 4 g =

g =

j – 14 + 14 = 18 +

2. Use the balance method to solve these equations.

j =

q + 32 = 51

b) r – 26 = 26

3 f – 19 = 17

= 17

3 f – 19

3 f =

3 f

f =

44 Scholar Zone Summer: Math

ISBN 978-981-09-0495-1

c) 3 s + 12 = 45

d) 6 t + 7 = 61

1 4

g + 11 = 16

1 4

= 16

g + 11

e) 4 u – 17 = 31

f) 7 v – 38 = 18

1 4

g =

1 4

e) 4 u – 17 = 31

f) 7 v – 38 = 18

g =

2. Use the balance method to solve these equations. e) 4 u – 17 = 31 f) 7 v – 38 = 18

q + 32 = 51

b) r – 26 = 26

1 6

1 4

w + 7 = 9

x + 16 = 20

1 6

1 4

w + 7 = 9

x + 16 = 20

1 6

1 4

w + 7 = 9

x + 16 = 20

c) 3 s + 12 = 45

d) 6 t + 7 = 61

1 5

1 8

y – 2 = 5

z – 4 = 4

1 5

1 8

y – 2 = 5

z – 4 = 4

1 5

1 8

y – 2 = 5

z – 4 = 4

ISBN 978-981-09-0495-1 Student Handbook 45

Math magazine WEEK 2 I DAY 2

In 1969, this woman’s calculations got astronauts to the moon and back

colleagues crunched the numbers in the equations used to design, test, and fly planes and spacecraft reliably and safely. Some equations had up to 35 variables! Together, their results helped launch rockets into space and safely transport astronauts into space—and back home again. Getting astronauts Armstrong and Aldrin to the moon was a spectacular scientific achievement. Getting them home was another hurdle. The astronauts had a small window of only a few hours to blast off from the moon’s surface and reconnect with the Apollo shuttle for the return journey. It was Johnson’s job to figure out the precise time that the two space vehicles should connect. This was a very complicated task, but one that Johnson considered her greatest contribution to the space program. “I found what I was looking for at Langley,” said Johnson, who died in 2020. “I went to work every day for 33 years happy. Never did I get up and say, ‘I don’t want to go to work.’” —Alexa C. Kurzius

Buzz Aldrin sets up an experiment on the moon’s surface.

To truly appreciate Johnson’s achievements, it’s necessary to understand the world she lived in. Johnson is black, and grew up during a time when segregation, or separating people by skin color, was legal in much of the South. African-Americans were forced to use separate bathrooms, attend separate schools, and eat at separate restaurants. Because of a labor shortage following World War II,

stronauts Neil Armstrong and Buzz Aldrin made history when they became the first

humans to set foot on the moon on July 20, 1969. The Apollo 11 mission was the result of decades of research, hundreds of scientific experiments, and the work of tens of thousands of dedicated people. But the contributions of one woman outshined the rest: Katherine Johnson. She was a NASA mathematician who calculated the detailed flight path the spacecraft would take from Earth to the moon. In 2017, a movie about Johnson and NASA’s other black female mathematicians hit theaters. Titled Hidden Figures , it’s based on a book of the same name.

Johnson and dozens of other black women were hired to work at Langley Research Center in Hampton, Virginia. Johnson started in 1953 as a “human computer.” In this job, Johnson and her female

aption tkDa vidis aut liqui cori nullacerit, omniminvella is as ium dolupta

Taraji P. Henson, as Katherine Johnson in

Hidden Figures , calculates the curved path of a rocket.

46 Scholar Zone Summer: Math

DRAWING ANGLES WITH A PROTRACTOR

When planning the Apollo 11 voyage, NASA scientists made a flight plan for the trip, including a step-by- step process to get the moon lander to the appointed spot on the surface. Katherine Johnson and her team calculated a series of angles for the moon lander to make before its descent. An angle is a figure made by two rays (a line with one endpoint) that meet at a point called a vertex. The difference between the two lines is measured in degrees.

EXAMPLE: Draw an angle of 52°.

Draw a ray and label the endpoint Y and add another point on the ray labeled X :

Align the baseline of your protractor with the ray. Point Y should be at your protractor’s origin. Make a point along the scale of the protractor at 52° and label it Z :

Draw a ray to connect point Y to point Z to complete the angle:

xyz

Name your angle using the points in the angle, with the vertex in the middle. This angle is ∠ XYZ .

Complete the diagram of the moon lander’s flight plan by drawing the angles that Johnson calculated. Line HMQ marks the horizon, or the line where the moon and sky appear to meet. Use point M (the moon’s surface) as the vertex for all angles.

✎

1 The moon lander traveled from left to right. When it was 35° above the moon’s horizon line, it began its landing. Draw a ray with a point of B to create this angle. What’s this angle’s name?

toward the moon and had moved an additional 16° above the horizon. Draw a ray with point C to create a 16° angle above the angle you drew in No. 1. What is the name of this new angle?

94° from the angle you drew in No. 2. Draw a ray with point D to make the angle and name it.

4 What is the measurement of ∠ DMQ that you created? Explain how you determined this.

3 Another 75 seconds later, the spacecraft was in position to detach the lander at

2 Forty seconds later, the spacecraft began tilting

Student Handbook 47

Practice WEEK 2 I DAY 2

Writing Equations

Name

Date

A Famous Author

C. S. Lewis is well known as the author of the series Chronicles of Narnia. Less well known is his full name. What do the initials C. S. stand for?

Answer: ________ ________ ________ ________ ________

5 n – 6 = 9

n ÷ 8 = 9

n (2 + 1) = 9

n +4=9 3( n + 1) = 9

n – 4 = 9 ________ ________ ________ ________ ________ ________ ________ n ÷ 2 + 5 = 9 3 n – 3 = 9

(3 n + 3) ÷ 3 = 9

n ÷8=9 3( n + 1) = 9 (3 n + 3) ÷ 3 = 9

To answer the question, write an algebraic equation for each sentence. Write the letter of each problem in the space above its equation. Hint: Some letters will be used more than once. Some will not be used.

V. 4 more than n is 9. ______________________________________________

T. 4 less than n is 9. ______________________________________________

L. n divided by 8 is 9. ______________________________________________

R. 3 times n is 9. ______________________________________________

P. 5 more than n divided by 2 is 9. ____________________________________________

C. 6 less than 5 times n is 9. ______________________________________________

N. n times 3 divided by 4 is 9. ______________________________________________

A. 3 times n minus 3 is 9. ______________________________________________

H. the sum of n and 4 divided by 2 is 9. ________________________________________

E. 3 times the sum of n and 1 is 9. ____________________________________________

S. the sum of 3 times n plus 3 divided by 3 is 9. ______________________________

I. n times the sum of 2 and 1 is 9. ___________________________________________

48 Scholar Zone Summer: Math

Name

Date

Solving Inequalities with Whole Numbers

Home, Sweet Home

Although our planet is big, all life exists in a relatively narrow band of land, sea, and sky. This part has the conditions life needs to survive. What is this part of Earth called?

Answer:

To answer the question, solve the inequalities. For each problem, four possible answers are given. Circle all answers that make each inequality true. When you are done, write the letters in order in the spaces.

3 + n > 14 R. 4

3 n > 26 D. 8 M. 7

B. 12 T. 10 I. 13

K. 3 H. 9

n − 6 < 3 H. 9 E. 10 O. 8 U. 12 n ÷ 4 > 6 S. 28 E. 24 C. 20 P. 32

2 n ÷ 4 > 3 E. 10

L. 6 T. 2 R. 8

4( n + 5) < 33 H. 4

S. 5 E. 3 I. 6

Student Handbook 49

PR1ME WEEK 2 I DAY 3

Lesson 2 Problem Solving

Learn Word problems Evan has z guppies and 21 angelfish. He has 38 fishes altogether. How many of his fishes are guppies ?

Understand the problem. 1

There are 38 fishes altogether. 21 of the fishes are angelfish. The rest are guppies. I have to find the unknown z , which is the number of guppies.

Plan what to do. 2

I can form an equation in terms of z to solve the problem.

Answer . 3

Work out the

z + 21 = 38 z + 21 – 21 = 38 – 21 z = 17

I can show this using a bar model.

Evan has 17 guppies.

is correct. 4

Check if your answer

When z = 17 ,

z + 21 = 17 + 21 = 38 ✓

My answer is correct.

1. Understand

2. Plan

3. Answer

4. Check

50 Scholar Zone Summer: Math

ISBN 978-981-09-0495-1

Where Math Gets Real Math magazine WEEK 2 I DAY 3

Where Math Gets Real

Angles in Orbit

(point S on the diagram) on January 1, 2017. (Note: The planets’ distances from the sun are not to scale.) Reread “Moon Math.” In that article, you drew angles to complete the diagram of the Apollo 11 moon lander’s flight plan. Use what you learned to draw five more angles to see the position of the planets orbiting the sun Where Math Gets Real

Where Math Gets Real

*with white behind logo

1. On January 1, Mercury (point M ) and Venus made a 70º angle with the sun as the vertex. Draw this angle using point M on the innermost ring, which is Mercury. Label Venus as point V on the second ring. What’s the name of this angle? 2. Earth made a 19º angle with Mercury that lies in between the angle Mercury and Venus made. Draw this angle, labeling Earth as E on the third ring. What’s this angle’s name? 3. Mars was to the right of Venus, making a 33º angle with Venus and the sun. Draw this angle and label Mars as point R on the fourth ring. What’s this angle’s name?

4A. Mars and Jupiter made a 180º angle with the sun in the center. Draw this angle and label point J for Jupiter on the fifth ring.

4B. Uranus also makes a 180º angle with the sun and Jupiter, named ∠ JSU . Mark Uranus as point U on the seventh ring.

5. Neptune is marked on the diagram as point N . Saturn was between Neptune and Jupiter, making a 68º angle with Jupiter and the sun. Draw this angle, labeling Saturn as T on the sixth ring. What’s this angle’s name?

JANUARY 16, 2017 > p. 14 Moon Math > DRAWING ANGLES WITH A PROTRACTOR

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7/23/18 9:57 AM

Math magazine (cont.) WEEK 2 I DAY 3

Where Math Gets Real

Angle Relationships When angles share a ray, they are called angle pairs. Knowing the relationships between angle pairs can help you find unknown measures of angles. Where Math Gets Real

YOUR TURN ✎ Use these definitions to classify angle pairs and find missing angle measures in the questions below.

*with white behind logo Complementary angles: Angles whose measures have a sum of 90° (a right angle) Supplementary angles: Angles whose measures have a sum of 180° (a straight line) Where Math Gets Real

Vertical angles: Angles opposite one another, formed when two lines intersect; these angles are always congruent (they have the same degree measure) Adjacent angles: Angles that have a common side and a common vertex (corner point) and do not overlap

66°

3A. Which pairs of angles shown above are vertical?

1A. Write and solve an equation to find the measure of angle m .

3B. Which pairs of angles are adjacent?

1B. Are the angles above complementary, supplementary, vertical, and/or adjacent?

3C. Angle b is 65°. What is the measure of angle a ?

3D. What is the measure of angle c ?

2. Angle s is complementary to 38°. Write and solve an equation to find the measure of angle s .

3E. What is the measure of angle d ?

38°

3F. What is the sum of the measures of angles a , b , c , and d ?

JANUARY 16, 2017 > p. 14 Moon Math > ANGLE PROPERTIES

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Where Math Gets Real

EXIT SLIP A

Moon Math > DRAWING ANGLES WITH A PROTRACTOR

Where Math Gets Real

Where Math Gets Real 1. The Solar Heliospheric Observatory (SOHO) is a satellite that orbits the sun to collect data on the sun’s interior and its solar winds. At one point in its orbit, SOHO makes a 60º angle between the Earth (point E ) and the sun (the sun is the vertex at point S ). Draw the angle that represents SOHO’s position on the diagram, below, using point H to represent the satellite.

Where Math Gets Real

*with white behind logo

2. What’s the name of

the angle that you drew?

Where Math Gets Real

EXIT SLIP B

Moon Math > DRAWING ANGLES WITH A PROTRACTOR

Where Math Gets Real

1. The Solar Terrestrial Relations Observatory spacecraft are two

*with white behind logo and the sun (the sun is the vertex at point S ). Draw and name this angle on the diagram. Where Math Gets Real satellites (STEREO-A and STEREO-B) that orbit the sun to capture images of the sun from different angles. In December 2016, STEREO-A made a 145º angle between the Earth (point E ) Where Math Gets Real

2. In December 2016, STEREO-B made a 65º angle between STEREO-A and the sun opposite the location of Earth. Draw the angle on the diagram.

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Practice WEEK 2 I DAY 3

Writing Equations

Name

Date

Balancing Act

Write an equation for each statement.

1. A number w increased by 2.5 is equal to 3.8. ____________________________

2. The difference between a number y and 82 is 47. ____________________________

3. A number n divided by 0.5 is equal to 2. ____________________________

4. The product of a number k and _3__

_7__ 8 . ____________________________

8 is 1

5. The quotient of a number z and 175 is 25. ____________________________

6. The sum of 1,231 and a number b is equal to 2,342. ____________________________

7. A number d multiplied by 64 is 960. ____________________________

8. A number 4,050 divided by a number x equals 81. ____________________________

9. Fifteen is equal to a number m divided by 75. ____________________________

10. A number v increased 160 times is equal to 1,760. ____________________________

54 Scholar Zone Summer: Math

Name

Date

A Sticky Situation

Writing Equations

In 1955, George D. Mestral invented a product that most Americans since then have used at one time or another. What is this product?

Answer:

3 × 12 = n 12 + 3 = n 16 − 12 = n 12 ÷ 3 = n 36 ÷ 3 = n 12 − 4 = n

To answer the question, write an equation for each problem. Then write the letter of the problem in the space above its equation. Let n stand for the missing numbers.

L. Joe had to complete 12 math

E. Tyrell can run a mile in 12 minutes. It takes his friend Ryan 3 minutes longer to run a mile. How long does it take Ryan to run a mile?

problems for homework. He copied his assignment incorrectly and completed 16 problems. How many extra problems did he do?

C. Danielle is selling wrapping paper to raise money for her class. The class will reach its goal if everyone sells 12 rolls. Danielle plans to reach this goal if she sells 3 rolls of paper per day. How many days will it take her to sell the wrapping paper? V. Marina is helping her teacher by cutting out circles for a class activity. There are three groups of students and each group needs a dozen circles. How many circles does Marina need to make?

O. Mike lost some of the pieces of his checkers set. He now has only 12 pieces, including 4 four red ones. How many black pieces does he have?

R. Marie and her two cousins are

planning refreshments for a family gathering. They need 3 dozen cupcakes. How many cupcakes should each girl bake if they are to bake the same amount?

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8:43 PM

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PR1ME WEEK 2 I DAY 4

Learn A baker bought 5 cartons of eggs. Each carton had y eggs. He used 12 eggs to make some sponge cakes and had 18 eggs left. How many eggs were there in each carton at first ?

5 y – 12 = 18 5 y – 12 + 12 = 18 + 12 5 y = 30 5 y ÷ 5 = 30 ÷ 5 y = 6

y y y y y

5 y

There were 6 eggs in each carton at first.

12 used 18 left

1. Understand

2. Plan

3. Answer

4. Check

Learn

Kristin bought a roll of red ribbon x meters long. She used 1 3 of the red ribbon and 8 meters of blue ribbon to decorate a stage. She used 11 meters of ribbon altogether. How long was the roll of red ribbon at first ?

1 3

x + 8 = 11

First, I need to form an equation in terms of x .

1 3 x + 8 – 8 = 11 – 8

1 3

x = 3

1 3

x × 3 = 3 × 3 x = 9

The roll of red ribbon was 9 meters long at first.

1. Understand

2. Plan

3. Answer

4. Check

56 Scholar Zone Summer: Math

ISBN 978-981-09-0495-1

Practice WEEK 2 I DAY 4

Writing Equations/ Word Problems

Name

Date

Give Y a Try!

Write an algebraic equation to represent and solve each problem. Solve three problems in a row to get Tic-Tac-Math!

Harold’s dad is 3 times his age. The sum of Harold’s age and his father’s age is 60 years. How old is Harold? How old is his dad?

A rectangle’s length is y cm. Its width is 2 cm. The perimeter is 10 cm. Find the rectangle’s width.

A rectangle’s length is y cm. Its width is 5 cm. Its perimeter is 34 cm. Find the length of the rectangle.

Harlan’s dad is 3 years more than 4 times Harlan’s age. The difference in their ages is 30 years. How old is Harlan? How old is his dad?

Ella is twice Bella’s age, and Stella is three times

Oriana is 5 years older than her brother Francisco. The sum of their ages is 27. How old is each child?

Bella’s age. The difference between Stella’s and Bella’s ages is 8 years. How old is each girl?

Ty, Malcolm, and Fred were playing basketball. Malcolm made 2 more baskets than Ty, and Fred made 4 more than twice the number that Ty made. Together, the boys made 42 baskets. How many baskets did each boy make?

Janet bought 3 dozen donuts from Delectable

Sally has twice as many hair ribbons as Natasha. Bethany has 3 less than Sally. The sum of all three girls’ ribbons is 32. How many hair ribbons does each girl have?

Donuts. She bought 3 times as many honey-dipped as plain. She bought 6 fewer chocolate-frosted than honey-dipped. How many of each did she buy?

Student Handbook 57

Math magazine (cont.) WEEK 2 I DAY 4

STATISTICS

BY JOANNA KLEIN

Y ou may have had a sandwich for lunch been no such thing. Legend has it that in the 1700s, English nobleman Found everywhere from diners to fancy restaurants, the triple-decker turkey club is an American classic. Here’s how to make it: What’s for Lunch? JOIN THE CLUB Found everywhere from diners to fancy restaurants, the triple-decker turkey club is an American classic. Here’s how to make it: What’s for Lunch? today, but more than 200 years ago there may have today, but more than 200 years ago there may have JOIN THE CLUB ou may have had a sandwich for lunch today, but more than 200 years ago there may have been no such thing. Legend has it that in the 1700s, English nobleman Found everywhere from diners to fancy restaurants, the triple-decker turkey club is an American classic. Here’s how to make it: JOIN THE CLUB

Y ou may have had a sandwich for lunch been no such thing. Legend has it that in the 1700s, English nobleman John Mantagu, the fourth Earl of Sandwich, was the first person to order a chunk of beef between two pieces of bread. With that, he revolutionized lunchtime. Forty-nine percent of Americans John Mantagu, the fourth Earl of Sandwich, was the first person to order a chunk of beef between two pieces of bread. With that, he revolutionized lunchtime. Forty-nine percent of Americans will eat some type of sandwich on any given day of the week, according to a 2016 survey by the U.S. Department of Agriculture. About 6,000 participants dished on everything they’d eaten the day before. The half who had eaten a sandwich also reported all of its ingredients. Of course, all sandwiches are not created equal. There’s a big difference between a PB&J, a turkey club, and a grilled cheese in terms of nutritional value. The survey also revealed that sandwiches contribute to one-fifth of America’s daily sodium intake. Another reason sandwiches’ nutritional value varies widely is that today’s definition of a sandwich difference between a PB&J, a turkey club, and a grilled cheese in terms of nutritional value. The survey also revealed that sandwiches contribute to one-fifth of America’s daily sodium intake. Another reason sandwiches’ nutritional value varies widely is that today’s definition of a sandwich isn’t as clear as it was back in the 1700s. For instance, some people consider hamburgers and hot dogs to be sandwiches. And a burrito is considered a sandwich for tax purposes in New York State, but not in Massachusetts. In 2006, after a fight between Panera Bread and Qdoba Mexican Grill, a judge in Worcester actually ruled that a burrito is not a sandwich! to be sandwiches. And a burrito is considered a sandwich for tax purposes in New York State, but not in Massachusetts. In 2006, after a fight between Panera Bread and Qdoba Mexican Grill, a judge in Worcester actually ruled that a burrito is not a sandwich! isn’t as clear as it was back in the 1700s. For instance, some people consider hamburgers and hot dogs will eat some type of sandwich on any given day of the week, according to a 2016 survey by the U.S. Department of Agriculture. About 6,000 participants dished on everything they’d eaten the day before. The half who had eaten a sandwich also reported all of its ingredients. Of course, all sandwiches are not created equal. There’s a big

John Mantagu, the fourth Earl of Sandwich, was the first person to order a chunk of beef between two pieces of bread. With that, he revolutionized lunchtime. Forty-nine percent of Americans will eat some type of sandwich on any given day of the week, according to a 2016 survey by the U.S. Department of Agriculture. About 6,000 participants dished on everything they’d eaten the day before. The half who had eaten a sandwich also reported all of its ingredients. Of course, all sandwiches are not created equal. There’s a big

TURKEY: 28 g

BREAD: 3 slices

MAYO: 2 tbsp

BACON: 4 strips

LETTUCE: 3 leaves

TURKEY: 28 g

BREAD: 3 slices

MAYO: 2 tbsp

BACON: 4 strips

LETTUCE: 3 leaves

TOMATO: 2 slices

Toppings

difference between a PB&J, a turkey club, and a grilled cheese in terms of nutritional value. The survey also revealed that sandwiches contribute to one-fifth of America’s daily sodium intake. Another reason sandwiches’ nutritional value varies widely is that today’s definition of a sandwich

✎ Answer the following questions using the information in the charts and graphs above. Answer the following questions using the information in the charts and graphs above. ✎ ✎

Answer the following questions using the information in the charts and graphs above.

isn’t as clear as it was back in the 1700s. For instance, some people consider hamburgers and hot dogs to be sandwiches. And a burrito is considered a sandwich for tax purposes in New York State, but not in Massachusetts. In 2006, after a fight between Panera Bread and Qdoba Mexican Grill, a judge in Worcester actually ruled that a burrito is not a sandwich!

1 How much more does a club sandwich cost in a hotel in Seoul, South Korea, than in Buenos Aires, Argentina? A $7.81 C $15.37 B $10.39 D $18.30 2 Which sandwich shop in the bar graph received the highest loyalty score? A Jersey Mike’s C Subway B Jason’s Deli D Arby’s 1 How much more does a club sandwich cost in a hotel in Seoul, South Korea, than in Buenos Aires, Argentina? A $7.81 C $15.37 B $10.39 D $18.30 2 Which sandwich shop in the bar graph received the highest loyalty score? A Jersey Mike’s C Subway B Jason’s Deli D Arby’s

3 What percent of respondents said that the toppings make a sandwich great? A 6% C 38% B 7% D 42% 4 What’s the ratio of bacon strips to slices of bread in a classic triple-decker turkey club sandwich? A 1:2 C 4:3 B 3:4 D 5:3 3 What percent of respondents said that the toppings make a sandwich great? A 6% C 38% B 7% D 42% 4 What’s the ratio of bacon strips to slices of bread in a classic triple-decker turkey club sandwich? A 1:2 C 4:3 B 3:4 D 5:3

So are you having a sandwich today?

58 Scholar Zone Summer: Math

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