Grade 7 Winter Holiday Student Activities
Module A – Integers, Coordinate Plane MA.7.A.3.1, MA.7.G.4.3,
Examples of MA.7.A.3.2 can be found on Module B
Activity #1 Addition and Subtraction of Integers – (STD MA.7.A.3.1)
(moderate complexity)(tested by MC)
Add Integers
To add integers with the same sign, add their absolute values. The sum is:
•
positive if both integers are positive.
•
negative if both integers are negative.
To add integers with different signs, subtract their absolute values. The sum is:
•
•
positive if the positive integer’s absolute value is greater.
negative if the negative integer’s absolute value is greater. To add integers, it is helpful to use a number line
Example 1 4 + (-­‐7)
Use a number line
• Start at 0
• Move 4 units to the right. Then
• 7 units to the left.
4 + (-­‐7) = -­‐3
Example 2 -­‐1 + -­‐3
Use a number line
• Start at 0
• Move 1 unit to the left. Then
• 3 more units to the left.
-­‐1 + -­‐3 = -­‐4
Subtract Integers
To subtract integers add its opposite
Example 1 Find 7 -­‐ 11.
Example 2 Find -­‐12 – (-­‐19).
7 – 11 = 7 + (-­‐11)
= -­‐4
-­‐12 – (-­‐19) = -­‐12 + 19
To subtract -­‐12, and 19
Simplify
=7
To subtract 11, add -­‐11
Simplify
Practice
1. The odometer of Ms. Smith truck read 57,234 miles before his trip and 58,619 miles after his trip. Which
integer represents the change in the odometer reading on Mr. Burdett’s truck?
A. -­‐1,385
B. -­‐385
C. 385
D. 1,385
2. A deep-­‐sea diver attached to a safety cable was lowered into the water to a depth of 500 feet. During
the next hour, the safety cable was let out 150 feet, pulled in 46 feet, pulled in 59 feet, let out 33 feet,
pulled in 41 feet, let out 58 feet, and pulled in 23 feet to allow the diver to explore. At the end of the hour,
what was the depth of the diver?
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Grade 7 Winter Holiday Student Activities
3. A team gained 6 yards on their first play of the game. Then they lost 8 yards. Find the total change
in yardage.
4. A roller coaster begins at 95 feet above ground level. Then it descends 120 feet. Find the height of the
coaster after the first descent.
5. Michele and Tom were digging in the sand at the beach. Michele dug a hole that was 16 inches below
the surface and Tom dug a hole that was 8 inches below the surface. Find the difference in the depths of
their holes.
Activity #2 Multiplying and Dividing Integers (STD MA.7.A.3.1)
(moderate complexity)(tested by MC)
Multiply Integers
Example 1 Find 6(-­‐3)
Example 2 Find -­‐4(-­‐5)
6(-­‐3) = -­‐18
-­‐4(-­‐5) = 20
If the integers have different
Signs. The product is negative.
If the integers have the same
Sign. The product is negative.
Divide Integers
The quotient of two integers with different signs is negative. The
quotient of two integers with the same sign is positive.
Example 1 Find 45 ÷ (-­‐5)
Example 2 Find -­‐150 ÷ -­‐10
45 ÷ (-­‐5)
Integers that have different signs
45 ÷ (-­‐5) = -­‐9 The quotient is negative.
-­‐150 ÷ -­‐10
The integers have the same
sign
-­‐150 ÷ -­‐10 = 15 The quotient is positive
Practice
1. Which integer is equal to the product of -­‐7 and the sum of 5 and -­‐1?
A. -­‐28
B. -­‐4
C. 4
D. 28
2. Which two integers have a positive quotient and a negative sum?
F. -­‐8 and -­‐3
G. -­‐5 and 2
H. 7 and 1
I. 9 and – 3
3. A drought can cause the level of the local water supply to drop by a few inches each week. Suppose
the level of the water supply drops 3 inches each week. How much will it change in 4 weeks?
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Grade 7 Winter Holiday Student Activities
4. Josh purchased 8 cans of tennis balls. The cans came with 4 balls in each can. How many balls did Josh
purchase?
5. The basketball team lost their last 6 games. They lost by a total of 54 points. Find their average number
of points relative to their opponents.
6. What is the value of the expression
−42 ÷ (−2)?
A. −21
B. −7
C. 7
D. 21
7. Over the past seven days, Mrs. Cho found that the temperature outside had dropped a total of
42 degrees. Find the average change in temperature each day.
8. The enrollment at Washington Middle School dropped by 70 students over a 5-­‐year period. What
is the average yearly drop in enrollment?
Activity #3 Coordinate Plane – (STD MA.7.G.4.3) (low complexity)
(tested by MC)
Example 1
Write the ordered pair that corresponds to
point Q. Then state the quadrant in which Q is
located.
• Start at the origin.
• Move 4 units left along the x-­‐axis.
• Move 3 units up on the y-­‐axis.
The ordered pair for point Q is (–4, 3).
Q is in the upper left quadrant or Quadrant II.
Example 2
Graph and label point N at (0, –4).
•
•
•
•
Start at the origin.
Move 0 units along the x-­‐axis.
Move 4 units down on the y-­‐axis.
Draw a dot and label it N
.
Practice
1. Which pair of coordinates describes a point in the second quadrant of a coordinate grid?
A. (2, 4)
B. (-­‐2, 4)
C. (2, -­‐4)
D. (-­‐2, -­‐4)
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Grade 7 Winter Holiday Student Activities
2. Chase’s home is represented by the ordered pair (0, 0) on the coordinate grid below.
Which ordered pair represents the location of the Library?
A. (-­‐4, 0 )
C. (4, 0)
B. (0, -­‐4)
D. (0,4)
Module B Fractions & Exponents MA.7.A.3.2, MA.7.A.5.1
Activity #4 Add and Subtract Unlike Fractions (STD MA.7.A.3.2)
(moderate complexity)(tested at MC, GR)
Example 1
Use the LCD, 15
then add the fractions
Practice
1. Kaitlyn completed of her project on Monday and of the project on Tuesday. How much of her project
is incomplete?
A.
B.
C.
D.
2. If of the students got an A and of them got a B, what fraction of the students got an A or a B?
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Grade 7 Winter Holiday Student Activities
3. If of the people in a water aerobics class are over age 65 and of the people in the class are under age
40, what fraction of the people in the class are either over 65 or under 40?
Activity #5 Add and Subtract Mixed Numbers (STD
MA.7.A.3.2)(moderate complexity)(tested by MC, GR)
To add or subtract mixed numbers:
• Add or subtract the fractions. Rename using the LCD if necessary.
• Then, add or subtract the whole numbers.
• Simplify if necessary.
Example 1
Find
Example 2
Write in simplest form
Write in simplest form
Rename the fraction using the LCD
Rename using the LCD
Add
Add
Example 3
Find
Find
Example 4
. Write in simplest form
Find
Rename the fraction using the LCD
Rename
Subtract
Subtract
Subtract
Practice
1. On Monday, Deborah ran 3 miles and on Tuesday she ran 4 miles. How many miles did she run on
these two days together?
2. Mr. and Mrs. Sampson went to two movies. The first movie lasted 2 hours and the second one lasted
1 hours. How much longer was the first than the second movie?
3. Sam and Sharon drove to the coast. Sam drove 38
miles. Then Sharon drove the last 51 miles. How
far did they drive to the coast?
Activity #6 Multiply and Divide Fractions (STD MA.7.A.3.2)(moderate
complexity)(tested by MC, GR)
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Grade 7 Winter Holiday Student Activities
Example 1
Find
Example 2
Write in simplest form.
Find
RENAME 4 AS AN IMPROPER
=
·
MULTIPLY BY THE RECIPROCAL OF
=
·
DIVIDE OUT COMMON
Rename
,
Multiply the numerators
MULTIPLY THE
DENOMINATORS
=
as an improper
fraction
MULTIP
= 15
. Write in simplest form.
Multiply
Simplify
Simplify
Example 3
Find 4 ÷ . Write in simplest form.
4 ÷ =
÷
1. One sixth of the students at a local college are junior. The number of sophomore students is 2 times
that amount. What fraction of the students are sophomores?
2. Bob bought some stock at $36 a share. The stock increased to 1 times its value. How much is the
stock per share?
3. Randy has three 27-­‐pound blocks of ice for his snow cone stand. If each snow cone requires
pound of
ice, how many snow cones can Randy make?
Activity #7 Powers of Exponents (STD MA.7.A.3.1)(low
complexity)(tested by MC)
exponent
4
4 = 4 ·∙ 4 ·∙ 4 ·∙ 4 = 256 base
common factors
The exponent tells you how many times the base is used as a factor.
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Grade 7 Winter Holiday Student Activities
Example 1
Example 2
Write 53 as a product of the same factor.
Evaluate 74.
The base is 5. The exponent 3 means that 5 is used as a
factor 3 times.
74 = 7 ·∙ 7 ·∙ 7 ·∙ 7
= 2401
53 = 5 ·∙ 5 ·∙ 5
Example 3
Write ·∙ ·∙ ·∙ ·∙ in exponential form.
The base is . It is used as a factor 5 times, so the
exponent is 5.
Write each power as a product of the same factor.
1. 63
2. 37
3.
5. 73
6. 84
Evaluate each expression.
4. 25
Write each product in exponential form.
7. 3 ·∙ 3 ·∙ 3 ·∙ 3
8. 6 ·∙ 6 ·∙ 6 ·∙ 6 ·∙ 6 ·∙ 6
9. Write 625 using exponents in as many ways as you can.
10. The school library contains 84 books. How many library books are in the school library?
11. The concession stand at the county fair sold 93 hot dogs on the first day. How many hot dogs did they
sell?
Activity #8 Terminating and repeating decimals – (STD
MA.7.A.5.1)(low complexity)(tested by MC
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Grade 7 Winter Holiday Student Activities
Practice
1. What decimal is equivalent to
2. The population of Florida is about
equivalent to
?
of the population of the entire United States. Which decimal is
?
A. 0.08
B. 0.8
C. 8.0
D. 18.88
Activity #9 Compare and Order Rational Numbers (STD
MA.7.A.5.1)9low complexity)(tested by MC)
To compare fractions, rewrite them so they have the same denominator. The least common
denominator (LCD) of two fractions is the LCM of their denominators.
Another way to compare fractions is to express them as decimals. Then compare the decimals.
Example 1
Which fraction is greater, , or ?
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Grade 7 Winter Holiday Student Activities
1. Because he sees movies at his local theater so often, Trisitan is being offered a discount. He
can have either off his next ticket or off his next ticket. Which discount should Delmar
choose? Explain.
2. In a recent pizza-­‐eating contest, Nora ate 1 pizzas, Aiden ate 1
pizzas, and Michael ate 1
pizzas. Which person won the contest?
Module C Proportion, Similarity
Activity #10 Proportional and Nonproportional Relationships(STD
MA.7.A.1.1)(high complexity)(tested MC, GR)
Two related quantities are proportional if they have a constant ratio between them. If two related quantities
do not have a constant ratio, then they are nonproportional.
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Grade 7 Winter Holiday Student Activities
1. A photo developer charges $0.35 per photo developed. Is the total cost proportional to the number of photos
developed?
2. A soccer club has 13 players for every team, with the exception of two teams that have 16 players each. Is the
number of players proportional to the number of teams?
Activity #11 Proportions (STD MA.7.A.1.1)
A proportion is an equation that states that two ratios are equivalent. To determine whether a pair of ratios forms a
proportion, use cross products. You can also use cross products to solve proportions.
1. A 12-­‐ounce bottle of shampoo lasts Enrique 15 weeks. How long would you expect an 18-­‐ounce
bottle of the same brand to last him?
2. A 6-­‐ounce package of fruit snacks contains 45 pieces. How many pieces would you expect in a 10-­‐
ounce package?
Activity #12 Apply Proportions to Measurement (STD MA.7.A.1.6)(moderate
complexity)(tested MC. GR)
A scale drawing represents something that is too large or too small to be drawn or built at actual size. Similarly, a scale
model can be used to represent something that is too large or built too small for an actual-­‐size model. The scale gives the
relationship between the drawing/model measure and the
actual measure.
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Grade 7 Winter Holiday Student Activities
1. Meagan’s family is driving from Daytona Beach to Savannah, a distance of approximately 195 miles. After 1 hour,
they have driven 65 miles. If they continue to travel at the same speed, about how much longer will it take them to
reach Savannah?
An interior designer made the scale drawing of a living room shown below.
The scale of the drawing is 1 inch = 60 inches. What is a good estimate of the actual length of the table?
A. .48 inches
B. 4.8 inches
C. 48.0 inches
C. 480 inches
Activity #13 Similar Figures (STD MA.7.A.1.3)(moderate complexity)(tested
MC. GR)
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Grade 7 Winter Holiday Student Activities
Module D Percents
Activity #14 Percent of a Number(STD MA.7.A.1.2)(high complexity)(tested
MC, GR)
To find the percent of a number, write the percent as a common fraction or decimal fraction and then
multiply.
Example 1
Find 20% of 60.
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Grade 7 Winter Holiday Student Activities
Example 2 What number is 25% of 200?
25% of 200 = 25% x 200 Write a multiplication expression.
= 0.25 x 200 Write 25% as a decimal
= 50
Multiply
25% of 200 is 50
Find each Number.
2. What is 55% of $400?
1. Find 20% of 50
3. Going into a recent election, only about 62% of people old enough to vote were registered. In a
community of about 55,200 eligible voters, how many people were registered?
Activity #15 The Percent Proportion(STD MA.7.A.1.2)(high complexity)(tested
MC. GR)
A percent proportion compares part of a quantity to a whole quantity for one ratio and lists the percent as a number
over 100 for the other ratio.
Find each number. Round to the nearest tenth if
necessary.
2. 12 is what percent of 40?
1. What number is 25% of 20?
3. Beth’s soccer team played 26 games and won 17 of them. What percent did the team
win?
Activity #16 Percent of Change (STD MA.7.A.1.2)(high complexity)(tested MC,
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Grade 7 Winter Holiday Student Activities
GR)
A percent of change is a ratio that compares the change in quantity to the original amount. If the original quantity is
increased, it is a percent of increase. If the original quantity is decreased, it is a percent of decrease.
1. A popular brand of running shoes costs a local store $78 for each pair. If the store sells the shoes for
$129, what is the percent of increase in the price?
2. The 2010 yearbook at Jacksonville Middle School had 246 candid pictures of students. The 2011 the
yearbook had 206 candid pictures of students. What was the percent of change in the number of candid
student pictures from 2010 to 2011 to the nearest tenth?
Activity #17 Sales Tax and Tip (STD MA.7.A.1.2)(high complexity)(tested MC,
GR)
Sales Tax is a percent of the purchase price and is an amount paid in addition to the purchase price.
Tip, or gratuity, is a small amount of money in return for service.
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Grade 7 Winter Holiday Student Activities
1. Josh went to the local hair cuttery to get his hair cut. It cost $18 for the haircut. Josiah tipped the stylist
15%. What was the total cost of the haircut including the tip?
2. The Johnson family had a meal catered for a Birthday dinner. The cost of the dinner was $526. There was a
7% sales tax and they left a 18% tip. What was the total cost including the sales tax and the tip?
Module E Linear Equations
Activity #18 Problem Solving Working Backwards (STD
MA.7.A.5.2)(high complexity)(tested MC, GR)
By working backward from where you end to where you began, you can solve problems. Use the four-­‐
step problem solving model to stay organized when working backward.
Example 1 Tom, put half of his birthday money into his savings account. Then he paid back the $11 that
he owed his brother for dance tickets. Lastly, he spent $4 on lunch at school. At the end of the day he was
left with $13. How much money did Jonah receive for his birthday?
Solve each problem by using the work backward strategy.
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Grade 7 Winter Holiday Student Activities
1. On Tuesday everyone was present in Mr. Brown’s class. At 11:00, 4 students left early for a fieldtrip.
At 1:15, half of the remaining students went to an assembly. Finally, at 1:00, 5 more students left for
a student council meeting. At the end of the day, there were only 6 students in the room. Assuming
that no students returned after having left, how many students are in Mr. Brown’s class?
2. Jake was trading baseball cards with some friends. He gave 14 cards to Conner and got 4 back. He
gave two thirds of his remaining cards to Caitlyn and kept the rest for himself. When he got home
he counted that he had 25 cards. How many baseball cards did Jake start with?
Activity #19 Solve One-­‐Step Addition and Subtraction Equations (STD
MA.7.A.3.3)(moderate complexity)(tested MC, GR)
Remember, equations must always remain balanced. If you subtract the same number from each side of an
equation, the two sides remain equal. Also, if you add the same number to each side of an equation, the
two sides remain equal.
Solve each equation. Show steps. Check your solution.
1. m + 6 = 20
2. -­‐9 = z – 11
3. A survey of teens showed that teens in Jacksonville aged 12-­‐17 spend 15.8 hours per week online.
Teens in Miami/Ft. Lauderdale spend 14.2 hours per week online. Write and solve an addition equation to
find the difference in time spent online by teens in these cities.
4. What is the value of m if m + 8 = −22?
A. −30
B. −14
C. 14
D. 30
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Grade 7 Winter Holiday Student Activities
Activity # 20 Solve One-­‐Step Multiplication and Division Equations (STD
MA.7.A.3.3)(moderate complexity)(tested MC, GR)
Use the Multiplication Property of Equality to solve division equations.
Use the Division Property of Equality to solve multiplication equations
Solve each equation. Check your solution.
1. 9k = –369
3. The number of 8th graders in Band is three times the number of 7th graders. If there are 49 8th
graders in band, how many 7th graders are in band?
4. There are 9 competitors in each ring for a Karate tournament. If there are 117 competitors in the
tournament, how many rings do they need?
Activity #21 Solve Two-­‐Step Equations (STD MA.7.A.3.3)(moderate
complexity)(tested MC, GR)
To solve a two-­‐step equation, undo the addition or subtraction first. Then undo the multiplication or
division.
Solve each equation. Check your solution.
1. 4y + 1 = 13
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Grade 7 Winter Holiday Student Activities
5. Susan has $145 in her savings account. She earns $36 a week mowing lawns. If Susan saves all of her
earnings, after how many weeks will she have $433 saved?
6. Mrs. Jackson earned a $600 bonus for signing a one-­‐year contract to work as a teacher. Her salary is $22
per hour. If her first week’s check including the bonus is $1,304, how many hours did Mrs. Jackson work?
Activity #22 Solve Equations with Variables on Each Side (STD
MA.7.A.3.4)(moderate complexity)(tested MC)
TO SOLVE AN EQUATION WITH VARIABLES ON EACH SIDE, USE THE PROPERTIES OF EQUALITY TO WRITE AN
EQUIVALENT EQUATION WITH THE VARIABLES ON ONE SIDE.
THEN SOLVE THE EQUATION.
1. Emily is solving the equation below.
–2x – 4 = 5x – 7
Which operations can Emily perform on her equation that would justify its equivalence to 3 = 7x?
A. Subtract 4 from both sides of the equation. Then divide both sides by –2.
B. Add 7 to both sides of the equation. Then divide both sides by 5.
C. Subtract 4 from both sides of the equation. Then add 2x to both sides.
D. Add 7 to both sides of the equation. Then add 2x to both sides.
2. Which of the following equations is equivalent to 8z -­‐ 3 = 2z?
A. 8z − 3 = 2z − 3
B. 16z − 3 = 4z
C. 8z = 2z + 3
D. 8z -­‐ 3 = 2z + 5
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