Download STAAR Ready Instruction Grade 6 Mathematics Sampler

Table of Contents
Unit 1: Ratios, Rates, and Percents
STAAR Reporting Categories 1 and 2
TEKS
6 4 C ♦, 6 4 D♦
Lesson 1
Ratios
Lesson 2
Represent Ratios and Rates
12
6 5 A♦
Lesson 3
Making Predictions and Comparisons Using Ratios
22
6 4 B✶
Lesson 4
Ratios, Fractions, Decimals, and Percents
32
6 4 E♦, 6 4 F♦, 6 4 G✶,
6 5 C♦
Lesson 5
Solve Problems with Percent
42
6 5 B✶
2
STAAR Practice
52
Unit 2: Number and Operations
STAAR Reporting Categories 1 and 2
Lesson 6
Fractions as Division
54
6 2 E♦
Lesson 7
Understand Division with Unit Fractions
62
6 3 A♦
Lesson 8
Multiply and Divide Fractions
68
6 3 E✶, 6 3 B♦
Lesson 9
Multiply and Divide Decimals
80
6 3 E✶
92
6 2 A♦
Lesson 10 Whole Numbers, Integers, and Rational Numbers
Lesson 11 Understand Positive and Negative Numbers
100
6 2 B♦, 6 2 C ♦
Lesson 12 Absolute Value and Ordering Numbers
106
6 2 C ♦, 6 2 D✶
Lesson 13 The Coordinate Plane
116
6 11 A✶
Lesson 14 Add and Subtract Positive and Negative Integers
124
6 3 C ♦, 6 3 D✶
Lesson 15 Multiply and Divide Positive and Negative Integers
136
6 3 D✶
STAAR Practice
146
✶ = STAAR Readiness Standard
♦ = STAAR Supporting Standard
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iii
Table of Contents
TEKS
Unit 3: Expressions and Equations
STAAR Reporting Categories 1 and 2
Lesson 16 Numerical Expressions with Exponents
150
6 7 A✶
Lesson 17 Algebraic Expressions and Equations
162
6 7 B♦
Lesson 18 Equivalent Expressions
174
6 7 C ♦, 6 7 D✶
Lesson 19 Understand Solutions to Equations
186
6 9 A♦, 6 10 A✶, 6 10 B♦
Lesson 20 Solve Equations
192
6 9 A♦, 6 9 B♦, 6 9 C ♦,
6 10 A✶, 6 10 B♦
Lesson 21 Solve Inequalities
204
6 9 A♦, 6 9 B♦, 6 9 C ♦,
6 10 A✶, 6 10 B♦
Lesson 22 Dependent and Independent Variables
216
6 6 A♦, 6 6 B♦, 6 6 C✶
Lesson 23 Additive and Multiplicative Relationships
226
6 4 A♦
STAAR Practice
234
Unit 4: Geometry and Measurement
STAAR Reporting Category 3
Lesson 24 Convert Measures
236
6 4 H✶
Lesson 25 Understand Conditions for Triangles
246
6 8 A♦
Lesson 26 Area of Polygons
252
6 8 B♦, 6 8 C ♦, 6 8 D✶
Lesson 27 Volume
262
6 8 C ♦, 6 8 D✶
STAAR Practice
272
✶ = STAAR Readiness Standard
♦ = STAAR Supporting Standard
iv
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Table of Contents
Unit 5: Data Analysis and Personal Financial Literacy
STAAR Reporting Category 4
TEKS
Lesson 28 Understand Statistical Questions
274
6 13 B♦
Lesson 29 Interpret Numeric Data
280
6 12 B♦, 6 12 C✶, 6 13 A✶
Lesson 30 Display Data on Dot Plots, Histograms, Box Plots,
and Stem-and-Leaf Plots
290
6 12 A♦, 6 12 C✶
Lesson 31 Interpret Categorical Data
302
6 12 D✶
Lesson 32 Checking Accounts
314
6 14 A♦, 6 14 B♦, 6 14 C ♦
Lesson 33 Understand Credit Reports
324
6 14 E♦, 6 14 F♦
Lesson 34 Understand Paying for College
330
6 14 G♦
Lesson 35 Understand Annual Salaries
336
6 14 H♦
STAAR Practice
342
✶ = STAAR Readiness Standard
♦ = STAAR Supporting Standard
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Focus on Math Concepts
Lesson 11
Part 1: Introduction
TEKS
6.2.B
6.2.C
Understand Positive and Negative Numbers
What are positive and negative numbers?
Positive numbers are greater than 0 and located to the right of 0 on a number line.
Negative numbers are less than 0 and located to the left of 0 on a number line. The
number zero is neither positive nor negative.
Negative
Zero
25 24 23 22 21
0
Positive
1
2
3
4
5
Positive and negative numbers are sometimes called signed numbers.
Positive numbers can be written with or without a plus sign.
Negative numbers are always written with a negative sign.
When solving problems with positive and negative numbers, it important to think about
how far from 0 the number is and in what direction.
Think
A thermometer shows positive and negative numbers.
Temperatures above 0 are positive.
Temperatures below 0 are negative.
Look at the thermometer.
F
120
50
100
40
80
20°F is 20 degrees above 0°F.
220°F is 20 degrees below 0°F.
230°C is 30 degrees below 0°C.
30°C is 30 degrees above 0°C.
100
C
60
40
20
Circle the negative
numbers labeled on
the thermometer.
30
20
10
0
210
0
220
220
230
240
240
L11: Understand Positive and Negative Numbers
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Part 1: Introduction
Lesson 11
Think Every positive and negative number has an opposite.
Numbers that are the same distance from zero but in opposite directions are called
opposite numbers. Every whole number, fraction, and decimal has an opposite.
The opposite of 4 is 24. Both numbers are the same distance from 0. To plot a point at 4,
count 4 units to the right of 0 and draw a point. To plot a point at 24, count 4 units to the
left of 0 and draw a point.
28 27 26 25 24 23 22 21
0
1
2
3
4
Think about folding the number line in half so that the fold
goes through 0. Numbers that line up are opposites.
All the whole numbers and their opposites are called
integers. All of the numbers labeled on the number line
above are integers:
5
6
7
8
The number line shows
that zero is its own
opposite.
28, 27, 26, 25, 24, 23, 22, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8
Reflect
1 Think about the numbers 210 and 10. How could you describe these numbers? What
is the same and what is different about these numbers?
L11: Understand Positive and Negative Numbers
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Part 2: Guided Instruction
Lesson 11
Explore It
A number line can help you understand positive and negative numbers.
Jana and a friend are playing a game that shows a number line from 27 to 7. The game is
played with 15 cards numbered with the integers from 27 to 7. Players draw a card from
a pile. They earn points for correctly locating the number on the card on the number line
and then identifying its opposite.
27
0
24
3
6
7
2 Finish labeling the number line.
3 Suppose Jana draws a card that shows 23. Draw a point at 23 on the number line.
4 What number is the opposite of 23?
. Explain your reasoning.
5 Jana’s friend draws a card that shows a 0. Draw a point at 0. What is the opposite of 0?
Explain.
6 The next card drawn is 26. How far from 0 is 26?
In which direction?
Draw a point at 26.
7 What number is the same distance from 0 as 26 but in the other direction?
8 Two numbers that are the same distance from 0 but on different sides of zero are
called
numbers.
Now try this problem.
9 Graph each integer and its opposite on the number line below.
5
21
4
22
28 27 26 25 24 23 22 21
102
0
1
2
3
4
5
6
7
8
L11: Understand Positive and Negative Numbers
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Part 2: Guided Instruction
Lesson 11
Talk About It
Solve the problems below as a group.
10 Look at the number lines on the previous page. There are numbers between the numbers
you graphed. Just as whole numbers can be positive or negative, fractions and decimals
can also be positive and negative.
The number 1.5 is between 1 and 2. The number 21.5 is between 22 and 21.
Draw a point at 1.5 and a point at 21.5 on the number line below. Label each point
with its value.
24
23
22
21
0
1
2
3
4
11 How is locating 21.5 on a number line the same as locating 1.5 on a number line?
How is it different?
12 Use the number line below to graph the following numbers. Label each point with its
value. Then graph and label the opposite of each number.
11
211
2
··
4
··
22
1
2 ··2
21
0
1
2
Try It Another Way
Work with your group to explore writing positive and negative numbers to
represent a situation.
13 Write a positive or a negative number to represent each situation.
A
you owe $25
B
a team has a gain of 20 yards in a football game
C
two floors below ground level
D 15 degrees above 0°C
E
a stock price fell 4.26 points
L11: Understand Positive and Negative Numbers
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Part 3: Guided Practice
Lesson 11
Connect It
Talk through these problems as a class, then write your answers below.
14 Conclude: What number is the opposite of the opposite of 5? What can you say
about the opposite of the opposite of a number?
15 Interpret: Positive and negative numbers can show an amount above or below zero.
They can also be used to show an amount above or below a certain point.
Students at Taft Middle School have a goal of collecting 1,000 pounds of recycling
materials each month. The following table shows their results over a 6-month time
period. Complete the table. The first month is done for you.
Month
January
Pounds Collected
985
February
March
April
May
June
1,010
995
1,050
975
980
Compared to 1,000
215
←15 less than 1,000
16 Analyze: Look at the number line below. The letters a, b, c, and d all represent
integers.
a
c
0
b
A Which letters represent negative integers?
B Which letters represent positive integers?
d
How do you know?
How do you know?
C If b and c are the same distance from 0, how can you describe them?
104
L11: Understand Positive and Negative Numbers
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Part 4 : Performance Task
Lesson 11
Put It Together
17 Use what you have learned to complete this task.
Write a problem about a real-life situation involving temperature or money. The
situation should include a number and its opposite that results in an answer of zero.
A Write your problem.
B Graph the numbers you used in your problem on a number line.
0
C Explain what zero means in this situation.
D What can you say about the sum of a number and its opposite?
L11: Understand Positive and Negative Numbers
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Develop Skills and Strategies
Lesson 12
Part 1: Introduction
TEKS
6.2.C
6.2.D
Absolute Value and Ordering Numbers
In Lesson 11, you learned how to locate positive and negative numbers on
a number line. In this lesson you will learn how to compare the numbers and find
their absolute value. Take a look at this problem.
The elevation of an object tells you its distance above or below sea level. Negative
numbers are used to represent objects below sea level. Positive numbers are used
to represent objects above sea level.
The table below shows the elevations of
four objects. Graph their locations on a
number line. Describe the distances of
the objects above or below sea level.
Object
Elevation (in km)
Mountain
2
Elevation
Ocean
Fish
21
Sunken Ship
24
Airplane
4
Explore It
Use the math you already know to solve the problem.
Sea level is marked and labeled on the number line. Mark and label the
elevation of the objects listed in the table above on the number line.
How far above sea level is the mountain?
How far below sea level is the school of fish?
Is the airplane above or below sea level?
0
Sea level
What two objects are the same distance from sea level? Explain how
you know.
Explain how you could find the distances of the objects from sea level.
106
L12: Absolute Value and Ordering Numbers
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Part 1: Introduction
Lesson 12
Find Out More
When you answered how far each object is from sea level, you found the absolute value
of a number.
The absolute value of a number is its distance from 0 on the number line.
|24| means the absolute value of 24.
24 is 4 units from 0.
|24| 5 4
The absolute value of 24 is 4 because 24 is 4 units from 0 on the number line.
24 23 22 21
0
1
2
3
4
4 units from 0
Absolute value represents distance, so its value is always greater than or equal to 0.
The absolute value of 0 is 0, or |0| 5 0.
The farther a number is from 0, the greater the number’s absolute value.
In real-world situations, the absolute value of a number is often used to describe the
situation. The elevation of the fish is 21 km, but you could also say that the fish is 1 km
below sea level. The elevation of the sunken ship is 24 km, but you could also say that
the sunken ship is 4 km below sea level.
Reflect
1 Look at your number line on the previous page. Which pair of numbers have the
same absolute value? How are the numbers related? Explain.
L12: Absolute Value and Ordering Numbers
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Part 2: Modeled Instruction
Lesson 12
Read the problem below. Then explore how to use a number line to compare
positive and negative numbers.
One morning it was 29°F in Columbus, Ohio and 27°F in Pittsburgh,
Pennsylvania. Was it warmer in Columbus or Pittsburgh?
Picture It
You can graph the numbers on a number line.
29 28 27 26 25 24 23 22 21
0
1
2
3
4
5
6
7
Model It
You can use the number line to write an inequality to compare the numbers.
29 is to the left of 27 on the number line.
This means that 29 is less than 27.
You can use symbols to compare the numbers.
The symbol , means is less than.
29 , 27
Model It
You can use the number line to write a second inequality to compare the numbers.
27 is to the right of 29 on the number line.
This means that 27 is greater than 29.
You can use symbols to compare the numbers.
The symbol . means is greater than.
27 . 29
108
L12: Absolute Value and Ordering Numbers
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Part 2: Guided Instruction
Lesson 12
Connect It
Now use the number line and the comparison statements to solve the problem.
2 Look at the number line in Picture It.
Where is 29 located?
Where is 27 located?
3 From left to right, does the number line show numbers from least to greatest or
greatest to least?
4 Which is the warmer temperature, 29°F or 27°F?
Which city was warmer?
5 Model It shows that you can write two inequalities to compare 29 and 27. Write two
inequalities to compare 26 and 5. Tell how you decided.
6 Explain how you can use a number line to compare any two numbers.
Try It
Use what you just learned to compare the numbers below. Use the number line to
help if needed.
210 29 28 27 26 25 24 23 22 21
0
1
2
3
4
5
6
7
8
9 10
7 Write two inequalities to compare 25 and 23.
8 Write two inequalities to compare 9 and 29.
L12: Absolute Value and Ordering Numbers
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Part 3: Modeled Instruction
Lesson 12
Read the problem below. Then explore how to use a number line to order positive
and negative numbers.
Five friends played a game where you earn positive and negative points. Their
final scores were 23.5, 2, 23, 21, 1.5. What was the highest score? What was the
lowest score?
Picture It
You can graph the numbers on a number line.
1.5
23.5
24
23
22
21
0
1
2
3
4
Model It
You can compare the positions of the numbers on the number line.
23.5 is to the left of 23.
23 is to the left of 21.
21 is to the left of 1.5.
1.5 is to the left of 2.
Model It
You can compare the positions of the numbers on the number line in another way.
2 is to the right of 1.5.
1.5 is to the right of 21.
21 is to the right of 23.
23 is to the right of 23.5.
110
L12: Absolute Value and Ordering Numbers
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Part 3: Guided Instruction
Lesson 12
Connect It
Now use the number line to order the numbers and solve the problem.
9 Look at the first Model It. Order the numbers from least to greatest.
10 Look at the second Model It. Order the numbers from greatest to least.
11 What was the lowest score? How do you know?
12 What was the highest score? How do you know?
13 Explain how to use a number line to order numbers.
Try It
Use what you just learned about ordering numbers to solve these problems. Use a
number line to help if needed.
14 Order the numbers from least to greatest.
A
28, 26, 25, 27
B
28.2, 6, 23.5, 8.2, 25
15 Order the numbers from greatest to least.
3
A
2··4, 21, 5, 2
B
20.5, 1.5, 0, 25, 1.25
4
··
L12: Absolute Value and Ordering Numbers
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Part 4: Guided Practice
Lesson 12
Study the student model below. Then solve problems 16–18.
Student Model
The student graphed the
numbers on a number
line to order them from
least to greatest.
A 6th grade class is studying transportation in New York City. They
collected this data about the heights above ground and depths
below ground of different structures. Write the names of these
structures in order from lowest elevation to highest elevation.
Verrazano Narrows Bridge 70 m
Holland Tunnel 225 m
George Washington Bridge 60 m
Lincoln Tunnel 230 m
230 225
Pair/Share
Are positive numbers
always greater than
negative numbers?
Will graphing the
numbers on a number
line help?
0
60
70
Solution: Lincoln Tunnel, Holland Tunnel, George Washington
Bridge, Verrazano Narrows Bridge
16 Eyeglass prescriptions use positive and negative numbers to describe
vision. In general, the farther away from zero the number on a
prescription is, the more vision correction you need. Negative numbers
mean you are nearsighted, positive numbers mean you are farsighted.
The table below shows prescription numbers for five patients.
Patient
Prescription
A
22.25
B
1.00
C
21.50
D
3.25
E
23.00
Which patients are nearsighted?
Which patients are farsighted?
Which patient is the most nearsighted?
Which patient is the most farsighted?
Pair/Share
Solution:
How do you compare
negative numbers?
112
L12: Absolute Value and Ordering Numbers
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Part 4: Guided Practice
Lesson 12
17 Which number is greater, 27 or 6? Which number has the greater
absolute value, 27 or 6? Explain your thinking. Use comparison
symbols and absolute value symbols when you write your answer.
What does absolute value
mean?
Solution:
Pair/Share
Can a negative number
have a greater absolute
value than a positive
number?
18 The table below shows elevations of different locations in the world.
List the elevations in order from greatest to least. Circle the letter of
the correct answer.
Location
Elevation (in ft)
Caspian
Sea
298
A
252, 298, 75, 92, 230
B
298, 252, 75, 92, 230
C
230, 92, 75, 252, 298
Mekong
Delta
230
Lake
Eyre
252
Senegal
River
75
Are negative numbers
always less than positive
numbers?
Iron Gate
92
D 230, 92, 75, 298, 252
Randy chose B as the correct answer. How did he get that answer?
Pair/Share
How can you tell that
Randy’s answer can’t be
correct by looking at
one number’s position in
his answer?
L12: Absolute Value and Ordering Numbers
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Part 5: TEKS Practice
Lesson 12
Solve the problems.
1 The lowest temperatures ever recorded in five of Earth’s continents are shown in the
table below.
Continent
Temperature (in °C)
South America North America Antarctica
239
266.1
289.2
Europe
258.1
Asia
268
Which continent has a lower recorded temperature than Asia?
A
South America
B
North America
C
Europe
D
Antarctica
2 On February 17, 1936, the following temperatures were recorded:
City
McIntosh, SD
Duluth, MN
Miami, FL
Temperature
258°F
226°F
78°F
Choose True or False for each statement.
A
The temperature difference between McIntosh, SD,
and Duluth, MN, was 84°F.
True
False
B
Duluth, MN, was 32°F warmer than McIntosh, SD.
True
False
C
The temperature difference between Miami, FL, and
Duluth, MN, was 52°F.
True
False
The temperature difference between the highest and
lowest temperatures was 136°F.
True
False
D
114
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Part 5: TEKS Practice
Lesson 12
3 From the list on the left, write in the correct temperature along the thermometer.
0°
Celsius
[not drawn
to scale]
278°
4°
276.8°
25°
°Celsius
4 A tour group is going sea diving. Sea level is 0 feet. The ocean floor is 218 feet. One diver is already
at 211 feet. The tour guide is keeping watch on the deck at 5 feet above sea level directly above the
diver. What is the distance from the tour guide to the diver? Draw and label a number line to justify
your answer.
feet
Answer
5 Look at the number line below. The letters a, b, c, and d all represent integers.
a
b
0
c
d
A
Write two inequalities to compare a and b.
How do you know?
B
Write two inequalities to compare b and 0.
How do you know?
C
If |a| 5 |d |, what can you say about a and d?
L12: Absolute Value and Ordering Numbers
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