MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Introduction
Standard 7.2(A) – Supporting
1
Complete the diagram to show the
relationship between the following sets of
numbers: Counting Numbers, Integers,
Rational Numbers, and Whole Numbers.
4
Label each statement as true or false.
Rewrite each false statement so that it is
true.
The set of integers is a subset of the set of
whole numbers.
____________________
___________________________________
____________________
___________________________________
________________
All counting numbers are whole numbers.
___________________________________
________
___________________________________
If a number is an element of the set of
rational numbers, it is also an element of the
set of integers.
___________________________________
___________________________________
Not every whole number is an integer.
2
Use the completed diagram above to
determine the set or sets to which each
number belongs.
___________________________________
___________________________________
2
-_
___________________________
5
0 ___________________________
- 13 ___________________________
5
5 ___________________________
List the set of numbers that matches each
description.
a. Counting numbers less than 6
__
0.3 ___________________________
________________________________
4 ___________________________
- __
b. Integers between -6 and 3, exclusive
2
________________________________
c.
3
List three numbers that belong to each of the
following number sets.
________________________________
Counting numbers _____________________
d. Rational numbers with a denominator of
Integers _____________________________
1
10 that lie between -_
and 0, inclusive
2
Rational numbers _____________________
________________________________
Whole numbers _______________________
©2014 mentoringminds.com
mentoringminds.com
motivationmath
Whole numbers that do not belong to the
subset of counting numbers
™
LEVEL 7
ILLEGAL TO COPY
7
MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Guided Practice
1
Standard 7.2(A) – Supporting
Which representation best shows the
relationship between whole numbers and
counting numbers?
3
To which of the following sets of numbers
7
does _
belong?
8
I. Counting numbers
II. Whole numbers
III. Integers
�
Whole
Numbers
IV. Rational numbers
Counting
Numbers
Whole
Numbers
4
� I and II only
� I, II, and IV only
� I and IV only
� IV only
Which diagram best demonstrates the
relationship between sets of numbers?
Rational Numbers
�
Counting
Numbers
�
Counting Numbers
Whole Numbers
Integers
Rational Numbers
�
Whole
Numbers
Integers
Counting
Numbers
�
Whole Numbers
Counting Numbers
Counting
Numbers
Rational Numbers
�
2
Integers
�
Whole
Numbers
Counting Numbers
Whole Numbers
Rational Numbers
Which of the following statements is NOT
true?
Integers
� All whole numbers are rational numbers.
�
� All integers are rational numbers.
Counting Numbers
� All integers are whole numbers.
Whole Numbers
� All counting numbers are whole numbers.
8
ILLEGAL TO COPY
mentoringminds.com
motivationmath
™
LEVEL 7
©2014 mentoringminds.com
MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Independent Practice
Standard 7.2(A) – Supporting
1
The Venn diagram represents the relationship
between integers and whole numbers.
4
If a number is a member of the set of
integers, then it must also be a member of
which other set?
� Rational numbers
Integers
� Counting numbers
� Whole numbers
Whole
Numbers
� Not here
Which number would be an element of the set
of Integers but not an element of the set of
Whole Numbers?
5
Which lists the correct labels for the diagram
shown?
� 0
� -3
d.
� 5
c.
b.
1
� -_
2
2
Set A = {0, 3, 8}. Set A is NOT a subset of
which set of numbers?
� a. Rational Numbers
b. Integers
c. Whole Numbers
d. Counting Numbers
� Rational numbers
� Integers
� a. Counting Numbers
b. Whole Numbers
c. Integers
d. Rational Numbers
� Whole numbers
� Counting numbers
3
a.
� a. Counting Numbers
b. Integers
c. Whole Numbers
d. Rational Numbers
Which of the following sets contains an
element that CANNOT be classified as
rational?
1
� {_
, 5.5, 13 _
, -4.5}
4
2
� a. Rational Numbers
b. Integers
c. Counting Numbers
d. Whole Numbers
3
_
43
� {0, 0.9, __
, -2}
3
5 _
9
� {-13.76, - _
, , 95}
2 0
1
� {2 _
, -7, 0.2323, _
2
3}
0
©2014 mentoringminds.com
mentoringminds.com
motivationmath
™
LEVEL 7
ILLEGAL TO COPY
9
MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Assessment
1
Standard 7.2(A) – Supporting
In which section of the diagram does the
6
number -_ belong?
3
3
Which of the following statements is always
true?
� All integers are counting numbers.
Rational Numbers
� All rational numbers are integers.
Integers
� All integers are whole numbers.
Whole Numbers
Counting
Numbers
� All counting numbers are whole numbers.
4
Aldine uses the diagram below to explain the
relationship between integers and rational
numbers.
� Rational Numbers
� Integers
Integers
Rational Numbers
� Whole Numbers
� Counting Numbers
Which of the following rational numbers does
NOT belong to the subset of integers?
6
� _
2
2
Which best describes all possible
classifications for the following set of
numbers?
� -4.0
15
� -__
3
{0, 4, 25, 32}
� 7.5
I. Counting numbers
II. Integers
III. Rational numbers
5
IV. Whole numbers
� IV only
12
, 8, and 10 only
� __
2
� I and IV only
� 8 and 10 only
� II, III, and IV only
� 0, 8, and 10 only
� I, II, III, and IV
10
12
, 8, 10},
Given the set of numbers {-2, 0, __
2
which elements belong to the set of counting
numbers?
ILLEGAL TO COPY
mentoringminds.com
12
, 8, and 10 only
� 0, __
2
motivationmath
™
LEVEL 7
©2014 mentoringminds.com
MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Critical Thinking
Standard 7.2(A) – Supporting
plication
Ap
1
Create a set of numbers, Set A, using the guidelines below.
• Must contain a minimum of 5 members
Apply
• Exactly 1 member must be a counting number
• Exactly 2 members must be whole numbers
• At least 1 member must be a rational number only
Set A = ____________________________________________________________________
Justify Set A is correct using a visual representation.
Analysis
2
Callen draws the diagram below to represent the relationship between sets of
numbers.
Analyze
Rational Numbers
Integers
Negative
Numbers
Positive
Numbers
Whole
Numbers
Based on what has been studied in this unit, is Callen’s diagram an accurate representation of
the relationship between sets of numbers? Justify your answer using words and creating your
own diagram above, if appropriate.
___________________________________________________________________________
___________________________________________________________________________
©2014 mentoringminds.com
mentoringminds.com
motivationmath
™
LEVEL 7
ILLEGAL TO COPY
11
MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Journal/Vocabulary Activity
Standard 7.2(A) – Supporting
Analysis
Journal
Consider the classications of each number below.
Analyze
15
- __
: Rational number, integer
5
7
_
: Rational number
3
Explain the similarities and differences between the two numbers, specically why they are
classied differently.
___________________________________________________________________________
___________________________________________________________________________
Vocabulary Activity
Create a concept web for the following vocabulary terms: rational numbers, integers, whole
numbers, and counting numbers. Provide at least two examples for each term.
Relationship between sets of numbers
12
term
term
term
term
examples
examples
examples
examples
ILLEGAL TO COPY
mentoringminds.com
motivationmath
™
LEVEL 7
©2014 mentoringminds.com
MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Motivation Station
Standard 7.2(A) – Supporting
It’s Written in the Numbers
Play It’s Written in the Numbers with a partner. Each pair of players needs a game board and
a paper clip to use with the spinner. Each player needs a different color pen or pencil. Player 1
begins by spinning to determine a number set, and then records a number in the appropriate
location on the diagram. If recorded correctly, player 1 earns points for the set rolled according
to the chart. He/she then records the number, number set, and points earned in the table, and
play passes to player 2, who repeats the process. If a player incorrectly records a number in the
diagram, he/she loses a turn. The game ends when each player has recorded 9 numbers in the
diagram. The player with more points wins.
Points Earned
Rational Number
5 points
Integer
4 points
Whole Number
3 points
Counting Number
2 points
Rational Numbers
Integers
Counting
Numbers
Rational
Numbers
Whole Numbers
Integers
Counting
Numbers
Whole
Numbers
Player 1
Number
©2014 mentoringminds.com
mentoringminds.com
Number Set
Player 2
Points
motivationmath
Number
™
LEVEL 7
Number Set
ILLEGAL TO COPY
Points
13
MATH | LEVEL 7
Student Edition Sample Page
Name __________________________________________
Unit 1 Homework
Standard 7.2(A) – Supporting
Refer to the diagram to answer the following questions.
Rational Numbers
Integers
Whole Numbers
Counting Numbers
1
Record the numbers described in the diagram.
3
Two numbers belonging only to the Rational
Numbers section
Record the numbers from the diagram below
that are incorrectly located. For each number
recorded, give the correct location.
Three numbers belonging only to the Integers
section
Rational Numbers
One number belonging only to the Whole
Numbers section
Integers
3
- __
4
Four numbers belonging only to the Counting
Numbers section
2
0.45
-2
Write a number set for each description given.
Counting
Numbers
a. The counting numbers between 20 and
30, exclusive
16
________________________________
24
- __
6
b. The rational numbers with a denominator
of 3 that lie between -1 and 1, inclusive
-5
________________________________
c. The integers that are multiples of 4, and
are greater than 0 but less than 20
___________________________________
________________________________
___________________________________
d. The whole numbers greater than or equal
to 0 and less than 8
___________________________________
___________________________________
________________________________
Connections
1. Research the origin of the term rational number. Write a brief paragraph detailing the origin of the term,
including who first used the term to describe numbers, in what country the term originated, and the
approximate year of origin.
2. Write a rap or a poem to aid you in remembering the sets of numbers and their relationships. Share
your creation with your family or friends.
14
ILLEGAL TO COPY
mentoringminds.com
motivationmath
™
LEVEL 7
©2014 mentoringminds.com
MATH | LEVEL 7
Teacher Edition Sample Page
Describe relationships between sets of rational numbers
Unit 1
TEKS 7.2(A) – Supporting
Unit 1 Standards
(Student pages 7–14)
Reporting
Category
1
Probability and Numerical Representations
The student will demonstrate an understanding of how to represent probabilities and
numbers.
Domain
TEKS
Student
Expectation
Number and Operations
7.2
The student applies mathematical process standards to represent and use rational
numbers in a variety of forms.
7.2(A) – Supporting Standard
Extend previous knowledge of sets and subsets using a visual representation to
describe relationships between sets of rational numbers.
Mathematical Process TEKS Addressed in This Unit
The student uses mathematical processes to acquire and demonstrate mathematical understanding.
7.1(E)
7.1(F)
7.1(G)
Create and use representations to organize, record, and communicate mathematical
ideas.
Analyze mathematical relationships to connect and communicate mathematical ideas.
Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Unpacking the Standards
In grade 6, students worked with whole numbers, integers, and rational numbers and were first
introduced to negative values. Sixth-grade students created and used graphic organizers to classify
and categorize numbers, determining whether a given number belonged to the set of rational numbers,
the set of integers, the set of whole numbers, or to multiple sets. In grade 7, students extend the
classification of numbers to include the set of counting (natural) numbers as a category. With the
exception of activities in which students create a model to show the relationship between number sets,
a model should be available for student reference throughout this unit. Irrational numbers are excluded
at this level. Although Venn diagrams are used most frequently to show the relationship between number
sets, other representations may be used as well, provided the representation makes clear the idea that
number sets are nested and not overlapping. Note: A rational number that simplifies to an integer or
15
simplifies to
counting number should be classified in the most descriptive set possible. For example, ___
3
5 and is classified as a counting number.
mentoringminds.com
mentoringminds.com
motivationmath™LEVEL 7
ILLEGAL TO COPY
39
MATH | LEVEL 7
Teacher Edition Sample Page
Unit 1
TEKS 7.2(A) – Supporting
Describe relationships between sets of rational numbers
Getting Started
Introduction Activity
The teacher displays a large nested Venn diagram.
All Students
7th-Grade Students
7th-Grade Boys
7th-Grade
Boys with
Glasses
The teacher gives sticky notes to several students and instructs them to write their names on the notes.
Each student places his/her sticky note in the most appropriate circle of the Venn diagram. The teacher
asks students to give their observations about the locations of the sticky notes. Possible responses
include: Students in the 7th-grade Boys with Glasses circle are included in all of the circles; No girls
are located in the two innermost circles; No notes were placed in the All Students circle (unless the
class is mixed-level.) The teacher then asks the students to record definitions in math journals for the
terms rational numbers, integers, and whole numbers. Student pairs share their definitions, clarifying and
recording one final definition. The teacher creates a nested Venn diagram to represent the relationship
between the sets of numbers, including the set of counting numbers, similar to the diagram shown below.
Rational
Numbers
Integers
Whole
Numbers
Counting
Numbers
The teacher asks students to give examples of numbers that would be located in the Counting Numbers
section of the diagram. The teacher records correct responses in the diagram, and incorrect responses
are written outside the diagram as a group. The teacher asks students to study the group of numbers
not recorded in the diagram and compare the numbers to those recorded in the diagram. Working
with an elbow partner, students write a definition for counting numbers based on their observations.
The teacher asks student pairs to share their definitions, recording key information on the board. The
40
ILLEGAL TO COPY
mentoringminds.com
motivationmath™LEVEL 7
mentoringmindsonline.com
MATH | LEVEL 7
Teacher Edition Sample Page
Describe relationships between sets of rational numbers
Unit 1
TEKS 7.2(A) – Supporting
teacher and students work together to write a clear definition for the set of counting numbers using
the information recorded. Students record the definition in math journals. Students sketch diagrams
similar to the one shown and record at least two numbers in each section, if possible. The teacher asks
students the following question: What number(s) belong in the Whole Numbers section of the diagram?
(Zero is the only number that fits in the Whole Numbers section since Counting Numbers are included.)
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.A, (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)3.D, (c)3.E, (c)4.F, (c)5.B)
Suggested Formative Assessment
Each student is given a blank Venn diagram composed of four nested circles labeled Rational Numbers,
Integers, Whole Numbers, and Counting Numbers.
Rational Numbers
Integers
Whole Numbers
Counting
Numbers
_
5
18
2 , -8, 3, ___
24 , -3.25) on the board, and students
The teacher lists ten numbers (e.g., - __
, 0, 3.3, __
, 1.5, - ___
7
3
6
3
record the numbers on their diagrams. The teacher asks the class probing questions such as the
following.
• Why did you classify 1.5 as a rational number instead of an integer?
• If a number fits into all four categories, where is it placed? Why?
Through examination of student Venn diagrams and answers, the teacher makes plans to provide
clarifications in future instructional activities.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)3.D, (c)3.H)
mentoringminds.com
mentoringminds.com
motivationmath™LEVEL 7
ILLEGAL TO COPY
41
MATH | LEVEL 7
Teacher Edition Sample Page
Unit 1
Describe relationships between sets of rational numbers
TEKS 7.2(A) – Supporting
Vocabulary Focus
The following are essential vocabulary terms for this unit.
counting numbers
negative number
set
exclusive
positive number
subset
inclusive
rational number
terminating decimal
integers
repeating decimal
Venn diagram
whole numbers
Vocabulary Activity
Stake Your Claim
The teacher creates cards labeled counting numbers, whole numbers, integers, and rational numbers,
divides the class into four groups, and randomly assigns one card per group. The students select
one member to represent the group, and he/she holds the card. The teacher calls numbers, including
positive and negative integers, fractions, and decimals. The group representative claims the number
called if it best fits in the classification assigned to the group. The group earns a point for each correct
claim, and the card is passed to another group member. The groups exchange cards after every five
numbers are called until each group has represented each classification.
(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)3.E)
Suggested Formative Vocabulary Assessment
On a sheet of paper, each student writes the terms counting numbers, whole numbers, integers, and
rational numbers. Next to each term, the student writes a brief definition of the classification and an
example of a number that fits that classification. The teacher examines student output to assess student
learning and plans additional review of the vocabulary as needed.
(DOK: 1, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)5.B, (c)5.G)
Suggested Instructional Activities
1. The teacher displays a set of numbers on the board. The teacher names a number classification.
Students hold their thumbs up if they agree the classification fits the numbers in the set or down
if they do not agree that the classification fits the numbers in the set. After naming all possible
classifications, the class discusses the most descriptive classification for the set. Some examples of
sets and their classifications are shown below.
•
12 , 5, 6.0} (thumbs up for all classifications; counting)
{___
•
-4 , 3} (thumbs up for all classifications except counting; whole)
{0, __
•
8
} (thumbs up for integers and rational numbers; integers)
{-2, 4, __
-1
1
{7, - __, 4.2} (thumbs up for rational numbers; rational numbers)
•
3
-2
2
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.D, (c)1.E, (c)1.H, (c)2.E, (c)2.G, (c)3.G, (c)4.G)
42
ILLEGAL TO COPY
mentoringminds.com
motivationmath™LEVEL 7
mentoringmindsonline.com
MATH | LEVEL 7
Teacher Edition Sample Page
Describe relationships between sets of rational numbers
Unit 1
TEKS 7.2(A) – Supporting
2. The teacher records the following statements on index cards, one statement per card.
•
All counting numbers are integers.
•
Some rational numbers are whole numbers.
•
Some integers are positive numbers.
The teacher prints two or more cards with each statement, so that there are enough statements for
each pair of students in the class. Student pairs work to create a model, including three numbers in
each section, to justify the statement is true. Each pair locates another pair in the class that has the
same statement to compare models.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D, (c)3.E)
a
3. The teacher assigns a specific positive or negative number written in the form __
to student pairs.
b
Students determine whether the assigned number is a repeating decimal or a terminating decimal.
Then the partners classify the number as a counting number, whole number, integer, and/or rational
number. Student pairs present the classifications to the class and explain their reasoning.
(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)2.C, (c)3.D, (c)3.E, (c)3.F)
4. The teacher randomly assigns a classification, counting numbers, whole numbers, integers, or
rational numbers, to each student. The student lists three numbers in the range from -10 to 10 that fit
into his/her assigned classification. At least one number should be written as a fraction or decimal.
The teacher selects students to share the assigned classifications and the three written numbers. The
class discusses any numbers classified incorrectly.
(DOK: 2, Bloom’s/RBT: Application/Apply, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.E, (c)2.I, (c)3.D)
Suggested Formative Assessment
The teacher creates a large, rectangular Venn diagram using tape on the floor of the classroom or
outside with string and stakes. A label is secured in the top corner of each section.
Rational Numbers
Integers
Whole Numbers
Counting Numbers
mentoringminds.com
mentoringminds.com
motivationmath™LEVEL 7
ILLEGAL TO COPY
43
MATH | LEVEL 7
Teacher Edition Sample Page
Unit 1
Describe relationships between sets of rational numbers
TEKS 7.2(A) – Supporting
Each student is given a card printed with a number, including number(s) that fit into each classification
on the diagram. Students move to the section of the diagram that best represents the given number.
Once each student has chosen a location, the teacher asks students to justify their locations. Students
may choose to move to another section of the diagram if they have made a mistake. When all students
agree on the placements, the students step out of the diagram, and the process is repeated with a new
set of numbers.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)2.E, (c)3.D, (c)3.E)
Suggested Reflection/Closure Activity
Students respond to the Journal prompt on page 12 of the student edition.
Consider the classifications of each number below.
7 : Rational number
__
3
15
- ___
: Rational number, integer
5
Explain the similarities and differences between the two numbers, specifically why they are classified
differently.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)4.G, (c)5.B, (c)5.G)
Suggested Formative Assessment
Students divide a sheet of paper into five columns labeled Number, Counting Number, Whole Number,
Integer, and Rational Number. The teacher reads a list of numbers, and students record each number
in the Number column. In the columns to the right, students record checks for each classification that
applies. An example is shown below.
Number
Counting Number
Whole Number
Integer
Rational Number
14












-45
9
__
3

0
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)4.G)
44
ILLEGAL TO COPY
mentoringminds.com
motivationmath™LEVEL 7
mentoringmindsonline.com
MATH | LEVEL 7
Teacher Edition Sample Page
Describe relationships between sets of rational numbers
Unit 1
TEKS 7.2(A) – Supporting
Interventions
1. The teacher displays a nested Venn diagram, similar to the one shown.
Rational Numbers
Integers
Whole Numbers
Counting
Numbers
The teacher places 12 to 15 numbers, including positive and negative decimals, fractions, whole
numbers, and zero, on sticky notes in the Rational Numbers section of the diagram. Students work
as a group to move the sticky notes to the Integers, Whole Numbers, or Counting Numbers sections
of the diagram, as appropriate. As students move the notes, the teacher asks questions to check for
student understanding.
•
Why do you think the (Integers, Whole Numbers, Counting Numbers) section is the best
placement for that number?
•
•
Why did you choose to leave (number) in the Rational Numbers section?
Why can (number) not be placed in the (Rational Numbers, Integers, Whole Numbers, Counting
Numbers) section?
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E)
2. The teacher displays a diagram showing the relationship between number sets, with ample room for
students to stand in front of the diagram. The teacher divides students into two groups. The groups
form two lines, and the first person in each line receives a flyswatter. The teacher calls out or displays
a number. The first student in each line runs to the diagram and swats the most specific section of
the diagram to show the number’s classification. The first student to swat the correct section earns a
point for his/her team. The students pass the flyswatter to the next student in line, and the process is
repeated until all students have a turn or until the teacher calls time. The team with more points wins.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.I)
mentoringminds.com
mentoringminds.com
motivationmath™LEVEL 7
ILLEGAL TO COPY
45
MATH | LEVEL 7
Teacher Edition Sample Page
Unit 1
TEKS 7.2(A) – Supporting
Describe relationships between sets of rational numbers
3. Each group of four students is given a set of cards with different numbers written on each card. Each
student selects a role: counting number, whole number, integer, or rational number. The students take
turns turning over one card at a time and raise their hands if the number fits their selected role. All
students in the group must agree on the classification before the next player’s turn.
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.C, (c)2.D, (c)3.D, (c)3.E, (c)3.F)
4. Each student creates a set of four nested boxes using index cards or card stock. Students label
the boxes with number classifications as shown. The teacher calls a number. Each student records
the number on a slip of paper and places the slip in the box labeled with the most descriptive
classification. The student then nests the box that contains the slip inside larger boxes, if possible,
and records all appropriate classifications of the number in a math journal. The teacher and students
repeat the process with other numbers.
Rational
Numbers
Integers
Whole
Numbers
Counting
Numbers
(DOK: 2, Bloom’s/RBT: Analysis/Analyze, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.I)
Suggested Formative Assessment
Individual students are given a blank Venn diagram. Working with each student individually, the teacher
displays several numbers, and the student explains where on the Venn diagram each number is placed.
The teacher displays as many numbers as necessary for the student to demonstrate an understanding
of classifying rational numbers. Based on student responses, the teacher plans additional interventions.
(DOK: 2, Bloom’s/RBT: Comprehension/Understand, ELPS: (c)1.C, (c)1.E, (c)1.H, (c)2.D, (c)2.E, (c)2.I, (c)3.D, (c)3.H)
Extending Student Thinking
Working in groups of 2–4, students use grade-appropriate Internet and library resources to research the
history of rational and irrational numbers, including the Egyptians’ Kahun Papyrus, Euclid’s works, and
the disagreement between Hippasus and Pythagoras over the existence of irrational numbers. Students
present the information in a creative format. Students might deliver a “postgame report” of an imaginary
debate between Hippasus and Pythagoras or act out a dramatic interpretation of an official presentation
of the Kahun Papyrus.
(DOK: 4, Bloom’s/RBT: Evaluation/Evaluate, ELPS: (c)1.E, (c)2.C, (c)2.I, (c)3.D, (c)4.G, (c)5.G)
46
ILLEGAL TO COPY
mentoringminds.com
motivationmath™LEVEL 7
mentoringmindsonline.com
MATH | LEVEL 7
Teacher Edition Sample Page
Unit 1
Describe relationships between sets of rational numbers
TEKS 7.2(A) – Supporting
Answer Codings
(Student pages 7–9)
Page Question
Answer
Process
TEKS
Bloom’s Original/
Revised
DOK
Level
ELPS
7.1(E)
Comprehension/Understand
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
7.1(G)
Analysis/Analyze
3
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.B, (c)5.G
7.1(F)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
Rational Numbers
____________________
____________________
Integers
Whole Numbers
________________
Counting
1
Numbers
________
- _2 : rational
5
7
2
0: rational, integer, whole
-13: rational, integer
5: rational, integer, whole, counting
_
0.3: rational
- _4 : rational, integer
2
3
4
5
8
9
Responses will vary.
False; statements will vary.
True
False; statements will vary.
False; statements will vary.
a. {1, 2, 3, 4, 5}
b. {-5, -4, -3, -2, -1, 0, 1, 2}
c. {0}
5 - __
3 - __
1 , 0} or
d. {- __
, 4 , - __
, 2 , - __
10 10 10 10 10
simplified fractions
1
B
7.1(E)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
2
H
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
3
D
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4
G
7.1(E)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
1
B
7.1(E)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
2
J
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
3
C
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4
F
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
5
B
7.1(E)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
mentoringminds.com
mentoringminds.com
motivationmath™LEVEL 7
ILLEGAL TO COPY
47
MATH | LEVEL 7
Teacher Edition Sample Page
Unit 1
Describe relationships between sets of rational numbers
TEKS 7.2(A) – Supporting
Answer Codings
(Student pages 10–14)
Page Question
1
10
Process
TEKS
Answer
B
7.1(E)
Bloom’s Original/
Revised
Analysis/Analyze
DOK
Level
ELPS
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
2
H
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
3
D
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
4
J
7.1(E)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
5
A
7.1(F)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
1
The set must include 0 and one other
counting whole number, and the
remaining members must be integers
or rational numbers.
The visual representation used should
reflect 1 value in the counting section,
0 in the whole number section, and
the remaining three values in the
rational section or integer section.
7.1(F)
7.1(G)
Application/Apply
3
(c)1.C, (c)1.E, (c)1.H, (c)4.G
2
Answers will vary but should include
that Callen’s diagram is incorrect
because zero is a whole number that
is neither positive nor negative.
Diagrams will vary.
7.1(E)
7.1(G)
Analysis/Analyze
3
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.B, (c)5.G
7.1(F)
7.1(G)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.B, (c)5.G
7.1(E)
Analysis/Analyze
2
7.1(E)
Analysis/Analyze
2
7.1(E)
Analysis/Analyze
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
7.1(F)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
7.1(E)
Application/Apply
2
(c)1.C, (c)1.E, (c)1.H, (c)4.G
11
Answers will vary but should include
Journal
12
that both are rational numbers _a
b
15
simplifies to an
where b ≠ 0, but - __
5
integer (-3), and _7 does not.
3
13
Vocabulary
Responses will vary.
Activity
Motivation
Results will vary.
Station
1
Responses will vary, but 0 is the only
number that can be placed in the Whole
Numbers section of the diagram.
(c)1.C, (c)1.E, (c)1.H,
(c)4.G, (c)5.B, (c)5.G
(c)1.C, (c)1.E, (c)1.H,
(c)3.E, (c)4.G
a. {21, 22, 23, 24, 25, 26, 27, 28, 29}
14
2
3
48
b. {- _3 , - _2 , - _1 , _0 , _1 , _2 , _3 }
3
3
3 3 3 3 3
c. {4, 8, 12, 16}
d. {0, 1, 2, 3, 4, 5, 6, 7}
-5, Integers
0.45, Rational Numbers
-2, Integers
ILLEGAL TO COPY
mentoringminds.com
motivationmath™LEVEL 7
mentoringmindsonline.com