Download (Unit 1) Operations with Rational Numbers - Grubbs

Teacher: LaToya Grubbs
Subject: 7th Grade Math
Date:
Standards:
MCC7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational
numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
MCC7.NS.1a Describe situations in which opposite quantities combine to make 0.
MCC7.NS.1b Understand 𝑝 + 𝑞 as the number located a distance |𝑞| from 𝑝, in the positive or negative direction
depending on whether 𝑞 is positive or negative. Show that a number and its opposite have a sum of 0 (are additive
inverses). Interpret sums of rational numbers by describing real-world contexts.
MCC7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, 𝑝 – 𝑞 = 𝑝 + (–𝑞). Show
that the distance between two rational numbers on the number line is the absolute value of their difference, and
apply this principle in real-world contexts.
MCC7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
MCC7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply
and divide rational numbers.
MCC7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that
operations continue to satisfy the properties of operations, particularly the distributive property, leading to products
such as (–1)(–1)=1 and the rules for multiplying signed numbers. Interpret products of rational numbers by
describing real-world contexts.
MCC7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of
integers (with non-zero divisor) is a rational number. If 𝑝 and 𝑞 are integers then –(𝑝/𝑞) = (–𝑝)/𝑞 = 𝑝/(–𝑞). Interpret
quotients of rational numbers by describing real-world contexts.
MCC7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
MCC7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational
number terminates in 0s or eventually repeats.
MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
KEY VOCABULARY: integers, negative, positive, additive inverse, number line, two-color counters, absolute
value, multiplicative inverse, natural numbers, rational numbers, repeating decimals, terminating decimals,
opposite numbers, zero pairs
ASSESSMENT STRATEGIES: Formative (Fluency Quiz, Math Journal, Self-Check, Opening Activities )
Summative (Performance Task, Test, Culminating Task, PAR)
DIFFERENTIATION: Scaffolding, Peer Tutoring, Manipulatives, Flexible Grouping,
WEEK 1: Aug. 26-30, 2013
INSTRUCTIONAL FRAMEWORK
Mon.
O- Math Using Words (Handout)
Math Journal
M- SE: Ch. 4.2 Adding Using a Number line (Problem 1a-f)

What is absolute value?
W- SE: Ch. 4.2 Adding Using a Number line (Problems 2 - 13)

Why is it always positive?
O- Math Using Words 2 (Handout)
Math Journal
M- Create your own number line (-15 thru 15)

What is the distance between -7 and 4?
W- SP: Ch. 4.1 Math Football/Using Models

Write a number sentence to represent
the distance between -7 and 4!
 Problems 1-10 (Teacher Directed0
Tues.
CLOSING
 Problems 11-20 (Independent & Peer Check)
 Problems 21-30 (Independent & Class Check)
Fri.
Thurs.
Wed.
 Problems 31-46 (Independent & Turn-in)---Use # 31/32
& 39/40 as EXAMPLES to explain the strategy.
Remind students on #39-46 they can only use
numbers 1-6 because it’s a number cube!
O- Integr Pairs (Handout)
Math Journal
M- WarmUp pg 195C (Handout)
If the absolute value of the positive integer
is greater than the absolute value of the
negative integer, the sum will be
…….Give 5 examples that have a sum of
10.
W- SP: Ch. 4.2 Walk the Line (Problems 1-28)
O- Integer Pairs 2 (Handout)
Math Journal
M- Follow Up pg 204-205C (Handout)
If the absolute value of the positive integer
is greater than the absolute value of the
negative integer, the sum will be
…….Give 5 examples that have a sum of
10.
W- Assignment 4.1 & 4.2
O- Integer Pairs 3 (Handout)
Math Journal
M- FollowUp 214A-215C
No Journal
W- Performance Task: Show Me Your Signs (Handout)
Math Using Words
Math Sentence
Number
Final
Sentence
Answer
1) What number is 6 more than -3?
-3 + 6 =
2) What number is 7 less than -2?
-2 + -7 =
3) What number is 5 more than -8?
4) What number is 9 less than 7?
5) What number is 4 less than 1?
6) What number is 2 less than -1?
7) What number is 5 more than -2?
8) What number is 3 more than -1?
9) What number is 8 less than 5?
10) What number is 7 more than -5?
Math Using Words 2
Math Sentence
1) What number is 8 more than -3?
2) What number is 5 less than -4?
3) What number is 2 more than -3?
4) What number is 9 less than 12?
5) What number is 12 less than 8?
6) What number is 7 less than -5?
7) What number is 8 more than -10?
8) What number is 3 more than -7?
9) What number is 5 less than 3?
10) What number is 6 more than -5?
Number
Final
Sentence
Answer
Integer Pairs






MatchUP 1 positive integer AND 1 negative integer that have a sum of (-15).
You must make at least 5 "integer pairs" to receive an 80.
You must find ALL 9 "integer pairs" to receive a 100.
Each number is used ONCE, so cross them out as you use them.
You have 5 minutes!
Write your solutions in Answer Key. (eg. -40 + 25 = -15)
Positive Integers
Negative Integers
5
8
11
18 -27
-4
-13
-17
21
2
57
19 -20
-34
-6
-36
36
42
28
12 -42
-5
-23
-51
20
14
35
16 -26
-32
-35
-15
Answer Key
1)
2)
3)
4)
5)
6)
7)
8)
9)
Integer Pairs 2






MatchUP 1 positive integer AND 1 negative integer that have a sum of (+15).
You must make at least 5 "integer pairs" to receive an 80.
You must find ALL 9 "integer pairs" to receive a 100.
Each number is used ONCE, so cross them out as you use them.
You have 5 minutes!
Write your solutions in Answer Key. (eg. -40 + 55 = 15)
Positive Integers
Negative Integers
5
47
11
18 -27
-4
-13
-10
21
2
57
19 -20
-34
-6
-36
36
42
28
12 -42
-5
-23
-51
20
14
36
16 -26
-32
-3
-21
Answer Key
1)
2)
3)
4)
5)
6)
7)
8)
9)
Integer Pairs 3






MatchUP 1 positive integer AND 1 negative integer that have a sum of (-20).
You must make at least 5 "integer pairs" to receive an 80.
You must find ALL 9 "integer pairs" to receive a 100.
Each number is used ONCE, so cross them out as you use them.
You have 5 minutes!
Write your solutions in Answer Key. (eg. -40 + 20 = -20)
Positive Integers
Negative Integers
5
17
21
18 -63
-45
-28
-10
25
12
51
29 -20
-34
-54
-36
32
22
8
35 -42
-41
-23
-51
58
43
34
16 -26
-37
-3
-49
Answer Key
1)
2)
3)
4)
5)
6)
7)
8)
9)
WEEK 2: Sept. 2-6, 2013
INSTRUCTIONAL FRAMEWORK
Mon.
O- Intro to Two Color Counter (Handout)
M- Representing a Number Sentence Using Tiles (Handout)
W- SE: Ch. 4.3 Two Color Counters (Problems 1- 16)
O- SP: Ch. 4.3 Two-Color Counters (Problems 1-6)
Tues.
M- SP: Ch. 4.3 Two-Color Counters (Problems 7- 14)
CLOSING
Math Journal

What is a zero pair? Give 5
examples.
Math Journal

How many zero pairs are there
if you model the number
sentence below. Explain your
answer

What is the solution?
W- SP: Ch. 4.3 Two-Color Counters (Problems 15-46)
Fri.
Thurs.
Wed.
-25 +17
O- SE: Ch. 4.4 Problem 1: Temperatures
Math Journal
M- Modeling Subtraction using Two-Color counters (Handout)
Why do you use zero pairs to model a
subtraction problem?
W- SE: Ch. 4.4 Problem 2: Modeling Subtraction (Zero Pairs)
Problem 3: Modeling Subtraction (Number line)
O- (SP) Ch. 4.4 What's the Difference? (Problems 1- 6)
Math Journal
M- (SP) Ch. 4.4 What's the Difference? (Problems 7-14)
Which method do you prefer and
WHY?
W- (SP) Ch. 4.4 What's the Difference? (Problems 15 - 48)
Number Line VS Two Color Counters
O- WarmUP 225C - 225D
Math Journal
M- FollowUp 238A - 238B
No Journal
W- Performance Task: Hot Air Balloons
Intro to Two-Color Counters
STEPS Activity
Step 1: What is a two-color counter?
One color represents a -1 (RED). The other color represents a +1 (YELLOW)
Draw a + sign in one circle and color it yellow. Draw a - sign in one circle and color it red.
= ZERO PAIR
Step 2: What is a ZERO PAIR?
Opposite numbers, such as -2 and +2 make up a ZERO PAIR. When you combine (or
add) opposite numbers, they are called ADDITIVE INVERSES. Additive inverses are
called Zero Pairs because they are "two numbers" that "always have a SUM of ZERO".
Fill-in the set of two-color counters to create a zero pair.
= 0
Step 3: Fill in the model to represent each value. Write a number sentence to represent the tiles.
= 4
Number Sentence:
Step 4: Manipulating the model. Write a number sentence to verify your answer.
1) What will be the value of the model if I add 3 negative tiles and 3 positive tiles?
2) What will be the value of the model if I add 4 negative tiles?
3) What will be the value of the model if I add 2 negative tiles and 4 positive tiles?
Represent the Number Sentence Using Tiles

Be sure to draw you tile using some type of pattern.

Cross out any zero pairs you see, AFTER YOU "ADD" the 2nd
TERM IN THE NUMBER SENTENCE.

Count what
-3 + 7 =
-7 + (-3) =
-4 + 1 =
2 + (-4) =
-5 + 6 =
-2 + 5 =
2 + (-6) =
Modeling Subtraction Using Tiles
Note:

When modeling ADDITION, you ADD IN tiles.

When modeling SUBTRACTION, you TAKE AWAY tiles.
You must be able to READ the number sentence properly, in order to MODEL it properly. Fillin the table below.
Number Sentence
-7 - 4
-7- (-4)
7-4
7 - (-4)
First term
-7
Sign in the middle
-
Second term
4
 Lets practice READING each number sentence.
 Circle the words that tell you how to model the problem.
Number
First Term
Sign in the middle
Second term
4-6
I start with 4 positives.
Then take away
6 positives.
4 - (-6)
I start with 4 positives.
Then take away
6 negatives.
-4-6
I start with 4 negatives.
Then take away
6 positives.
- 4 - (-6)
I start with 4 negatives.
Then take away
6 negatives.
Sentence
5 - 10
5 - (-10)
-5 - 10
-5 - (-10)
WEEK 3: Sept. 9-13 , 2013
INSTRUCTIONAL FRAMEWORK
Mon.
O- Integer Pairs 4
Math Journal
M- Assignment 4.3 Problem 1

What is absolute value?
W- Assignment 4.3 Problem 2-4

Why is it always positive?
O- Fluency Quiz 1
Tues.
CLOSING
Math Journal
M- MathShell: Temperature Changes

What does "difference between mean?
W-

Write a number sentence to represent the
follwing statement.
Fri.
Thurs.
Wed.
What is the difference between 8 and -5?
O- Fluency Quiz 2
Math Journal
M- Assignment 4.4 Problem 1a
W- Assignment 4.4 Problem 1b-h
Why do you use zero pairs to model a subtraction
problem?
O- Performance Task: Debits & Credits-Situation 1
Math Journal
M- Performance Task: Debits & Credits-Situation 2
Which method do you prefer and WHY?
W- Performance Task: Debits & Credits-Situation 3
Number Line VS Two Color Counters
O- Introduce Culminating Task
Math Journal
M- FollowUp 238A - 238B
No Journal
W- Performance Task: Hot Air Balloons
Integer Pairs 4






MatchUP 1 positive integer AND 1 negative integer that have a sum of (18).
You must make at least 5 "integer pairs" to receive an 80.
You must find ALL 9 "integer pairs" to receive a 100.
Each number is used ONCE, so cross them out as you use them.
You have 5 minutes!
Write your solutions in Answer Key. (eg. -40 + 20 = -20)
Positive Integers
Negative Integers
5
19
30
18 -22
-45
-21
-20
25
12
51
39 -20
-34
-16
-36
32
40
38
35 -7
-1
-12
-51
44
13
34
23 -9
-26
-3
-5
Answer Key
10)
11)
12)
13)
14)
15)
16)
17)
18)
Fluency Quiz 1
Solve
-8 + 12 =
Solve
-12 + 8 =
Solve
-8 - (-12) =
Solve
-12 - 8 =
Subtract
3
/4 - 2/3 =
Add
8
/10 + 2/3 =
Simplify
Simplify
52
36
(Write the number sentence and
solve it)
What number is 7 less than -5?
(Write the number sentence and
solve it)
What number is 9 more than -4?
/46 =
/45 =
Fluency Quiz 2
Solve
7 + (-8) =
Solve
-7 + 8 =
Solve
-7 - (-8) =
Solve
-8 - (-7) =
Subtract
1
/2 - 1/3 =
Add
5
/ 6 + 8/ 9 =
Simplify
Simplify
18
72
(Write the number sentence and
solve it)
What number is 4 less than 2?
(Write the number sentence and
solve it)
What number is 5 more than -7?
/4 =
/80 =
Fluency Quiz 3
Solve
14 + (-10) =
Solve
-14 + 10 =
Solve
-14 - (-10) =
Solve
-14 - 10 =
Subtract
8
/7 - 4/5 =
Add
6
/11 + 2/6 =
Simplify
Simplify
40
27
(Write the number sentence and
solve it)
What number is 18 less than 10?
(Write the number sentence
and solve it)
What number is 12 more than -9?
/12 =
/54 =
WEEK 4: Sept. 16-20, 2013
INSTRUCTIONAL FRAMEWORK
Mon.
O- Fluency Quiz 3
M- (SE): Ch. 5.1 Problem 1: Multiplying Integers
Tues.
Wed.
M- (SP): Equal Groups Problems 1-14
W- (SP): Equal Groups Problems 15- 48
(SE) TALK to TALK pg. 262
Math Journal

Model each problem below
using a number line.
-6(4) AND 20/-5
O- Fluency Quiz 5
Math Journal
M- (A) Equal Groups Problem 1
Write a word problem that represents
the following number sentence:
W- (A) Equal Groups Problem 2-3
5(-2)
O- Fluency Quiz 6
Thurs.
Math Journal
W- (SE): Ch. 5.1 Problem 2: Division of Integers
O- Fluency Quiz 4
Fri.
CLOSING
Math Journal
M- Performance Task: Multiplying Rational Numbers
KWL Chart
W- Performance Task: Multiplying Rational Numbers
"Adding, Subtracting, Dividing,
Multiplying Integers"
O- Fluency Quiz 7
Math Journal
M- Performance Task: Patterns of Multiplying/Dividing
No Journal
W- Performance Task: Patterns of Multiplying/Dividing
Fluency Quiz 3
Solve
14 + (-10) =
Solve
-14 + 10 =
Solve
-14 - (-10) =
Solve
-14 - 10 =
Subtract
8
/7 - 4/5 =
Add
6
/11 + 2/6 =
Simplify
Simplify
40
27
(Write the number sentence and
solve it)
What number is 18 less than 10?
(Write the number sentence and
solve it)
What number is 12 more than -9?
/12 =
/54 =
Fluency Quiz 4
Solve
-8 + (-10) =
Solve
-8 - 10 =
Solve
-8 - (-10) =
Solve
8- (-10) =
Subtract
6
/7 - 2/3 =
Add
3
/10 + 5/6 =
Simplify
Simplify
37
36
(Write the number sentence and
solve it)
What number is 12 less than -5?
(Write the number sentence and
solve it)
What number is 3 more than -1?
/10 =
/45 =
Fluency Quiz 5
Solve
4 + (-7) =
Solve
4-7=
Solve
4 - (-7) =
Solve
-4 - (-7) =
Subtract
8
/9 - 5/6 =
Add
2
/5 + 9/10 =
Simplify
Simplify
50
24
(Write the number sentence and
solve it)
What number is 3 less than -5?
(Write the number sentence and
solve it)
What number is 2 more than -1?
/12 =
/30 =
Fluency Quiz 6
Solve
20 + (-16) =
Solve
20 - 16 =
Solve
20 - (-16) =
Solve
-20 - (-16) =
Subtract
18
/20 - 4/5 =
Add
5
/6 + 3/4 =
Simplify
Simplify
35
60
(Write the number sentence and
solve it)
What number is 5 less than 3?
(Write the number sentence and
solve it)
What number is 9 more than -5?
/9 =
/75 =
Fluency Quiz 7
Solve
-4 + (-14) =
Solve
-4 + 14 =
Solve
-4 - (-14) =
Solve
-4 - 14 =
Subtract
4
/5 - 2/3 =
Add
9
/10 + 2/3 =
Simplify
Simplify
80
24
(Write the number sentence and
solve it)
What number is 8 less than 5?
(Write the number sentence and
solve it)
What number is 3 more than -7?
/25 =
/64 =