Accentuate the Negative
The Learning will apply and extend previous understandings of operations with fractions to add,
subtract, multiply, and divide rational numbers.
Reasoning-DOK2
Created by Melissa Majeski – Warren Woods Middle School
7.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.
7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to divide rational numbers.
7.NS.3 Solve real-world problems involving the four operations with rational numbers.
**Skills needed in order to master learning target. Will not be tested individually on final assessment.
Proficiency Level 3
R-DOK2
Rules for Adding: If the signs are the same, add and keep the sign. If the signs are different, subtract and
keep the sign of the larger absolute value.
Jessica made the addition model below of the expression (-5) + (-2) + 3
Jessica used the number line to conclude that the sum of the 3 numbers is -4. If she correct? Explain
your thinking.
Explain Thinking: Jessica solution, -4, is correct because since -5 and -2 have the same sign, you add
them together and keep the sign, to get -7. Then you take -7 and add a positive 3. Since the signs are
different, you subtract 3 from 7 to get 4. The final answer is a -4, because when you take the absolute
value of -7 and 3, 7 is greater, so you take the sign of 7.
AN5: I can show algorithms for adding rational numbers
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
R-DOK2
Rational Numbers: Any number that can be written as a fraction.
Examples: 3, -1, 0.04, -2.1, -½ , ¼ , 84%
Non-Examples: 0.3333, √2, 𝜋
3 −1
Explain Thinking: Since 3, -1, 0.04, -2.1 and 84% can be written as 1 ,
1
4
1
84
, 100 , −2 10 , 100, they are
rational. Since 0.3333, √2, 𝜋 are repeating decimals or decimals that go on forever, they cannot
be writing as a simple fraction.
**AN1: I can explain and identify rational numbers
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
R-DOK2
Compare the following numbers using, <, >, =, ≤, or ≥.
0.64 > 47%
7/10 = 0.7
-0.44 < 0.44
Order the following set of numbers from least to greatest.
5
-0.2, ½ , 0.3, -2, 8
Least to Greatest
5
-2, -0.2, 0.3, ½, 8
Explain Thinking: To order rational numbers, first I converted ½ to 0.5 and 5/8 to 0.625. Then, I
used a number and located each number on the number. The larger the positive number, the
further to the right of zero. The smaller the negative number, the further left of zero.
**AN2: I can compare/order positive/negative rational
numbers.
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
K-DOK1
**AN3: I can locate rational numbers on a number line
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
R-DOK2
Find the absolute value of each number. Then, order them from least to greatest.
1
| | , |−3|, |2|
2
Least to Greatest
1
, 2, 3
2
Explain Thinking: Since absolute value of a rational number is the distance from zero, and
distance cannot be negative, ½ has the shortest distance from zero, and 3 has the largest
distance from zero.
**AN4: I can order the absolute value of rational
numbers.
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
R-DOK2
Rules for Subtracting: Add the additive inverse (opposite). Change the subtraction sign to an addition
sign. Change the sign of the second number. Then follow the rules of addition.
Explain what is meant by the following: p – q = p + (-q).
Explain Thinking: Subtracting a number is the same as adding it’s opposite. For example:
p = 4, q = 6
p – q = 4 – 6 = -2
is the same as
p + (-q) = 4 + (-6) = -2
AN6: I can use algorithms to subtract rational numbers.
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
R-DOK2
Rules for Multiplying: If the signs are the same, the product is positive. If the signs are different, the
product is negative.
Generate real-world situations that can be modeled by each of the following multiplication problems.
Use the Integer
Game as a resource.
4 x (– 7) = -28
If I lose 7 pounds per month for 4 months, my weight will change by -28 pounds total.
AN7: I can use algorithms to multiply rational numbers
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
R-DOK2
Rules for Dividing: If the signs are the same, the quotient is positive. If the signs are different, the
quotient is negative.
Are the answers to the three quotients below the same or different? Why or why not?
a) −14 ÷ 7 = −2
b) 14 ÷ (−7) = −2
c) −(14 ÷ 7) = −2
The answers in the problems are the same: -2 because for (a) and (b) since the signs are different, the
quotient is negative. For part (c) the negative in front of the parentheses changes the value inside the
parentheses to its opposite. The value in the parentheses is 2, and its opposite is -2.
AN8: I can use algorithms to divide rational numbers
Created by Melissa Majeski – Warren Woods Middle School
Proficiency Level 3
R-DOK2
Order of Operations: Parenthesis, Exponents, (Multiplication/Division from Left to Right),
(Addition/Subtraction from Left to Right)
10
5
10
= 2(3 +16) -1 + 5
10
= 2(19) – 1 +
5
2(3+ 42) -1 +
= 38 – 1 + 2 = 37+ 2
= 39
AN9: I can use order of operations to simplify expressions
and solve problems.
Created by Melissa Majeski – Warren Woods Middle School