Download UnderstandAddition of Positive and Negative Integers

Focus on Math Concepts
Lesson 1
Part 1: Introduction
CCLS
Understand Addition of Positive and
Negative Integers
7.NS.1.a
7.NS.1.b
When do we add positive and negative integers?
You can use positive and negative integers to represent quantities you see in sports, games,
business, science, and in other areas of your life.
For instance, in a game, you might gain 5 points if you answer the question correctly and
lose 5 points if you answer the question incorrectly. The numbers 5 and 25 are on opposite
sides of the number line and have the same distance from 0 on the number line. This means
that the numbers have the same absolute value.
| 5 | = 5
| –5 | = 5
–5
–4
–3
–2
–1
0
1
2
3
4
5
Think What happens when you add an integer to its opposite?
On the number line
below, circle the arrow
that represents 25.
You can use a number line to picture what happens when you
add an integer to its opposite.
Look at the number line above. The distance from 0 to 25 is
represented by an arrow pointing to the left. The distance from 0 to
5 is represented by an arrow pointing to the right. Because | 5 | 5 | 25 |, you know the
distances and arrows are equal in length.
The sum of 5 and 25 is shown on the number line below. If we move 5 units in the positive
direction and then move 5 units in the negative direction, we will be back at 0.
–5
+5
–5
–4
–3
–2
–1
0
1
2
3
4
5
Two numbers that have a sum of zero are additive inverses. In this case, 25 is the additive
inverse of 5 because 5 1 (25) 5 0. For the same reason, 5 is the additive inverse of 25.
2
L1: Understand Addition of Positive and Negative Integers
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Part 1: Introduction
Lesson 1
Think How do you model integer addition on a number line?
When adding or subtracting a negative number from another number, you write the
negative number in parentheses to separate it from the operation symbol.
Correct
3 1 (25)
4 2 (23)
Incorrect
3 1 25
4 2 23
The number line below represents 22 1 (24). You start at 22 and move left 4 units, ending
at 26. The sum of 22 1 (24) is 26. When adding two negative numbers, you start on the
left side of 0 and always move left, so the answer is always negative.
–4
–6
–5
–4
–3
–2
–1
0
The number line below represents 7 + (25). You start at 7 and
move left 5 units to add 25. You end at 2, so 7 1 (25) 5 2.
Will the sum of 28
and 13 be positive or
negative? Explain.
25
1
2
3
4
5
6
7
You can use this same process to add 5 + (27). You start at 5
and move left 7 units. You end at 22, so the sum of
5 + (27) = 22.
27
23
22
21
0
1
2
3
4
5
6
7
Reflect
1 How is adding integers similar to adding whole numbers? How is it different?
L1: Understand Addition of Positive and Negative Integers
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3
Part 2: Guided Instruction
Lesson 1
Explore It
You can use additive inverses to help you understand how to add integers.
2 A fisherman drops his net to a depth of 28 feet below the surface of the water. How far
does he need to raise the net to bring it back to the surface of the water? 3 A bird is 7 feet above the ground. What integer would you use to represent the distance
that the bird needs to fly to get back to the ground? Using a number line helps to visualize what is happening when adding integers.
4 Use the number line below to show 6 1 (26). The sum 6 1 (26) 5 .
22
21
0
1
2
3
4
5
6
7
8
5 Use the number line below to show 11 1 (28). The sum 11 1 (28) 5 .
2
3
4
5
6
7
8
9
10
11
12
6 Use the number line below to show 24 1 (27). The sum 24 1 (27) 5 .
–12
–11
–10
–9
–8
–7
–6
–5
–4
–3
–2
7 Use the number line below to show 24 1 7. The sum 24 1 7 5 .
–6
4
–5
–4
–3
–2
–1
0
1
2
3
4
L1: Understand Addition of Positive and Negative Integers
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Part 2: Guided Instruction
Lesson 1
Talk About It
Solve the problems below as a group.
8 Jason’s football team lost 6 yards from their starting position and then lost another
5 yards. What number represents a loss of 6 yards? a loss of 5 yards? 9 Use a number line to find the team’s total loss.
–12
–10
–8
–6
–4
–2
0
2
4
6
8
10 On the next play, the team gains 12 yards. Will the team be at their original starting
position? Explain.
11 A weather forecaster says the temperature will be about 258C “give or take” 10 degrees.
What is the greatest possible temperature? What is the least possible temperature? 12 Explain how you found your answers to problem 11.
Try It Another Way
You can add integers by decomposing numbers to form additive inverses that add to 0.
For example, to add 28 1 10, you can think of 10 as 8 1 2.
28 1 10 5 28 1 (8 1 2)
5 (28 1 8) 1 2
5012
52
Use the method shown above to do the problems below. Show your steps. 13 10 1 (24) 14 212 1 7 L1: Understand Addition of Positive and Negative Integers
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5
Part 3: Guided Practice
Lesson 1
Connect It
Talk through these problems as a class and write your answers below.
15 Compare: Show 7 1 (23) on the number line below.
–10
–8
–6
–4
–2
0
2
4
6
8
10
0
2
4
6
8
10
Show 23 1 7 on the number line below.
–10
–8
–6
–4
–2
What do you notice about the results? Explain why your number lines end on the same number.
16 Explain: Chase drew the number line below to show 24 1 (23). Is his model accurate?
If not, tell what is wrong with his model.
–3
–4
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
17 Analyze: On the number line below, the numbers x and y are the same distance from 0.
What is x 1 y? Explain how you found your answer.
y
0
x
6
L1: Understand Addition of Positive and Negative Integers
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Part 4: Common Core Performance Task
Lesson 1
Put It Together
18 Use what you have learned in this lesson to complete this task.
Mari is participating in National Lemonade Stand Day. She spends $18 for start-up
costs, which include supplies to make the lemonade, cups, and advertising.
ADescribe in detail how Mari could end up with the lemonade stand breaking even.
(“Breaking even” means “a profit of 0,” or that she makes enough money to pay for
her start-up costs but has no money left over.) Your description must include:
•the cost of each type of supply (lemonade, cups, and advertising), with each cost
represented as a negative number and in dollars
•the price Mari charges for 1 cup of lemonade, in dollars
•the total amount of sales, in dollars
•the money she has left over after covering her start-up costs, in dollars
•a mathematical expression and model that use the concepts in this lesson to show
the amount of profit
BRepeat Part A for the situation where Mari’s lemonade stand makes a profit (meaning
she has enough money to pay for her startup costs and has some money left over).
Draw your number line on a separate sheet of paper.
L1: Understand Addition of Positive and Negative Integers
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7
Focus on Math Concepts
Lesson 1
(Student Book pages 2–7)
Understand Addition of Positive and Negative Integers
Lesson Objectives
The Learning Progression
•Understand that opposite numbers combine to make
zero in mathematical and real-world situations.
In previous grades, students mastered basic operations
with positive whole numbers, fractions, and decimals.
In Grade 6, they expressed values less than 0 as
negative numbers and learned that absolute value is the
distance from zero. In Grade 7, students extend their
understanding of operations to include positive and
negative numbers, and they use rational numbers in
describing real-world contexts.
•Understand the relationship between addition and
subtraction.
•Represent p 1 q as the distance |q| from p on a
number line.
Prerequisite Skills
•Recognize that the difference between two positive
numbers on a number line represents the distance
between the numbers.
•Understand that absolute value is the distance from
0 and use absolute value symbols.
•Understand that numbers that are equidistant from
0 but in opposite directions are called opposites.
In this lesson, students apply and extend their previous
understandings of addition and subtraction to include
these operations on integers. Students will represent
addition and subtraction on a number line and describe
situations in which opposite quantities combine to
make zero. Students will also show that a number and
its opposite have a sum of zero as an introduction to
the additive inverse property.
Toolbox
Vocabulary
absolute value: a number’s distance from 0 on the
number line
additive inverses: two numbers whose sum equals
zero
Teacher-Toolbox.com
Prerequisite
Skills
Ready Lessons
7.NS.1.a
7.NS.1.b
✓
Tools for Instruction
Interactive Tutorials
✓
CCLS Focus
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.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its
two constituents are oppositely charged.
b. Understand p 1 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.
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 2–4 (see page A9 for full text)
L1: Understand Addition of Positive and Negative Integers
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1
Part 1: Introduction
Lesson 1
At a Glance
Focus on Math Concepts
Lesson 1
Students explore the concept of additive inverses to
develop an understanding that opposite numbers
combine to make zero.
Part 1: introduction
CCLs
Understand Addition of Positive and
Negative Integers
7.ns.1.a
7.ns.1.b
When do we add positive and negative integers?
Step By Step
You can use positive and negative integers to represent quantities you see in sports, games,
business, science, and in other areas of your life.
•Introduce the Question at the top of the page. Allow
time for students to discuss everyday situations that
involve positive and negative numbers, including
video games, football, temperature, and debt.
Support students in making the connections between
the number line, arrows, 25 and 5.
think What happens when you add an integer to its opposite?
•Read Think with students.
You can use a number line to picture what happens when you
add an integer to its opposite.
For instance, in a game, you might gain 5 points if you answer the question correctly and
lose 5 points if you answer the question incorrectly. The numbers 5 and 25 are on opposite
sides of the number line and have the same distance from 0 on the number line. This means
that the numbers have the same absolute value.
| 5 | = 5
| –5 | = 5
–5
–4
–3
–2
–1
0
1
2
3
4
5
on the number line
below, circle the arrow
that represents 25.
Look at the number line above. The distance from 0 to 25 is
represented by an arrow pointing to the left. The distance from 0 to
5 is represented by an arrow pointing to the right. Because | 5 | 5 | 25 |, you know the
distances and arrows are equal in length.
•Guide students to recognize that the sum of opposite
numbers has a value of zero.
The sum of 5 and 25 is shown on the number line below. If we move 5 units in the positive
direction and then move 5 units in the negative direction, we will be back at 0.
•Guide students to understand additive inverses.
–5
•If students need additional support with additive
inverses, use a number line to provide further
examples.
+5
–5
ELL Support
Use a number line to review and reinforce the
meaning of the phrases “opposite sides of the
number line” and “distance from 0.” Review the
meaning of “integer” and have students locate 3 to 4
integers and name their absolute values.
SMP Tip: Students model with mathematics
(SMP 4) when they describe and represent everyday
situations with integers, including addition and
subtraction of integers. From time to time, point out
and discuss situations in which we work with
positive and negative numbers.
2
–4
–3
–2
–1
0
1
2
3
4
5
Two numbers that have a sum of zero are additive inverses. In this case, 25 is the additive
inverse of 5 because 5 1 (25) 5 0. For the same reason, 5 is the additive inverse of 25.
2
L1: Understand Addition of Positive and Negative Integers
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Mathematical Discourse
•Provide a situation where you might use additive
inverses. Do others agree or disagree? Explain.
Listen for students to represent values which
represent opposite but equivalent distances
from zero.
•Do you think the concept of additive inverses holds
true for numbers other than integers? Explain.
Extend student thinking into decimal and/or
fractional values. Students should understand
that additive inverses don’t have to be integers.
L1: Understand Addition of Positive and Negative Integers
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Part 1: Introduction
Lesson 1
At a Glance
Students explore modeling addition of integers on a
number line.
Step By Step
Part 1: introduction
Lesson 1
think How do you model integer addition on a number line?
When adding or subtracting a negative number from another number, you write the
negative number in parentheses to separate it from the operation symbol.
Correct
3 1 (25)
4 2 (23)
•Read Think with students.
•Discuss the need for parentheses as a way to separate
the operation from the sign of the integer.
•Prompt students to start at zero and move to the first
addend. Adding a negative value is represented by
moving left on the number line.
•Reinforce the movement on the number lines for
each example.
•Ask students to provide real-world examples which
might represent adding a negative number or moving
to the left on the number line.
Incorrect
3 1 25
4 2 23
The number line below represents 22 1 (24). You start at 22 and move left 4 units, ending
at 26. The sum of 22 1 (24) is 26. When adding two negative numbers, you start on the
left side of 0 and always move left, so the answer is always negative.
–4
–6
–5
–4
–3
–2
–1
0
The number line below represents 7 + (25). You start at 7 and
move left 5 units to add 25. You end at 2, so 7 1 (25) 5 2.
Will the sum of 28
and 13 be positive or
negative? Explain.
25
1
2
3
4
5
6
7
You can use this same process to add 5 + (27). You start at 5
and move left 7 units. You end at 22, so the sum of
5 + (27) = 22.
27
23
22
21
0
1
2
3
4
5
6
7
reflect
•Have students read and reply to the Reflect directive.
Hands-On Activity
Model integer addition on a number line.
1 How is adding integers similar to adding whole numbers? How is it different?
you can add integers and whole numbers on a number line. When you add
integers, you move left to represent a negative number instead of always
moving right. When you add integers, you can get a sum of 0.
L1: Understand Addition of Positive and Negative Integers
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Materials: masking tape to create number lines on
the floor, paper
•Pairs of students model the addition of integers
using a life-size number line.
•Students start at zero on the number line. They
should then walk in the correct direction to model
the first addend and then the addition of the
integer.
•Students who are not walking on the number line
should record the expression that the movement
of their classmate represents.
•Repeat as needed.
•Extend this activity by asking students to walk
the number line and the audience to determine
the addition expression being represented.
L1: Understand Addition of Positive and Negative Integers
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3
Mathematical Discourse
•Explain the steps for modeling addition on a number
line.
Note that the sign of the integer determines the
direction on the number line. Previously,
students have been concerned only with
numbers to the right of 0 on the number line.
Now, when modeling addition on a number
line, students might move both right and/or left
on the number line to reach the sum.
•Will adding a negative always result in a negative
answer? How can you explain this to a peer?
Listen for students to describe the number with
the larger absolute value as determining the
sign of the sum.
3
Part 2: Guided Instruction
Lesson 1
At a Glance
Part 2: guided instruction
Students use horizontal number lines and the
knowledge of additive inverses to add integers.
explore it
you can use additive inverses to help you understand how to add integers.
Step By Step
2 A fisherman drops his net to a depth of 28 feet below the surface of the water. How far
that the bird needs to fly to get back to the ground? 27 feet
using a number line helps to visualize what is happening when adding integers.
22
Materials: computer and/or writing materials
•Students may work in groups, pairs, or
individually to create an integer-based newspaper.
•Use the expressions in problems 4–7 as a basis for
writing news stories to use in a newspaper. Each
expression should guide students in writing about
a real-world situation which could be seen in a
newspaper.
•Be creative and remember to include the sums in
the written piece.
4
21
0
1
2
3
4
5
6
2
3
4
5
6
7
8
9
–11
–10
–9
–8
–7
–6
–5
10
–6
4
–5
–4
–3
–2
–1
0
1
.
11
12
211
–4
–3
3
7 Use the number line below to show 24 1 7. The sum 24 1 7 5
8
3
6 Use the number line below to show 24 1 (27). The sum 24 1 (27) 5
–12
.
7
5 Use the number line below to show 11 1 (28). The sum 11 1 (28) 5
•Take note of students who are still having difficulty
and wait to see if their understanding progresses as
they work in their groups during the next part of the
lesson.
Make real-world connections.
0
4 Use the number line below to show 6 1 (26). The sum 6 1 (26) 5
•As students work individually, circulate among them.
This is an opportunity to assess student
understanding and address student misconceptions.
Use the Mathematical Discourse questions to engage
student thinking.
Concept Extension
8 feet
does he need to raise the net to bring it back to the surface of the water?
3 A bird is 7 feet above the ground. What integer would you use to represent the distance
•Tell students that they will have time to work
individually on the Explore It problems on this page
and then share their responses in groups. You may
choose to work through the first problem together as
a class.
STUDENT MISCONCEPTION ALERT: Students
may not have worked with negative numbers before
and may forget to include the negative sign in front
of the number. Direct students to highlight the signs
of numbers as a visual cue.
Lesson 1
2
.
–2
.
3
4
L1: Understand Addition of Positive and Negative Integers
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Mathematical Discourse
•Sam believes the answer to problem 5 is 219. Do you
agree or disagree? How would you respond to Sam?
Explain.
Students should be clear on the starting points
and the direction in which they are moving on
the number line to determine the sum.
•Explain why some sums are positive, others are
negative, and still others are 0.
Listen for students to make connections
between the absolute value of the addends as a
determinant in the sign of the sum.
•If the order of the addends were changed, how might
this affect your answer? Can you prove this to me?
The order doesn’t matter; the commutative
property of addition holds true for integers as
as whole numbers.
L1: Understand Addition of Positive and Negative Integers
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Part 2: Guided Instruction
Lesson 1
At a Glance
Students use number lines to show addition of integers.
Students use the decomposition of numbers to create
additive inverses to add integers.
Step By Step
•Organize students into pairs or groups. You may
choose to work through the first Talk About It
problem together as a class.
•Walk around to each group, listen to, and join in on
discussions at different points. Use the Mathematical
Discourse question to help support or extend
students’ thinking.
•Remind students to use a number line as they work
through problems 11 and 12. This is a good time to
introduce a vertical number line.
•Direct the group’s attention to Try It Another Way.
Have a volunteer from each group come to the board
to explain the group’s solutions to problems 13
and 14.
•Support students in decomposing an addend to
create additive inverses and to then apply the
associative property.
Concept Extension
Extend to addition of two-digit integers.
Part 2: guided instruction
Lesson 1
talk about it
solve the problems below as a group.
8 Jason’s football team lost 6 yards from their starting position and then lost another
5 yards. What number represents a loss of 6 yards? a loss of 5 yards?26 and 25
9 Use a number line to find the team’s total loss.
–12
–10
–8
–6
–4
–2
0
2
4
6
8
10 On the next play, the team gains 12 yards. Will the team be at their original starting
position? Explain.
no; the team will have reached their original starting position and then gone
past it by 1 yard.
11 A weather forecaster says the temperature will be about 258C “give or take” 10 degrees.
What is the greatest possible temperature?
What is the least possible temperature?
58C
2158C
12 Explain how you found your answers to problem 11.
Possible solution: i drew two number lines: i started at 25 and added 10 to get 5.
i started at 25 on the second number line and added 210 to get 215.
try it another Way
You can add integers by decomposing numbers to form additive inverses that add to 0.
For example, to add 28 1 10, you can think of 10 as 8 1 2.
28 1 10 5 28 1 (8 1 2)
5 (28 1 8) 1 2
5012
52
Use the method shown above to do the problems below. Show your steps.
13 10 1 (24) (6 1 4) 1 (24) 5 6 1 (4 1 (24)) 5 6 1 0 5 6
14 212 1 7 (25 1 (27)) 1 7 5 25 1 (27 1 7) 5 25 1 0 5 25
L1: Understand Addition of Positive and Negative Integers
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5
Mathematical Discourse
•Model the addition of two-digit integers using a
number line.
•Can you think of some ways to add integers without
using a number line?
Possible answers include decomposition and
the combination of opposites.
•Ask students to think of situations where the
addition of two-digit integers may be utilized.
SMP Tip: Asking students to share their thinking
Materials: number lines
•Create a story based on this situation.
•Individuals and pairs of students should exchange
stories to model the addition on a number line.
provides them with an opportunity to practice
critiquing the reasoning of others (SMP 3) by
rephrasing, asking for clarification, or identifying
misconceptions.
•Challenge students to use decomposition and the
associative property without the aid of a number
line.
L1: Understand Addition of Positive and Negative Integers
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5
Part 3: Guided Practice
Lesson 1
At a Glance
Part 3: guided Practice
Students demonstrate their understanding of adding
integers.
Lesson 1
Connect it
talk through these problems as a class and write your answers below.
Step By Step
15 Compare: Show 7 1 (23) on the number line below.
•Discuss each Connect It problem as a class using the
discussion points outlined below.
–10
–8
–6
–4
–2
0
2
4
6
8
10
0
2
4
6
8
10
Show 23 1 7 on the number line below.
–10
–8
–6
–4
–2
What do you notice about the results? they are the same. they both equal 4.
Compare:
Explain why your number lines end on the same number.
the order in which you add two numbers does not change the sum.
•You may choose to have all students model their
responses on a mini-whiteboard or paper and hold
them up.
16 explain: Chase drew the number line below to show 24 1 (23). Is his model accurate?
If not, tell what is wrong with his model.
–3
–4
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
no; both arrows are in the negative direction, but instead of starting both arrows
Explain:
at 0, the second arrow should start where the first arrow left off.
•Read the problem together as a class. Ask students to
work in pairs to discuss and write their responses
about what Chase did wrong.
17 analyze: On the number line below, the numbers x and y are the same distance from 0.
What is x 1 y? Explain how you found your answer.
y
•This problem focuses on the significance of moving
in the correct direction when modeling with a
number line.
•Stress the importance of starting at zero, moving to
the first addend (to the right if it is positive and to
the left if it is negative), and then moving accordingly
for the second addend.
0
x
x and y are the same distance from 0, but they are on opposite sides of 0. if we
start at x and move the same number of units to the left, we will be back at 0. We
know that y 5 the opposite of x and that the sum of a number and its opposite is
0. therefore, x 1 y 5 x 1 (2x) 5 0.
6
L1: Understand Addition of Positive and Negative Integers
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Analyze:
•Remind students to refer to a number line.
•Ask students to share strategies in answering this
question.
SMP Tip: Students are asked to understand the
meaning of the variables as related to x 1 y and then
decontextualize to manipulate the symbolic
representation (SMP 2) as seen with additive
inverses.
6
L1: Understand Addition of Positive and Negative Integers
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Part 4: Common Core Performance Task
Lesson 1
At a Glance
Part 4: Common Core Performance task
Students describe situations in which the addition of
integers can be applied and supported with a
mathematical model.
Put it together
18 Use what you have learned in this lesson to complete this task.
Mari is participating in National Lemonade Stand Day. She spends $18 for start-up
costs, which include supplies to make the lemonade, cups, and advertising.
Step By Step
a Describe in detail how Mari could end up with the lemonade stand breaking even.
(“Breaking even” means “a profit of 0,” or that she makes enough money to pay for
her start-up costs but has no money left over.) Your description must include:
•Direct students to complete the Put It Together task
on their own.
• the cost of each type of supply (lemonade, cups, and advertising), with each cost
represented as a negative number and in dollars
•As students work on their own, walk around to
assess their progress and understanding, to answer
their questions, and to give additional support, if
needed.
• the price Mari charges for 1 cup of lemonade, in dollars
• the total amount of sales, in dollars
• the money she has left over after covering her start-up costs, in dollars
• a mathematical expression and model that use the concepts in this lesson to show
the amount of profit
Possible answer: Mari’s costs are 2$12 for lemonade mix, 2$4 for plastic
cups, and 2$2 for poster board. Mari sells lemonade for $0.75/cup.
•If time permits, have students share one of their
descriptions with a partner, being sure to support
their description with a model on a number line.
24 people buy lemonade. her total sales are $18. her start-up costs total
2$18 and her sales are $18. because (218) 1 18 5 0, Mari breaks even.
+18
–2
Scoring Rubrics
–20
–18
–4
–16
–14
–12
–12
–10
–8
–6
–4
–2
0
b Repeat Part A for the situation where Mari’s lemonade stand makes a profit (meaning
she has enough money to pay for her startup costs and has some money left over).
Draw your number line on a separate sheet of paper.
See student facsimile page for possible student answers.
A
Lesson 1
Possible answer: Mari’s costs are 2$12 for lemonade mix, 2$4 for plastic
cups, and 2$2 for poster board. Mari sells lemonade for $0.50/cup. 42 people
Points Expectations
2
1
0
The response demonstrates the student’s
mathematical understanding of
representing integers on a number line,
additive inverses, and the addition of
integers.
An effort was made to accomplish the task.
The response demonstrates some evidence
of verbal and mathematical reasoning, but
the student’s questions may contain some
misunderstandings.
buy lemonade. her total sales are $21. her start-up costs total 2$18 and her
sales are $21. because 218 1 21 5 3, Mari’s profit is $3.
L1: Understand Addition of Positive and Negative Integers
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B
Points Expectations
2
The response demonstrates the student’s
mathematical understanding of adding
integers and modeling on a number line.
1
An effort was made to accomplish the task.
The response demonstrates some evidence
of verbal and mathematical reasoning, but
the student’s questions may contain some
misunderstandings.
0
There is no response or the response shows
little or no understanding of integer
addition and/or the modeling of integer
addition using a number line.
There is no response or the response shows
little or no understanding of the concepts in
this lesson.
L1: Understand Addition of Positive and Negative Integers
©Curriculum Associates, LLC Copying is not permitted.
7
7
Differentiated Instruction
Lesson 1
Intervention Activity
On-Level Activity
Use a vertical number line to calculate
temperature differences.
Create a mathematical model to solve
a problem.
Have students solve the following:
Have students solve the following:
•The temperature was 12 degrees on Monday. It
dropped 13 degrees later that night.
•Joe had $22 in his bank account. He went to the
bank on Sunday and made a transaction. His
balance on Monday was 2$32.
•The temperature was 13 degrees on Tuesday. It
dropped 12 degrees later that night.
•Use a vertical number line to determine the
night-time temperatures for Monday and Tuesday
nights.
•Determine what Joe did on Sunday. Provide
mathematical support to your reasoning and be
sure to include a model.
Challenge Activity
Explain mathematical reasoning in solving a problem.
Have students solve the following situation:
Sam and Nick love to climb rocks. One day, they start at different elevations.
•Sam starts at 123 feet below sea level and climbs 237 feet.
•Nick starts at 50 feet above sea level.
•How far must Nick climb to end up at the same elevation as Sam? Explain how you found your answer.
[64 feet; To find Sam’s final elevation, start with 2123 and add 237. Sam climbed to 114 feet above sea level.
Nick starts at 50 feet above sea level. To get to the same elevation as Sam, 114 feet above sea level, he must climb
64 feet, because 114 2 50 5 64.]
8
L1: Understand Addition of Positive and Negative Integers
©Curriculum Associates, LLC Copying is not permitted.