Adding Rational Numbers-Lesson Plan

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Teacher: Wyche/Smith Unit: Number System
Lesson: Finding the Additive Inverse Date: 2/11/2019 2 Days
IS 349’s Suggested Lesson Plan Template
CCSS:
The Number System CCSS:
7.NS.1a: Describe situations in which opposite quantities combine to make “0”.
7.NS.1b:Apply and extend previous understandings of operattions with fractions.
7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.
Mathematical Practice: MP.2-Reasoning It calls for students to organize and communicate mathematical ideas.
Students use a number line to add two rational numbers that have different signs.
This will be provided after Setpetmber 4, 2018’s PL session)
■
2018-19 Instructional Focus for IS 349:
‘If all teachers use results from common pre and post unit assessments and collaborate to provide strategic interventions
then all students will demonstrate progress towards proficiency.” (Note: This will be adjusted after September 4
8
Aim: (Takes the form of a “How” or “Why” question that is small enough to tackle in on
class period, but this promotes student thinking. The “Aim” should appear visible to
students at the front of the room for the entire period. This question is often the “Exit”
assessment. It takes the class period to answer and should be displayed infront of the room
for the entire period.)
How can you add rational numbers?
Answer: If the two numbers have the same sign you can add them
together and give the sum the same sign as the two numbers. If the
sum of two numbers have different signs, find the difference of their
absolute values and use the sign of the number with the greater
absolute value.
BEFORE READING/LEARNING
With what will my students struggle?
__x_ need for prior knowledge
_x__ new concepts
___ text complexity (sentence length/type)
___ (academic)1vocabulary
___ vocabulary
How will I get them ready to learn?
___ review previous lesson
__x_ background knowledge to frame text
___ preview vocab and/or concepts
___ anticipation guide
Additional Notes:
EQUITABLE CLASSROOM PRACTICES
___ welcome students by name
__x_ use visual aids
___ materials reflect culture of students
___ random response strategies
___ use probing, clarifying techniques
___ acknowledge all comments
_x__ adequate wait time
___ seek multiple perspectives
___ survey students about instruction
___ give specific feedback
__x_ provide individuals w/assistance
Additional Notes:
DIFFERENTIATION
Content
__x_ Think-Pair-Share
___ Read/Summarize
___ Read/Question/Answer
___ Double Entry-Diary
__x_ Visual Organizer
___ Books on Tape
[Type text]
___ Highlighted Texts
__x_ Note-taking Organizers
___ Varied Texts
___ Varied Supplementary Material
___ Chunking / length of text
Process:
___ Graphic organizer
___ Choices (Intelligences)
___ Tiered lessons
___ Scaffoling by____________________
___ Activities and/or Excercieses
Additional Notes:
Product:
___ Differntatied tasks
EX:_________________________
_________________________
_________________________
___ Choices – readiness & interest
___ Clear expectations
___ Timelines
___ Checklists
___ Rubric
___Student self/peer assessment with
feedback opportunity
8
[Type text]
Learning Objective(s): (This is a short statement of what the intended learning is for
students. Best practice is to make the learning objective in student-facing language that
maps directly back to the “Aim”.)
Students will be able to:
 Apply previous knowledge and understanding of adding and
subtracting decimals and fractions.
 Explain how to use a number line to find the additive inverse , or
opposites of a number.
[Type text]
Procedure/ Sequence of learning activities: (All learning activities/student tasks
such as “Do Now”, “Think-Pair-Share”, “Annotation” are to map directly back to
the learning objective.)
Do Now: All students will be able to use a calculator to solve the
problems if needed.
281-Higher Learners
Benjamin
Nas
Haley
Malik
Jose
Joshua
281-Lower Learners: will need counters as a visual before starting the
lesson
Julio
Tony
Reina
Marisa
740 Higher Learners
Anthony
Aldo
Axel
Paycent
Denisse
Tristan Rivera
740 Lower Learners:will need counters as a visual before starting the
lesson
Sherline
Wendy
Fabian
Geovani
Tristan Loubriel
Jeremiah Rivera
Katelyn Pena
Higher Learners: These students have the ability to grasp the knowledge of
reviewing a word problem, using the CUBES method if needed to find out what
the problem is asking.
Day 1
Arlene has a gift card for a local lawn and garden store. She uses the gift card to
rent a tiller for 4 days. It cost $35 per day to rent the tiller. She also buys a rake
for $9.
Find the change to the value on her gift card.
Tiller: a machine that gets soil ready for planting.
Answer: 4(-35) -9= -149; 149 less
Day 2:
Directions: Answer the following questions on this sheet.
Yvonne bought 4 𝟕/𝟖 yards of material to make her dress.
a. What is 4 7/8 written as an improper fraction?_____39/8______________
[Type text]
b.
What is 4 7/8 written as a decimal?___4.875____________________
Day 3:
While reviewing last month’s finances, Jacob noticed that he had spent $300 on
a robot and deposited $300 that he had earned from selling books to a used
bookstore. What is the change in Jacob’s savings?
Answer: 0
Lower Learners: These students may still need support with using the
operations to solve problems with out using so many words to find the answer.
They are capable of handling a word problems, but may need more time.
Keeping the account of the time when doing a “Do Now”.
Day 1
Evaluate each expression.
1) 4(-1) +7
2) (-10) / (-2) +9
Answer: 1) 3
2) 14
Day 2:
Write each rational number as a decimal. Use the calculator to support with solving
you answer.
1. 4/7
Answer: 0.571428…
2
2. 1/3
Answer: 0.333…
3. 9/20
Answer: 0.45
Day 3:
While hiking, Jing went up 100 meters. If Jing started at 200 meters above sea
level, what is his elevation now?
Answer: 300
Vocabulary:
Tiller: a machine that gets soil ready for planting.
Absolute Value(Valor Absoluto):2
The distance of number from zero on a number line; show by
l l Example: l 5 l = 5; l -5 l = 5
Additive Inverse: Opposite of a number in the same distance from 0 on a
number line as the original number, but on the other side of 0.
Materials:
Do Now Handouts
Go Math Workbook
Number Line Worksheets for Whole, Halves, Quarters
Notebook
Pencil
[Type text]
Mini Lesson:
What do you notice different about these two types of number line sheets?
Answer: One sheet has whole numbers negative and positive, and the other
sheet has numbers in ½ (halves) both negative and posit2ive.
In this lesson, we will be looking at number in halves and whole using both
negative and positive to solve for an answer. We will also be looking at halves
and whole number with both decimals and fractions to show how both types of
numbers can be written differently, but have the sa2me value.
Example: 4.5 (Four and five-tenths) Student prior knowledge is that we have
been working on place value beyond the decimal. Students will recite the what
the represents.
Misconception may exist here because as a fraction the number will appear
different. In a fraction the whole number and decimal will be written as 4 ½.
Students will be explain that when you reduce 5/10 it will equal ½.
Teacher will also explain that any decimal that represents .5 is considered as ½
in a fraction.
Differentiated Instruction:
 Some students will have a number line that have whole numbers and
other students who will need the visual will have two different number
lines that have halves and whole numbers to discriminate the two
different types of numbers.
 Students may also need counters red and yellow. Red: ½ and Yellow:
whole
 Teacher will mark the counter so that they can discriminate.
Example 1:
A. Malachi hikes 2.5 miles and stops for lunch. Then he hikes for 1.5 more
miles. How many miles did he hike altogether?
Question: What are the key words in this scenario that will help us solve this
problem? (Posed to all students to see if they are able to point out the target words.)
Key words: more; altogether (2this means that we will add the two value together to
get and answer. Students will circle the keywords in their work book.
On the number line hand out sheet they will identify the first stop that Malachi made
to the next stop he made after lunch. Paraprofessionals will walk around to see that
students have identify the start and final points that Malachi made.
Step 1: Use positive numbers to represent the distance Malachi hiked.
Step 2: 2.5 + 1.5
Step 3: Find 2.5 on the number line + 1.5 spaces to the (right) that he hiked.
Step 4: The result is 4. Malachi hiked 4 miles (unit)
Note: Students will record the signs on the end of the number on both left and
right side in order to support their answer for the “Exit Ticket”
Guided Practice:
[Type text]
B. Kyle pours out ¾ liter of liquid from a beaker. Then he pours out
another ½ liter of liquid. What is the overall change in the amount of
liquid in the beaker?
Underline the key words in this scenario ”pours out”
Note: “Pours out” represent (-) in this scenario.
Teacher will expresses interest on this word.
Step 1. Use negative numbers to represent amounts the change each time Kyle
pours liquid from the beaker.
Step 2: Find -3/4 + (-1/2)
Step 3 Find -3/4 on the number line.
Step 4 Move l -1/2 l = ½ (Absolute Value) The result is -1 ¼. The amount of
liquid in the beaker has decreased by 1 ¼ liters. Note: Students will identify
that the word “decrease” which is the target/key word that supports (-) in this
problem.
Day 2:
Adding Rational Numbers with Different Signs:
To add rational numbers with different signs, find the difference of their
absolute values. Then use th sign of the rational number with the greater value.
Example 2:
A. During the day, the temperature increase by 4.5 degrees. At night, the
temperature decreases by 7.5 degrees. What is the overall change in
temperature.
Step 1: Use a positive number to represent the increase in temperature and a
negative number to represent a decrease in temperature.
Step 2: Find 4.5 + (-7.5).
Step 3: Start with 4.5
Step 4: Move l-7.5 l = 7.5 units to the left because the second addend is negative.
The result is negative -3.
The temperature decrease by 3 degree overall.
When using a number line, how is finding the sum where the two numbers have
the same sign similar to finding a sum wehre the two numbers (addend) have
different signs, and how is it different? In both methods the sign of the second
number (addend determines which direction to move to find the sum on the
number line. When the two numbers (addend) have different signs, the sum
has the sign of the number (addend) with the greatest absolute value.
B. Ernesto writes a check for $2.50. Then deposits
$6 in his checking account. What is the overall increase or decrease in
the account balance?
Step 1: Use a positive and negative to represent a deposit and a negative
number to represent a withdrawal or a check.
Step 2: Find -2.5 + 6
[Type text]
Step 3: Start at -2.5
Teacher will create a number line on chart paper.
Step 4: Move l6l = 6 uits to the right because the second addend is positive.
The result is 3.5.
The account balance will increase by $3.50.
Guided Practice:
Use the number line to find the sum.
1. -8 + 5 = -3
2. 2½ + (3/4)= -1/4
3. -1 + 7 = 6
Independent Practice:
4. ¼ + ½ =3/4
5. -1 ½ + (-1 ½) = 3
6. 3 + (-5) = -2
Day 3:
Mini-Lesson:
Finding the Additive Inverse: Opposite
p.70
Example 3:
A. A football team loses 3.5 yards on their first play. On the next play, they
gain 3.5 yards. What is the overall increase or decrease in yards (yds).
Step 1: Use a positive number to represent the gain in yards and a
negative number to represent the loss in yards.
Step 2: Find -83.5 + 3.5
Step 3: Use a number line and start at “-3.5”.
Step 4: Move l -3.5 l = 3.5 units to the right, because the second addend
is positive.
The result is 0. This means the overall change is 0 yards.
B. Kendrick adds ¾ cup of chicken stock to a pot. Then he takes ¾ cup of
stock out of a pot. What is the overall increase or decrease in the
amount of chicken in the pot?
Step 1: Use a positive number to represent chicken stock added to the
pot ad a negative number to represent chicken stock taken out of the
pot.
Step 2: Find ¾ + (- ¾ )
Step 3: Start at ¾, by plotting the point on the number line.
Step 4: Move l – ¾ l = ¾ units to the left because the second addend is
negative. The result is 0. This means the overall change is 0 cups.
[Type text]
Teacher will provide students with a Stick-It Together resource while in
the classroom. Students will work with a pair in a small group. Each
student will work together on a problem or question on a sticky note.
They will place all their sticky notes on a common page and read
through their answers. Taking the best part of each person’s answer,
they discuss and work together to build the best possible answer they
can.
Assessment Methods: (Best practice is to have 3 assessments in place for one class
period: Initial Assessment, Medial Assessment, and Final Assessment.)
Initial:
Answers to the Do Now.
8
Medial:
Independent Practice:
1. ¼ + ½ =3/4
2
2. 2-1 ½ + (-1 ½) = 3
3. 3 + (-5) = -2
Day 3: Your Turn:
Use the number line to find each sum.
9. 2 ½ + (- 2 ½ ) = 0
10. -4.5 + 4.5 = 0
Check for Understanding: Explain how to use a number line to find the
additive inverse or opposite of any number negative or positive.
Final : Exit Ticket
Exit Ticket:
1. S2amuel walks forward 19 steps. He represents the movement with a
positive 19 How would he represent the opposite of this number? -19
2. A contestant on a game show has 30 points. She answers a question
correctly to win 15 points. Then she answers a question incorrectly
and loses 25 points. What is the constestant’s final score? 30 + 15+ (25) = 20; the final score is 20- points.
[Type text]
Student Groupings:
 current data (such as assessment results, classwork, formative
assessments, etc.)
 student needs
 personality/strengths
Group/Pairings practice
Students are paired in groups of 3 in 740 in small working groups.
In 281, students are paired in groups of 3-4. Some students need to be
individ2ualized based on their level of understanding and work 1:1 with
a paraprofessional on areas of misunderstanding.
Group Work
Students will work on P. 72 problems 1-2 (Lower Learners) They will use the
number line to support with solving the answer.
Problems P. 72 3, 4, 5 (Higher Learners) Number line if needed.
Day # 3
All students will work on the same problem using the Stick-It Together
problem solving chart. Students will record all information on there.
1. At the start of the summer, Joan got a haircut that took off 1.75
inches. By the end of the summer her hair had grown 1.75
inches. What is the overall increase or decrease to Joan’s hair
inches.
Note: Students will create a number line that will range from -2 to +2
-2 -1.75 -1.50 -1.25 -1 -0.75 -0.50 -0.25 0 0.25 0.50 0.75 1 1.25 1.50 1.75 2
2. Victor borrowed $21.50 from his mother to go to the theater. A week
later, he paid her back $21.50. How much does he owe her? $0
3. Sandra used her debit card to buy lunch for $8.74 on Monday. On
Tuesday, she deposited $8.74 back into her account. What is the
overall increase or decrease in her bank account? $ 0
[Type text]
Domains of Knowledge (DOK)
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