Week 1-Mathematics Lesson Plan

WEEK 1—MATHEMATICS LESSON PLAN

Positive and Negative Numbers

Note to the teacher: We want this to be an exciting and challenging start to math this year.  Students need to feel that math will not be as usual.  One goal throughout the year is to tie math to real life so that students see the connection of math to every day events.

Day One:

A Daring Beginning. We will use the You Tube Video in which a girl explains how she feels about math.  Students will watch the video and then react to it using a computer to table blog their reaction.

After watching the video, have the students discuss their reaction to the girl’s comments and plan a response that will be shared through the blog site.

Blog on the following site:

Conclude that while many students probably share her reaction to math, maybe it is because she learned math through a textbook and the student never really learned why the math she was doing could be useful…besides, she has many mistaken ideas.  Throughout the year, we will be learning things she brought up, and by the end of the year, the students in this class will listen to her again and find her mistakes and give the correct explanation.  We will even plan to make our own You Tube Video version of why we need math.

Day Two:

Our first Math unit is going to focus on negative and positive numbers.

So who cares?

Show the following pictures:

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Ask the students to discuss what they saw in these pictures that indicates we really do care about negative and positive numbers.  What did they see, how do these numbers bear on our lives?

Activity:

Twenty one students are given cards: negative ten through positive ten.  The first task of this group is to have them situate themselves in the correct order.  Those remaining in the seats are to check and see if the number line is correct.

Then the students who are sitting down are asked to take the place of numbers standing there (eg. Take the place of negative six.)

Activity:

Students are given a strip of adding machine tape 42 inches long.  Teacher guides the students from a living number line which was just created, to a paper number line using numbers negative twenty to positive twenty.

Folder the paper in half for the zero point, mark one inch intervals on both sides and then help the students put in the numbers.  Use the extra inch for arrow spaces. ( this should be kept in the pocket of the student notebook binder.)

Activity:

Tour the number line with the students.  Have them put their finger on:

Negative six, positive ten, zero, fifteen, negative twenty, positive three, etc.

Activity:

Use the number line to solve problems:

  1. Mary had five dollars and received three more.
  2. Mary had twenty dollars and paid six Itunes.
  3. Jose noted the temperature was five degrees outside yesterday and suddenly it dropped twelve degrees…what is the temperature now?
  4. The fish were swimming at 8 feet below sea level and jumped up five feet above the water, how far did they travel?

Conclusion: Positive and Negative numbers are a part of our lives and are important to learn.

Day Three

We are going to use something other than a number line today for positive and negative numbers.

Activity:

Students will be given a zip lock bag full of twenty positive and twenty negative tile spacers.

Keep the bag closed while an explanation is given.

Teacher Explanation:

A positive tile represents positive one.

A negative tile represents negative one

What happens when we put them together?

( -1 + 1 = 0)       They become a zero sum pair.

Teacher explanation continued:

What happens when you have four positive tiles and two negative tiles?

(teacher demonstration)

Two positive tiles remain.

Show the equation:   +4 +-2 = +2

What happens when you have six negative tiles and three positive tiles?

(teacher demonstration on the overhead)

Three negative tiles remain.

Show the equation:      -6 + +3 = -3

Now it is the student’s turn. Each student uses their own bag and a white piece of paper.

Teacher will give verbal situations for the students to work out in tiles and then write on the paper the equation.

  1. 8 positive tiles, four negative tiles
  2. 10 positive tiles, fifteen negative tiles
  3. 6 negative tiles, thirteen positive tiles
  4. 0 positive tiles, seven negative tiles!

WHAT HAPPENS!?

Teacher demonstrates again:

Now we are going to move on when we have all negative or all positive tiles.

Demonstrate: three positive tiles and five positive tiles.

Show the equation: + 3  +   + 5  =  +8

Demonstrate: negative two plus negative seven tiles

Show the equation: -2  + -7  =  -9

Now students try on their own with the paper and the tiles:

  1. You are scuba diving at seven feet below sea level and you dive down five feet deeper.  At what depth are you now?
  2. You had ten dollars in your savings account and you deposited five dollars more.  How much money do you have saved now?

Teacher Explanation:

All subtraction problems we change to adding the opposite.  For example:

  • +5 –  2 gets changed to +5 + the opposite of two which is -2.  Now it is the same as what we were doing in addition and we can proceed with no problem!
  • -5 – +2 gets changed to -5 +  the opposite of positive  two which is -2.
  • -5 + -2 = -7
  • -5  – -7 gets changed to -5  +  the opposite of the negative seven which is +7
  • -5  +  + 7= +2
  • +5  – +7 gets changed to +5 + the opposite of the positive seven which is -7
  • +5  +  -7 =  -2

Now the students try on their own with the paper and the tiles:

  1. You have ten dollars but you need fifteen for a purchase, how much do you need to borrow?
  2. You are swimming at three feet below sea level and you dive down six more feet.  What depth are you now?
  3. Three minus negative eight

Day Four

Teacher Explanation:

We did a great job with tiles, but what happens when we do not have enough titles to figure out a problem AND the two signs are different

Example

  • + 50  +  +30  = +80
  • – 34   +  – 18  =  – 52

Now when the signs are different:

  • +82  +  -67  =

Ignore the signs

Chose the larger number’s sign  ( 82 is bigger so put that sign in your answer.)

Then take the difference of the two numbers ( smaller from the larger regardless of the sign)

  • ( 82-67 = 15 )
  • + 82  +  -67  =  + 15
  • + 32  +  -60  +

Ignore the signs

Chose the larger number’s sign ( 60 is bigger so put that sign in your answer)

Then take the difference of the two numbers ( smaller from the larger

Regardless of the sign)

  • (60-32 = 28)
  • +32 +  -60  = -28

Students will now practice this with their white boards:

  1. -48  +  +26  =
  2. +15  +  – 25  =

Remember what to do if it is subtraction when doing this practice:

  1. -31   –   +16  =
  2. -42  –   –  21  =

Students will watch a silent power point made by the girl they met the first day.  She was asked to explain positive and negative numbers without getting her audience confused.  Let’s see how she does. This power point is a slide show that runs by itself. When she gets to problems to solve, students can say the answer before she shows it, it they like.

http://www.lexington1.net/technology/instruct/ppts/mathppts/Numeracy%20&%20Concepts/integers1.ppt.ppt#264,2,Definition

After the slide show:

  • How did she do?
  • Was anything confusing?
  • Would you have liked to have watched this before we learned what we have this week? Or was it better after the work we have done?  Why?

Teacher Explanation:

Students need a one inch notebook with binder paper for each unit.  Today is our first day for notes.   To show students how nicely notes should be written, they will be given this page of notes, with some spots to fill in and the entire page should be discussed with the class.  Each student will be given a color which they will write in their agenda which they need to know for the next day.

Positive and Negative Numbers: Unit One

Vocabulary:

  • Integer: a positive or negative whole number and zero
  • Positive : more than zero
  • Negative: less than zero
  • Opposite: a integer and its counterpart ( +3, -3)
  • Zero Sum Pair: when a number and its opposite are added together the result is zero.
  • Number line: negative numbers are on the left, positive numbersare on the right and zero is in the middle.

Notes:

Throughout the year, we will be learning things the video girl  brought up, and by the end of the year, the students in this class will listen to her again and find her mistakes and give the correct explanation.  We will even plan to make our own You Tube Video version of why we need math.

Positive and negative numbers are used everyday in many situations:

List three:

  1. __________________________________
  2. ___________________________________
  3. ____________________________________

Number lines are one way to do operations with positive and negative numbers.  ( refer to the number line in the pocket of your binder)

  • A positive tile represents positive one.
  • A negative tile represents negative one

What happens when we put them together?

  • ( -1 + 1 = 0)       They become a zero sum pair.

Illustrate using hand drawn spacers to show zero sum pairs

What happens when you have four positive tiles and two negative tiles?

  • Two positive tiles remain.
  • Show the equation:   +4 +-2 = +2

Illustrate this process using hand drawn spacers

What happens when you have six negative tiles and three positive tiles?

  • Three negative tiles remain.
  • Show the equation:      -6 + +3 = -3

Illustrate this process using hand drawn spacers

When we have all negative or all positive tiles.

Demonstrate: three positive tiles and five positive tiles.

  • Show the equation: + 3  +   + 5  =  +8

Demonstrate: negative two plus negative seven tiles

  • Show the equation: -2  + -7  =  -9

SUBTRACTION

All subtraction problems we change to adding the opposite.  For example

  • +5 –  2 gets changed to +5 + the opposite of two which is -2.  Now it is the same as what we were doing in addition and we can proceed with no problem!
  • -5 – +2 gets changed to -5 +  the opposite of positive  two which is -2.
  • -5 + -2 = -7
  • -5  – -7 gets changed to -5  +  the opposite of the negative seven which is +7
  • -5  +  + 7= +2
  • +5  – +7 gets changed to +5 + the opposite of the positive seven which is -7
  • +5  +  -7 =  -2

How to work with integers  when the signs are different:

  • +82  +  -67  =

Ignore the signs

Choose the larger number’s sign  ( 82 is bigger so put that sign in your answer.)

Then take the difference of the two numbers ( smaller from the larger regardless of the sign)

  • ( 82-67 = 15 )
  • + 82  +  -67  =  + 15
  • + 32  +  -60  +

Ignore the signs

Choose the larger number’s sign ( 60 is bigger so put that sign in your answer)

Then take the difference of the two numbers ( smaller from the larger

regardless of the sign)

  • (60-32 = 28)
  • +32 +  -60  = -28

When subtracting unlike signs, you must do the rules for the subtraction and then add the opposite, then choose the larger number sign for your answer, and then take the difference of the two numbers.

  • -42  –  -31   =

Do the rules for subtraction first:

Add the opposite

  • -42   +   +31  =

Ignore the signs

Choose the larger number’s sign (42 is bigger so put that sign in your answer)

Take the difference of the two numbers ( smaller from the larger

regardless of the sign)

  • (42-31 = 11)
  • -42  +  +31  = -11

I have taught these notes to at least one parent at home.  The problems given on the practice sheet were also completed.

Parent Signature _________________________________ Date_______

Name ____________________________________________

Practice Sheet

Refer to your notes and show your work.

  1. -3 + +8  =
  2. +6  + -14 =
  3. +5   –  + 8  =
  4. – 7  –  -14  =
  5. +62  +  -32 =
  6. -36   +  +20 =
  7. -58   –   +20 =
  8. +35  –   -35

More:

  1. Billy was scuba diving in the ocean.  He started swimming at 10 feet below sea level.  He then chased a fish that swam 8 feet towards the bottom of the ocean.  What depth is Billy now?
  2. The high temperature for this day is 108 degrees F.  The low for the same day in history is -27 degrees F during the ice age.  What is the difference between the high and the low for this day?

Day Five    Circuit Review and Quiz Assessment

Today is the review for the first week. Center  circuit will be used.  Students need to learn the rules for stations and they need to have the overview for each station before beginning.  Each station will last eight minutes.  15 minutes is needed at the end for the first assessment quiz.

Rules

  • students must remain in the assigned group
  • no one is talk loudly in groups
  • no movement out of group
  • when the timer goes off, students push in chairs, and move to the next group and waste no time.
  • One timer is selected for the circuit.

Center  One:  Checking Answers

Needed:

  • Homework practice sheet

Directions:

review answers in this group and be sure that everyone has the same answers and understands the process.

Center  Two: Vocabulary Practice

Needed

  • Laptop with a power point of the vocabulary
  • White board and markers

Directions:

Each student in the group must give the definition for each word

Wrap up:

One word at a time, each writes the word and definition and check within the group.

Center Three: Note Correlation and review

Needed

  • Practice sheet and notes

Directions:

Find in the section in the notes that explains how to do each practice problem and re-read that section of notes no matter how many times it is used.

Center  Four: Practice as a group

Needed:

  • White boards and markers

Each member of the group makes up a problem for the group to solve.  The one who give the problem must be able to check the answers.

Station Five: Teacher  Re-Teach

  • Needed: practice sheet, agenda, and notes

This station is teacher guided and stresses word problems

The teacher will check to see if notes are signed and practice sheet is done.

Comments can be made in the agenda

Once the circuit is completed, students return to their assigned seats and the quiz is given.

Name ____________________________________________ Unit One Quiz 1

Show your work.

  1. -5 +  +12  =
  2. +4  + -17 =
  3. +3   –  + 6  =
  4. –9  –  -16  =
  5. +56  +  -21 =
  6. -43   +  +26 =
  7. -72   –   +35 =
  8. +31  –   -156 =
  9. Sandra is working on a sail boat.  She begins the day working on top of the sails which are 27 feet above sea level.  By the end of the day she is working on the bottom of the boat which is twelve feet below sea level.  What is the distance from the top to the bottom of the boat?
  10. Yesterday’s temperature in Alaska was 18 degrees F below zero.  Today it was 22 degrees cooler.  What is today’s temperature?

Vocabulary: write the word that is described

1. _____________  +3  +  -3  = 0

2.   _____________   + 4, -5, -16, +16, + 33, 0

3. ______________   positive numbers on the right, negative numbers

on the left

4. ______________   below zero

5. ______________   +4   -4;    +15   -15;  -8  +8

6. ______________   above zero

Why should you care about positive and negative numbers?

 

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