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Over the course of the summer, I designed and implemented a six-week
lesson plan in mathematics. During the course, my two classes studied
fractions, decimals, and percentage, but we also covered a unit on negative
numbers. Here are six of the lessons I did with the class throughout the
summer. (Each lesson was designed for 45 minute block).
Introduction to Fractions
Objectives:
Students will be able to:
- Write a fraction representing a picture or situation (i.e. fraction
of given balloons that are red).
- Identify the numerator and denominator of a fraction
- Explain, in their own words, what a fraction is
Materials:
- M&M challenge sheets
- M&Ms (a mix of peanut and plain)
- Markers
- Pencils
- Napkins
Procedure:
Review the concept of a fraction with the students, introducing the
terms numerator and denominator. (Students had seen fractions in
their education - so in part this was a review). Explore some common
fractions the students might have seen: such as pieces of a pizza or
of a candy bar, or the fraction of total students in the room wearing
sneakers.
Pass out m&ms and a copy of the M&M challenge worksheet to
each student. Explain to students how to make a "fraction wheel"
by counting up the total of m&m's and dividing up a circle into
that many "equal parts." Have students spend the rest of the
period working through the sheets and drawing fraction wheels. Examples
of Student Work
Assessment:
Students' ability to make fraction wheels.
Homework:
Worksheet
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The Amazing Multiple
Objectives:
Students will be able to:
- Understand what a multiple is and find some multiples of a given
number
- Find the lowest common multiple between two numbers
- Identify fractions that are equivalent
Materials:
- "Go Fish"
Cards (specially adapted to have equivalent fractions on
them)
- A large sheet of paper with the numbers 1-60 pre-written on it.
Procedure:
Ask the students if they know what a multiple is? Either way, discuss
with the students what a multiple is.
The Multiple Song:
Have the list of numbers up on the board. Explain to students that
they will be making a "multiple song." One student will be
assigned to read the numbers one through sixty aloud slowly. Two other
students will be assigned to make a noise of their choosing when a multiples
of a their number is called. (Each student will have a different numbers)
The noise could be clapping, stomping, etc.
As the students are playing the "song," ask students to observe
what happens when they reach the lowest common multiple (without using
this terminology). When the students say that what happened was that
both people made noise, draw out that this number must be a multiple
of BOTH numbers. Define this as the lowest common multiple.
Have the students play a few more rounds, this time coming up with
predictions for what the LCM will be. Then have the students brainstorm
strategies for finding the LCM.
Review of material covered in previous class:
With the remaining time have the students play Equivalent Fraction
Go Fish (in each deck are four equivalent fractions, students must make
pairs of two equivalent fractions to discard them from their pile).
Assessment:
Observation of kids during multiple activity and go fish game.
Homework:
Worksheet
Adding Fractions with Different
Denominators
This was the second time students had seen this concept
presented in the classroom.
Objectives:
Students will be able to:
- Add and subtract fractions with different denominators by first
converting the fractions to fractions with the same denominator
- Demonstrate visually why you need to convert the fractions to ones
with the same denominator
Materials:
- Scissors
- Glue
- Construction Paper with pre-made slots for the activity below (including
+ and = signs)
- Copies of the packet of circles (see attached) one per group
Procedure:
Activity:
Have the students break up into groups of two or three. Give each group
a pair of scissors, glue, some construction paper, and a packet of fraction
circles (circles that are broken up into varying numbers of equal pieces).
Have the students solve the following addition problems in the following
way. First, they should cut out the fraction of the wheel that represents
the two addends. In the example to model this (1/2 + 1/4 = 2/4 + 1/4
= 3/4) it is one-half and one-quarter Next they should convert these
fractions visually to ones with common denominators by cutting out one-half
as two quarters and one quarter as one-quarter. In the last image, they
should glue down the answer, which is three-fourths. Model this on the
board with an example:
Then have students solve the following two examples by cutting out
the appropriate fraction pie pieces, and reassembling them visually
to demonstrate the equivalence and addition of the fraction pairs:
1/12 + 5/6 =
3/4 + 1/6 =
Links to Student Work
Extra Time?
If the students finish early, they can play games of 24.
Assessment:
Look at the products of student work.
Homework:
Students will continue working on a "textbooks"
on fractions.
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What is a Decimal?
Objectives:
Students will be able to:
- identify the place values in a decimal and say what each place value
represents
- understand what place value after the decimal represents and begin
to understand the connection between fractions and decimals
- add and subtract numbers in decimal form as pertaining to money
Materials:
- A round object to be used as a decimal point in the human decimal
- Pieces of construction paper with numbers written on them
- Guess Who with numbers
boards (one per student)
- Paper receipt paper made from half of an index card (two-three per
student)
- Index cards with picture and prices of food items for a classroom
supermarket
- Fake paper and coin money
Procedure:
Hook:
Ask students what math skills they need when they are out shopping
at a supermarket. List these on the blackboard. Ask students what type
of number money is written out as (most of the students should already
have learned something about decimals in school).
Activity 1:
Reintroduce the concept of place value by placing a price on the board.
Have the students try to label each place value.
Activity 2:
Write out the various place values on the board. Then, have the students
stand against the board holding a construction paper number in front
of one place value. Hold a decimal point where the decimal point begins.
The students are now a human decimal. Have them read the number aloud
(4 hundred and thirty and seven and two tenths, for example). Then have
the students reorganize themselves and read out the new number a couple
of more times.
Activity 3:
Play Guess Who with decimals! Have the
students ask questions such as "does your number have a six in
the tens place." Each student gets a board and will cross off numbers
when they have eliminated them.
Activity 4:
Playing Supermarket: Have the students use prior knowledge to go shopping
in the supermarket. Set up index cards with food items and prices on
them against the blackboard. Have students get in pairs. One student
is given twenty dollars and should pick up a couple of items. They will
give these items to their partner who will write up a receipt totaling
the item prices and finding the change from twenty dollars. The pairs
should then switch roles. Examples of receipts.
Assessment:
Look at the receipts the students have produced.
Homework:
Worksheet and creation of a restaurant menu
for use in class tomorrow
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Review for the Decimal and Percentage
Exam
Objectives:
- Students will review the material for the upcoming exam (adding and
subtracting decimals, long division with decimal answers, rounding,
percentage)
Materials:
- Student homework from previous night
- Envelopes for each scavenger hunt location containing a clue.
- Copies of each scavenger hunt questions
- Copies of each scavenger hunt reward letter and the final code
Procedure:
Ask the students to take out their homework from the night before (a
review sheet in which they had the correct answers given to them). Then
ask them which questions they got wrong and go over those problems,
taking suggestions from the rest of the class.
Prior to the lesson, the teacher should have set up envelopes with
a review problem in them outside in the hallway. Students start off
with one problem. When the solve their problem, they should check their
answer with the teacher. If they get the problem correct, then they
are handed a new clue of a location to look for a problem. On the back
of each problem is a letter and number. When the students get all of
the clues correct, they will get an answer code, which tells them in
what order (based on the number) to put the letters on the back of the
clues in. This will spell out a location in the school where they should
go to find their "surprise." (This surprise was that we would
be eating munchkins after tomorrow's test)
Assessment:
Are the students able to answer the questions?
Homework:
Study for Exam
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Introduction to Negative
Numbers
Objectives:
Students will be able to:
- understand what a negative number is
- give a couple of real world examples of them
- subtract any two whole numbers to get either a positive or negative
number
Materials:
- Guided Note-Taking Sheet on Negative Numbers (see attached).
- Bingo Sheets with positive and negative numbers
- Construction Paper and Markers
- Staircase labeled as a number line with sheets of paper.
Procedure:
Hook:
Tell the class that you are going shopping in a store. Use the following
questions
to introduce negative numbers.
Questions for discussion: Imagine I have twenty dollars, do I have
enough to pay for a $15 skirt? Now imagine I have twenty dollars and
I want to buy a $25 dollar skirt. Will I have enough? How much more
would I need?Well, let's say my friend was with me and she lent me the
$5 dollars. How much money would I have at the end of the day?
What is a negative number?
Introduce the idea that you really have a debt of $5. Tell the students
that this is a negative number, or less than 0 dollars. Go through the
guided note sheet (see attached) and have students write in the definitions
of negative and positive numbers as less and greater than zero, respectively.
Then have the students give examples of negative and positive numbers,
which will be written on the board for students to copy in their note
sheet. Then draw a number line on the board and have the students supply
answers for what goes in what place on the line. They will copy this
onto their sheet.
Subtracting Two Positive Numbers:
Have students create their own number lines on pieces of construction
paper and markers. Then have them get up and follow you out of the room
into the labeled staircase. Have a landing labeled as 0, and steps going
down labeled as negative numbers, stairs going up labeled as positive
numbers. Have students move along the stairs to simulate adding and
subtracting whole numbers. (i.e. for 2 - 4, have a student stand on
the +2 step and move down 4 spaces to get to the answer -2).
Now have students answer the five questions on the back of the guided
note-taking sheet. Go over these questions in the large group.
Ask students if they see any pattern to the answers. Hopefully a student
will notice that the answers to 5 - 4 and 4 - 5 are the same except
for sign. Derive the rules for determining the sign (if the first number
is bigger, etc.) with the children.
Practice Time:
Give each child a bingo sheet. Explain the rules of bingo. You will
be calling out a subtraction problem and they should cross off the appropriate
answer to this problem on their bingo sheet. After each problem is called,
have one student relay the answer to the class so that no one crosses
of the wrong number and problems in comprehension can be addressed.
List of Possible Bingo Calls:
8-8 = 0
7-8 = -1
9-15 = -6
10-3 = 7
2-9 = -7
15-11 = 4
8-2 = 6
8-10 = -2
5-4 = 1
14-18 = -4
6-3 = 3
3-6 = -3
10-5 = 5
5-14 = -9
3-8 = -5
16-8 = 8
8-16 = -8
11-2 = 9
1-10 = -9
12-2 = 10
1-11 = -10
22-11 = 11
2-13 = -11
24-12 = 12
Evaluation:
Students will be evaluated with respect to their verbal answers during
bingo and their written answers during the five questions.
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