Math Lessons

Estimated Time: 45 minutes
Lesson Topic/Subject: Comparing fractions and incorporating technology/Mathematics
Grade Level: 5
Comparing Fractions

• I. Goal: Learn strategies effective in comparing fractions.
  
• II. Objectives:
  The students should be able to:
  (5)1.9 identify fractional parts of regions and sets
  (5)1.10 compare and order fractions and/or decimals with like and unlike denominators [NS 1.6.6]
  (5)1.11 describe the place of fractions (including decimal notations) in the number system
  (5)1.12 identify and/or generate equivalent fractions
  
• III. Prerequisite learning or experiences: Students should know basic addition and be able to identify improper and proper fractions. Students should also understand the concept of ½.
  
• IV. Materials:
  · Math notebook for note taking for each student (retrieved from desk cubby)
  · One overhead projector and projection screen
  · 5 blank sheets of transparency paper for overhead notes
  · Overhead marker
  · One large whiteboard
  · Whiteboard marker
  · Fraction Circles (Model) kit from UNLV Curriculum Materials Library kit collection
  · Overhead Dot Dice from UNLV Curriculum Materials Library kit collection
  · Overhead Fraction Strips (Model) from UNLV Curriculum Materials Library kit collection
  · Worksheet pg. 95 from textbook blackline master (one for each student)
  · Textbook for each student turned to page 419 (retrieved from desk cubby)
  · Teacher’s guide textbook pages 416-419
  
• V. Procedures:
  a. Introduction: Students will engage in creating a chart of activities recently experienced during recess earlier that day (transparency 1). From this chart, the students will work out the results into fractions which they will compare.
  i. Which is greater, the number of students who played basketball or the number of students who jumped rope?
  ii. What do you notice about the fractions we came up with? All have same denominator.
  iii. Is there a way we can compare these proportions (fractions) with a symbol? Introduce or re-teach > < and =" (<"> 4/6
  2. Does this work for improper fractions?
  10/7 <> 5/3
  5. Students derive second concept:
  When the numerators are the same, the fraction with the lesser denominator is greater.
  
  With a pizza, the more slices you’ll need to cut, the smaller each piece will be.
  
  iii. Fractions relative to ½:
  1. Have one student from each table stand up and orally name a fraction equivalent to ½.
  Display the fraction strips chart I’ve created hiding behind overhead roll down screen.
  In a loud voice and using the math terms we know (numerator/denominator), describe the relationship with these fractions. The numerator is half the denominator.
  What would the denominator be for 120 if we wanted an equivalent fraction to ½? 240
  2. Comparing fractions to ½
  If I had 4/6, would I have more than ½ or less than ½?
  Compare 4/6 > 2/8 (note: we don’t have the same numerators or
  denominators but we can look at each fraction compared to ½)
  3. If there is extra time, mention fractions relevant to 1 whole.
  Compare 6/7 <>

Estimated Time: approximately 1 hour
Lesson Topic/Subject: Fractions and decimals/Mathematics
Grade Level: 5
Fractions and Decimals

• I. Goal: Learn how to write decimals from fractions.
  
• II. Objectives:
  The students should be able to:
  (5)
• III. Prerequisite learning or experiences: Students should know how to write equivalent fractions and solve division equations with smaller dividends than divisors.
  
• IV. Materials:
  · Math textbook for each student retrieved from desk cubby
  · Math notebook for each student retrieved from desk cubby
  · Overhead projector and display screen
  · Whiteboard and transparencies (2)
  · Markers for white board and overhead transparencies
  · 6 small whiteboards with markers (one for each table cluster)
  · 1 beach ball labeled with fractions
  · 38 pairs of decimal numbers and names on heart cut-outs (provided by
  · teacher and copied from Fractions & Decimals by Terri Breeden and Andrea Sukow,
  · pg. 28-29)
  · Red butcher paper for cut-out mounting and mounting tape
  · 1 sheet of construction paper for each student
  
• V. Procedures:
  
  a. Introduction: (7 minutes)
  Students will engage in a sponge activity that requires them to toss a beach ball around and orally name a fraction written on it. From this exercise, I will write the fractions named on the white board.
  
  6/10 13/100 8/100 17/1,000 3 14/100 22 1/1000
  
  i. Let’s write out these fractions by their names.
  (Six tenths, thirteen hundredths, three and fourteen hundredths, etc)
  ii. Note spelling on the margin of the white board.
  iii. We’re going to examine the different place values in a decimal.
  
  b. Developmental Activities:
  i. Creating place value guide (7 minutes)
  Students will fold construction paper and label the columns of place value.
  - Label tens, ones, ., tenths, hundredths, thousandths
  - Post for easy viewing
  - Incorporate the use of fractions when dividing paper in segments
  
  ii. Writing Decimals (4 minutes)
  The first transparency will be projected onto the whiteboard and I will
  demonstrate how to write the fractions written on the board as decimals
  using the place value guide.
  - Ask which decimal values are smaller and shortly discuss why
  - Explain the “and” of the decimal and why we do not say three hundred
  and seventy-six to represent 376 (three hundred seventy-six)
  
  iii. Reviewing the Concept with Hearts (5 minutes)
  The students will read their paper heart cut-out and find the corresponding
  heart of another student. The pair will tape their hearts onto the red
  butcher paper.
  
  iv. Converting Fractions to 10ths and 100ths (5 minutes)
  - I will teach the students that finding equivalent fractions with
  denominators 10 and 100 make it easier to write decimals.
  - Transparency 2 will model how to convert
  
  4 = 4 x 2 = 8 = 0.8 3 = 3 x 5 = 15 = 0.15
  5 5 x 2 10 20 20 x 5 100
  
  v. Practice and Review (10 minutes)
  - Students will practice on their whiteboards at the tables clusters. One
  student will use equivalent fractions to determine a decimal and then pass
  it on to another student at their table, using the following fractions.
  
  ½ 6 3/5 7/50 6/20 2/500
  
  0.5 6.6 0.14 0.3(discuss) 0.004
  
  vi. Working Backwards (7 minutes)
  - Students will practice converting decimals back into fractions on their
  white boards. Same passing technique applies so all students have
  chances to write and hold up their results.
  
  0.6 4.04 0.082
  
  vii. Using Division to Convert Fractions to Decimals (10 minutes)
  - Explain that 4/5 means 4 divided by 5.
  
  
  
  - Use division to model how to convert fractions into decimals:
  
  4/5 3/4
  0.8 0.75
  - How can you check these?
  - Re-convert 0.8 to 8/10 and remind students to simplify.
  
  viii. Review
  - 2 students will model their division and explain their steps for the
  following:
  
  1/4 5/8
  
  ix. Quarters and Benchmark Fractions
  - If there is enough time, talk about 4ths with students.
  1/4th = Quarter, $0.25
  2/4th = Two quarters, ½, $0.50
  3/4th = Three quarters, $0.75
  
  c. Culminating activities:
  - Students will be asked to open their texts to pg. 427 for the Check section. As a
  class, we will successfully give oral answers. Afterward, students will work on
  the Practice on the following two pages.
  - After ample time, the class will reconvene and share answers and questions.
  
  d. Extension:
  - Students who finish early will engage in an enrichment activity, Triple Treat, available as a blackline master (copies with me).
  - Additional review requires two students to play a matching memory game with decimal, fraction and image game cards also available with me. Another game for early finishers is a guessing game where one student writes a secret decimal number and the other students have to ask questions to figure out what the number is (i.e. Is the number in the tenths place even?)
  
• VI. Student Evaluation:
  During group work I will walk amongst the students and answer any questions they may have. In addition, I will take note of their strategies and commend students who derive new strategies and encourage others to do the same. At the end of the allotted time for seat work, I will address any questions students had about answers they could not understand.

Estimated Time: approximately 70 minutes
Lesson Topic/Subject: Circles/Math
Grade Level: 5
Segments and Angles Related to Circles

• I. Goal: Identify relationships between parts of a circle such as center, radius, diameter, chord, and central angle.
  
• II. Objectives:
  The students should be able to:
  (5)4.2 identify, define, draw, and describe points, line segments, rays, angles, and planes [NS/PS 4.5.6]
  (5)4.3 identify, define, draw, and describe intersecting, parallel, and perpendicular lines [NS/PS 4.5.6]
  (5)4.5 identify and draw circles and parts of circles and describe the relationships between the various parts such as arcs, diameter, and central angles [NS/PS 4.5.1]
  (5)4.10 describe uses of geometry in practical problems and situations
  (5)9.1 link new concepts to prior knowledge [NS 9.1]
  (5)9.3 use models to explain the relationship of concepts to procedures [NS/PS 9.3]
  
• III. Materials:
  · Sheet of butcher paper with vocabulary and diagram
  · Labeling marker
  · Overhead, projector, transparencies, marker and eraser
  · Whiteboard compass and protractor, regular compass, whiteboard marker
  · Whiteboard and marker for each table of students (6)
  · Circle stencils (6)
  · One math notebook and textbook for each child (in desk)
  · Colored and labeled ribbon (4 different colors, each 8 ft)
  · Sidewalk chalk
  · Stapler (to secure the ribbon around the students’ ankle)
  
• IV. Procedures:
  a. Introduction: (5 minutes):
  The students will brainstorm as a table any words they
  know of related to circles. A poster will be on the white board with a circle and lines of radii, diameter and a chord; the right half of the poster will be covered by the overhead screen. As a class we will talk about some of the vocabulary the students had come up with. This is a pre-assessment activity for me to know how much the students already know.
  
  b. Developmental Activities: ( 35 minutes)
  Students will trace a stencil of a circle into their notebooks while I illustrate one on the overhead and label the following, while introducing key characteristics. Students will label these segments and angles in their notebooks also.
  
  · Compass: tool used to draw circles
  · Circle, center: equal points from one center, how we name circles
  · Radius: 2r=d any line segment that connects the center to a point on the circle
  · Diameter: any line segment through the center that connects two points on the circle
  · Chord: any line segment that connects two points on the circle
  · Central Angle: an angle whose vertex is the center, 360˚ total
  
  We will review these concepts on the white board by revealing the vocabulary box and having students come to the poster and label the segments and angles.
  
  We will step onto the playground and create a human circle with a human compass. One student will stand at the center with a piece of ribbon tied around his/her ankle. I will stretch out the length of the ribbon and draw a circle. The students will stand in the circle and I will become the point. Circle G will be labeled by the students who have named ribbons. The ribbons will be of different colors and the students are to create and identify a radius, diameter, chord and central angle within our circle.
  
  c. Culminating activities (20 minutes):
  Student will complete pages 337 and 338 of their textbooks.
  
  d. Extension:
  Students who finish early will use a compass to practice drawing circles. They will label the key elements of a circle and will write a math word problem that requires one to know the basics we’ve learned about today.
  
• V. Student Evaluation (10 minutes): Throughout the delivery I will be asking students questions to determine whether they are following my pace. I will slow down or speed up as necessary. After 20 minutes I will go over the answers to the assigned problems and students will check their work and make corrections where needed.

Estimated Time: 70 minutes
Lesson Topic/Subject: Mean, Median, and Mode/Math
Grade Level: 5
Mean, Median, and Mode

• I. Goal: To Find the mean, median, mode, and range of a set of data, and choose the measure that best represents a given set of data.
  
• II. Objectives:
  The students should be able to:
  · (5)5.1 collect, organize, read, and interpret data using a variety of graphic representations including tables, line plots, stem and leaf plots, scatter plots, and histograms [NS/PS 5.5.1]
  · (5)5.7 model and compute measures of central tendency including mean, median, and mode[NS/PS 5.5.4]
  · (5)6.8 use technology, including calculators, to solve problems and verify solutions [NS 6.13]
  · (5)7.8 express mathematical ideas and use them to define, compare, and solve problems orally and in writing [NS/PS 7.16]
  
• III. Materials:
  · One math textbook and notebook for each student
  · Practice worksheets for each student (approx. 25)
  · Overhead, screen, writing sheet (2) and marker
  · One flower sales poster
  · Desk-bell
  
• IV. Procedures:
  a. Introduction: (10 minutes)
  
  Sponge Activity (5 min): On the overhead I will create a data file drawn from the students’ responses of their shoe size. I will plot these values on a line plot. By doing so, we have organized our information.
  
  Anticipatory Set Qs (5 min):
  · What information can we identify easily now that we have our data plotted this way? Category with the most, highest and lowest values.
  · What number occurs most frequently?
  · What value is the largest shoe size? Smallest?
  · If we were to re-write our data, what order can we now arrange them in?
  · How can we use an ordered set of values?
  
  b. Developmental Activities:
  Teaching the new ideas (20 min):
  Get out math notebooks to a clean page and hand out practice sheets.
  
  I will ring the class desk-bell a total of 10 sets, each set with the following amount of rings:
  
  6 8 4 3 8 3 8 9 7
  
  Students are to write down these values on the practice sheet in the Data File box.
  I will teach the following concepts to the students on the overhead as they take notes in their notebooks. After each concept I will stop briefly and have the students fill in a new portion of the practice worksheet.
  Mean: the average
  Median: the middle number
  Mode: the most frequently occurring
  Range: the difference between the highest and lowest values
  · How is the range useful? Good to know for scaling when graphing.
  
  Talk about it (4 min):
  1. In finding the mean, median, and mode of a set of data, in which case do you need to add all the data in the set? In which case do you need to order the data from least to greatest? Mean; median
  2. If there are 9 values listed in order, which value will be in the middle? If 8 values are listed in order, how do you find the middle value? The fifth value; find the mean of the fourth and fifth values
  3. Can a set of values have more than on mode? No mode? Explain. Yes; yes. A set of values has more than one mode when 2 or more values appear the same number of times. A set of values does not have a mode when all values appear the same number of times
  
  Check (8 min): (use poster on whiteboard)
  Ask volunteers to:
  1. Find the mode
  2. Find the median; how many values are above/below the median?
  3. Find the mean
  4. What is the range?
  5. If the gardener becomes upset and complains that too many flowers are being picked by each student, which value would you use to describe the amount of flowers each child picked?
  6. If this contest was for each student to sell the most flowers, which value would you use?
  
  c. Culminating activities (20 minutes):
  Students will complete pg. 284 from their math textbook. We will review the answers at the end of the class.
  
  d. Extension:
  Students who finish early will:
  · Create a set of five numbers for which the mean, median and mode are equal
  · Complete #18 on pg. 285
  
• V. Student Evaluation: To determine whether the students have understood the material I will informally assess their progress through questions during the instructional period. While they are doing seatwork from the textbook, I will walk around and overlook their answers, listen to solution strategies and answer any questions pertaining to understanding. The answer review at the end of the period will additionally inform me of the students’ progress and understanding levels.