Title:
Objective:
Students will gain an understanding of perimeter, measure perimeters using various measurement tools and practice estimating perimeters.
Materials:
Tools for measurement in both English and metric measures (yard sticks, rulers, meter sticks, measuring tapes, metal construction rules), twine or rope
Audience targeted/level:
Type of setting:
Time required:
30 min or more, depending on the number of areas to measure
Activity:
Using various measurement tools each group will measure around items in the room. The following are examples of the types of items students can find the perimeter of and the lifeskill involved.
windows - weather stripping or molding classroom - baseboard or wallpaper borders (Students can develop thinking skills when they determine what part of the perimeter of the room would not need baseboard or borders.) posters - molding required for a frame
Estimation skills can be developed by measuring off lengths of twine in various lengths. I like to use one and ten foot lengths. Having pieces of twine in these two measurements enables students to develop a sense of size without the necessity of a specific measurement.
Evaluation:
Students have fun with this activity and develop useful life skills.
Recommended Resources:
Modifications:
Title:
Objective:
To develop an understanding of the concept of perimeter and to use nonstandard units to measure perimeter,
Materials:
Audience targeted/level:
Type of setting:
Time required:
Activity:
Using one side of the green triangle as the measurement "unit" the groups will determine the perimeter of each of the other shapes. After each group has determined the perimeter of all the shapes, each member of the group can make a design or pattern and calculate the perimeter. Students can calculate the perimeter of each others designs.
Evaluation:
Recommended Resources:
Modifications:
Title:
Objective:
To develop an understanding of volume, to calculate simple volumes
Materials:
Cardboard, tape, rulers, mat knives,
Audience targeted/level:
Type of setting:
Time required:
30 minutes prep time (to be done once)
Preparation:
Before class or during if desired, cut pieces of cardboard (large boxes work well) into square foot pieces. Six of these pieces can be assembled with wide tape into a one cubic foot block. This block enables students to see what a cubic foot looks like. Over time many of these blocks can by constructed and be temporarily assembled into a cubic yard. Cubic inch blocks can be constructed also or wood blocks can be purchased.
Activity:
With the cubic inch blocks construct a cubic foot. With the cubic foot blocks construct a cubic yard. Count the blocks necessary to make each shape. Using cubic inch blocks fill various boxes to estimate the volume of each box.
Use cubic foot blocks to estimate the volume of a file cabinet, storage cabinet or closet. This can be done by estimating how many blocks would fill each drawer or shelf Using cubic inch blocks build shapes with blocks. Students might construct regular and irregular shapes similar to illustrations in GED® books. Students can use the volume formula to calculate the volume of each solid shape. By counting the blocks required to Construct each shape the results of the volume formula can be verified.
Evaluation:
By building shapes with blocks, especially irregular shapes, students can better visualize the many ways the volume can be calculated.
Recommended Resources:
GED® text book with illustrations of irregular shaped volume problems.
Modifications:
Any size small block (ABC, or 2 cm.) can be used for this activity. Instead of using cubic inches use cubic units.
Title:
Objective:
To understand the concept of area, measure the area of shapes and estimate the area of shapes.
Materials:
Large sheets of cardboard. paper, graph paper, rulers, knives and scissors.
Audience targeted/level:
All levels of ABLE students
Type of setting:
Time required:
Activity:
Either before or during the activity each group will measure and cut out a square foot out of cardboard. Students will then estimate how many square inches it will take to cover the square foot. Using paper, students will measure and cut out square inch pieces of paper and glue them to the square foot. How close was the estimate? (Students usually do not need to cover the entire piece of cardboard to develop an understanding of area.)
Using square foot pieces of cardboard, the students can construct a square yard of cardboard. This activity gives visually meaning to the size of a square yard.
Floor tiles are frequently a square foot in size. These can be used to determine area of a floor and give understanding to the unit "square foot."
Using graph paper mark off shapes. How many square units is it? On graph paper draw a rectangle or square of a specific size (8 by 4). Calculate the area using the area formula. Then check your answer by counting the square units inside the shape.
After calculating the area of a square or rectangle, cut the shape in half on the diagonal. This is an easy way to illustrate why the area of a triangle is A=1/2 BH.
Evaluation:
Recommended Resources:
Modifications:
Title:
Objective:
To visualize the volume of shapes
Materials:
Worksheet (follows), blocks if desired
Audience targeted level: All levels of ABLE students
Type of setting:
Small group or individual activity. This works well as a start up activity for class as there will likely be a lot of difference in time required for completion.
Time required:
Activity:
Allow a students the opportunity to work in groups to determine the number of cubes in each shape. After allowing time to initially solve the problem ask if students would like to use cubes. Does this make the problem easier? Did any answers change? What would the volume of each shape be?
Evaluation:
Recommended Resources:
Modifications:
Cube Count
Can you calculate how many cubes are in each of the shapes below?
Title:
Circles - Radius, Diameter, Circumference
Objective:
To understand radius, diameter, circumference, and pi and the relationship between these concepts pertaining to circles.
Materials:
Plastic lids in a variety of diameters, tape measures, rulers, & calculators
Audience targeted/level:
Type of setting:
Time required:
Activity:
Most plastic lids have a dot or a bubble in the center. Use this dot as the center of the circle. Measure from the dot to an edge. this is the radius. Try measuring from the dot to several points on the edge of the circle. (radii should be equal.)
Measure from edge to edge (ruler or tape measure should cross the dot on the lid) This represents the diameter. Measure 2 radii. Is there a relationship between the diameter and the radius?
Use the tape measure and measure the outer edge/around the lid. (This can also be done with string. Just wrap the string around the, cut it to length, then use a ruler to measure the string.) This measurement represents the circumference. Divide the circumference by the diameter. Divide to the nearest tenth.
Tabulate the values of the various lids.
Compare C/D values. They should all be at least 3! Explain what pi (the ratio of C to D). Circumference formula C =piD. The students are now ready to use the circumference formula to solve problems.
Evaluation:
This activity works well with all levels of ABLE students. By working in groups those students with lower math skills can receive assistance with the division of C/D. Calculators are great to use with this activity too. Have had students comment several weeks after the class how much they enjoyed this activity. They gain an understanding of pi and how math makes sense.
Recommended Resources:
Modifications:
If you don't have enough variety in size of plastic lids use other round objects (paper plates, cans, etc.). This lesson helps students realize they can estimate the value of pi as the number 3.
Title:
Area of Squares and Rectangles
Objective:
To develop strategies for finding the area of squares and rectangles
Materials:
Audience targeted/level:
Type of setting:
Time required:
Activity:
Draw several squares and rectangles or various sizes on graph paper.
Calculate the areas. Do a number of problems. Develop a formula to show how the area was found.
Evaluation:
Recommended Resources:
Modifications:
This same activity could be done except this time the perimeter of the rectangle or square could be found.
Title:
Lines and Angles All Around Me
Objective:
Students will identify right, obtuse and acute angles. Students will identify perpendicular and parallel lines.
Materials:
Classroom supplies, manuscript alphabet, city maps, etc.
Audience targeted/level:
Type of setting:
Time required:
10 minutes or more if desired
Activity:
Using objects in the room, students look for examples of different types of angles and line relationships. The groups might compete to see which group can find the most examples in each category.
Using an alphabet chart or sample manuscript alphabet, students will look for examples of angles and line relationships.
Evaluation:
This can activity can serve as a quick way to reinforce understanding of angles and line relationships.
Recommended Resources:
Modifications:
A city map can be used to look for angles and line relationships.
Title:
Visual Thinking Triangles
Objective:
To learn there are many different shapes in a simple diagram.
Materials:
Visual Thinking worksheet (follows) or a similar drawing with questions
Audience targeted level:
Type of setting:
Individual or small groups
Time required:
Activity:
Part 1 - Discuss how to name a triangle (using the vertices). Review the properties of the following triangles: equilateral, isosceles, scalene, acute, right, and obtuse.
Part 2 - Use the discovery method. Let the class determine how many triangles there are for each question before it is discussed.
Part 3 - Talk about methods used to be sure that answers are correct. trace triangles with colored pencils or their fingers. Use a ruler to measure sides to be sure sides are equal. Use a comer to a sheet of paper to prove there is a right angle. Be sure to talk about how triangles overlap and to visualize just the triangle they are looking at.
Evaluation:
Recommended Resources:
Modifications:
This same diagram could be used to look for right angles, acute angles, obtuse angles, straight angles and reflex angles.
Visual Thinking
The triangle below has three sides of equal length. Answer the following questions by studying the triangle. Don't foget - the triangles may overlap!
1. How many triangles can be foind in the figure above?
2. How many equalateral triangles are there?
3. How many scalene triangles are there?
4. How many isisceles triangles are there?
5. How many right triangles are there?
6. How many acute triangles are there?
7. How many obtuse triangles are there?
8. How many quadrilaterals can be found in the figure?
Title:
Objective:
To introduce students to the geometric concepts of measuring, length, width and area, Students will gain skills in wallpapering, measuring, area formula slid working in a group.
Materials:
Inexpensive, leftover rolls of wallpaper, (purchased with a discount as a math teacher), scissors, rulers, yardstick, tape, chalk board or tables.
Audience targeted/level:
Type of setting:
Groups of three to four students
Time required:
1 1/2 to 2 hours, depending on length of introduction to the concepts and formulas for area and perimeter.
Activity:
Evaluation:
Students learned cooperation and problem-solving in a group. Most were enthusiastic about the project. In fact, they were so enthusiastic that a member of each group took home the remainder of the roll and the cut pieces to use at home.
Students also learned the importance of accuracy and dedication to their project. Group skills were noted and discussed. Rewards were given to the whole class for their cooperation and one group was singled out for an extra prize for their outstanding professionalism.
Recommended Resources:
Modifications:
Title:
Objective:
To distinguish between perimeter and area, to apply the theoretical concepts of perimeter and area to practical situations
Materials:
Floor plans from the local newspaper or home magazines (Better Homes and
Gardens, ). Copy and enlarge the plans, add dimensions for the rooms if needed. See example which follows.
Audience targeted/level:
Type of setting:
Time required:
30 to 45 minutes. More depending on the number of tasks and calculations required.
Activity:
Use this lesson as a review or reinforcement of the concepts of area and perimeter. Students will practice finding perimeters for "baseboards" and areas for cement and carpeting. Calculate the number of square tiles (I foot and 9 inch) for bathrooms and basements. The activity also reinforces decimal multiplication.
Evaluation:
Recommended Resources:
Contemporary's Real Numbers: Geometry Basics (p. 45) has a good example of this type of activity.
Modifications:
This activity can be extended even more by actually calculating costs for the carpet (changing square feet to square yards is necessary for this), baseboard, amount of paint needed in rooms, etc.
Title:
Triangles, Triangles, Triangles
Objective:
To evaluate a group of triangles for differences.
Materials:
Paper, pencils, and scissors
Audience targeted level:
Type of setting:
Classroom or small groups
Time required:
Activity:
Draw a series of 5 triangles. After the first one is drawn, make sure each of the next ones is different in some way. Write down the reasons why each triangle is different.
Evaluation:
This activity can be done on many different levels. The amount of knowledge of geometry which a student has will influence their statements.
Recommended Resources:
Van De Walle, John A. Elementary School Mathematics: Teaching Developmentally-2nd, edition, Longman Group Ltd., New York, 1994.
Modifications:
Title:
Objective:
To study the differences in perimeter of several shapes with an area 10.
Materials:
Isometric dot grid paper (see next page), plain paper which can be used for tracing (if desired), pencils
Audience targeted/level:
Type of setting:
Individuals, pairs or small groups.
Time required:
Activity:
Using a sheet of dot grid paper, each individual will draw several figures each having an area of 10 small triangles. All students must construct their figures so these rules are followed:
1. Lines must connect adjacent dots only.
2. All shapes must be simple closed figures.
After drawing 3 to 4 different shapes students will determine the perimeter of each figure and record it next to each figure. What observations can be made about the shapes? Draw more figures to explore and study the observations.
Evaluation:
Discuss with the students the types of figures drawn, etc. Did everyone in the group draw the same type or style of figure?
Recommended Resources:
Modifications:
Try this activity with square grid paper. How would the area and perimeter relate then. What would the shape with the largest and smallest perimeter look like? What would happen if you built three-dimensional boxes out of cubes? How would the surface area of the box change?
Title:
Geometry in the Bathroom: Tile Patterns
Objective:
To study how shapes fit together to form patterns.
Materials:
Colored paper, shapes for tile patterns (See below), scissors, pencils
Audience targeted/level:
Type of setting:
Individual or small groups
Time required:
Activity:
Each person will make at least 8 copies of one of the tile shapes given. (One way to do this is to fold the colored paper into 8 thicknesses. Trace the shape on the top sheet and cut out through all 8 layers.) The pieces which have been cut out are your bathroom tiles. Your job is to design a tiling pattern. (Tiling pattern made with one shape have two important properties. 1. There are no gaps or wholes in the pattern. 2. The pattern repeats and could go on forever.) Play with the files until you decide on a pattern you like.
Evaluation:
Recommended Resources:
Van De Walle, John A. Elementary School Mathematics: Teaching developmentally- 2nd Edition, Longman Group Ltd., New York, 1994.
Modifications:
Tiling patterns can also be done with pattern blocks,
Title:
Cooperation Squares and Circles
Objective:
To demonstrate working cooperatively with a team on a common task. To practice spatial skills be assembling squares and circles.
Materials:
Directions for Cooperative Squares and Circles (follows), Packets of 15 pieces (one packet per work crew - patterns follow), job descriptions for four different Job Observes (follows), process questions to use after game (follows)
Audience targeted/level:
Type of setting:
Time required:
Activity:
Form "work crews" of three students. Select one or more Job Observers to make each of the Following reports: Cooperation and Teamwork, Non-verbal Communication, Leadership and Management, Infractions of Company Policy. Give the job description to each Job Observer. These students are not part of the work crews. Play the game (refer to rules). Remember work crews can not communicate orally to complete the task. Upon completion of the game ask the process questions and have job observers give their reports.
Evaluation:
This is a great activity to reinforce spatial skills and job skills. The process questions can be completed as a group activity or as a written assignment. This is a good activity to use as an introduction or follow-up to a discussion of learning styles.
Recommended Resources:
Ideas that Work for ABE,: Activities and Resources for
Competency-based Adult Basic Education, Oregon CBE Curriculum Committee, 1990-
91. (Funded by a 353 Grant under the Adult Education Act)
Modifications:
The role of the job observers could be used in many Cooperative learning situations. The same activity could be done with shapes other than squares.
Cooperation Squares and Circles
A wonderful way to demonstrate work maturity skills
Directions:
You work in a Perfect Square (Circle) assembly factory called Cooperation Squares/Circles Corporation. Your supervisor will give your work crew a packet of cut pieces. Each packet contains 15 pieces. Your work crew's job is to assemble five (5) squares that each meet the following criteria:
Each square is made up of 3 pieces
All 5 sqaures are the same size
This is a noisy factory, so you must communicate with your co-workers though eye contact, gestures, and motioning only. No talking is allowed.
Please cooperate with your co-workers to complete the assembly of these squares.
Variation:
Use large pieces and put a tab with the name of a player on some pieces in each pack. That player can "work" with the pieces with her/his name on them and must work with others to move the pieces into squares (or circles).
Job Observers: Job Observers are in charge of "Quality Control for the Cooperation Squares Corporation. While the work crews are assembling the squares (circles), four different types of Job Observers will be watching the crews for specific behaviors that demonstrate cooperation and teamwork, leadership and management, non-verbal communication, and infractions ofthe company policy. The Job Observers will report to the supervisor at the end of the work shift.
Process Questions After the Play:
In what ways was cooperation important (useful) during the game?
How did you feel when someone held a piece and did not see the solution?
What was your reaction when someone finished one square and then sat back without seeing that s/he held a key piece to the other squares?
What were your feelings if you finished a sqaure then began to realize that you would have to break it up and give it away to make ALL of the squares work?
How did it feeel to be the fisrt/last group to finish?
How can you relate this to working with others...
- when someone works too slow?
- when someone takes tools/jobs away from you before you can do it yourself?
- when you like to look things over, then take action, but others are jumping in and moving things around?
- when you would like to jump in and get things done, but others are planning and thinking it all through first, and taking too long to get the job done (by your standards)?
How can you learn to adjust/adapt to others' work pace/quality standards while on the job?
Job Observer
Cooperation and Teamwork
You are in charge of 'Quality Control' for the Cooperation Squares Corporation. It is your job to watch the employees work (without interacting with them in any way while they are 'on the job"), make specific observations, report to the workcrew (at the end of the workshift), and eventually report to your Supervisor - who will report to the Board of Directors.
Notice and report to the group examples of Cooperation and Teamwork on the job. This could include:
Offering pieces to a co-worker
Guessing to keep the activity moving
Two co-workers working on the same square together
Job Observer
Non-verbal Communication
You are in charge of 'Quality Control' for the Cooperation Squares Corporation. It is your job to watch the employees work (without interacting with them in any way while they are 'on the job), make specific observations, report to the workmen (at the end of the workshift), and eventually report to your Supervisor - who will report to the Board of Directors.
Notice and report to the group examples of Non-verbal Communication on the job. This could include:
pointing
finger clicking to call attention to a move you propose
eye contact
Job Observer
Leadership or Management
You are in charge of 'Quality Control' for the Cooperation Squares Corporation. It is your job to watch the employees work (without interacting with them in any way while they am 'on the job), make specific directions, report to the workmen (at the end of the workshift), and eventually report to your Supervisor - who will report to the Board of Directors.
Notice and report to the group examples of Leadership or Management skills demonstrated by any of the employees on the job. This could include:
Offering pieces to a co-worker
Cmturing to keep the activity moving
TwiD co-workers working on the same square together
Job Observer
Infractions of Company Policy
You are in charge of 'Quality Control' for the Cooperation Squares Corporation. It is your job to watch the employees work (without interacting with them in any way while they are 'on the job), make specific observations, report to the workcrew (at the end of the workshift), and eventually report to your Supervisor - who will report to the Board of Directors.
Notice and report tothe group any B you observed on the job. This could include.
Verbal communication
Attempting to touch or move another worker's 'tools' ( pieces of squares)
Attempting to assemble a square with the wrong number of pieces (only 3 per square)
67
Pattern for cut pieces of Perfect Squares
Cut out 5 6" squares
Cut each square into 3 pieces as shown here
Include all 15 pieces in one packet
Title:
Objective:
To discover that the distance around a circle divided by the distance across equals 3.4 or pi
Materials:
Circular items: i.e. coffee can, plate, umbrella, round table, Frisbee, etc.
Measuring tapes, one per group
Recording chart (sample follows)
Audience targeted/level: ABLE levels II and III
Type of setting:
Time required:
Activity:
Put numbers on circular items. Place items on tables around the room. Divide the class into teams of three. The three team members rotate roles with each new item:
Recorder - record measurements, division answer
Measurer - measures items
Divider - does division
Teams rotate from item to item and do the following:
Measure distance across and distance around
Divide distance across into the distance around.
Record answers on the chart.
After all groups have measured each item, answers can be compared in the large group.
Evaluation:
If the work was done correctly all answers should be about 3.
Recommended Resources:
Ideas that Work for ABE- Activities and Resources for Competency-based Adult Basic Education Oregon CBE Curriculum Committee. 199091.
Modifications:
Title:
Objective:
To develop skill in working with spatial relationships, to develop problem solving skills, and practice creating equal areas and shapes.
Materials:
Audience targeted/level:
Type of setting:
Time required:
Activity:
All students are given a supply of toothpicks. The object is to arrange to the toothpicks into straight lines to make triangles. Students first attempt to make a triangle with 3 toothpicks, then 4, 5, and so on. Before they attempt of construct each triangle they determine if a triangle is possible. They then sketch the solution. They then determine if another solution possible with the same number of picks. Students might make a chart of their findings. they should be encouraged to examine why certain triangle are impossible and certain concepts. ( i.e. The sum of any 2 sides of a triangle must be greater than the third side.)
Students can also attempt to construct various triangles, hexagons and other geometric figures as directed (see next page). The activities give them practice in problem solving and analytical thinking.
Evaluation:
Doing spatial problems similar to these enable other students to excel.
Your best students may not be best with these activities.
Recommended Resources: Downie, Diane.
MAth for Girls and Other Problem Solvers EQUALS, Lawrence Hall of Science, University of California, 1981.
Other useful toothpick problems can be found in kids math puzzle books.
Modifications:
After completing several toothpick puzzles the students can make up original puzzles to share with one another.
Title:
Objective:
To measure the area of the room and use this information in practical applications.
Materials:
Tape measures or steel rules, and shopping ads for carpeting, paint, window blinds, etc.
Audience targeted level:
Type of setting:
Small groups, individuals if desired.
Time required:
Activity:
Students measure and record the area of classroom floors, windows, and walls. Next they find the cost of carpeting, window blinds, and paint at local stores that would be needed to do a "classroom makeover."
Evaluation:
Recommended Resources:
Ideas that Work for ABE- Activities and Resources for
Competency-based Adult Basic education. Oregon CBE Curriculum Committee. 199091.
Modifications:
Students could measure rooms in their homes to "decorate."
Toothpick Activities
1. Construct this shape using 17 toothpicks.
Try to remove 5 toothpicks so 3 squares remain. Can you remove 6 toothpicks so 2 squares are left?
2. Construct this hexagon with 12 toothpicks.
Can you remove 4 toothpicks so 3 triangles are left? Try to move 4 toothpicks to form 3 triangles.
3. Use 8 toothpicks and a cheerio to form this fish.
Can you move 3 toothpicks and the cheerio to make the fish swam the opposite direction.
4. Two families own land in this shape.
The first family wants to divide their land evenly among their 3 children. Add 4 toothpicks to form 3 parcels of land of equal size and identical shape.
The second family wants to divide their land evenly among their 4 children. Using 8 toothpicks divide the land into 4 lots of equal size and identical shape.
5. Use 9 toothpicks to construct this triangle.
Remove 2 toothpicks and leave 3 triangles. Remove 3 toothpicks and leave I triangle.
Remove 6 toothpicks and get I triangle. Remove 4 toothpicks and get 2 triangles.
Remove 2 toothpicks and get 2 triangles.
6. Can you use 6 toothpicks to construct 4 equilateral triangles (You may need to change your perspective for this one
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