Measurement,
Perimeter
& Area


Grade 7, 8, 9

By
Greg Brososky
Fairview Middle School
Swift Current, Saskatchewan
&
Michael Neufeld
Rabbit Lake Central School
Rabbit Lake, Saskatchewan
1994


EDITOR'S NOTE:

The following abbreviations are used for the Common Essential Learnings (CELs).


I. TOPIC: LINEAR MEASUREMENT

II. FOUNDATIONAL OBJECTIVES:

The student should demonstrate:

III. SPECIFIC LEARNING OBJECTIVES:

The student should be able to:

IV. STRATEGIES:

V. METHODS:

VI. DESCRIPTION:

A.

Students construct a "Personal Data Sheet" containing individual body measurements. Students can use cloth tapes and work in groups or in pairs. Room can be left on the card for students to add other measurements suggested by the teacher.

PERSONAL DATA SHEET
Height ____cm
Finger tip to finger tip____cm
Top of head to chin____cm
Top of head to eyes____cm
Around neck____cm
Around bisceps____cm
Length of foot____cm
Elbow to wrist____cm

Students may find it interesting to explore the ratios between the various measurements.

B.

Scavenger hunt. Students are given a list of objects to measure both within the school and the classroom and outside the school. Groups are supplied with record sheets, tape measures and trundle wheels. The results can be shared, not so much to ensure accuracy as to ensure the use of appropriate units.

C.

To reinforce the metric ladder conversion method, large colorful signs can be constructed. Place these signs on a staircase and having students move from one step to another while announcing the change in the original value. Students gain a working knowledge of how the ladder is used to convert metric units.

VII. ASSESSMENT TECHNIQUES:

VIII. CELs:

Students should develop their abilities to:


I. TOPIC: PERIMETER

II. FOUNDATIONAL OBJECTIVES:

The student should demonstrate:

III. SPECIFIC LEARNING OBJECTIVES:

The student should be able to:

IV. STRATEGIES:

V. METHODS:

VI. DESCRIPTION:

A.

Have students, perhaps during art classes, construct mobiles out of coat hangers or other wire. The shapes could vary. All, or selected ones, could be hung from the ceiling to act as a reminder and reference when the topic changes to area.

B.

Students are given geo-boards and asked to construct shapes with given perimeters. There may be a variety of correct answers depending upon the number chosen for the perimeter. Students can exchange their work and examine the variety of shapes constructed. Discuss the various figures created. Encourage the use of shapes with 90 degree angles or be prepared to handle questions that arise regarding sloping distances. This limits it to rectangles or squares.

C.

Have students cut out a square, 25 cm. X 25 cm., and find the perimeter of the square. Have them cut another square, 10 cm. X 10 cm., from the top right corner of the first square. Have them find the perimeter of the new shape formed when the smaller square is removed. Ask the students to cut out other squares of their choice and cut from the top right corner, squares of different sizes. Have them find the perimeter. Ask students to list any observations that they see. Note that the loss of the area as the square removed does not affect the perimeter. This should point out that perimeter is not related to the area of the figure.

D.

Students use string, cloth tape and/or a trundle wheel to measure the circumference of various circles (cup, can, barrels, jump circle in gym etc.). They also record the diameter of the circles. This information can be recorded in a chart which when brought back to the class can be shared using a chart on the board. Students are asked to determine the relationship between the two to gain an understanding of the value of pi and it role in the formula for the circumference of a circle.

E.

Students cut circles out of paper. (Encourage students to use circles with diameters which are whole numbers....this will make the connection between diameter and area more easily observed.) They then cut the circles in half by cutting along the diameter. Each half is then cut into small slices running from the circles center to the outside edge. When finished the edges of the circle are laid side by side and measured to arrive at an approximation of the circumference.

VI. ASSESSMENT:

VII. CELs:

Students should develop their abilities to:


I. TOPIC: AREA

II. FOUNDATIONAL OBJECTIVES:

The student should demonstrate:

III. SPECIFIC LEARNING OBJECTIVES:

Students should develop their abilities to:

IV. STRATEGIES:

V. METHODS:

VI. DESCRIPTION:

A.

Have students, perhaps during art classes, cut flat shapes out of cardboard. These shapes would be covered with paper mâché and painted with bright acrylic paint. Coating the shapes with varnish will add to their visual impact. All, or selected ones could be hung in a region of the room (perhaps hung from the ceiling) to act as visual reference. If done in conjunction with the coat hanger mobiles, it will make a valuable contrast between the two concepts. Formulae could be attached to the side of each shape. A variety of shapes (triangles, rectangles, parallelograms) should be displayed.

B.

Students are given geo-boards. Students are asked to create shapes with various given areas. Students chart the length and width of the shapes as well as the perimeter along with the area that was given to them. Students can be asked to draw conclusions about the relationship between the length, width and the area. Relationships between area and perimeter can also be discussed. This same activity could be accomplished with building cubes (base ten blocks).

C.

Students cut out rectangles and then calculate and record the area using the formula. A sloping vertical line is drawn across the rectangle. Students cut along this line dividing the shape in two. The right and left sides are reversed creating a parallelogram. The area has not changed. Students record the dimensions of the new shape. During the discussion that follows students should be led to the understanding that a new formula (not LxW) is required to find the area of the parallelogram, and that base and height are now more appropriate.

D.

Students cut parallelograms out of squared paper. The parallelogram is cut into triangles. Both the areas of the parallelogram and the triangles are recorded (use formula for the parallelogram and counting for the triangle). By using different methods, students may arrive at slightly different answers. Students share their results in a chart on the board and are led to the conclusion that the areas of the triangles are half of the area of the original parallelogram and thus to the formula for the area of the triangle.

E.

To help students better understand the method of calculating the area of rectangular shapes, have the students draw the images on grid paper. Students can then cut out the shapes, calculate the area of individual areas and then paste them together again. The total area is then seen to be the total of the individual areas.

F.

Students are given a sheet of grid paper containing an irregular polygon. They calculate the area and the perimeter. Students are then asked to draw a shape on a second sheet of grid paper where the perimeter remains the same but the area is the largest possible. Similarly, with the same perimeter but the smallest area possible. Calculating the area of an irregular polygon could be interesting. How might they do this? Geoboards, or by counting or dividing into triangles, calculations and sums? Their written description of the process might be worthwhile.

G.

Each student is given an orange (or other round edible item...ie pizza, bannock) and asked to record dimensions associated with the item (see chart below). Cut a slice about one centimetre thick from the center of an orange. Lay the slice on a piece of paper. Measure and record the radius of the slice. Cut the slice in half. Separate the sections in each half. This can be done easily if the students did not cut through any of the triangular sections inside the orange. Arrange the sections as shown below. Use the formula for the area of a parallelogram to calculate the area of the constructed shape. Student results are recorded on the board and students, through trial and error are encouraged to determine any relationships between the various elements. After much foraging students will see the constant connection (pi) between the area and the radius. An alternate method would be to have students work in groups to arrive at an appropriate formula and then present their findings to the rest of the class.

H.

Papers containing the following shapes are distributed to the students. Either individually or in groups, the students calculate the area of the white regions in each dark square and the dark area surrounding them. This should give the student experience in subtracting to arrive at the area of a specific region. The results showing the areas to be the same in each of the squares will be very interesting.

VI. ASSESSMENT

(samples provided in appendix):

VII. CELs:

Students should develop their abilities to:

REFERENCES:

A Teacher's Guide to Math Works, Agency for Instructional Technology, 1985

Daily Mathematics, Critical Thinking and Problem Solving, McDougal, Littel & Co.

Intermediate Math 1, Dottori D., Knill G., et. al., McGraw-Hill Ryerson Ltd., 1981

Math In Context, Ebos F., McKillop D., et. al., Nelson Canada, 1992

Math Quest, Alexander B., Folk S., & Worth J., Addison-Wesley Publisher, Ltd., 1989


APPENDIX A-1

Checklist to Assess Student's Ability to Use Information

Student Name:_______________________________________________

Date or Time Period of Assessment:_________________________________________________

Check all applicable criteria.

CriteriaYes/No
1.  Student is able to state the purpose for
   the collection of the information.
_______
2.  Student is able to gather information from
   own recall of past learning.
_______
3.  Student is able to identify main elements
   needed in information.
_______
4.  Student is able to organize information
   into usable units.
_______
5.  Student is able to identify related details.
_______
6.  Student is able to recognize relationship
   of information gathered to information
   remembered.
_______
7.  Students is able to clearly state ideas that
   fit with the topic being addressed.
_______
8.  Student is able to give evidence of checking
   information for accuracy.
_______

(This instrument may be adapted
 for use as a rating scale.)

Student Evaluation Handbook, 1991


The following rating scale could be used to record observations of a group involved in a collaborative project. Teachers could use this scale to describe each student's contribution to the group and the development of co-operative skills.

Co-operative Group Learning (Teacher Assessment)

Date:_______________________________________________

Group:______________________________________________

Task:________________________________________________

5      4      3      2      1

High Low

Names of Group Members

________ ________ ________ ________ ________ ________
Negotiates roles and responsibilites of each group member ___ ___ ___ ___ ___ ___
Contributes ideas and suggestions ___ ___ ___ ___ ___ ___
Encourages the involvment of all group members ___ ___ ___ ___ ___ ___
Is receptive to peer questions and criticism ___ ___ ___ ___ ___ ___
Listens to the suggestions of others ___ ___ ___ ___ ___ ___
Modifies personal thinking to incorporate the ideas of others or new information ___ ___ ___ ___ ___ ___
Respects and accepts the contributions of each group member ___ ___ ___ ___ ___ ___
Completes individual commitment to the group ___ ___ ___ ___ ___ ___

Additional Comments:

__________________________________________________

__________________________________________________

__________________________________________________

__________________________________________________

__________________________________________________

__________________________________________________

English Language Arts
A Curriculum Guide for the Elementary Level

June 1992, Saskatchewan Education


Students could discuss questions such as the following to assess the group's ability to work co-operatively.

Co-operative Group Learning (Group Assessment)

1. Was your group successful in working together? What co-operative skills did the group use to make working together enjoyable?

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

2. What co-operative skills improved as the group project progressed?

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

3. What co-operative skills need to be further developed?

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

4. What was the most important thing your group learned about working together during this project?

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________

English Language Arts
A Curriculum Guide for the Elementary Level

June 1992, Saskatchewan Education


Assessment of Cooperative Learning

~ Individual ~ Pair ~ Group

Student Name:_____________________________________

Partner/Group Members:_____________________________

_________________________________________________

_________________________________________________

_________________________________________________

Date:____________

DIRECTIONS:

Please meet with your group and use the rating scale below as a basis for discussing how effectively your group is working. Complete the rating scale and return it to your instructor.

DID YOUR GROUP:

POORLY........................................EXTREMELY WELL

  • Identify specific goals?
  •   1           2           3           4           5           6
  • Make noticeable progress towards those goals?
  •   1           2           3           4           5           6
  • Share information, ideas, and opinions with each other?
  •   1           2           3           4           5           6
  • Make decisions that were based on the views of all members?
  •   1           2           3           4           5           6
  • Listen with attention to each other?
  •   1           2           3           4           5           6
  • Actively encourage each other to participate in the group activities?
  •   1           2           3           4           5           6

    Some suggestions for improving our group work next time:

    ________________________________________________

    ________________________________________________

    ________________________________________________

    ________________________________________________

    >From Business Education Accounting 16, 26, 36
    Saskatchewan Education 1992
    Student Evaluation: A Teacher Handbook, 1993


    Rating Scale for Cooperative Group Learning

    Student Name:________________________

    Date or Time Period of Assessment:____________________

    1. The student works with a wide range
    of peers, not just with close friends.
        1          2            3             4          5
      never                 sometimes                 always
    2. The student willingly shares materials
    and ideas with others.
        1          2            3             4          5
      never                 sometimes                 always
    3. In group work the student shows
    respect for others by listening and
    considering other points of view.
        1          2            3             4          5
      never                 sometimes                 always
    4. The student follows group work
    rules as established for the activity.
        1          2            3             4          5
       never                 sometimes                 always
    5. The student fulfills her/his work
    responsibilities in the group.
        1          2            3             4          5
      never                 sometimes                 always
    6. The student exhibits appropriate work
    behaviors during time set aside for groups.
        1          2            3             4          5
      never                 sometimes                 always
    7. The student participates in discussions
    during the time set aside for group work.
        1          2            3             4          5
      never                 sometimes                 always
    8. The student contributes ideas to
    the group efforts during the
    discussions in the time set aside for
    group work.
        1          2            3             4          5
      never                 sometimes                 always

    This instrument may be adapted for use as a checklist.

    Student Evaluation Handbook, 1991


    Anecdotal Record

    Student Name:_________________________

    Class:________________________________

    Term:________________________________

    After an anecdotal notion is written on a pre-pasted note, the teacher may add it to this anecdotal record sheet. The teacher will circle the focus for each anecdotal entry.

    Date: __________________________________
    
    Focus:	     Knowledge	     Application	     Technical Skills	    Attitude
    
    
    
    
    
    
    Date: __________________________________
    
    Focus:	     Knowledge	     Application	     Technical Skills	    Attitude	
    
    
    
    
    
    
    
    Date: __________________________________
    
    Focus:	     Knowledge	     Application	     Technical Skills	    Attitude	
    
    
    
    
    
    
    
    
    

    From
    Business Education Accounting 16, 26, 36
    Saskatchewan Education 1992

    Student Evaluation: A Teacher Handbook, 1993


    Template 1

    Anecdotal Record-Keeping Form

    Date:_________________________

    Unit:_________________________

    td>

      Student's Names  

    Criteria/Objectives	    	

    
    
    
    
    
     
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    

    Special Comments:

    ________________________________________________

    ________________________________________________

    ________________________________________________

    ________________________________________________

    Student Evaluation: A Teacher Handbook, 1993

    Arts Education
    A Curriculum Guide for Grade 1

    September, 1991, Saskatchewan Education


    Data Collection/Notebook Checklist*

    Name:_________________________

    Date:__________________________

    A checkmark indicates that the criterion is satisfactory. No mark indicates that the criterion is either missing or unsatisfactory.

  • Documentation is complete.
  • 	
  • The information or data collected is accurate.
  • 	
  • Written work is neat and legible.
  • 	
  • Tables and diagrams are completed neatly.
  • 	
  • Each new section begins with an appropriate heading.
  • 	
  • Errors are crossed out but not erased.
  • 	
  • Spelling and language usage are edited and corrected.
  • 	
  • Information is recorded in a logical sequence.
  • 	
  • Technological aids are used appropriately.
  • 	
  • Notes are collected in a folder or binder.
  • 	
  • Color or graphics are used to enhance the appearance.
  • 	
  • Rough work is done separately.
  • 	

    Comments/Overall Impressions:

    ________________________________________________

    ________________________________________________

    ________________________________________________

    ________________________________________________

    * This checklist may be used by teachers, or by students for self-evaluation. It may be used to evaluate notebooks, laboratory data collection done during investigations, or more formal written laboratory reports. Students should be made aware of these criteria at the start of the term.

    Student Evaluation: A Teacher Handbook, 1993

    Science
    A Curriculum Guide for the Secondary Level

    September, 1991, Saskatchewan Education


    This unit comes from the The Stewart Resources Centre which provides library resources and teacher-prepared materials for teachers in Saskatchewan. To borrow materials or obtain a free catalogue listing unit and lesson plans contact :
    Stewart Resources Centre,
    Sask. Teachers' Federation,
    2317 Arlington Avenue,
    Saskatoon, SK S7J 2H8;
    phone 306-373-1660; fax 306-374-1122,
    e-mail src@stf.sk.ca.
    http://www.stf.sk.ca/

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