As of September 30, 2005, the North Central Regional Technology in Education Consortium is no longer in operation.
NCRTEC Professional Development Planning and Evaluation Teaching and Learning

Major Learning Activities

Activity One: Fractional Amounts (Allow one class period for the lesson and one or more class periods for assessment depending on the number of assessments chosen.)

Materials:

Lesson:

Students may work individually or in groups in lab setting. Students go to The Amazing Picture Machine Web site. In the "Search for" box, enter flags, click on "and", and in the "Second search term" box, enter countries. Students are then asked to find flags that could easily be divided into halves, thirds, fourths, etc

Assessment:

  1. Students must explain to the teacher, another student, or a journal why they believe their flag is easily divided into particular fractional amounts.

  2. The teacher may decide to have several other flags for students to categorize. The teacher will develop a table including the fractional amounts he or she is assessing, leaving room for students to include other categories they may find. Many flags may fit into more than one category, and students need to have justification for each category into which they place the flag. (See an example in the Assessment section.)

  3. Ask students to design their own flags (or other objects) that easily depict thirds, fourths, sevenths, etc.

  4. Have students search The Amazing Picture Machine Web site (search keyword might be "shapes") and locate pictures other than flags that demonstrate the use of fractions. Students present to their classmates how fractions are used in the picture(s) they locate. Listening students could predict how they think fractions are used and then compare their predictions with their classmates' presentations. A computer with a projection device would be useful for this activity. (See example in the Assessment section below.)

  5. Students design a collage (using pictures from magazines) showing fractional amounts.

Activity Two: Equivalent Fractions.(Allow one class period for the lesson and one or more class periods for assessment, depending on the number of assessments chosen.)

Lesson Outcome(s):

The students will demonstrate equivalent fractions through visual representation, written description, and real world representation.

Lesson:

Students may work individually or in groups in a lab setting. Students go to The Amazing Picture Machine Web site. In the "Search for" box, enter flags, click on "and", and in the "Second search term" box, enter countries. Students are then asked to find a flag that shows equivalent fractions. For example, the flag of Uzbekistan has 12 stars, so students could show that 3 out of 12 stars = 1/4.

Assessment:

  1. Students must explain to the teacher, another student, or a journal what equivalent fractions are depicted and where.

  2. Students look through other pictures of flags and/or other objects to find equivalent fractions. Students draw, fill out a chart, or explain in writing which equivalent fractions they find. (See example in the Assessment section below.)

  3. Ask students to design their own flags (or other objects) that easily depict equivalent fractions.

  4. Ask students to find examples of equivalent fractions in everyday life. For example, 25 cents is equivalent to one-fourth of a dollar.

Activity Three: Addition/Subtraction with Fractions. (Allow one class period for the lesson and one or more class periods for assessment depending on the number of assessments necessary.)

Lesson Outcome(s):

The students will demonstrate addition and subtraction of fractions (both like and unlike denominators) using pictures.

Materials:

Addition:

Students may work individually or in groups, or the teacher may demonstrate the lesson using a computer and projection device. Students go to the Mazda Hubcap picture, http://www.ncrtec.org/images/tire/tire1.htm . Have students break the hubcap into halves, thirds, fourths, and sixths. Demonstrate to students that 1/12 + 1/12 = 2/12. Students have already broken hubcaps into sixths, so they should be able to determine that 2/12 = 1/6. Demonstrate 1/3 (4/12) + 1/4 (3/12) = 7/12.

Subtraction:

Students may work individually or in groups in a lab setting, or the teacher may demonstrate lesson using a computer and projection device. Students go to the Mazda Hubcap picture, http://www.ncrtec.org/images/tire/tire1.htm. Have students break the hubcap into halves, thirds, fourths and sixths. Demonstrate to students that 5/12 - 1/12 = 4/12. Students have already broken hubcaps into thirds, so they should be able to determine that 4/12 = 1/3. Demonstrate 1/3 (4/12) - 1/4 (3/12) = 1/12, but that 1/4 (3/12) - 1/3 (4/12) cannot be done in this situation.

Assessment:

  1. Students take problems from their math books and find pictures that illustrate addition or subtraction. Encourage students to look for interesting and unique pictures.

  2. Optional assessment: Using a digital camera, scanner and photos, and multimedia software such as HyperStudio or ClarisWorks, have students create a presentation depicting addition and/or subtraction of fractions.
Activity Four: Multiplication and Division. (Allow one or more class periods, depending on the assessment(s) chosen.)

Lesson Outcome(s):

The students will use observation and investigation skills to discover and demonstrate that division by a whole number is the same as multiplication by the reciprocal of that number.

Materials:

Lesson:

Students may work individually or in groups in a lab setting, or the teacher may demonstrate the lesson using a computer and projection device.

Students go to the Mazda Hubcap picture, http://www.ncrtec.org/images/tire/tire1.htm. Have the students divide the hubcap into three parts. Then have the students find one-third of the hubcap holes.

Students go to ftp://ftp.sunet.se/pub/pictures/flags/united-states-of-america.gif (USA flag). Have students divide the stars into five groups. Then have students find one-fifth of the stars.

Students go to the soda pop cans site, http://www.ncrtec.org/images/diag/dm5.htm. Have students divide pop cans into four groups. Then have students find one-fourth of the cans.

Introduce the idea of reciprocals and guide students to the realization that division by a whole number is the same as multiplication by the reciprocal of that number.

Assessment:

  1. Students write in journals or have a conference with the teacher to explain how division by a whole number is the same as multiplication by the reciprocal of that number.

  2. Students locate pictures in magazines and books or take their own pictures and demonstrate how division by a whole number is the same as multiplication by the reciprocal of that number. Students could be assigned specific problems from their math books to illustrate this concept.

  3. Students use pattern blocks or other manipulatives to demonstrate how division by a whole number is the same as multiplication by the reciprocal of that number.

  4. Use some short oral problems. For example, find one-third of 24 or find one-fifth of 35.

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