Fractions,Decimals,and Percents

2. Tell participants that this course is about fractions, decimals and percents and is designed to serve three purposes:
• To expand their understanding of mathematics
• To experience mathematical activities that can be used with their children at home
• To have fun!

3. Tell participants that the course will be more enjoyable if we get to know one another and learn each other’s names.
• Give each participant an index card.
• Ask each participant to fold the card to form a tent.
• Ask them to write their name in large letters and to draw their children on the card. (See sample in the notes to the right.)

4. After the name cards are completed, ask participants to introduce themselves and talk about their children with others at their table.

The name cards should be collected at the end of each class and handed out at the beginning of each session.

Encourage parents to talk about their children, telling their ages, personalities, etc. After all, their children are the reason they are here!

2. Ask participants to work with a partner to try to use all seven pieces to form each of the shapes shown on the Tangram Pattern Sheets. Let them know that it is not necessary to solve all of the puzzles , but that they should try several of them.

The Value of a Tangram Piece
1. Tell participants that they will now do another activity with the tangram pieces. Say:
• Imagine that a person could buy the whole set of tangrams for $8.00, or just buy individual pieces. What would be the value of each of the individual pieces?
• Assume that the value of a piece depends on its size (area) in comparison to the other pieces.

2. Encourage participants to work with a partner so that they have the opportunity to talk about their thinking. If some groups complete the task quickly, see notes for extension questions.

3. Solutions to tangram problems are provided on page 7.

Processing
1. Have several participants present the reasoning they used to determine each piece’s value. Encourage them to use the overhead tangram pieces when demonstrating their reasoning. As participants share, record the mathematical language they are using. They might be using terms such as parts, half, twice as much, compared to, fraction of, percent, or ratio.

2. It is important to validate every participant’s contribution as they complete their sharing by pointing out the strategy that they used. After all the volunteers have presented, celebrate the variety of strategies that have been shared.

3. If many groups solved the $12, $1.60, and $1.00 problems.
Ask:

How did the solution to the $8.00 problem help you to solve the other problems?

4. After participants have shared, point out that the problem was solved in many ways, but in all cases they were using the ideas of fractions, decimals, and percents. Participants were considering the relationship of the parts to the whole and of the parts to each other. This kind of thinking and reasoning is basic for understanding fractions, decimals, and percents.

5. Take a few minutes to explain the use of manipulatives in today’s classroom. It might be appropriate to bring in a sampling of the manipulatives that will be used during this course. Research has shown that manipulatives can be a very effective aid in learning mathematics.

6. Let them know that in the next few classes they will continue to use manipulatives and problems to help illuminate more ideas about fractions, decimals, and percents.
• Sessions 2 – 4 will focus on fractions,
• Sessions 5 – 6 will focus on decimals,
• Sessions 7 – 8 will focus on percents.

Tangrams are believed to have originated as a puzzle in China around 1800 .

During group work, be sure to walk around and listen to the conversations in order to know what the participants are thinking.

If some groups complete this task quickly, pose these additional challenges:
• If the completed shape is worth $12, what is the value of each piece?
• If the completed shape is worth $1.60, what is the value of each piece?
• If the completed shape is worth $1.00, what is the approximate value of each piece?

Participants may be reluctant to come to the front of the room to share. Be sure to offer support and acknowledgement to those who volunteer. Allow partners to come to the overhead together and offer your assistance to them as they present.

This is an appropriate time to take a short break, if desired.

Applications in daily life
1. Remind participants that this course is focused on the mathematical ways we represent parts of things using fractions, decimals, and percents. These topics are heavily represented at the elementary and middle school level. Explain that one reason for this emphasis is the practical usefulness of fractions, decimals, and percents in daily life.
Say:

The object of this next activity is to brainstorm lots of everyday uses for fractions, decimals, and percents

2. Ask for volunteers to share places they use fractions, decimals, and percents at work or at home. After a few examples have been shared, ask participants to generate a short list of additional examples at their table. Say:
We will be sharing our ideas soon, but before we do, let’s expand our lists by looking through some magazines and newspapers for more ideas.

Newspaper Search
1. Hand out newspapers and magazines and allow participants to cut out additional fraction, decimal, and percent examples.

2. If their list contains additional examples that are not found in the paper, they may write each idea on a Post-it®.

3. Have participants work in groups to collect examples.

Sharing ideas
1. After 5 minutes, have each group post their examples on the Fraction-Decimal-Percent Charts, while sharing what they have found. If an idea has already been shared, ask them to state it again and post the clipping or Post-it® note on top of the others with the same idea. This will indicate which uses of fractions, decimals and percents are the most common.

2. Once all items have been posted, ask participants to look for ideas that are common to the three lists. For example, many examples will likely have to do with making comparisons, measurement, and money. Ask:
Why do you suppose that fractions, decimals and percent are often taught together?

Encourage participants to consider the things they see as they drive, watch TV, read the newspaper, go shopping, banking, or do chores at home.
Examples:
• Interest rates
• Sports statistics
• Shopping advertisements, surveys
or graphs
• Radio station call numbers
• Stock market changes
• Cooking
• Shopping prices

Ask participants to use markers rather than pens or pencils when writing on the Post-it® notes and to write large enough for it to be seen from a distance.

Possible entries for the Fraction-Decimal-Percent charts are listed on page 8. The chart made by each class should reflect participants’ ideas. It will not be necessary to include all the items listed on page 8.

Some reasons might include:
• They are used in similar ways as the fraction-decimal-percent chart shows
• They are used to express a part-whole relationship
• They can be interchanged
(0.5 = 50% = 1/2).

4. Record responses on the same Math Class Web transparency using a different color pen.

5. Tell participants that one goal of this class is to provide them with many experiences that reflect the current approach to teaching and learning mathematics. Through these experiences they will be better able to assist their children in learning mathematics.

2. Participants will need to take a set of Tangrams home in order to complete the Bringing Mathematics Home 1 activities.

3. Encourage participants to try at least one of the activities listed either with their children, their spouse or on their own

2. Fold or roll the Fraction-Decimal-Percent charts in a way that preserves the items posted on it and bring it to the next class.

3. Save the Chart It! and bring it to the next class. If desired, you may have the log typed and distributed to participants at the next class.