This lesson helps students to relate decimal fractions to common fractions and reinforces the fact that decimals are fractions written in a different symbolic form.
When you are counting items that have parts less than one we use decimals. Decimals are used in our place value system to write fractions in tenths, hundredths, thousandths, and so on. We use a dot as a symbol to separate the whole number part from parts that are less than one. The dot is called a decimal point. The decimal indicates that the position to the left is being counted as units or ones. Numbers that are written with a decimal point are called decimals. Decimals follow the same place value pattern as whole numbers. When you are using a base ten system, no matter what place you are looking at, its value increases ten times the value of the place to its right and when you move to the right on this system each piece gets smaller by one-tenth.
Students need to read 2.7, as two and seven-tenths. This helps them to relate decimal fractions to common fractions and reinforces the fact that decimals are fractions written in a different symbolic form. When we read numbers with decimals in them we say "and" when we get to the decimal point.
5. Connect mathematical ideas within mathematics, to other disciplines, and to everyday experiences.
Invitation to Learn
Model the following sharing problems as a whole class. Ask students to volunteer and come to the front of the class to help solve each problem. You can use real items or paper representations of the items. Ask the students to represent the remainder as a fraction.
Share five cookies between four people. How much does each person get?Share seven cookies among three children. How much does each child get?
Divide nine apples between two people. How much does each person get?
Divide seven brownies among four children. How much does each person get?
Divide a whole pie among ten people. How much does each person get?
Ask the students what answers they would get if they used a calculator? Have a group use a calculator to solve the problem. Explain that the answer is a decimal number and that it is the way a calculator represents a number that is between two whole numbers. The decimal number and the fraction are the same amounts, they are just written two different ways. Our place value system is a decimal system so that we can write numbers less than one using digits.
Instructional Procedures
Lesson 1 - Decimals
Lesson 1 - Make that Number!
Family Connections
Jensen, E. (2000). Moving with the brain in mind. Educational Leadership, 58 (3), 34-37. Retrieved January 18, 2007 from http://www.newsletteronline.com/
Brain research has shown that physical movement -- moving, stretching, and acting out concepts, can increase the learning process. Active learners remember the information longer and better than sedentary learners. Teachers should have students: engage in a variety of postures throughout the day, engage in movement during class, use their bodies to demonstrate concepts, role play and include a variety of physical activities to help students learn and if these ideas are not possible then students should at least stop and stretch every 20 minutes.
Marzano, R.J., Pickering, D.J., & Pollock, J.E. (2001). Nonlinguistic Representations. In classroom instruction that works, (72-83). Alexandria, Virginia: ASCD.
Researchers believe that students learn and store information in two different ways. The first form is a linguistic form where the learner either listens to the information or reads it in a book. In the second form, non-linguistic, the learner forms a mental image or a physical sensation by touching, smelling, listening, tasting, or kinesthetic association. Research has shown that when students learn using both forms their achievement improves greatly. After a non-linguistic form of learning has taken place students should be asked to explain and justify what they have learned. When students are able to explain their thinking and reasoning to others their knowledge increases and they are able to recall it easier. Non-linguistic representations include: making physical models, using manipulatives, drawing pictures, graphic organizers, or engaging in kinesthetic activities.