Exploring Decimals By: Amy Benjamin Math- Grade 4/5 6 day unit plan Technologies Used: *Computers *Class set of calculators(ti80)

Transcription

1 Exploring Decimals By: Amy Benjamin Math- Grade 4/5 6 day unit plan Technologies Used: *Computers *Class set of calculators(ti80) * TI-84+ graphing calculator *Overhead unit for calculator *Overhead projector *Overhead manipulatives (transparent decimal grid paper,transparent fractions squares and overhead calculator) *Fraction cubes

2 Overall Objectives Students discuss common uses of decimals. They will become familiar with a calculator, representing decimals on grids and the use of an overhead with manipulatives. Standards Addressed NCTM Number and Operations *understand numbers, ways of representing numbers, relationships among numbers, and number systems *understand meanings of operations and how they relate to one another Problem Solving *build new mathematical knowledge through problem solving Connections *recognize and use connections among mathematical ideas * understand how mathematical ideas interconnect and build on one another to produce a coherent whole *recognize and apply mathematics in contexts outside of mathematics New York State Content Strand- Number Systems *5.N.4- Create equivalent fractions, given a fraction *5.N.5- Compare and order fractions including unlike denominators *5.N.9- Compare fractions <,>,= *5.N.11- Understand that percent means part of 100, and write percents as fractions and decimals *5.N.19-Simplify fractions to lowest terms Resources Akers, Joan. Investigations in Number, Data and Space: Name that Portion, Teacher Notes.Cambridge,Mass:TERC; 1998 Dennis, J. Richard. Fractions are parts of things. New York:Thomas Y. Crowe; Ernst, Lisa Campbell. Sam Johnson and the Blue Ribbon Quilt. New York: Lothrop, Lee and Shepard, 1983 Page Two

3 Materials and Equipment Needed *Computers *Class set of calculators(ti80) *Overhead projector *Overhead manipulatives (transparent decimal grid paper,transparent fractions squares and overhead calculator) *Fraction cubes *Newspaper sports sections Overview Day One- Interpreting Decimals Students discuss common uses of decimals. Using a calculator to solve division problems. To explore application of decimals children can choose sports teams to follow over a two week period, keeping track of win/loss records and making predictions and changes in the percentage of games won. Day Two- Decimals on Grids Students represent tenths and hundredths on grids. Then they play a decimal game. Fill Two, which involves combining decimals on grids. Day Three and Four- Decimal Games Students will rotate between 3 decimal games that involve ordering decimal numbers expressed in tenths, hundredths, and thousandths: Smaller to Larger, Decimals in-between and Capture Decimals. Day Five and Six- Fractions to Decimals Students find decimals of up to three digits that have a value between that of two given decimals. Students then find decimal equivalents for fractions on the calculator, making a Fraction to Decimal Division Table for all fractions with numerators and denominators from 1 to 12. They identify and explain patterns within the table. Page Three

4 Interpreting Decimals Lesson Summary Students discuss common uses of decimals. Using a calculator, they find several division problems that have answers of 0.5,0.25,0.75, and other familiar decimals. Materials Calculators TI-84+ calculator Overhead adapter Newspaper sports section Opening Show students the following examples of decimals: Car odometer Baseball player s batting average-.346 Rainfall in the last 24 hours inch Total rain for the month inches Allow a few minutes for students to read each decimal number and decide with your partner what it means. Listen for student understanding about decimals. Do they recognize that 0.25 inch is ¼ inch or that 5.43 inches is almost 5 ½ inches? Lesson Description Write on the board: How would you read these decimals? (one- place decimal-tenths, two-place decimal-hundreths) What familiar fractions are these decimals equal to? 0.5= ½ 0.25= ¼ If fractions and decimals are two ways of writing the same thing, why do you think we need both forms? Decimals are easier to work with. Decimals are always expressed in multiples of 10-tenths,hundredths, and thousands Fractions have all kinds of different denominators-thirds, sevenths,twelfths I want to express these fractions (1/2, ¼) as decimals, but I didn t know how. Who knows how I can use my calculator to find out? Remind students that a fraction is another form of division. Any fraction can be thought of as a division problem. The line between the numbers is like a division sign. (1/2 represents 1 divided by 2-1 divided into 2 parts) Doing the division on the calculator gives us the decimal equivalent on the display. Page Four

5 Challenge students to find several other ways to get the same decimals on A calculator, using different division problems. When we divide 1 by 2 on the calculator, we get 0.5 on the display. What other numbers could you divide to get 0.5? Write 0.5 on the board, and list the division problems that students suggest. Write them both with a division sign and fractions. As a challenge give then part of another problem, such as 50 divided by? divided by 2 ½ 2 divided by 4 2/4 3 divided by 6 3/6 50 divided by? 50/? Assessment Explain that students will be making similar lists for some other decimals they have seen. Write 0.25 and a few other decimals familiar to students, such as 0.75, 0.1 and 2.5. Students take a moment to think and talk to their neighbors about what fractions these decimals are equivalent to. Then they search with a calculator for 3 or 4 division problems that result in each decimal, keeping a list of each one. Homework Students could be given a list of fractions to be converted to decimals. Page Five

6 Decimals on Grids Lesson Summary Student use a model decimal grid representing tenths and hundredths on grids. Then they play a decimal game, Fill Two which involves combining decimals on a grid. Materials Blank squares **Decimal grids (tenths, hundredths,thousandths,ten-thousandths) **Decimal grid transparency **Decimal cards (set A and B) **Directions for Fill Two Overhead projector Crayons/Markers Opening Show students the blank square you have prepared. Explain that this is one whole. Place a transparency of Decimal Grids on the overhead projector. These grids are similar to those you used to show fractions and percents, but these show how one whole can be divided into decimals. How are the four grids different? Allow students time to figure and discuss the number of parts in each grid. The first grid is divided into 10 equal parts, the second into 100, the third into 1000, and the fourth into 10,000. Lesson Description Write 0.1 on the board or overhead. Have volunteers come to the overhead and color in one-tenth on each of the grids. Which grid clearly shows one-tenth? How would we write one tenth as hundredths,as thousandths, and as ten-thousandths. For each grid write it both as decimal and a fraction. Students discuss the question in small groups, write down their answers and then share responses. Write 0.25 and 0.3 on the board. Which of these decimals is greater? Invite students to illustrate answers on their grids. Write 0.05,0.5 and 0.50 on the board. What s the difference between these three decimals? Which is worth the least? How do you know? Encourage students to discuss this in small groups. Page Six

7 Assessment/Homework Introduce the game Fill Two. Two students can model the game for others. Circulate and assess while students are playing the game. Cards and directions can be copied for play at home. ** Some students may find it helpful to write the percent equivalents on all the Decimal Cards. Have them write it lightly in pencil on their cards. Remind students to record below the grid each decimal they color in. Page Seven

8 Decimal Games 2 day lesson Lesson Summary Students will play three decimal games that involve ordering decimal numbers expressed in tenths, hundredths, and thousandths. Their work will focus on reading and writing decimals, ordering decimals and adding decimals. Materials **Decimal Cards (set A and B) **Decimal Grids **Directions for Smaller to Larger (student sheet) Decimals in Between (student sheet) Capture Decimals (see below) Opening Games can be introduced by modeling. Teacher and student or student to student with the teacher facilitating. Allow students time to practice each game. Capture Decimals Capture decimals is played by pairs. The deck of decimal cards is dealt out into two facedown piles, one for each player. Both players turn their top card faceup at the same time. The player who turns up the highest value takes both cards and puts them aside. As in the other two games, encourage students to use Grids or to try writing the decimals as fractions when they need help comparing the value of the two decimals. Assessment See Teacher Checkpoint Observing Decimal Games Homework All games and cards can be reproduced to play at home. Page Eight

9 Fractions Decimals 2 day lesson Lesson Summary Students find decimals of up to three digits that have a value between two given decimals. Students then find decimal equivalents for fractions on the calculator, making a Fraction to Decimal Division Table for all fractions with numerators and denominators from 1 to 12. They identify patterns within the table. Materials Calculators Overhead projector **Student Sheet (Fraction to Decimal Division Table) Opening This is a division table. It is similar to a multiplication table: The numbers we start with are shown across the top and down the left side, and the answers are recoreded in the inside boxes. You can use this division table for recording fraction and decimal equivalents. The numbers in the top row represent numerators of fractions. The numbers in the left column are denominators. Model the procedure for completing the table. For example, point to 1 in the top row and 2 in the left column, ask students what fraction that would represent, or what the decimal equivalent is (0.5), and where that number should be recorded Distribute student sheet- Fraction to Decimal Table for students to complete. Students start by filling in decimal equivalents for fractions they already know before using the calculator. Encourage students to stop and look for patterns. Assessment Students can be given a list to find equivalents Homework Additional charts can be completed at home. Page Nine

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