Decimal Place Value. Student Probe Read the number 1.285

Transcription

1 Decimal Place Value Student Probe Read the number.285 Answer: One and two hundred eighty five thousandths (While reading a number correctly does not indicate fluency with decimal place value, reading the number incorrectly does indicate lack of fluency.) Lesson Description In this lesson students will use base ten blocks to extend their understanding of the place value in the base ten system to decimals to the thousandths place. Rationale The base ten place value system extends infinitely on two directions: to tiny values as well as large values. It is important for students to understand that between any two place values, the ten to one ratio exists. The decimal point is simply a convention to designate the units position. Decimal numeration and notation is essential in understanding the density of the rational numbers and also for approximating irrational numbers. Preparation Distribute base ten blocks to each student. At a Glance What: Extending place value structures to include decimals. Common Core State Standard: CC.5.NBT.3a. Read, write, and compare decimals to thousandths. (a) Read and write decimals to thousandths using base ten numerals, number names, and expanded form. Mathematical Practices: Attend to precision. Look for and make use of structure. Who: Students who cannot extend place value structures to include decimals Grade Level: 4 Prerequisite Vocabulary: place value, ones, tens, hundreds, tenths, hundredths, thousandths, decimal Prerequisite Skills: place value understanding of whole numbers (ones, tens, hundreds, etc.) Delivery Format: Individual, pairs, small groups Lesson Length: 5 30 minutes Materials, Resources, Technology: Base ten blocks, sticky notes, visual display Student Worksheets: None

2 Lesson The Expect students to say or do If students do not, then the. We are going to use the base ten blocks, but we are going to use them in a different way. 2. Look at the large cube. What amount does it usually represent? 3. Pick up a flat. What amount does it usually represent? How many flats would fit in a large cube? 4. Pick up a rod (stick). What amount does it usually represent? How many rods are in a flat? How many rods are in a large cube? 5. Look at the small cubes. How many small cubes are in a rod? How many small cubes are in a flat? How many small cubes are in a large cube? 000 There are 000 small cubes in it. 00 There are 00 small cubes in it. 0 I can stack up 0 flats to get the same size as a large cube. 0 There are ten small cubes in it There are 0 rods in a flat and 0 flats in a large cube. Since 0 x 0 = 00, there must be 00 rods in a cube How many small cubes will fit in the large cube? How many small cubes will fit on the flat? Let s stack some flats up until they are the same size as the large cube. How many flats does it take? How many small cubes will fit on a rod? Let s count them. Lay the rods on a flat to show there are 0 rods in a flat. Count them.

3 The Expect students to say or do If students do not, then the 6. This is the change we are going to make: We are going to make the large cube represent. (Place a sticky note on a large cube and label it.) 7. That changes other things, too! We know that the large cube will contain 0 flats. What does that make one flat? (Place a sticky note on a flat and label it 0.) 8. We know the large cube contains 00 rods. What does that make one rod? (Place a sticky note on a rod and label it 00.) 9. We know that the large cube contains 000 small cubes. What does that make one small cube? (Place a sticky note on a small cube and label it 000.) There are 0 flats in the large cube. What part of the large cube is one flat? There are 00 rods in the large cube. What part of the large cube is one rod? There are 000 small cubes in the large cube. What part of the large cube is one small cube?

4 The Expect students to say or do If students do not, then the 0. I am going to model a number with the base ten blocks. Place a large cube and Count out the blocks saying, one unit, one tenth, as you touch each block. What number have I represented? Let s write that using fractions. (Write these on a visual display.). We could count all of the small cubes. How many are there? How did you do that so quickly? 2. Since each small cube is of the unit (large 000 cube), what can we call the 27? 3. That is a lot of writing! Mathematicians have a shorthand way of writing these numbers:.27. The decimal point separates the units form the parts. It always goes to the right of the units place. 4. When we read this number we say, One AND one hundred twenty One unit, one tenth, two one hundredths and 7 one thousandths small cubes Model counting the cubes for students. Prompt students.

5 seven thousandths. The Expect students to say or do If students do not, then the 5. Repeat Steps 0 4 with a variety of examples. 6. Now I am going to give you a decimal number. I want you to model it with our base ten blocks. Model the number (Say the number orally. Do not write it.) 2 large cubes and Prompt students. After allowing time for students to work, ask for a student volunteer to demonstrate for the class. Ask the volunteer to say the number, pointing to the appropriate blocks. 7. Who can write the decimal using fractions? (Ask for the same or another volunteer.) Two and two hundred fortynine thousandths Point to the blocks saying, two units, two tenths,. How many small cubes are there altogether? 8. How do we write this number as a decimal? (Ask for the same or another volunteer.) 9. Here is another number to model: (Write the number. Do not say it orally.) After allowing time for students to work, ask for a student volunteer to demonstrate for the class. If students need help adding fractions see Addition of Fraction How many units are there? How do we name the unit? How many thousandths are there? 3 large cubes and Prompt students. How many units are there? How do we name the unit? How many thousandths are there?

6 Ask the volunteer to say the number, pointing to the appropriate blocks. Three and forty two thousandths. The Expect students to say or do If students do not, then the 20. Who can write the decimal using fractions? Repeat Steps 6 9 with a variety of examples. Point to the blocks saying, three units, four hundredths,. How many small cubes all together? If students need help adding fractions see Addition of Fraction Teacher Notes. Review of place value of whole numbers and modeling with the base ten blocks prior to this lesson may be appropriate. 2. In this lesson the standard values of the base ten blocks will be altered as follows: the large cube will represent the unit, the flat will represent tenths, the rod (stick) will represent hundredths, and the small cube will represent thousandths. 3. Since decimals are simply another way of writing fractions, this lesson will first use decimal notation. Students will then use the standard decimal notation. 4. Emphasize that the decimal point, always located after the units digit, names the unit. 5. When teaching students to read and extend their knowledge of place values beyond the decimal point, emphasize the proper reading of the digits and decimal point. 6. Students will develop maximum fluency and flexibility if they are asked to model the decimals and write the decimals using standard notation, using words, and using fractional form. Variations None Formative Assessment Say the number 2.3 orally to the student(s). Represent this number with base ten blocks. Write it as a fraction. Write it as a decimal.

7 Answer: 2 large cubes and

8 References Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide Response to Intervention in Mathematics. Retrieved 2 25, 20, from rti4sucess Institute of Educational Sciences (IES). (200). Developing effective fractions instruction for Kindergarten through 8th grade. Retrieved September 5, 200 Van de Walle, J. A., & Lovin, L. H. (2006). Teaching Student Centered Mathematics Grades 5 8 Volume 3. Boston, MA: Pearson Education, Inc.