Model Decimals with Base-10 Blocks

Transcription

1 Model Decimals with Base- Blocks Objectives To model decimals with base- blocks; and to review decimals with money. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Use base- blocks and grids to model tenths and hundredths and write money amounts in dollars-and-cents notation; read and write decimal numbers through hundredths. [Number and Numeration Goal 1] Use base- blocks and grids to represent decimal and fraction equivalencies. [Number and Numeration Goal 5] Compare and order decimals on -by- grids. [Number and Numeration Goal 6] Key Activities Children use money and base- blocks to extend their understanding of decimal notation for tenths and hundredths. They compare and order decimal numbers. Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 138. [Number and Numeration Goal 1] Ongoing Assessment: Informing Instruction See page 354. Key Vocabulary tenths hundredths Materials Math Journal 1, pp. 114 and 115 Home Link 5 6 Math Masters, p. 138; pp. 126 and 127 (optional) transparency of Math Masters, p. 425 overhead base- cubes and longs (if available) base- flat per partnership: at least cubes and longs slate (optional) Displaying Data on a Line Plot Student Reference Book, pp , 89A, and 89B Math Journal 1, p. 64 Math Masters, p. 166A transparency of Math Masters, p. 166A (optional) Children display data of their hand spans on a line plot. Math Boxes Math Journal 1, p. 116 Children practice and maintain skills through Math Box problems. Home Link Math Masters, p. 139 Children practice and maintain skills through Home Link activities. READINESS Exploring Equivalent Names for Coins Math Masters, pp. 426 and 427 per group: pennies, dimes, slate, calculator Children explore equivalent names for a penny and a dime. ENRICHMENT Writing Names on Hundred Grids Math Masters, p. 140 optional: calculator, scissors, construction paper, glue Children find decimal values for each letter in their first names. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 132 Children add the terms tenths and hundredths to their Math Word Banks. Advance Preparation Cut apart copies of Math Masters, page 138 and place the slips near the Math Message. Set aside space on the board or class Data Pad for children to record their hand-span measures. For the optional Readiness activity in Part 3, assemble a -by- grid from Math Masters, pages 426 and 427 for each small group. Teacher s Reference Manual, Grades 1 3 pp. 60, Unit 5 Place Value in Whole Numbers and Decimals

2 Getting Started Mental Math and Reflexes Dictate numbers as children write them on their slates or on Math Masters, pages 126 or 127. Suggestions: 213,789; 506, ,002; 304,500 7,000,304; 9,078,415 For each number, ask such questions as: Which digit is in the thousands place? What is the value of the digit x? How many ten-thousands are there? Math Message Take a Math Message slip. Follow the directions. Turn to Math Journal 1, page 64. Record the measure of your hand span on the board. Home Link 5 6 Follow-Up Children share their number stories for others to solve. 1 Teaching the Lesson Math Message Follow-Up (Math Masters, p. 138) Children read their answers aloud. The word and in three dollars and fifty-one cents is used to denote the decimal point. There are dimes in a dollar, so one dime is 1_ of a dollar. Similarly, there are pennies in a dollar, so one penny is 1_ of a dollar. In dollars-and-cents notation, the first digit to the right of the decimal point stands for dimes, or tenths of a dollar; the second digit stands for pennies, or hundredths of a dollar. Make sure that all children have recorded their hand-span measures on the board or Class Data Pad. The measures will be used for the Part 2 line-plot activity. Exploring Tenths with Base- Blocks (Math Journal 1, p. 114; Math Masters, p. 425) Explain that base- blocks can be used to model tenths and hundredths. Display the transparency of Math Masters, page 425. Demonstrate that the grid has the same area as the top of a flat. Using the overhead transparency and overhead or regular base- blocks, guide children through the activities on journal page 114 as they follow along in pairs. 1. Children place a long on the inside edge of the grid on the journal page. Ask: How many longs do you need to cover the whole grid? What fraction of the grid is one long? 1_ Math Message Write the following amounts using a dollar sign and a decimal point: 1. 3 dollar bills, 5 dimes, and 1 penny $ dimes and 6 pennies $ dollar bills and 7 dimes $ pennies $0.09 Math Message Write the following amounts using a dollar sign and a decimal point: Math Masters, page 138 Adjusting the Activity Ongoing Assessment: ELL To support English language learners, clarify the difference between the ordinal meaning of tenth and a tenth as part of something; for example, tenth in line vs. tenth of a dollar. When saying the decimal place-value names, exaggerate the th sound in the word. AUDITORY KINESTHETIC TACTILE VISUAL Math Message Informing Instruction Use the Math Message to assess children s progress toward reading and writing money totals in decimal notation. Children are making adequate progress if they are able to record the money amounts for the problems, with coins and bills. Some children may be able to record the money amounts without coins and bills. [Number and Numeration Goal 1] py g g p py g g Lesson 353

3 Date 5 7 Student Page Time Place Value in Decimals If the grid is ONE, then which part of each grid is shaded? Write a fraction and a decimal below each grid Hold up a flat in one hand and a long in the other. If this (the flat) is ONE, then what is this? (Hold up the long.) 1_ 3. Write 0.1 on the board. Explain that this is another way of writing 1_ ; 0.1 is read as one-tenth. Next to 0.1 write one-tenth and 1_. 4. Write 0.2 on the board. Partners show this number on their grids with base- blocks. Place two longs on the grid. How do you read this decimal? Two-tenths Next to 0.2, write two-tenths and 2_. Repeat with other tenths, such as 0.3 and 0.4. cube long flat big cube 1 fraction: 2 5 or or or 0.50 fraction: 8 fraction: Math Journal 1, p. 114 ONE 1, one-tenth two-tenths three-tenths four-tenths ONE The value of the base- blocks depends on which block is ONE. Ongoing Assessment: Informing Instruction A Flat Teaching Aid Master Watch for children who are having difficulty understanding that the value of base- blocks can change. Explain that base- blocks model numbers, but their values can change depending on which block is defined as the ONE. For decimals, it s often better to define the flat as the ONE. Exploring Hundredths Using Base- Blocks (Math Journal 1, p. 114) Go through the following procedure with the class: 1. Children place a single cube in a corner along the inside edge of the grid on journal page 114. Ask: How many cubes do you need to cover the whole grid? What fraction of the grid is one cube? 1_ 2. Hold up a flat in one hand and a cube in the other. If this (the flat) is ONE, then what is this? (Hold up the cube.) 1_ Math Masters, p Unit 5 Place Value in Whole Numbers and Decimals

4 3. Write 0.01 on the board and remind the class that this is another way of writing 1_. Explain that 0.01 is read as onehundredth. Next to 0.01, write one-hundredth and 1_. 4. Write 0.05 on the board and ask children how to show this number with base- blocks on their grids. Place five cubes on the grid. How do you read this decimal? Five-hundredths Next to 0.05, write five-hundredths and 5_. Repeat with other hundredths, such as 0.13 and Date Student Page Time Place Value in Decimals continued 4. Which decimal in each pair is greater? Use the grids in Exercises 1 3 to help you. 0.5 or or or Color part of each grid to show the decimal named. 5. Color 0.7 of the grid. 6. Color 0.07 of the grid. 7. Color 0.46 of the grid. Comparing and Ordering Decimals on a Square Grid (Math Journal 1, pp. 114 and 115) PROBLEM SOLVING 8. Write 0.7, 0.07, and 0.46 in order from smallest to largest. Use the grids in Exercises 5 7 to help you Try This Color part of each grid to show the fraction named. 9. Color 4_ of the grid.. Color 1_ 2 of the grid. 11. Color 23_ of the grid. Children write fractions and decimals naming the shaded parts of square grids and use the grids to compare decimals. They color other grids and use them to order decimals from smallest to largest. 12. Write 23_ as a decimal Math Journal 1, p Ongoing Learning & Practice Displaying Data on a Line Plot (Math Journal 1, p. 64; Math Masters, p. 166A; Student Reference Book, pp , 89A, and 89B) Explain to children that they will make a line plot to show handspan measures for the class. As needed, review landmark data and line plots with children using Student Reference Book, pages 79-82, 89A, and 89B. Have children copy the class set of hand-span measures from the board or Class Data Pad onto blank paper in order from shortest to longest. Distribute Math Masters, page 166A to children. Draw a line for the line plot on the board or display a transparency of Math Masters, page 166A. Have children label the vertical axis Number of Children on page 166A while you write it on the board or transparency. Ask children to suggest a label for the horizontal axis and write it on the line. Sample answers: Measures of Hand Spans in Inches; Hand-Span Lengths in Inches In a similar manner, ask children to suggest a title for the line plot. Sample answer: Class Measures of Hand Spans Next, discuss the scale for the line plot. The data on hand spans shows measures to the nearest 1_ inch, so the scale should begin 2 with the shortest hand span, increase in 1_ -inch increments, and 2 end with the measurement of the longest hand span. Model writing the scale on the board or transparency while the class writes the scale on page 166A. Have children draw s to represent the class data on their line plot. Adjusting the Activity To illustrate the importance of knowing what the ONE is, hold up a flat in one hand and a long in the other. Ask: If this (the long) is ONE, what is this? (Hold up the flat.) If this (the cube) is ONE, what is this? (Hold up the flat.) AUDITORY KINESTHETIC TACTILE VISUAL Number of Children Hand Spans (Inches) Lesson 355

5 Line Plot Teaching Master Answers vary. Use the line plot to have children identify the maximum, minimum, range, and mode of the hand-span data. Next, find the median measurement of class hand spans by having children cross off an from each end of the line plot one after another until one or two remain. Math Boxes (Math Journal 1, p. 116) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-5. The skill in Problem 6 previews Unit 6 content. Title: Math Masters, p. 166A Home Link (Math Masters, p. 139) Home Connection Children write fractions and decimals naming the shaded parts of square grids. They use the grids to compare the decimals. They also color grids and use them to order decimals from smallest to largest. 3 Differentiation Options Date 1. Solve. Math Boxes = = = ,000 = 9,016 Time 2. For the number 5,749,862 the 4 means 40,000 the 5 means 5,000,000 the 8 means 800 the 7 means 700,000 the 9 means 9, ,000 = 90, What is another name for 3 dollar bills and 6 pennies? Fill in the circle for the best answer. A $3.60 B $3.06 C $30.60 D Write a division story by filling in the blanks. There are 48 chairs in 6 rows. How many chairs are in each row? 8 Write a number model = 8 Student Page Unit Solve using any method you wish Unit 6. Use a straightedge. Draw a 7-sided polygon. Sample answer: READINESS Exploring Equivalent Names for Coins (Math Masters, pp. 426 and 427) SMALL-GROUP Min To provide experience with decimals using a concrete model, have children arrange pennies on the -by- grid. Ask: How many dollars are on your grid? One dollar How many pennies are on your grid? pennies What part of a dollar is a penny? 1_ of a dollar Write one penny in decimal notation on your slate. $0.01 Children count their pennies using calculators. Have them share their ideas about what they need to enter into the calculator to count the hundredths of a dollar. Casio key sequence: 0.01 [+] [+] 0 [=] [=]... TI key sequence: 0.01 [+] [=] [=]... They choral count as the calculator counts up: one hundredth, two hundredths, and so on Math Journal 1, p Unit 5 Place Value in Whole Numbers and Decimals

6 Children exchange each row of pennies on their -by- grid for a dime. Ask: Do the coins on the grid still add up to one dollar? yes How many dimes are on your grid? dimes What part of a dollar is a dime? 1_ Write 1 dime in decimal notation on your slate. $0. Children count their dimes using calculators. Have them share their ideas about what they need to enter into the calculator to count the tenths of a dollar. Casio key sequence: 0. [+] [+] 0 [=] [=]... TI key sequence: 0. [+] [=] [=]... As soon as they put in the first [=], most calculators will change the display and drop the 0 in the hundredths place. Review with children that this is another way to write tenths. Children choral count as the calculator counts up: one tenth, two tenths, and so on. HOME LINK 1. fraction: Home Link Master Understanding Decimals Family Your child has been using grids like the ones below to understand the meaning of decimals. Note The grid is made up of squares. Each square is 1_ or 0.01 of the grid. Ten squares is 1_ or 0. of the grid. 0.8 is read as eight-tenths is read as four-hundredths is read as fifty-three hundredths Please return this Home Link to school tomorrow. If the grid is ONE, then what part of each grid is shaded? Write a fraction and a decimal below each grid. 2. 3_ or _ or 0.30 fraction: 9_ _ fraction: Which decimal is greater? Use the grids to help you. 0.3 or or or Color 0.8 of the grid. 6. Color 0.04 of the grid. 7. Color 0.53 of the grid. 8. Write 0.8, 0.04, and 0.53 in order from smallest to largest. Use the grids to help you ENRICHMENT Writing Names on Hundred Grids (Math Masters, p. 140) Min Math Masters, p. 139 To further explore representing decimal numbers on a grid, have children write each letter of their first names on a separate grid. (See margin.) They figure out the decimal value of each letter and label the letter with the decimal number. If appropriate, have children use a calculator to add the values of individual letters to figure out the total value of the letters in their names using the grid as the whole. You may want to have children cut out the grids they have made, paste them onto construction paper to form their names, label each letter with its decimal value, and display them in the room. The value of this letter K on a hundred grid is 0.2 or.20. Teaching Master Writing Names on Hundred Grids ELL SUPPORT Building a Math Word Bank (Differentiation Handbook, p. 132) SMALL-GROUP 5 15 Min To provide language support for decimals, have children use the Word Bank template found on Differentiation Handbook, page 132. Ask children to write the terms tenths and hundredths, draw a picture representing each term, and write other related words. See the Differentiation Handbook for more information. Math Masters, p. 140 Lesson 357

7 Line Plot Title: Copyright Wright Group/McGraw-Hill 166A