Decimal Addition and Subtraction

Transcription

1 Decimal Addition and Subtraction Objective To extend methods for whole-number addition and subtraction to decimals. 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 Model decimals through hundredths with base-10 blocks. Express the values of digits in decimals. Add and subtract decimals to the hundredths place. [Operations and Computation Goal 2] Judge the reasonableness of solutions to decimal addition and subtraction problems. [Operations and Computation Goal 6] Key Activities Students discuss different methods in which to add and subtract decimals, including modeling with base-10 blocks and using algorithms. Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 118. Ongoing Assessment: Informing Instruction See page 263. Materials Math Journal 1, p. 87 Student Reference Book, pp B Study Link 4 4 Math Masters, p. 118; pp. 427 and 428 (optional) base-10 blocks quarters, nickels, dimes, pennies (optional) slate Analyzing Circle Graphs Math Journal 1, p. 88 Students compare population data presented in circle graphs. Math Boxes 4 5 Math Journal 1, p. 89 Students practice and maintain skills through Math Box problems. Study Link 4 5 Math Masters, p. 119 Students practice and maintain skills through Study Link activities. READINESS Investigating a Decimal Version of the Number Grid Math Masters, p. 427 Number-Grid Poster Students use a decimal version of the number grid to model decimal addition and subtraction. ENRICHMENT Solving Hiking Trail Problems Math Masters, pp. 120 and 121 Students compute various distances on a hiking trail. Advance Preparation For Part 1, copy and cut apart Math Masters, page 118 so that each student has one answer sheet for the Math Message. Place these sheets near the Math Message. Teacher s Reference Manual, Grades 4 6 pp Unit 4 Decimals and Their Uses

2 Getting Started Mental Math and Reflexes Pose decimal addition and subtraction problems within a money context. Suggestions: $ $0.75 = $1.25 $ $0.60 = $0.90 $ $0.70 = $0.30 $ $0.40 = $0.40 Math Message Take an answer sheet (Math Masters, page 118 ) and complete it. $ $0.25 = $1.45 $ $0.10 = $1.28 $ $1.25 = $0.50 $ $0.30 = $1.11 Study Link 4 4 Follow-Up $ $0.46 = $1.85 $ $0.63 = $3.03 $ $0.33 = $0.31 $ $0.28 = $0.17 Draw students attention to Problems 4 and 5. Problem 4 describes what should be added to the length of one tunnel to get the length of another. This is an example of a comparison situation involving addition. Problem 5 describes what one tunnel length should be multiplied by to get another tunnel length. This is an example of a comparison situation involving multiplication. Descriptions of these problem types are on Student Reference Book, pages B. Refer to these pages as you lead a discussion about the difference between these two types of comparisons. You might suggest that students sketch a situation diagram for each problem. 1 Teaching the Lesson Math Message Follow-Up (Math Masters, p. 118) PROBLEM SOLVING WHOLE-CLASS Have students discuss why the answer to the problem is incorrect. There are many ways to explain the mistake. Mention the following, if no one brings them up: Model the problem with base-10 blocks or pictures of base-10 blocks. (See margin.) This gives a total of 9 longs and 6 cubes, or Write the problem in dollars-and-cents notation = $0.76 and 0.2 = $0.20. Think of the 7 in $0.76 as 7 dimes and the 6 as 6 pennies. Think of the 2 in $0.20 as 2 dimes and the 0 as no pennies. This gives a total of 9 dimes and 6 pennies, or $0.96. Think in terms of place value = 7 tenths and 6 hundredths, and 0.2 = 2 tenths. This gives a total of 9 tenths and 6 hundredths, or Rename 0.2 as 0.20 so that both addends name hundredths. Then use an addition algorithm (0.2 = 0.20) Math Message What s wrong with this problem? What is the correct answer? Sample answer: The digits are not in the correct columns. Six hundredths plus 2 tenths is not 8 hundredths. The correct answer is Math Masters, p. 118 Lesson

3 Ongoing Assessment: Recognizing Student Achievement Math Message Use the Math Message to assess students understanding of the values of decimal digits. Students are making adequate progress if their responses indicate that the digit 6 stands for or represents 6 hundredths and the digit 2 stands for or represents 2 tenths. Some students may be able to describe how a ballpark estimate can be used to check the answer to the problem. Algorithm Project In this lesson, students use various methods to add and subtract decimals. To teach U.S. traditional addition and subtraction of decimals, see Algorithm Projects 2 and 4 on pages A5 and A15. Adding and Subtracting Decimals Using an Algorithm WHOLE-CLASS Ask: Is it possible to use the same methods for adding and subtracting decimals that you use for whole numbers? yes As with whole numbers, all digits of a given place value must be lined up correctly. One way to make sure the digits align correctly is to rename the numbers so that each has the same number of digits after the decimal point. For example, if adding or subtracting decimals in tenths and hundredths, rename the tenths as hundredths by adding a zero to the end of the numbers. When the digits are aligned correctly, the decimal points will also align. Pose several decimal addition and subtraction problems. Ask students to model their answers with base-10 blocks (or symbols). Suggestions: =? =? =? =? The zeros in boldface have been appended so both numbers have the same number of digits after the decimal point Links to the Future Do not be concerned if students use manipulatives such as base-10 blocks or bills and coins to add and subtract decimals. Students will be expected to do so without the use of manipulatives in Grade Unit 4 Decimals and Their Uses

4 Practicing Decimal Addition and Subtraction (Math Journal 1, p. 87) Students solve decimal addition and subtraction problems. Date 4 5 Student Page Time Decimal Addition and Subtraction Add or subtract mentally or with a paper-and-pencil algorithm. Pay attention to the and symbols Adjusting the Activity ELL Have base-10 blocks, coins and bills (Math Masters, page 428), and a decimal number grid (Math Masters, page 427) available. Encourage students to think in terms of the partial-sums algorithm Add the 1s: Add the 0.1s: Add the 0.01s: Find the total: A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L 7. Choose one of the problems from above. Explain the method you used to solve the problem. Sample answer: Problem 6; I rewrote the problem as $1.00 $0.67. Then I mentally thought how I would make change. $0.03 $0.05 $0.25 $0.33. Math Journal 1, p. 87 Ongoing Assessment: Informing Instruction Watch for students who do not correctly align the digits when adding and subtracting. All digits of a given place value must be written in the same column. Encourage students to use computation grid paper and record the place-value heading above each column. 2 Ongoing Learning & Practice Analyzing Circle Graphs (Math Journal 1, p. 88) Links to the Future ELL Students compare population data presented in circle graphs. To support English language learners, discuss the terms population,, and. Creating and interpreting circle graphs are Grade 5 and Grade 6 Goals. Date 4 5 Circle Graphs Time Percent is the number of people out of 100 who live in towns or cities. Percent is the number of people out of 100 who live in the countryside. Each circle graph below represents the percent of the and population of an African country. Burundi Lesotho Source: The United Nations Student Page Cameroon Namibia Central African Republic 1. For each pair, circle the country with the larger population. a. Congo Uganda b. Rwanda Gabon c. Burundi South Africa d. Namibia Lesotho 2. Which country has the greatest percentage of people living in areas? Rwanda 3. Which two countries have the greatest percentage of people living in areas? 4. Which two countries have about 1 of their people living 2 in areas and 1 2 of their people living in areas? Congo South Africa Gabon Uganda Gabon Burundi, Uganda Congo, Cameroon Try This 5. Write a question that can be answered from the information in the graphs. Then answer the question. Question: Which country has about two-thirds of its population living in areas? Answer: Namibia Math Journal 1, p. 88 Lesson

5 Date Insert,, or. Math Boxes a b c d e Fill in the missing numbers. 49 a. 28, 35, 42,,, 7 Rule: b. 56, 48, 40,,, Rule: 8 c. 81, 72, 54 45, 63,, 9 Rule: Student Page Time 2. a. Measure the length of this line segment to the nearest 1 2 centimeter. About 5.5 b. Draw a line segment 3 centimeters long. cm Solve each open sentence. a. 5.9 T 5 T 0.9 b. 9.4 K 3 K 6.4 c M 0.43 M 0.38 d. F F 8.9 e S 1.06 S 1.37 f. R R Math Boxes 4 5 (Math Journal 1, p. 89) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-7. The skill in Problem 6 previews Unit 5 content. Writing/Reasoning Have students write a response to the following: Explain how you found the value of S in Problem 4e. Sample answer: Since I knew the whole (2.43) and one of the parts (1.06), I subtracted 1.06 from 2.43 to find the value of S. 5. Add 9 tens, 8 hundredths, and 3 tenths to What is the result? Math Journal 1, p Add mentally or with a paper-and-pencil algorithm. a. 6 b , ,196 1, Study Link 4 5 (Math Masters, p. 119) Home Connection Students add and subtract decimals. They also write <, >, or = symbols to make true number sentences. Encourage students to continue bringing examples of decimals to display in the Decimals All Around Museum. 3 Differentiation Options Study Link Master READINESS Investigating a Decimal Version of the Number Grid (Math Masters, p. 427) SMALL-GROUP 5 15 Min STUDY LINK 4 5 Addition and Subtraction of Decimals Add or subtract. Show your work To explore the use of a visual organizer for understanding the base-ten place-value system for decimals, have students use a decimal version of the number grid. Have students compare the Number-Grid Poster with the decimal version. Ask: What are some similarities and differences? Possible answers: Patterns in the digits are similar in that the hundredths digit stays the same as you move down a column, and the tenths digit stays the same as you move across a row. The numbers increase by 0.01 as you move a step to the right; the numbers increase by 0.1 as you move a step down. Write,, or to make each statement true Sample answers: 9. Name two 3-digit numbers whose sum is Name two 3-digit numbers whose difference is Practice s s º g 24 g / p 6 p 14. m / 9 8 m 72 Math Masters, p Unit 4 Decimals and Their Uses

6 Ask students to solve addition or subtraction problems by counting on the grid. Examples: Write on the board. Have students put their fingers on 0.02 and count by hundredths as they move their fingers 7 steps to the right one step for each hundredth Write on the board. Have students put their fingers on 0.14 and count by hundredths as they move their fingers 10 steps to the right one for each hundredth. Or, move down one row for each tenth Teaching Aid Master Number Grid (Decimal Version) ENRICHMENT Solving Hiking Trail Problems (Math Masters, pp. 120 and 121) PARTNER 5 15 Min Math Masters, p. 427 To apply students understanding of computation with decimals to the hundredths place, have them find distances on a hiking map. 4 5 A Hiking Trail The Batona Trail is a hiking trail in southern New Jersey. The Batona Hiking Club measured the trail very carefully and found that it is about kilometers long. The trail crosses several roads, so it can be reached by car at a number of places. Carpenter Spring is at the north end of the trail. Washington Road, near Batsto, is at the trail s south end. Go to Math Masters, page 121. Teaching Master Batsto River N Hay Road Map of Batona Trail 70 Carranza Memorial WHARTON STATE Quakerbridge Carpenter Spring Deep Hollow Pond Lebanon Headquarters & Fire Tower FOREST CHATSWORTH Apple Pie Hill Fire Tower BATONA TRAIL Scale of Kilometers 563 Pakim Pond 4 5 Teaching Master A Hiking Trail continued The following table shows distances from several points of interest from the north to the south end of the trail. Fill in the missing distances. Batona Trail Point of Interest Distance from Distance from Carpenter Spring (km) Washington Road (km) Carpenter Spring Deep Hollow Pond Route Lebanon Headquarters Pakim Pond Route Route Route Apple Pie Hill Fire Tower Carranza Memorial Hay Road Quakerbridge Washington Road Batsto Lake BATSTO 542 Washington Road Batsto Historical Area New Jersey Area of this map How can you check your answers? Sample answer: Finding the sum of the two entries on each line should give you the distance of the whole trail: km. Source: Batona Hiking Club of Philadelphia Math Masters, p. 120 Math Masters, p. 121 Lesson