T344 Mathematics Success – Level Fntnmath.kemsmath.com/LEVEL F TEACHER NOTES/LEVEL F LESSON 12 LESSON NOTES.pdfT344 Mathematics Success – Level F LESSON 12: Add and Subtract with

Mathematics Success – Level FT344

LESSON 12: Add and Subtract with Decimals

[OBJECTIVE]

The student will add and subtract with decimals to the thousandths place.

[MATERIALS]

Student pages S113–S123Transparencies T354, T356, T358, T360, T362, T364, T3671 sheet of paper per student for decimal foldable

[ESSENTIAL QUESTIONS]

1. Why is it important to know how to add decimals?2. Why is it important to know how to subtract decimals?3. How can you add and subtract decimals with different place values?

[WORDS FOR WORD WALL ]

decimals, addend, minuend, subtrahend, place holder, place value, tenths, hundredths, thousandths, sum, difference

[GROUPING]

Cooperative Pairs (CP), Whole Group (WG), Individual (I)

[LEVELS OF TEACHER SUPPORT]

Modeling (M), Guided Practice (GP), Independent Practice (IP)

[MULTIPLE REPRESENTATIONS]

SOLVE, Verbal Description, Pictorial Representation, Graphic Organizer

[WARM-UP] (5 minutes – IP, WG, I) S113 (Answers on T353.)

• Have students turn to S113 in their books to begin the Warm-Up. Students will practice identifying the place values of digits in decimals, including decimals to the thousandths place. Monitor students to see if any of them need help during the Warm-Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Verbal Description, Graphic Organizer}

[HOMEWORK] (5 minutes)

Take time to go over the homework from the previous night.

[LESSON] (50–60 minutes – M, GP, IP, CP, WG, I)

Mathematics Success – Level F T345


SOLVE Problem (2 minutes – GP, WG) T354, S114 (Answers on T355.)

Have students turn to S114 in their books, and place T354 on the overhead. The fi rst problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to add and subtract decimals to the thousandths place. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE}

Recognize Decimals (2 minutes – GP, WG) T354, S114 (Answers on T355.)

For Problems 1–5 on S114, work through the problems with the students and discuss the answers as a class. Have students write “0.2 = 0.20” under the models on S114. {Pictorial Representation, Verbal Description, Graphic Organizer}

Add Decimals (7 minutes – M, GP, WG) T356, T358, T360, S115–S117 (Answers on T357, T359, T361.)

Use the following modeling activity to build the concept of adding decimals through hundredths. {Verbal Description, Pictorial Representation, Graphic Organizer}

MODELING

Adding Decimals to Hundredths

Step 1: Complete Problems 6 and 7 on S115 (T356) with students. For each problem, work with students to shade the models; write each problem, lining up the decimals; bring the decimal point straight down to the answer; and fi nd the sum. Tell students that the decimal points in the decimals must always be lined up, one above the other, when adding them. Refer to each decimal as an “addend,” and to the solution as a “sum.” The steps for Problem 6 are shown below.


Step 2: Next, complete Problem 1 on S116 (T358) with students. Have students shade the models as you do the same on T358. Ask students to look at the decimals. One is written in tenths (0.3), while the other is written in hundredths (0.20). Tell students that in order to add decimals with different numbers of decimal places (like 0.3 and 0.20), not only should they line up the decimal points in the decimals, but it is also best to rewrite one or more of the decimals to make sure all of the addends have the same number of decimal places. Ask students how they hold a place value in any number. (Use a 0.) Ask students if 0.3 is equal to 0.30. (Yes.)Direct students’ attention to the decimal chart on S116. Have students complete Problem 2 by fi lling in the chart as you model on T358 and then answering the questions below the chart.

Step 3: Have students turn to S117 in their books, and place T360 on the overhead. Ask students to compare Problem 1 to the ones they have been doing and describe any differences (e.g., there are whole numbers involved).Ask students to determine what decimal addend each model represents. Write the problem in the chart on T360, as students do the same on S117. Ask students how to write 1.4 so it can be added to 1.25. (It needs a 0place holder.) Remind students that 1.4 is equal to 1.40. Have students write 1.4 as 1.40 in the chart, bring the decimal point straight down, and fi nd the sum.

Add More Decimals (2 minutes – IP, CP, WG) T360, S117 (Answers on T361.)

Have students work in cooperative pairs to complete Problem 2 on S117 (T360). Monitor students closely as they complete the problem and make sure they do not have any questions. Go over the answer to Problem 2 on T361. {Verbal Description, Pictorial Representation, Graphic Organizer}

Decimals to Thousandths (2 minutes – M, GP, WG) T360,S117 (Answers on T361.)

Use the following modeling activity to build the concept of adding decimals through the thousandths. {Verbal Description, Graphic Organizer}




MODELING

Adding Decimals to Thousandths

Step 1: Ask students what would happen if they needed to add decimals to the thousandths place. Have students look at Problem 3 on S117. Ask students how many 0’s must be written in the number 0.51 in order to give both decimals the same number of decimal places. (one)

Step 2: Model how to rewrite the problem on T360 as students do the same in their books. Write the 0 in the thousandths place for the fi rst addend to create 0.510. Remind students that decimal points in the decimal addends must always be lined up, one above the other. Make connections to the problems they just did with adding the 0 as a place holder. Model for students how to write the problem in the place-value chart. Complete the problem with students, bringing the decimal point straight down in the answer and writing the sum. The steps for Problem 3 are shown below. Tell students that they follow the same rules for adding decimals to the thousandths place as they did for decimals to the hundredths place.

0.510 Write the 0 in the thousandths place of the fi rst addend.

Write the problem inside and outside the

place-value chart.

0.510

+ 0.236

0.746

Bring the decimal point straight down and fi nd

the sum.

Subtract with Decimals (4 minutes – M, GP, IP, WG, CP) T362, S118(Answers on T363.)

3 minutes – M, GP, WG: Have students turn to S118 in their books, and place T362 on the overhead. Use the following activity to review with students how to subtract with decimals to tenths.



MODELING

Subtracting with Decimals to Tenths

Step 1: Complete Problem 1 on S118 (T362) with students. Have students shade in 0.9 of the 0.9 model as you do the same. Then model for – 0.3 students how to cross out 3 of the shaded

tenths (0.3) in the problem. Ask students how many shaded tenths are left. (6) Write the problem numerically, lining up the decimal points.

Step 2: Tell students that the top number in a subtraction problem is called the minuend, the number being subtracted is called the subtrahend, and the answer is called the difference. Explain to students that decimalsmust always be lined up, one above the other, when subtracting with them.

Step 3: Solve the problem with students, bringing the decimal 0.9 point straight down in the answer, and stressing – 0.3 mathematical vocabulary. 0.6

1 minute – IP, CP, WG: Have students work in cooperative pairs to complete Problem 2 on S118 (T362). Monitor students closely as they complete the problem and make sure they do not have any questions. Go over the answer as a class using T363. {Verbal Description, Pictorial

Representation}

Subtract with More Decimals (4 minutes – M, GP, IP, WG, CP) T362, S118(Answers on T363.)

3 minutes – M, GP, WG: Use the following activity to model for students how to subtract with decimals to hundredths.



MODELING

Subtracting with Decimals to Hundredths

Step 1: Complete Problem 3 on S118 (T362) with students. Have students shade in 0.56 of the model as 0.56 you do the same. Then model for students how – 0.30 to cross out 0.30. Ask students how many shaded hundredths are left (26). Write the problem numerically, lining up the decimal points.

Step 2: Remind students that the top number in a subtraction problem is called the minuend, the number being subtracted is called the subtrahend, and the answer is called the difference. Remind students that decimalsmust always be lined up, one above the other, when subtracting with them.

Step 3: Solve the problem with students, bringing the decimal point 0.56 straight down in the answer, and stressing mathematical – 0.30 vocabulary. 0.26

1 minute – IP, CP, WG: Have students work in cooperative pairs to complete Problem 4 on S118 (T362). Monitor students closely as they complete the problem and make sure they do not have any questions. Go over the answer as a class using T363. {Verbal Description, Pictorial Representation}

Subtract with More Decimals (3 minutes – M, GP, IP, WG, CP) T364, S119(Answers on T365.)

2 minutes – M, GP, WG: Have students turn to S119 in their books, and place T364 on the overhead. Use the following activity to continue to model for students how to subtract decimals.


MODELING

Subtracting Decimals with Whole Number Parts

Step 1: Ask students to compare Problem 1 to the subtraction problems they have been doing and describe any differences (e.g., there are whole numbers involved). Ask students to determine what decimal the model represents(1.5).

Step 2: Model how to cross out 1.2 by crossing out one whole and two tenths on the model. Have 1.5 students do the same in their books. – 1.2 Write the problem numerically, lining 0.3 up the decimal points. Then complete

the rest of Problem 1 with students.

1 minute – IP, CP, WG: Have students work in cooperative pairs to complete Problem 2 on S119 (T364). Monitor students closely as they complete the problem and make sure they do not have any questions. Go over the answer as a class. {Verbal Description, Pictorial Representation}

Decimals to Thousandths (2 minutes – M, GP, WG) T364, S119 (Answers on T365.)

Use the following modeling activity to build the concept of subtracting decimals through the thousandths. {Verbal Description, Graphic Organizer}

MODELING

Subtracting with Decimals to Thousandths

Step 1: Ask students what would happen if they needed to subtract with decimals to the thousandths place. Have students look at Problem 3 on S119. Ask students how many 0’s must be written in the number 0.01 in order to give both decimals the same number of decimal places. (one)

Step 2: Model how to rewrite the problem on T364 as students do the same in their books. Write the 0 in the thousandths place for the subtrahend to create 0.010. Remind students that decimal points in the decimals must always be lined up, one above the other. Complete the problem with students, bringing the decimal point straight down in the answer and writing the difference.




Add and Subtract Decimals (10 minutes – IP, WG, CP) T364, S119, S120(Answers on T365, T366.)

Have students work in cooperative pairs to complete Problems 4–6 on S119 (T364) and Problems 1–10 on S120. On S120, ask one partner to do even problems and the other partner to do odd problems and then partner check. Monitor students closely as they complete the problems and make sure they do not have any questions. Review the answers using T365 and T366. {Verbal Description}

Decimal Foldable – Addition and Subtraction (5 minutes – M, GP, WG)

MODELING

Decimals Foldable – Add and Subtract

Step 1: Have students place a sheet of paper on their desks in front of them. The sheet of paper should be horizontal (wider across).

Step 2: Have students fold the paper in half from left to right and crease the fold.

Step 3: Have students fold the paper again from left to right and crease the fold.

Step 4: Next, have students open the paper back up to see that they have created four sections.

Step 5: Label the fi rst two sections: Adding Decimals and Subtracting Decimals, from left to right. Write the steps for adding decimals in the fi rst section and for subtracting decimals in the second section. Create a transparency to model for students what should be written on each fl ap.

SOLVE Problem (5 minutes – GP, WG) T367, S121(Answers on T368.)

Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (In order to solve the problem, students will need to know how to subtract decimals.) {SOLVE, Verbal Description}



If time permits… (10 minutes – IP, I) S122 (Answers on T369.)

Have students complete Problems 1–10 on S122. Ask students to partner check and then come back together to discuss answers. {Verbal Description}

[CLOSURE] (2 minutes)

To wrap up the lesson, go back to the essential questions and discuss them with students.

• Why is it important to know how to add decimals? (Answers will vary, but dealing with money is an example of an appropriate answer.)

• Why is it important to know how to subtract decimals? (Answers will vary, but dealing with money is an example of an appropriate answer.)

• How can you add and subtract decimals with different place values? (Using 0 as a place holder, so the decimals have the same number of place values.)

[HOMEWORK] Assign S123 for homework. (Answers on T370.)

[QUIZ ANSWERS] T371

The quiz can be used at any time as extra homework or to see how students did on adding and subtracting with decimals.


Documents

T344 Mathematics Success – Level Fntnmath.kemsmath.com/LEVEL F TEACHER NOTES/LEVEL F LESSON 12 LESSON NOTES.pdfT344 Mathematics Success – Level F LESSON 12: Add and Subtract with