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1 T276 Mathematics Success Grade 6 [OBJECTIVE] The student will add and subtract with decimals to the thousandths place in mathematical and real-world situations. [PREREQUISITE SKILLS] addition and subtraction of whole numbers, decimal place value [MATERIALS] Student pages S134 S148 1 sheet of colored paper 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, difference, sum [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] (IP, I, WG) S134 (Answers are on T285.) Have students turn to S134 in their books to begin the Warm-Up. Students will practice identifying the place value of digits in decimals, including decimals to the thousandths place. Monitor students to see if any of them need help during the Warm-Up. Have students complete the problems and then review the answers as a class. {Verbal Description, Graphic Organizer} [HOMEWORK] Take time to go over the homework from the previous night. [LESSON] [1 2 Days (1 day = 80 minutes) M, GP, WG, CP, IP] SOLVE Problem (WG, GP) S135 (Answers on T286.) Have students turn to S135 in their books. The first 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, Verbal Description, Graphic Organizer}

2 Mathematics Success Grade 6 T277 Recognizing Decimals Adding Decimals to Hundredths (CP, IP, WG) S135 (Answers on T286.) IP, CP, WG: Have students complete Problems 1 5 on S135. Students will review the meaning of the value of decimals. Discuss the answers as a class. Have students write 0.2 = 0.20 beside the models in Problem 1. {Pictorial Representation, Verbal Description} Adding Decimals to Hundredths (M, GP, CP, WG, IP) S135, S136, S137 (Answers on T286, T287, T288.) M, GP, CP, WG: Use the following modeling activity to build the concept of adding decimals through hundredths. Assign the roles of Partner A and Partner B. {Verbal Description, Pictorial Representation, Graphic Organizer} Step 1: Have students look at Problem 6 on the bottom of S135. Have students shade in two tenths of the first model. Have the students shade in four tenths of the second model. Partner A, if the two shaded decimal models were added together, what would the sum be? (six tenths) Partner B, how would you write six tenths as a decimal? (0.6) Record. Partner A, how can we write the number sentence? (Two tenths plus four tenths is equal to six tenths.) Record. The steps for Problem 6 are shown below. Shade the models. addend 0.2 addend sum 0.6 Find the sum. Step 2: Have students complete Problem 7 using the same procedure as in Step 1. Students will be adding decimals with hundredths.

3 T278 Mathematics Success Grade 6 Step 3: Have students turn to page S136. Have students describe how the model for the problem on the top of S136 is different from the two problems on S135. (One of the problems on S135 has two addends that are tenths and the other problem has two addends that are hundredths. The problem on the top of S136 has one addend that is tenths and one addend is hundredths.) Have students shade in three tenths (0.3) in the first model. Have students shade in twenty hundredths (0.20) in the second model. Step 4: Partner A, what do you notice about the models? (The square models represent equal amounts of space.) Record. Have student pairs fill in the first addend in the chart in Problem 2. (0.3) Record. Have student pairs fill in the second addend in the place value chart in Problem 2. (0.20) Record. Step 5: Partner B, what is the sum of the two addends? (0.5 or 0.50) Record. Partner A, how can we write the number sentence using the decimals with the hundredths? (Thirty hundredths plus twenty hundredths is equal to fifty hundredths.) Record. Partner B, what did we do to the first addend so that the two addends would have the same number of places behind the decimal point. (added a zero as a place holder) Partner A, did adding the zero as a place holder change the value of the decimal? (No, because 0.3 is equivalent to 0.30.) Have students look at Question 5. If 0.50 is equal to (0.5), 0.20 is equal to (0.2) and 0.30 is equal to (0.3), how could you write the decimal number sentence that is equivalent to the one in Question 4 using tenths. Record. (Three tenths plus two tenths is equal to five tenths.) Record. CP, IP, WG: Have students work in cooperative pairs to complete Problems 1 and 2 on page S137. Students will use the model to write the addition problems in the table and then write the addition problem to determine the sum. Review the answers as a whole group. {Verbal Description, Pictorial Representation, Graphic Organizer}

4 Mathematics Success Grade 6 T279 Adding Decimals to Thousandths (M, GP, CP, WG) S137 (Answers on T288.) M, GP, CP, WG: Students will extend the addition of decimals from the hundredths to the thousands. Make sure students know their designation as Partner A or Partner B. {Verbal Description, Pictorial Representation, Graphic Organizer} Adding Decimals to Thousandths Step 1: Have students look at Problem 3 on S137. How is this problem different from Problems 1 and 2? (There is no pictorial model.) Partner A, what is the first addend? (fifty-one hundredths) Record in the graphic organizer. Partner B, what is the second addend? (two hundred thirty-six thousandths) Record in the graphic organizer. Step 2: Partner A, what can we do so that both addends have the same number of place values? (Add a zero as a place holder.) Ones. Tenths Hundredths Thousandths Sum Write the 0 in the thousandths place of the first addend. Write the outside the place-value chart Bring the decimal point straight down and find the sum. Partner B, what is the sum? (0.746) Record.

5 T280 Mathematics Success Grade 6 Subtracting with Decimals (M, WG, GP, CP) S138 (Answers on T289.) M, GP, CP, WG: Students will explore subtraction of decimals. Make sure students know their designation as Partner A or Partner B. {Verbal Description, Pictorial Representation, Graphic Organizer} Subtracting with Decimals Step 1: Have students look at Problem 1. Partner A, when creating a model for subtraction, which value do we represent? (the first value) Have students shade the nine tenths for Problem 1. Have students cross out three tenths. Partner B, how many tenths are left? (0.6) Record. Have students write the subtraction problem. Partner A, what do you know about the decimals when subtracting? (The decimal points must be lined up.) Record. Step 2: Have students complete Problem 2 using the procedure from Step 1. Review the answer for the subtraction problem. Step 3: Have students look at Problem 3. Partner A, how many hundredths do we shade? (fifty-six hundredths) Have students shade in the figure. Partner B, how do we model the subtraction of the thirty hundredths? (Cross them out on the model.) Partner A, what is the difference? (0.26) Record. Have students write the subtraction problem. Partner B, what do you know about decimals when subtracting? (The decimal points must be lined up.) Record. Step 4: Have students complete Problem 4 and review the answers as a whole group.

6 Mathematics Success Grade 6 T281 Subtracting with Decimals with Mixed Numbers (M, WG, GP, CP) S139 (Answers on T290.) M, GP, CP, WG: Students will extend the subtraction of decimals to mixed numbers. Make sure students know their designation as Partner A or Partner B. {Verbal Description, Pictorial Representation, Graphic Organizer} Subtracting Decimals with Mixed Numbers Step 1: Partner A, what is different about Problem 1 from the problems we have been subtracting? (The decimal value of the minuend is greater than 1.) Partner B, what does the model represent? (1.5) Step 2: Model how to cross out 1.2 by crossing out one whole and two tenths on the model. Have students do the same in their books. Write the problem numerically lining up the decimal points. 1.5 minuend 1.2 subtracted 0.3 difference Partner A, how many shaded tenths are left? (3) Record. Have students write the subtraction problem. Partner B, what is true about decimals? (When subtracting the decimal points must be lined up.) Record. Step 3: Have students complete Problem 2 creating the model and writing the subtraction problem.

7 T282 Mathematics Success Grade 6 Subtracting with Decimals to Thousandths (WG, CP. M, GP, IP) S139 (Answers on T290.) Subtracting with Decimals to Thousandths Step 1: Have students look at Problem 3. Partner A, what is different about this problem from other subtraction problems that we have worked with? (There is no pictorial model.) Partner B, explain how we can rewrite the problem so that we can line up the decimal points. (Write it in a vertical orientation.) Have students write the problem and subtract. Partner A, what do we need to remember when subtracting decimals? (Always line up the decimal points.) Partner B, what is the difference for Problem 3? (0.019) Step 2: Have students complete Problems 4 6 and then review the answers as a whole group. Add and Subtract Decimals (CP, IP, WG) S140 (Answers on T291.) IP, CP, WG: Have students work in cooperative pairs to complete Problems 1 10 on page S140. Students will need to rewrite the decimal problems and align the decimal points. Review the answers as a whole group. {Verbal Description, Graphic Organizer}

8 Mathematics Success Grade 6 T283 Decimal Foldable Addition and Subtraction (M, GP) Decimal Foldable Addition and Subtraction 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 first two sections Add with Decimals and Subtract with Decimals, from left to right. Write the steps for adding decimals in the first section and for subtracting decimals in the second section. SOLVE Problems - Add and Subtract with Decimals (GP, WG) S141-S146 (Answers on T292-T297.) 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, Algebraic Formula, Verbal Description} IP, CP, WG: Have students complete the SOLVE problems on S142-S146 {SOLVE, Verbal Description, Graphic Organizer, Algebraic Formula}

9

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