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1 Objectives To guide children as they make ballpark estimates; and to provide opportunities to model and practice the partialsums algorithm for - and -digit numbers. Teaching the Lesson Key Activities Children add - and -digit numbers, discuss solution methods, and make ballpark estimates to check addition results. Key Concepts and Skills Model multi-digit numbers with base- blocks. [Number and Numeration Goal ] Use basic facts to solve extended fact problems with the partial-sums algorithm. [Operations and Computation Goal ] Use base- blocks to extend the partial-sums algorithm to -digit addends. [Operations and Computation Goal ] Make ballpark estimates as a check for reasonableness of answers. [Operations and Computation Goal 5] Key Vocabulary partial-sums algorithm ballpark estimate partial-sums method Ongoing Assessment: Recognizing Student Achievement Use journal page 5. [Operations and Computation Goal ] Ongoing Learning & Practice Children play Target 5. Children practice and maintain skills through Math Boxes and Home Link activities. Differentiation Options READINESS Children use base- blocks to model -digit numbers. ENRICHMENT Children make up and solve -digit addition number stories based on a mileage map. ELL SUPPORT Children write ballpark estimate using the Word Bank template. materials Math Journal, p. 5 Student Reference Book, pp. 9 9 Home Link Teaching Master (Math Masters, p. 5; optional) base- blocks overhead base- blocks, optional materials Math Journal, p. Student Reference Book, p. Home Link Master (Math Masters, p. 5) materials Student Reference Book, pp. and 5 Teaching Aid Masters (Math Masters, pp. and ) Teaching Aid Master (Math Masters, p. ) Game Master (Math Masters, p. 5) number cards 9; base- blocks Differentiation Handbook base- blocks number cards 9, of each; paper Technology Assessment Management System Journal page 5 See the itlg. Lesson 5

2 Getting Started Mental Math and Reflexes Ask such questions as the following: Is closer to or 5? Is 5 closer to 5 or? Is 95 closer to 9 or? Same distance away Is 5 closer to or? Same distance away Is closer to or? Is 99 closer to 9 or,?, Is, closer to, or,?, Is, closer to, or,5?, Is,5 closer to, or,? Same distance away Math Message Add. 5 9 Unit miles Home Link Follow-Up Review answers as necessary. Have a few children share their strategies for solving the number stories. Teaching the Lesson NOTE Partial sums may be calculated in either order it does not matter whether you add the tens or the ones first. When discussing and using the partial-sums algorithm, emphasize the following paper-and-pencil method. Example:. Add the tens: [tens] [tens] [tens] or. Write below the line.. Add the ones: [ones] [ones] [ones] or. Write below the.. Add the partial sums: Draw a second line beneath and. Write beneath this line. Math Message Follow-Up Ask children how they calculated the answers. Record children s different strategies on the board. During the discussion, have children name the value in each place, not just the digits. In the first problem, for example, if a child says, I added the and the remind the class to say they added and, or tens and tens. Possible Strategies for WHOLE-CLASS DISCUSSION 5; 5; and This strategy uses the partial-sums algorithm. Take from, getting 5, and add the to ;, and 5 5. Think of as ; 5; and 5 5. s s Making Ballpark Estimates (Student Reference Book, pp. 9 9) WHOLE-CLASS. Add the s.. Add the s.. Add the partial sums. Remind children that answers should always be checked to see whether they make sense. This is true for number story problems and for problems where there is no story like those in the Math Message. Children should make a close enough, or ballpark estimate of the answer either before or after calculating by changing the addends to close but easier numbers and then adding them. Have children read about estimation on pages 9 9 in their Student Reference Books. Unit Adding and Subtracting Whole Numbers

3 Ask children to make ballpark estimates for the problems below and tell how they arrived at their estimates. Note that there is often more than one acceptable estimate. 9 is close to 9 is close to 9 5 is close to 5 5 is close to 5 or 5 is close to 9 or. Point out that because 5 is halfway between and on the number line, either or may be used as an easier substitute for 5. Name Date Time LESSON Example: Addition: The Partial-Sums Method s s. Ballpark estimate: Teaching Master s 9 Ballpark estimate:. Ballpark estimate: s s s s s s Modeling the Partial-Sums Method for -Digit Addends (Math Masters, p. 5) WHOLE-CLASS. Ballpark estimate:. Ballpark estimate: s s s s s s Remind children that in Second Grade Everyday Mathematics they used the partial-sums method to add -digit addends. Today you will show them that the partial-sums method works in the same way with -digit addends. Math Masters, p. 5 Write these problems on the board in vertical form: Ask children to gather in a circle as you demonstrate with base- blocks, or use base- blocks on the overhead projector. Refer to flats as hundreds, longs as tens, and cubes as ones. For each problem, model addition as a four-part operation: add the s, add the s, add the s, and then add the partial sums. + Example : Model 5 with base- blocks. Count out flat, longs, and 5 cubes to represent 5. Count out flats, longs, and cubes to represent. Arrange the blocks like the addition problem in vertical form. Gather the hundreds into one pile, the tens into a second pile, and the ones into a third pile. Count the hundreds. hundreds, or Count the tens. tens, or Count the ones. ones, or Add the hundreds, tens, and ones. Ask children how they would record this procedure on paper. You may use Math Masters, page 5 if you wish. s s s 5. Add the s.. Add the s.. Add the s.. Add the partial sums. Lesson

4 Adjusting the Activity Write each addend in expanded notation before adding. For example, in 5 rewrite each number in expanded notation Write out each partial sum based on the expanded notation. 5 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. Add the s.. Add the s.. Add the s.. Add the partial sums. Date LESSON s Time s Make a ballpark estimate. Write a number model to show your estimate. Choose at least two problems to solve using the partial-sums method and show your work. You may choose any method you wish to solve the other problems. Sample estimates given. Example: Ballpark estimate: Addition Methods. Ballpark estimate: s 9 5 Unit miles. Ballpark estimate: 9 9 Partial-Sums Method 9 s + s s 9. Ballpark estimate:. Ballpark estimate: 5. Ballpark estimate: 9 9 Student Page 9 Example : Model 9 5 with base- blocks. Count out and arrange the blocks as before. Gather the hundreds, tens, and ones into separate piles. Children might notice that the tens can be replaced by hundred and tens. The ones can be replaced by ten and ones. Make these substitutions, but leave the hundred and tens in the tens pile, and leave the ten and ones in the ones pile. Add the hundreds, tens, and ones:. Show children how to record this procedure on paper. Try more -digit addition problems as needed. Practicing the Partial-Sums Algorithm and Other Addition Methods (Math Journal, p. 5; Math Masters, p. 5) Children should show their work on the journal page. Remind them to make ballpark estimates for checking their answers and for finding mistakes if an answer seems unreasonable. Provide base- blocks for children to use. Children may share their answers with a partner. If there is a disagreement, encourage them to discuss their strategies with each other and do the problem again until they both can agree on an answer. Abundant practice will be found on Home Link and Math Boxes pages in future lessons. Additional problems may be created on Math Masters, page 5. Ongoing Assessment: Recognizing Student Achievement Journal Page 5 Problems and Use journal page 5, Problems and, to assess children s ability to solve multidigit addition problems. Children are making adequate progress if they are able to solve Problems and correctly, with or without the use of manipulatives. Some children may be able to solve the rest of the problems on the page, with or without manipulatives. [Operations and Computation Goal ] Math Journal, p. 5 Unit Adding and Subtracting Whole Numbers

5 Ongoing Learning & Practice Playing Target: 5 (Student Reference Book, p. ; Math Masters, pp. and 5) Children practice multidigit addition and subtraction with base- blocks by playing Target: 5. Go over the rules for Target: 5 on page in the Student Reference Book. NOTE The Target: 5 Record Sheet on Math Masters, page 5 may be used as an assessment tool. Have children record one series of turns taken to reach 5. Math Boxes (Math Journal, p. ) SMALL-GROUP Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons -5 and -9. The skill in Problem previews Unit content. Writing/Reasoning Have children write an answer to the following: Explain how you found the length of the fence in Problem. Sample answer: I added all of the sides. Date LESSON. Use addition or subtraction to complete these problems on your calculator. Enter Change to How?,5,5 5,, 9, 9,. In,5, the means the 5 means, 5 the means the means,,, 9, 9 5. Austin read his book for 5 minutes on Monday and for 5 minutes on Tuesday. How many more minutes did he read on Monday? Quantity minutes Quantity Math Boxes 5 5? Difference Math Journal, p. Student Page 5 Time. What s My Rule? in out 9 Answers vary.. Write at least 5 names for,., Sample answers:,,,, How long is the fence around the flowers? feet feet feet feet in Rule Add 9 feet out 5 5 Home Link (Math Masters, p. 5) Home Connection Children solve addition problems using - and -digit numbers. Since the partial-sums algorithm might not be familiar to parents, you might want to send home the Student Reference Book. Home Link Master Name Date Time HOME LINK The Partial-Sums Addition Method Family Note Today your child learned about adding two -digit numbers using a procedure called the partial-sums method. Your child may choose to use this method or may prefer a different procedure. For more information, see pages 5 and 5 in the Student Reference Book. 5 5 Please return this Home Link to school tomorrow. Solve each addition problem. You may want to use the partial-sums method. Use a ballpark estimate to check that your answer makes sense. Write a number model to show your estimate. Sample estimates given.. Ballpark estimate: 5 5. Ballpark estimate:. Ballpark estimate: 5 55 s s s Ballpark estimate: 5. Ballpark estimate:. Ballpark estimate:, , Math Masters, p. 5 Lesson 9

6 Differentiation Options READINESS Modeling -Digit Numbers With Base- Blocks (Math Masters, p. ) 5 5 Min To explore place-value concepts using a concrete model, have children build numbers with base- blocks. Children draw two cards and place them on a Place-Value Mat to make a -digit number. They put longs in the tens column to show the tens digit and cubes in the ones column to show the ones digit. On a half-sheet of paper, children draw a picture to show what they did. They write the number in standard notation and in expanded notation under the picture. (See margin.) NOTE The numbers indicate distances between cities based on routes usually followed by motorists, except for Hawaii and Alaska, which are distances by air. ENRICHMENT Making Up Addition Problems from a Mileage Map (Student Reference Book, pp. and 5; Math Masters, p. ) SMALL-GROUP 5 5 Min Social Studies Link To apply children s understanding of addition, have them write and solve addition number stories. Children study the U.S. mileage map in the Student Reference Book, on pages and 5. Pose problems like the following to be sure that children understand how to read the map. Find Minneapolis, Minnesota. Which city on the map is 5 miles from Minneapolis? Bismarck, North Dakota Find Seattle, Washington. How would you determine the number of miles from Seattle to Salt Lake City, Utah, by way of Boise, Idaho? Add the distance from Seattle to Boise to the distance from Boise to Salt Lake City. Children pose new addition problems to each other using the mileage map. Children may record one or two of their stories on Math Masters, page. ELL SUPPORT Building a Math Word Bank (Differentiation Handbook) SMALL-GROUP 5 5 Min To provide language support for estimation, have children use the Word Bank template found in the Differentiation Handbook. Ask children to write the term ballpark estimate, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information. Unit Adding and Subtracting Whole Numbers

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