# Objective To introduce and practice the partial-sums addition algorithm.

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1 Objective To introduce and practice the partial-sums addition algorithm. 1 Teaching the Lesson Key Activities Children are introduced to the partial-sums algorithm using base-1 blocks and paper-and-pencil computation. Children practice adding - and -digit numbers using the partial-sums algorithm and make ballpark estimates to check their answers. Key Concepts and Skills Identify the value of digits in multidigit numbers. [Number and Numeration Goal ] Use base-1 blocks and fact extensions to add two -digit whole numbers. [Operations and Computation Goal ] Use ballpark estimates. [Operations and Computation Goal ] Show understanding of addition and subtraction symbols. [Patterns, Functions, and Algebra Goal ] Key Vocabulary algorithm Ongoing Assessment: Recognizing Student Achievement and Reflexes. [Operations and Computation Goal ] Use Mental Math materials Math Journal 1, pp. 1 and 1 Home Link base-1 blocks: flats, 1 longs, 1 cubes overhead base-1 blocks (optional): longs, 1 cubes slate (optional) See Advance Preparation Ongoing Learning & Practice materials Children answer questions about the times before or after a given time of an event. Children practice fact extensions by playing the Fact Extension Game. Children practice and maintain skills through Math Boxes and Home Link activities. Differentiation Options READINESS Children use base-1 blocks to review place-value concepts. ENRICHMENT Children explain addition strategies. EXTRA PRACTICE Children solve problems using multiples of 1. Math Journal 1, pp. 1 and 11 My Reference Book, pp. 1 and 1 Home Link Master (Math Masters, p. 11) materials Teaching Masters (Math Masters, pp. 11 and 11) Teaching Aid Master (Math Masters, p. ) Minute Math +, p. per partnership: number cards labeled (optional: number cards) 1 die per partnership number cards base-1 blocks: cubes, longs, flats number grid Additional Information Background Information The problems in Mental Math and Reflexes give children practice with quickly solving mental addition. This skill is needed for making ballpark estimates and carrying out the partial-sums algorithm. Advance Preparation Plan to spend three days on this lesson. Decide how you will demonstrate the partial-sums algorithm using base-1 blocks on a flat surface with children gathered around or with blocks on the overhead projector. Technology Assessment Management System Mental Math and Reflexes See the itlg. Addition and Subtraction

2 Getting Started Mental Math and Reflexes Pose pairs of problems, such as the following:????? 1? 1, Math Message Make a ballpark estimate for each answer. Write a number model for each estimate.? 1? people Home Link Follow-Up Review answers and ask volunteers to explain the strategies they used to add and to make ballpark estimates. Problems 11 and 1 involve adding -digit numbers. Ongoing Assessment: Recognizing Student Achievement 1 Teaching the Lesson Math Message Follow-Up Mental Math and Reflexes Use Mental Math and Reflexes to assess children s progress toward solving problems involving addition of multidigit multiples of ten. Children are making adequate progress if they are able to successfully complete Level 1. Some children may be able to solve problems that have a -digit number as a sum. [Operations and Computation Goal ] On Day 1 of this lesson, children should complete the Math Message Follow-Up and be introduced to and practice the partial-sums addition algorithm using base-1 blocks. Then children should play the Fact Extension Game in Part. On Day of this lesson, children should be introduced to and practice the partial-sums algorithm as a paper-and-pencil method. Then children should complete journal page 1 in Part. On Day of this lesson, children should continue to practice the partial-sums algorithm. Then have children complete the other Part activities. Remind children that one way to make a ballpark estimate is to change the numbers in the problem to close but easier numbers that can be added mentally. For example: is close to, or 1, or, or. The exact answer to should be close to 1. is close to, or, or, or. The exact answer should be near. Or notice that is. That leaves, which is close to, or 1. Thus, is close to 1, or. Introducing the Partial-Sums Addition Algorithm Using Base-1 Blocks Today children will learn and practice a single strategy for addition. (Encourage children to continue using other favorite strategies they may have for adding numbers.) Lesson

3 Date 1 Partial-Sums Addition Using Base-1 Blocks Draw base-1 blocks and write the number sentence to solve each problem. 1. Example: Example 1: Example : books Answer: books. 1 Answer: Write these two problems on the board, in vertical form: Ask children to gather around as you demonstrate how to use base-1 blocks. You may wish to use an overhead. Refer to the longs as tens and the cubes as ones. For each problem, model addition as a three-part operation: adding the, adding the, and then adding the partial sums. Example 1: Model with base-1 blocks. 1. Make a ballpark estimate before or after solving the problem. Sample answers: ; ;. Count out tens and ones to represent. Count out tens and ones to represent.. Arrange the blocks so that they resemble the vertical addition problem. (See the first model in the margin.). Collect the tens into one pile. Collect the ones into a second pile.. Count the tens. tens, or. Count the ones. ones, or. Add the counts of tens and ones. Record the answer on the board. The ballpark estimates are close to this answer, so the answer is reasonable. Example : Model with base-1 blocks. For the second example, follow the same procedure. When you count the ones, some children may notice that 1 cubes in the ones pile can be replaced by 1 long; you can make this substitution. There are still two piles of blocks: the tens pile (with tens), and the revised ones pile (with ones). Summary These examples using base-1 blocks illustrate the steps of the partial-sums method for addition: 1. Add the tens.. Add the ones.. Add the partial sums of tens and ones to obtain the final answer. Children do several problems at their desk. Have them describe exactly what they are doing at each step.. 1 Answer: 1. Answer: 1 Practicing Addition Using Base-1 Blocks (Math Journal 1, p. 1) PARTNER Partners use base-1 blocks to practice the partial-sums algorithm. Math Journal 1, p. 1 Addition and Subtraction

4 Introducing the Partial-Sums Algorithm as a Paper-and- Pencil Method Date Addition Practice Write a number model to show your ballpark estimate. Solve the problem. Show your work. Use the ballpark estimate to check whether your exact answer makes sense. Sample estimates: Review the partial-sums addition with base-1 blocks using the same two problems: and. Next, on the board or overhead, demonstrate the paper-and-pencil method for solving these problems. As a reminder of place value, write and above the columns and use the same language to describe and. Example: 1. Find a ballpark estimate. ; ;. Add the tens. tens tens tens, or. Write below the line.. Add the ones. ones ones ones, or. Write below.. Add the partial sums. Draw a second line beneath and. Write beneath this line. In this example, the tens were added first. However, the partial sums may be calculated in either order it does not matter whether the tens or the ones are added first. For the second example, follow the same procedure again to find and add the partial sums and 1, checking the answer against a ballpark estimate. Tell children that the method illustrated by these examples is called an algorithm. An algorithm is a step-by-step set of instructions for doing something. Write algorithm on the board. Practicing the Partial-Sums Algorithm Write several multidigit addition problems on the board. Start by adding together a -digit and a 1-digit number. Most problems should have -digit addends. Using slates or paper, have children describe exactly what they are doing at each step. Correct errors in calculation and in method, making sure the numbers are aligned in columns. Continuing Practice with the Partial-Sums Algorithm (Math Journal 1, p. 1) Review the partial-sums algorithm. Most problems should have -digit addends, but include at least one with -digit addends. When you discuss the problem with -digit addends, write,, and above the columns as a reminder of place value. Most children will realize that the partial-sums method works the same way for -digit numbers as for -digit numbers. 1. Ballpark estimate:. Ballpark estimate:. Ballpark estimate: 1 1. Ballpark estimate:. Ballpark estimate:. Ballpark estimate: Math Journal 1, p Links to the Future This is the first time that children have been exposed to a formal paper-and-pencil addition algorithm. They will have plenty of opportunities to practice the partial-sums algorithm throughout the year. Do not expect all children to be able to perform the algorithm at the conclusion of this lesson. 1 NOTE Provide base-1 blocks for children to use when working on journal page 1. This concrete experience is essential to prepare children for the transition from concrete to abstract thought. Lesson

5 Date The of Day For Problems 1, draw the hour hand and the minute hand to show the time. 1. Luz got up at :. 1 1 She had breakfast an hour later. Show the time when she had breakfast.. The second graders went on a field trip. They left school at 1:. They got back hours later. Show the time when they got back.. Tony left home at :1. It took him half an hour to get to school. Show the time when he arrived at school.. Ming finished reading a story at 1:. It took her 1 minutes. Show the time when she started reading.. The clock shows when Bob went to bed. He went to sleep 1 minutes later. At what time did he go to sleep? : Math Journal 1, p Ongoing Learning & Practice Reviewing Telling (Math Journal 1, p. 1) Children answer questions in which they determine the times before or after the given time of an event. This activity is related to the partial-sums algorithm. In adding an initial time and an elapsed time, a common strategy is to add the hours and minutes separately and then trade minutes for an hour if the total number of minutes is or greater. Playing the Fact Extension Game (My Reference Book, pp. 1 and 1) Children practice fact extensions through the Fact Extension Game first introduced on page in Lesson -. PARTNER Math Boxes (Math Journal 1, p. 11) Date Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons - and -. The skill in Problem previews content. Writing/Reasoning Have children draw, write, or verbalize their answers to the following: In Problem, what time will it be in 1 hours? Explain how you solved this problem. Sample answer: :1. I counted up 1 hours. :1, :1, :1, 1:1, and so on. Math Boxes 1. I bought a radio for \$.. I paid with \$1.. How much change did I get? \$.. What is the temperature? Circle the best answer. A. F B. F C. F D. F F Home Link (Math Masters, p. 11) Home Connection Children use the partial-sums algorithm to solve multidigit addition problems.. Write three even and three odd -digit numbers. Circle the even numbers. Sample answers: 1. What time is it? : What time will it be in 1 minutes? 1 : 1 1 Differentiation Options. Find the rules Math Journal 1, p. 11. Use your Pattern-Block Template. Draw the triangles. What is the difference between the triangles? One is larger. READINESS Reviewing Place-Value Concepts (Math Masters, pp. 11 and ) PARTNER + Min To provide experience with place value, have children use base-1 blocks to explore a strategy for using the fewest base-1 blocks. Addition and Subtraction

6 Use base-1 blocks: Partners shuffle number cards, place the deck facedown between them, and draw two cards. They place the first card in the ones column on the Place-Value Mat (Math Masters, page ) and the second card in the tens column. They use the fewest base-1 blocks possible to build the number. On a sheet of paper, they record the number shown, as well as the number of tens (longs) and the number of ones (cubes). Then partners switch the two cards on the mat and repeat the procedure. Vary the activity by having children draw three cards to make -digit numbers. Use Math Masters, page 11: For each group of base-1 blocks, children represent the same number using the fewest flats, longs, and cubes possible. ENRICHMENT Using Addition Strategies (Math Masters, p. 11) 1 Min To apply children s understanding of multidigit addition, have them determine the steps of an addition strategy on Math Masters, page 11. Have children explain how the strategies work. Briefly discuss which strategy they thought was easier and why. Name Date HOME LINK Place Value Family Note Your child is learning a method for addition that focuses on place value. The child is asked to first find a ballpark estimate. (For more on ballpark estimates see page in the My Reference Book.) Find Ballpark estimate: Write a number model for your ballpark estimate. Find each sum. 1. Ballpark estimate:. Ballpark estimate:. Ballpark estimate: Ballpark estimate:. Ballpark estimate:. Ballpark estimate: Home Link Master Add the tens ( ) and write the sum. Add the ones ( 1) and write the sum. Combine the tens and ones ( 1 ) to find the final sum. Encourage your child to use the correct place-value language when using this method. For example, when adding tens in the example, say, not. We only recently introduced this method, so allow plenty of time for practice before expecting your child to be able to use it easily. 1 Please return this Home Link to school tomorrow. 1 1 Math Masters, p. 11 Try This EXTRA PRACTICE Minute Math+ SMALL-GROUP 1 Min Children practice adding multiples of 1. Model this, using the number grid to find the answer. See the following page in Minute Math: p.. Name Date Base-1 Blocks For each problem, draw a new set of base-1 blocks that uses the fewest possible number of flats, longs, and cubes Teaching Master Teaching Master Name Date Addition Strategies Addition Strategies Look at the two addition strategies below. See if you can figure out how they work. Louisa s Strategy Li s Strategy?? Now try to use either Louisa s Strategy or Li s Strategy to solve the problems below.? Sample answers: Louisa s Strategy Li s Strategy Which strategy do you think is easier? Explain. Sample answer: Louisa s strategy is easier because she is adding the tens and then adding the ones. She doesn t have to subtract anything. Math Masters, p. 11 Math Masters, p. 11 Lesson

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