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Open Number Line Banner - Decimals Congratulations on your purchase of this Really Good Stuff® Open Number Line Banner Decimals—an introduction to the open number line strategy for solving addition and subtraction problems with decimals. This Really Good Stuff® product includes: • Open Number Line Banner - Decimals, laminated • This Really Good Stuff® Activity Guide Displaying the Open Number Line Banner Decimals Before displaying the Open Number Line Banner Decimals, make copies of this Really Good Stuff® Activity Guide, cut apart the reproducibles, and file the pages for future use. Or, download another copy of it from our Web site at www.reallygoodstuff.com. Hang the Banner where students will be able to see it easily. Introducing the Open Number Line Banner Decimals As you draw a horizontal line on the board and label it with the numbers 1, 2, 3, and 4, remind students that the number line shows the numbers that we count. Then draw arrows on each end and review that the arrows indicate that the number line goes on forever in both directions. Explain that in between each whole number there are an infinite number of places that we can label with fractions or decimals because they are part of a whole number. For example, as you mark 1.5 on your number line, remind students that 1.5 is halfway between 1 and 2. Then ask students where the number 2.8 should be marked along the number line. Show additional decimals along the number line, if necessary. Emphasize that the open number line is a powerful problem-solving tool because it will let them use whatever part of the number line they need. Pointing to the Open Number Line Banner Decimals, indicate that you are going to use the Banner to show them how to use an open number line to solve problems that require addition and subtraction of decimals. Read the first problem on the Banner. Say, “From this, I know that Tory starts with 4.8 meters and needs 0.64 meters more. I need to find how much fabric she needs altogether. First, I need to find 4.8 on the number line and then add or move up the number line by 0.64. The whole number of 4 tells me that 4.8 is greater than 4 and less than 5 and the .8 tells me that it is between 4 and 5.” Point to 4.8 on the Banner. “Next, I need to think about getting to a ‘friendly’ number. When I work with decimals, I try to get to whole numbers for ‘friendly’ numbers. I know 4.8 is eight tenths away from 4, so it is two tenths away from 5. My first jump will be to 5, and I know two tenths can be written as 0.2.” Point to the +0.2 arrow and say, “I have moved two tenths of the 0.64 that I need to move up the number line, so I need to figure out the difference between two tenths (0.2) and sixty-four hundredths (0.64).” Think aloud and say, “Two tenths is equal to twenty hundredths and the difference between 20 and 64 is 44, so I need to move forty-four hundredths (0.44) farther up the number line. Because I am starting from a friendly whole number, it is easy to make this jump.” Move your finger from 5 to 5.44 and say, “Tory needed a total of 5.44 meters of fabric.” Read the next problem on the Banner. Think aloud and say, “I know Samantha had a race time of 55.28 seconds and that she wants to shave 3.1 seconds off her time. That means she wants to be 3.1 seconds faster than she is right now. To solve this, I need to start at 55.28 and subtract 3.1 or jump 3.1 down the number line. Since I’m subtracting and moving down the number line, the larger number in the problem (55.28) is labeled at the right-hand end of the line. As I think about jumping 3.1 down the number line, I need to get to a friendly number. In this problem, the closest friendly number is 55, so I am going to subtract 3. I know 55 – 3 = 52, therefore, 55.28 – 3 = 52.28. I need to move one All activity guides can be found online: Helping Teachers Make A Difference® © 2011 Really Good Stuff ® 1-800-366-1920 www.reallygoodstuff.com Made in USA #159714 Open Number Line Banner - Decimals tenth (0.1) farther down the number line, so I need to think that twenty-eight hundredths (.28) minus ten hundredths (.10) equals eighteen hundredths, so I end at 52.18. We know Samantha’s goal is 52.18 seconds.” Introducing the Adding and Subtracting Decimals Along an Open Number Line Reproducible Copy and distribute the Adding and Subtracting Decimals Along an Open Number Line Reproducible. Write the first problem 6.8 + 2.35 = on the board. Draw a number line and say, “The addition sign tells us that we will be making jumps up the number line.” Make an exaggerated arrow at the right-hand end of the line. Say, “Let’s start with the bigger number of 6.8,” and write it on the left-hand side of the number line.” Say, “The closest whole number, or friendly number, is 7, so let’s jump there. That’s a jump of +0.2.” Label the jump. Then say, “Because we jumped an extra two tenths to reach the whole number of 7, we need to subtract it from 2.35, that is 2.35 – .2 = 2.15. That means, we have 2.15 left to jump, and 7 plus 2.15 is 9.15.” Label 9.15 and the jump of +2.15. identify 58 as the closest “friendly” number and say, “Let’s get to 58 because that is the closest whole number and from there we can jump whole numbers: from 58 to 59 to 60 to 61. This means we have already jumped 3.2 up the number line. How much do we still need to jump? (Guide them, if necessary, to do: 3.6 – 3.2 = .4.) That’s right, from 61, we need to jump .4 more. So we know that Felix weighed 61.4 at the end of fifth grade.” Answers: 1) 61.4 pounds, 21.8 points, 38.88 seconds, 9.95 feet Thinking Flexibly At times, it may make sense to “over jump.” For example, write the problem 3.4 + 2.98 = on the board. Say, “This problem asks us to jump up 2.98, which is very close to the whole number 3, so we can jump up 3 to 6.4 and then back .02 to 6.38.” Challenge students to come up with multiple ways to solve the same problem. Have students compare their work with a partner and point out the similarities and differences in their strategies. Answers: 1) 9.15, 2) 4.12, 3) 44.58, 4) 14.13, 5) 30.2, 6) 14.82 Introducing the Decimals Problem Solving Along an Open Number Line Reproducible Copy and distribute the Decimals Problem Solving Along an Open Number Line Reproducible. Read the first problem together. Then say, “This problem is asking us to find how much Felix weighs now, so we need to add 57.8 and 3.6.” Label 57.8 along the number line, and explain that the class will need to jump 3.6 up the number line. Lead students to Making Connections to Other Strategies Have students solve one of the problems using other addition or subtraction strategies. Help students to recognize that there are multiple ways to solve the same problem. Encourage them to make connections between the two methods. Urge them to notice things about the order they solve the problem and the place value. Remind students that the open number line can help them keep track of their jumps a little easier. All activity guides can be found online: Helping Teachers Make A Difference® © 2011 Really Good Stuff ® 1-800-366-1920 www.reallygoodstuff.com Made in USA #159714 Adding and Subtracting Decimals Along an Open Number Line Reproducible Helping Teachers Make A Difference® © 2011 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in USA #159714 Decimals Problem Solving Along an Open Number Line Reproducible Helping Teachers Make A Difference® © 2011 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in USA #159714