Close Enough!

Est. Class Sessions: 3

Developing the Lesson

Part 1. Rounding Numbers Using Benchmarks

Compare Using Benchmarks and Base-Ten Pieces. To begin this activity, students will work with a partner. The pair will need the two Hundreds Template pages from the Student Activity Book. Ask student pairs to tape the two copies of the Hundreds Template page together as shown in Figure 1. The other student will save their template pages to use later, as needed.

Ask students to cover each of the four grids with a flat.

Ask:

How many bits are in one flat? (100)
If we skip count by 100s to find the total number of bits covering the grids, what numbers would we say? (100, 200, 300, 400)

Have students clear the flats from their pages. Ask them to work with their partner to place skinnies on each row going down and to count by tens until they reach 400. Students should record the numbers they say at the end of each row as shown in Figure 1. If students run out of skinnies before they reach 400, they can replace the skinnies on a filled grid with a flat and then continue counting by ten. Once students have completed this activity, ask them to clear their grids.

Ask students to place 1 flat, 2 skinnies, and 3 bits on the template, filling it in from the top and from left to right. See Figure 1.

Ask:

How many bits are on the board? (123)
Is 123 closer to 100 or 200? How do you know? (100; Possible response: It is just two rows back to 100. It is almost 7 rows to 200.)
123 is between which tens? (120 and 130)
Which ten is it closer to? How do you know? (120; Possible response: 123 is only 3 away from 120. It is 7 away from 130.)

Ask students to use base-ten pieces to cover 167 on the template.

Ask:

167 is between which hundreds? (100 and 200)
Which hundred is 167 closer to? How do you know? (200; Possible response: There are fewer rows to get to 200 than to go back to 100.)
167 is between which tens? (160 and 170)
Which ten is it closer to? (170)

Ask students to use base-ten pieces to cover 201 on the template.

Ask:

Which hundred is closer to 201? (200)
201 is between which two tens? (200 and 210)
Which ten is it closer to? (200)
Why does it make sense to say that 200 is the closest “ten”? (Because when we count by tens, 200 is between 190 and 210.)

Continue these types of problems choosing a variety of numbers such as 329, 303, 199, 216, 98, or 300. Make sure students focus on both hundreds and tens and the issue of which hundred or ten is closer.

Round Using Base-Ten Pieces. Explain that rounding is one estimation strategy that can be used when an exact number is not needed. When you round up you round to the closest ten or hundred benchmark that is larger than the given number and when you round down you round to the closest ten or hundred benchmark that is smaller than the given number. For now, numbers that end in 5 or 50 can be rounded either up or down since they are exactly midway between any given benchmark. The Content Note provides more information about rounding numbers that end in 5 or 50.

Rounding numbers that end in 5 or 50. Learning to round numbers without a context can be problematic. Students need to develop flexible skills that they can apply when solving problems. For example, if an estimate for the sum of 125 widgets and 146 widgets is needed, a good choice is to round 125 down to 120 and 146 up to 150. Rounding 125 down reduces the error caused by rounding 146 up. On the other hand, if you are standing in the store and trying to decide if you have enough change to buy items that cost 35¢, 89¢, and 88¢, it is prudent to round all the items up to the next dime to be sure that you have enough money.

Provide additional practice using base-ten pieces to round to the nearest ten or hundred using numbers larger than 400 such as 456, 478, 529, or 872.

For each number, ask:

To round to the nearest hundred, which two hundreds are the benchmarks we use?
Which hundred is it closest to? How do you know?
To round to the nearest ten, which two tens are the benchmarks?
Which ten is it closest to? How do you know?

Round with Number Lines. After students have practiced finding the nearest ten or hundred for a given number using the Hundreds Template page, ask them to find 23 on their desk number line.

Ask:

23 is between which two tens? (20 and 30)
Which ten is it closer to? (20) How do you know? (23 is only 3 away from 20 but it is 7 away from 30.)

Now ask students to find 97 on their desk number line.

Ask:

97 is between which two tens? (90 and 100)
Which ten is it closer to? (100)
Which hundred is it closer to? (100)

Point to 123 on the class number line.

Ask:

When you round a number to the nearest ten or hundred, you find the ten or hundred that it is closer to. Which ten is 123 closer to? (120) Explain how you decided. (Possible response: When I look at the number line, I see that 123 is between 120 and 130. 123 is 3 away from 120 and 7 away from 130, so it is closer to 120.)
Round 123 to the nearest hundred. (100) Explain how you decided. (Possible response: I looked at the number line and saw that 123 was between 100 and 200. 123 is closer to 100 because 150 would be halfway between, and 123 is less than 150.)

Direct students to the first Rounding Numbers page in the Student Activity Book, and show a display of the page. Ask students to locate 87 on their desk number lines, then work with a partner to decide about where 87 is located on the number line on the Rounding Numbers page. Ask a student to place a point on the number line in Question 1 and label it with 87.

Ask:

Do you and your partner agree with where [student's name] put 87 on the number line? Why or why not? (Possible response: We agree because we put it at about the same place. We started at 50 and counted by tens until we got to 80. Then we decided that the dot for 87 should be closer to the 90 mark than to the 80 mark, because 87 is closer to 90 than 80.)
Using your dot as a guide, round 87 to the nearest ten. (The nearest ten is 90.)
Round 87 to the nearest hundred. (The nearest hundred is 100.)

Ask students to look at the table in Question 2. Question 2A shows how to fill in the table by rounding 87 to the nearest ten and hundred. Ask students to place 36 and 25 on the number line and complete the table for Questions 2B and 2C.

For Question 2C, ask:

How did you decide where to place 25 on the number line? (We found the marks for 20 and 30 and we put it halfway in between.)
What did you write in the table? What is the nearest ten to 25?

Encourage discussion about this point. Since 25 is exactly halfway between 20 and 30, there are two “closest tens.” Students can write either 20 or 30 in the table for the closest ten. See the Content Note.

Ask students to complete the Rounding Numbers pages in class. As students work ask questions similar to those in the discussion prompts to elicit student thinking and to check their understanding of rounding to the nearest ten or hundred.

Assign the Homework section of the Rounding Numbers pages in the Student Activity Book for homework. This section is similar to the pages that students just completed, except that they work with numbers up to 400.

Student Guide:

Student Activity Book: 177 181 182

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