OA4-16 Rounding on a Grid Pages 86 87 STANDARDS 4.NBT.A.3 Goals Students will round whole numbers to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. PRIOR KNOWLEDGE REQUIRED Knowing which multiples of ten, a hundred, or a thousand a number is between Finding which multiple of ten, a hundred, or a thousand a given number is closest to. Rounding on a grid (without regrouping). Show students how numbers can be rounded on a grid. Follow the steps shown below to round 12,473 to the nearest thousand. Step 1: As before, underline the digit you are rounding to and put your pencil on the digit to the right. If the digit under your pencil is 5, 6, 7, 8, or 9, you will round up; write round up beside (or above) the grid. If the digit under your pencil is 0, 1, 2, 3, or 4, you will round down; write round down. The hundreds digit here is 4, so we write round down. Step 2: To round up, add 1 to the underlined digit; to round down, keep the digit the same. In this case, we are rounding down, so we copy the 2. 2 Isolate Step 2. If any students are struggling with Step 2, make up several examples where the first step is done for them so that they can focus only on rounding the underlined digit up or down. Sample questions: Exercises: Round the underlined digit up or down as indicated: 1 6 4 7 3 2 0 7 5 2 Once all students have mastered Step 2, move on. 5 8 2 1 5 D-9
Step 3: Change all numbers to the right of the rounded digit to zeros. Leave all numbers to the left of the rounded digit as they were. The number 12,473 rounded to the nearest thousand is 12,000. 1 2 0 0 0 Rounding with regrouping. When students have mastered rounding without regrouping, give them several examples that demand regrouping as well. Warn them that the digits to the left of the rounded digit might change now. Round the 9 up to 10 and then regroup the 10 hundreds as 1 thousand and add it to the 7 thousand. Regroup 10 0 0 1 8 0 0 0 Another way to do this rounding. Do an example together: Underline the digit you want to round to and decide whether to round up or down, as before, then change all numbers to the right of the rounded digit to zeros. We obtain (for the same example as above): 0 0 Then ASK: Which two hundreds is the number between? PROMPT: How many hundreds are in 17,978? (179 hundreds are in 17,978, so the number is between 179 hundreds and 180 hundreds) Remind students that we are rounding up (point to the picture) because the tens digit is 7 the number is closer to 180 hundreds than to 179 hundreds. Complete the rounding by writing 180, not 179, as the number of hundreds. 1 8 0 0 0 Point out that both ways of rounding get the same answer. Rounding larger numbers. Show grids with larger numbers, where regrouping does not occur. Ask students to round 538,226 to the nearest ten thousand. Here is the result they should obtain: 5 3 8 2 2 6 5 4 0 0 0 0 D-10 Teacher s Guide for AP Book 4.1
Repeat with numbers where there is regrouping. Ask students to round 745,391 to the nearest ten. Here is the result they should obtain: 7 4 5 3 9 6 7 4 5 4 0 0 Round three more large numbers that require regrouping as a class: a) round 439,889 to the nearest thousand b) round 953,219 to the nearest hundred thousand c) round 595,233 to the nearest ten thousand Students can round more such numbers individually. Exercises: Round each number to the given digit. a) thousands b) hundreds 3 9 6 7 3 1 2 9 7 1 c) ten thousands d) hundreds 1 2 9 9 3 4 6 9 9 8 7 2 Extensions 1. Regrouping twice when rounding. If you have an advanced class, you can try teaching this to the whole class. SAY: Sometimes rounding forces you to regroup two or more numbers. Let s see what to do when this happens. We want to round 3,999 to the nearest ten. First, we round 90 up to 100. 10 Then we regroup the 10 tens as 1 hundred and add it to the 9 hundreds. This gives 10 hundreds (1,000). 10 0 D-11
Now we regroup the 10 hundreds as 1 thousand and add it to the 3 thousands. 4 0 0 To finish, we complete the rounded number by adding any missing zeros. 4 0 0 0 SAY: Let s do another example with a bigger number, such as 799,994. We will round this number to the nearest hundred. First, we round 900 up to 1,000. 10 Then we regroup the 10 hundreds as 1 thousand and add them to the 9 thousands in the original number. Now we have 10 thousands. 10 0 ASK: What s the next step? (We regroup the 10 thousands as 1 ten thousand and add it to the 9 ten thousands in the original number. Now we have 10 ten thousands, or 1 hundred thousand (100,000).) 10 0 0 ASK: What s the next step? (We add 1 to the hundred thousands.) 8 0 0 0 ASK: How do we finish the rounding? (We complete the rounded number by adding any missing zeros.) 8 0 0 0 0 0 D-12 Teacher s Guide for AP Book 4.1
Have students round 3,997 to the nearest hundred and to the nearest ten; 73,992 to the nearest hundred and to the nearest ten; and 39,997 to the nearest hundred and to the nearest thousand. 2. If 48,329 is rounded to 48,300, what digit has it been rounded to? (MP.1) 3. a) Write down all numbers that round to 40 when rounded to the nearest ten. How many such numbers are there? b) Write down all numbers that round to 800 when rounded to the nearest ten. How many such numbers are there? c) What is the smallest number that rounds to 800 when rounded to the nearest hundred? What is the largest number that rounds to 800 when rounded to the nearest hundred? How many numbers round to 800 when rounded to the nearest hundred? Hint: If you wrote down all the numbers from 1 to the largest number you found, and took away all the numbers that don t round to 800, how many numbers would still be in the list? Answers a) 35, 36, 37, 38, 39, 40, 41, 42, 43, 44; there are 10 such numbers b) 795, 796, 797, 798, 799, 800, 801, 802, 803, 804; again, there are 10 such numbers c) 750 is the smallest such number, and 849 is the largest. There are 849 numbers from 1 to 849. We don t want to include all the numbers from 1 to 749. So there are 849 749 = 100 numbers in the list. D-13