the number line models the expression 359 + 278. enter numbers to label each jump. first jump to the nearest…

Explanation:

Step1: Find the nearest hundred jump

The number we start with is 359. We want to jump to the nearest hundred. The nearest hundred to 359 when adding 278: first, we can think of 278 as 300 - 22 (since 300 is the nearest hundred above 278? Wait, no, the problem says "first jump to the nearest hundred then jump back the extra amount". Wait, actually, when adding 359 + 278, we can decompose 278 as 300 - 22. So first, we add 300 to 359. So 359 + 300 = 659? Wait, no, wait. Wait, 359 + 300 would be 659, but then we have to jump back the extra amount. Wait, the extra amount is 300 - 278 = 22. So first jump: from 359, add 300 to get to 359 + 300 = 659? Wait, no, that can't be. Wait, maybe I misread. Wait, the number line has 359, then a jump to a number, then a jump back, and then 659? Wait, no, the final point is 659? Wait, no, the sum of 359 and 278 is 359 + 278 = 637? Wait, that's a mistake. Wait, 359 + 278: 359 + 200 = 559, 559 + 78 = 637. Wait, maybe the number line is modeled as 359 + 300 - 22. So first, jump from 359 to 359 + 300 = 659 (that's the first box), then jump back 22 (the extra amount, since 300 - 278 = 22) to get to 659 - 22 = 637. Wait, but the final point on the number line is 659? No, that must be wrong. Wait, maybe the number line is: start at 359, first jump to the nearest hundred (of the addend 278, which is 300), so 359 + 300 = 659 (first box), then jump back the extra amount (300 - 278 = 22), so the middle box is 659 - 22 = 637, and the sum is 637. Wait, but the number line has 659 as a point? Maybe I messed up. Wait, let's recalculate 359 + 278: 359 + 278. Let's do 359 + 200 = 559, 559 + 70 = 629, 629 + 8 = 637. So the sum is 637. Now, the method is first jump to the nearest hundred of 278, which is 300. So add 300 to 359: 359 + 300 = 659 (that's the first jump, the top box). Then, since we added 300 instead of 278, we have to subtract the extra 22 (because 300 - 278 = 22). So we jump back 22 from 659, so 659 - 22 = 637 (the middle box, the point before the final jump). Wait, but the final point on the number line is 659? No, that doesn't make sense. Wait, maybe the number line is: start at 359, first jump to 359 + 300 = 659 (top box), then jump back 22 to get to 659 - 22 = 637 (the sum). Wait, but the number line has 659 as a point? Maybe the diagram is: 359 -> (first jump) 659 -> (jump back 22) 637. So the first box (top) is 659, the middle box (the point after jumping back) is 637, and the small jump back is 22. Wait, but the problem says "Enter numbers to label each jump. First jump to the nearest hundred then jump back the extra amount. Enter the sum of 359 and 278 above the number line." Wait, maybe the sum is 637, the first jump (top box) is 359 + 300 = 659, the jump back amount is 22, and the middle box (the point before the final sum) is 659 - 22 = 637. Wait, let's check: 359 + 300 - 22 = 359 + 278 = 637. Yes, that works. So:

First jump (top box): 359 + 300 = 659

Extra amount (jump back): 300 - 278 = 22

Sum: 359 + 278 = 637

Wait, but the number line has 659 as a point? Maybe the diagram is: start at 359, jump to 659 (first box), then jump back 22 (small box) to get to 637 (sum). So the labels are:

Top box (first jump): 659

Middle box (after jumping back): 637

Small jump back: 22

Sum: 637

Wait, but let's verify the addition: 359 + 278. Let's do 359 + 278:

359 + 278 = 359 + (300 - 22) = (359 + 300) - 22 = 659 - 22 = 637. Yes, that's correct. So the first jump is to 659 (359 + 300), then jump back 22 (the extra), resulting in 637 (the sum).

Step2: Calculate the sum

359 + 278 = 637. Alternatively, using the number line method: 359 + 300 = 659, then subtract 22 (since we added 300 instead of 278, the difference is 22) to get 659 - 22 = 637.

Step3: Label the jumps

• First jump (top box): 359 + 300 = 659
• Jump back amount (small box): 300 - 278 = 22
• Middle box (after jumping back): 659 - 22 = 637 (which is the sum)

Wait, but the problem says "Enter numbers to label each jump. First jump to the nearest hundred then jump back the extra amount. Enter the sum of 359 and 278 above the number line." So the sum is 637, the first jump (top) is 659, the jump back is 22, and the middle point (after jumping back) is 637.

Answer:

Top box (first jump): 659

Small jump back: 22

Middle box (sum): 637

Sum: 637

(Note: Depending on the number line's structure, the labels might be: top box: 659, middle box (sum): 637, small jump back: 22)