Which number could be labeled with this point on the number line?

There are 85 students on the playground. There are 57 fewer students in the classroom than on the playground. How many students are in the classroom? Explain or show your reasoning.

Jada says she can find \(87 - 59\) by taking away 60 from 87 and adding 1, so it is the same as \(27 + 1\) or 28. Explain or show why Jada’s method to calculate \(87-59\) makes sense.

Find the value of \(316 + 514\). Explain or show your reasoning.

Write < or > in the blank to make each statement true.

1. \(197\, \underline{\hspace{1.05cm}}\, 311\)
2. \(567\, \underline{\hspace{1.05cm}}\, 555\)
3. \(908\, \underline{\hspace{1.05cm}} \,809\)

Find the value of each expression.

1. \(206 + 543\)
2. \(327 + 181\)
3. \(674 - 129\)

Select all representations of the number four hundred twenty-three.

The height of the Empire State Building in New York City is 443 meters. The Burj Khalifa (BURJZH kah-LEE-fah) in Dubai (doo-BAI) is 828 meters. How many meters taller than the Empire State Building is the Burj Khalifa?

Find the value of each sum in any way that makes sense to you. Explain or show your reasoning.

1. \(456 + 231\)
2. \(372 + 165\)

Here are 3 different ways to find the value of \(157 + 436\).

How are the methods alike? How are they different? Explain your reasoning.

Here is Elena's algorithm for finding \(273 + 481\).

1. Where does the 100 that Elena wrote in Step 2 come from?
2. Use Elena's method to find \(255 + 372\).

1. What do the 1s above the 2 and the 5 in 253 mean in this calculation?

   

2. Use an algorithm or another strategy to find the value of each sum.

   1. \(572 + 268\)
   2. \(726 + 199\)

Here is Lin’s strategy to find the value of \(596 + 385\): “I added 600 to 385, and then took away 4.”

1. Explain why Lin’s strategy works. Then use it to find the value of \(596 + 385\).

2. For which of these expressions would you use Lin’s strategy? Explain or show your reasoning.

   1. \(436 + 173\)
   2. \(517 + 255\)
   3. \(787 + 135\)
   4. \(247 + 395\)

Write an addition problem with 3-digit numbers that you think is well suited for each of the following methods. Then find the value of the sum, using that method.

1. mental strategies
2. base-ten blocks
3. an algorithm