Standard

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Student language:

• "I can add and subtract large numbers using the standard algorithm."

Explanation

About the Math, Learning Targets, and Rigor

This is the first-grade level in which students are expected to be proficient at using the standard algorithm to add and subtract.

*See Addition Strategy Sheet and Subtraction Strategy Sheet for previous strategies that build towards the standard algorithm.

Note for subtraction: Students should know that it is mathematically possible to subtract a larger number from a smaller number but that their work with whole numbers does not allow this as the difference would result in a negative number.

Students should be able to explain why the algorithm works.

3892 + 1567

Student explanation for this problem:

1. Two ones plus seven ones is nine ones.
2. Nine tens plus six tens is 15 tens.
3. I am going to write down five tens and think of the 10 tens as one more hundred.(notates with a 1 above the hundreds column)
4. Eight hundreds plus five hundreds plus the extra hundred from adding the tens is 14 hundreds.
5. I am going to write the four hundreds and think of the 10 hundreds as one more 1000. (notates with a 1 above the thousands column)
6. Three thousands plus one thousand plus the extra thousand from the hundreds is five thousand.

3546 - 928

1. There are not enough ones to take 8 ones from 6 ones so I have to use one ten as 10 ones. Now I have 3 tens and 16 ones. (Marks through the 4 and notates with a 3 above the 4 and writes a 1 above the ones column to be represented as 16 ones.)
2. Sixteen ones minus 8 ones is 8 ones. (Writes an 8 in the ones column of answer.)
3. Three tens minus 2 tens is one ten. (Writes a 1 in the tens column of answer.)
4. There are not enough hundreds to take 9 hundreds from 5 hundreds so I have to use one thousand as 10 hundreds. (Marks through the 3 and notates with a 2 above it.) (Writes down a 1 above the hundreds column.) Now I have 2 thousand and 15 hundreds.
5. Fifteen hundreds minus 9 hundreds is 6 hundreds. (Writes a 6 in the hundreds column of the answer).
6. I have 2 thousands left since I did not have to take away any thousands. (Writes 2 in the thousands place of answer.)

Resources

Videos

• Teaching Video (1:05-5:17)
• Khan Academy (scroll to find 4.NBT.4, click on a skill, find videos on left side in each skill)
• Learn Zillion
  • Videos
• Virtual Nerd

EngageNY Lessons

• Module 1, Topic D, Lesson 11: Use place value understanding to fluently add multi-digit whole numbers using the standard addition algorithm and apply the algorithm to solve word problems using tape diagrams.
• Module 1, Topic E, Lesson 13: Use place value understanding to decompose to smaller units once using the standard subtraction algorithm and apply the algorithm to solve word problems using tape diagrams.
• Module 1, Topic E, Lesson 14: Use place value understanding to decompose to smaller units up to 3 times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.
• Module 1, Topic E, Lesson 15: Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.
• Module 1, Topic F, Lesson 17: Solve additive compare word problems modeled with tape diagrams.

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 4th grade at bottom, then 4.NBT.4
• Common Core Sheets

Released Assessment Questions

PARCC

4.NBT.4-1

Fluently add multi-digit whole numbers using the standard algorithm.

• The given addends are such as to require an efficient/standard algorithm (e.g., 7263 + 4875). Addends in the task do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 16,999 + 3,501).
• Tasks do not have a context.
• Grade 4 expectations in CCSSM are limited to whole numbers less than or equal to 1,000,000; for purposes of assessment, both of the given numbers should have 4 digits.
• Tasks are not timed.

4.NBT.4-2

Fluently subtract multi-digit whole numbers using the standard algorithm.

• The given subtrahend and minuend are such as to require an efficient/standard algorithm (e.g., 7263 – 4875 or 7406 – 4637). The subtrahend and minuend do not suggest any obvious ad hoc or mental strategy (as would be present for example in a case such as 7300 – 6301).
• Tasks do not have a context.
• Grade 4 expectations in CCSSM are limited to whole numbers less than or equal to 1,000,000; for purposes of assessment, both of the given numbers should have 4 digits.
• Tasks are not timed.

Performance Indicators: 4.NBT.4-1, 4.NBT.4-2, 4.Int.7, 4.Int.8

Level 5: Exceeds Expectations

Solves multiple-step word and other problems by adding or subtracting multi-digit whole numbers using the standard algorithm.

Level 4: Meets Expectations

Solves two-step word problems and other problems by adding and subtracting multi-digit whole numbers using the standard algorithm.

Integrated Standards

4.Int.7

Solve one-step word problems involving adding or subtracting two four-digit numbers.

• The given numbers are such as to require an efficient/standard algorithm (e.g., 7263 + 4875, 7263 – 4875, 7406 – 4637). The given numbers do not suggest any obvious ad hoc or mental strategy (as would be present, for example, in a case such as 6,999 + 3,501 or 7300 – 6301).
• Word problems shall include a variety of grade-level appropriate applications and contexts.

4.Int.8

Solve addition and subtraction word problems involving three four-digit addends, or two four-digit addends and a four-digit subtrahend.

• The given numbers are such as to require an efficient/standard algorithm (e.g., 7263 + 4875 + 6901). The given numbers do not suggest any obvious ad hoc or mental strategy (as would be present, for example, in a case such as 6,999 + 3,501 - 5,000).

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