# Place Value, Rounding, Addition, and Subtraction

## Objective

Fluently add multi-digit whole numbers using the standard algorithm involving up to two compositions. Solve one-step word problems involving addition.

## Materials and Resources

• Base ten blocks  — Optional

## Common Core Standards

### Core Standards

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• 4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.

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• 3.NBT.A.2

## Criteria for Success

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1. Add multi-digit numbers with up to two compositions.
2. Solve one-step word problems involving addition with up to two compositions, using a letter to represent the unknown (MP.4).

## Tips for Teachers

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• When discussing how to line up numbers in order to add or subtract them vertically, emphasize that units need to be lined up because one can only add or subtract like units (ones with ones and tens with tens) as opposed to saying that numbers need to be lined up from right to left. This is an important distinction since lining numbers up from right to left no longer works when students begin working with decimals (e.g., adding 6.4 and 2.08 would result in an incorrect sum if lined up from right to left).
• Students have solved one-step word problems involving addition in previous grade levels (1.OA.1, 2.OA.1, 3.OA.8), so the intention here is to have students solve contextual problems that involve computations expected of this grade level (4.NBT.4) as well as prepare students to solve multi-step word problems involving addition and subtraction later in the unit, and eventually multiplication (Unit 3) and division (Unit 4) (4.OA.3).
• Before the Problem Set, you could have students play "Climbing Chimney Rocks" from Building Conceptual Understanding and Fluency Through Games by the Public Schools of North Carolina. (This game only includes small computational cases, so it may be especially helpful if students would benefit from some practice with smaller values that can be modeled using proportional base ten blocks before working with larger values.)

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Ms. Cole and Ms. Dowling want to know the largest number they can represent with their base ten blocks.

Ms. Dowling has 3 thousands, 3 tens, 1 hundred, and 4 ones. Ms. Cole has 2 thousands, 4 hundreds, 9 tens, and 3 ones. What’s the largest number they could represent with their base ten blocks? Show or explain how you know.

### Problem 2

Estimate. Then solve.

1.    40,762 + 30,473 = _________
2.    _________ = 258,209 + 48,906

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 7 > Topic B > Lesson 11Concept Development

Grade 4 Mathematics > Module 7 > Topic B > Lesson 11 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 3

The Lane family took a road trip. During the first week, they drove 907 miles. The second week they spent more time in each place they visited and only drove 287 miles. How many miles did they drive during both weeks?

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic D > Lesson 11Concept Development

Grade 4 Mathematics > Module 1 > Topic D > Lesson 11 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

## Discussion of Problem Set

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• Look at #1b. What is the largest place value in the sum? What is the largest place value in each of the addends? Why are they different?
• Look at #1g. Did anyone solve a different way? Are either or both addends near benchmark numbers that can be added together and then adjusted for after adding? How could you use a similar strategy for #2?
• Look at #3. What was Elizabeth’s mistake? How did you fix it?
• Look at #5. This seems to be a takeaway problem. So why can you solve it using addition?
• Do you prefer adding on a place value chart or with the standard algorithm? Why?
• How is recording the regrouped number in the next column when using the standard algorithm related to regrouping on the place value chart?
• If you have 2 addends, can you ever have enough ones to make 2 tens, or enough tens to make 2 hundreds, or enough hundreds to make 2 thousands? Try it out with your partner. What if you have 3 addends?