Lesson 16 | Place Value, Rounding, Addition, and Subtraction | 4th Grade Mathematics

Objective

Fluently subtract multi-digit whole numbers using the standard algorithm involving up to two decompositions. Solve one-step word problems involving subtraction.

Common Core Standards

Core Standards

The core standards covered in this lesson

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

Number and Operations in Base Ten

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

Foundational Standards

The foundational standards covered in this lesson

3.NBT.A.2

Number and Operations in Base Ten

3.NBT.A.2 — Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Subtract multi-digit numbers with up to two decompositions.
Solve one-step word problems involving subtraction with up to one decomposition, using a letter to represent the unknown (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

As noted previously, 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).
It is important not to say things like “you cannot take a bigger number from a smaller number” when discussing subtraction, since this is in fact possible to do, it would just result in a negative number, which students won’t see until Grade 7 (7.NS.1). Instead, you can say things like “there are not enough ones/tens/etc., to subtract.”
When subtraction requires decomposition, doing all necessary decomposition before subtracting will help to avoid errors. Take 425 – 278, for example. “The total 425 does not have enough tens or ones to subtract the 7 tens or 8 ones in 278. Therefore one hundred is decomposed to make ten tens and one ten is decomposed to make ten ones. These decompositions can be done and written in either order; starting from the left is shown because many students prefer to operate in that order. In the middle step, one hundred has been decomposed (making 3 hundreds, 11 tens, 15 ones) so that the 2 hundreds 7 tens and 8 ones in 278 can be subtracted. These subtractions of like units can also be done in any order. When students alternate decomposing and subtracting like units, they may forget to decompose entirely or in a given column after they have just subtracted (e.g., after subtracting 8 from 15 to get 7, they move left to the tens column and see a 1 on the top and a 7 on the bottom and write 6 because they are in subtraction mode, having just subtracted the ones)” (NBT Progression, p. 10). Thus, decomposing first both allows students to decompose in any order as well as avoid common errors. This process would look like this:

Students have solved one-step word problems involving subtraction in previous grade levels (1.OA.1, 2.OA.1, 3.OA.8), just not yet with whole numbers of this magnitude. So, the intention of the word problems in this lesson 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).

Lesson Materials

Base ten blocks (4 thousands, 2 hundreds, 15 tens, and 9 ones per student or small group) — See Anchor Task 1 for more information.
Millions Place Value Chart (1 per student) — Students might need more or less depending on their reliance on this tool.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Sets of utensils for lunch come in cartons of ten. Those cartons of ten come in boxes of ten. Those boxes of ten come in packages of ten.

Ms. Ruizdeporras has 4 packages, 2 boxes, 5 cartons, and 9 individual sets. After one week, she has 2 packages, 1 box, 7 cartons, and 1 individual sets left. How many sets of utensils did Ms. Ruizdeporras use in one week?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic E > Lesson 13 — Concept Development

Grade 4 Mathematics > Module 1 > Topic E > Lesson 13 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 Fishtank Learning, Inc.

Problem 2

Estimate. Then solve.

a. __________ = 22,397 – 3,745

b. 214,290 = 193,007 + __________

Guiding Questions

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Problem 3

The paper mill produced 73,458 boxes of paper this month. Last month, it produced 65,606 boxes of paper. How many more boxes of paper did it produce this month compared to last month?

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Compare your answers for #1(a) and (b). How are your answers the same when the problems are different?
Compare #1(a) and (f). Does having a larger whole in 1(a) give an answer greater than or less than 1(f)?
What pattern did you notice between #1(d) and (e)?
Look at #3. What mistake did Danny make? What should his answer have been?
What values did you come up with for #7(a)? (b)? (c)? (d)?
When do we need to unbundle to subtract?
What are the advantages and disadvantages to modeling subtraction using a place value chart? With the standard algorithm?
Why must the units line up when subtracting? How might our answer change if the digits were not aligned?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve. Show or explain your work.

a. $$\begin{align} 7,396 \\ {–\ 2,145}& \\ \hline \end{align}$$

b. $$87,625-5,031=$$ ______

c. $$\begin{array}{r} &19,850\\ -\!\!\!\!\!\!&15,761\\ \hline \end{array}$$

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 15

Lesson 17

Lesson Map

Topic A: Place Value of Multi-Digit Whole Numbers

Review place value understanding for numbers within 1,000.

4.NBT.A.1 4.NBT.A.2 4.NBT.A.3 4.NBT.B.4

Build numbers to 10,000 and write numbers to that place value in standard, unit, and expanded form.

4.NBT.A.1 4.NBT.A.2

Model and write numbers to 10,000 with more than 9 of any unit in standard and unit form.

4.NBT.A.1 4.NBT.A.2 4.NBT.B.4

Build numbers to 1,000,000 and write numbers to that place value in standard and unit form.

4.NBT.A.1 4.NBT.A.2

Multiply and divide single units by 10. Recognize that a digit represents 10 times the value of what it represents in the place to its right.

4.NBT.A.1

Multiply and divide multiple units by 10. Apply the property of “ten times greater” in the context of problems.

4.NBT.A.1

Topic B: Reading, Writing, and Comparing Multi-Digit Whole Numbers

Read and write multi-digit numbers using base-ten numerals, number names, and expanded form.

4.NBT.A.2

Locate multi-digit numbers on a number line and explain their placement.

4.NBT.A.2 4.NBT.A.3

Compare numbers based on the meanings of the digits using >, <, or = to record the comparison.

4.NBT.A.2

Topic C: Rounding Multi-Digit Whole Numbers

Round multi-digit numbers to their largest place.

4.NBT.A.3

Round multi-digit numbers to any place.

4.NBT.A.3

Round multi-digit numbers to any place in more complex cases, including those involving real-world contexts and/or assessing the reasonableness of that estimate.

4.NBT.A.3

Topic D: Multi-Digit Whole-Number Addition and Subtraction

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

4.NBT.B.4

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

4.NBT.B.4

Solve multi-step word problems involving addition, using rounding to assess the reasonableness of answers.

4.NBT.B.4 4.OA.A.3

Fluently subtract multi-digit whole numbers using the standard algorithm involving up to two decompositions. Solve one-step word problems involving subtraction.

4.NBT.B.4

Fluently subtract multi-digit whole numbers using the standard algorithm involving multiple decompositions. Solve one-step word problems involving subtraction.

4.NBT.B.4

Solve multi-step word problems involving subtraction, using rounding to assess the reasonableness of answers.

4.NBT.B.4 4.OA.A.3

Solve multi-step word problems involving addition and subtraction, using rounding to assess the reasonableness of answers.

4.NBT.B.4 4.OA.A.3

Place Value, Rounding, Addition, and Subtraction

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Foundational Standards

Number and Operations in Base Ten

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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