Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. 4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place.

Anchor Standard/Mathematical Practice(s)

MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.6. Attend to precision. MP.7. Look for and make use of structure.

Information Technology Standard

Use technology tools and skills to reinforce classroom concepts and activities.

Revised Bloom's Level of thinking

Understanding Analyzing

Learning Target/Task Analysis

4.NBT.1 This standard calls for students to extend their understanding of place value related to multiplying and dividing by multiples of 10. In this standard, students should reason about the magnitude of digits in a number. Students should be given opportunities to reason and analyze the relationships of numbers that they are working with. Example: How is the 2 in the number 582 similar to and different from the 2 in the number 528? Students should be familiar with and use place value as they work with numbers. Some activities that will help students develop understanding of this standard are: Investigate the product of 10 and any number, then justify why the number now has a 0 at the end. (7 x 10 = 70 because 70 represents 7 tens and no ones, 10 x 35 = 350 because the 3 in 350 represents 3 hundreds, which is 10 times as much as 3 tens, and the 5 represents 5 tens, which is 10 times as much as 5 ones.) While students can easily see the pattern of adding a 0 at the end of a number when multiplying by 10, they need to be able to justify why this works. Investigate the pattern, 6, 60, 600, 6,000, 60,000, 600,000 by dividing each number by the previous number. Misconceptions There are several misconceptions students may have about writing numerals from verbal descriptions. Number4s like one thousand do not cause a problem; however a number like one thousand two causes problems for students. Many students will understand the 1000 and the 2 but then instead of placing the 2 in the ones place, students will write the numbers as they hear them, 10002 (ten thousand two). There are multiple strategies that can be used to assist with this concept, including place-value boxes and vertical-addition method. Students often assume that the first digit of a multi-digit number indicates the "greatness" of a number. The assumption is made that 954 is greater than 1002 because students are focusing on the first digit instead of the number as a whole. 4.NBT.2 This standard refers to various ways to write numbers. Students should have flexibility with the different number forms. Traditional expanded form is 285 = 200 + 80 + 5. Written form is two hundred eighty-five. However, students should have opportunities to explore the idea that 285 could also be 28 tens plus 5 ones or 1 hundred, 18 tens, and 5 ones. Students should also be able to compare two multi-digit whole numbers using appropriate symbols. The expanded form of 275 is 200 + 70 + 5. Students use place value to compare numbers. For example, in comparing 34,570 and 34,192, a student might say, both numbers have the same value of 10,000s and the same value of 1000s however, the value in the 100s place is different so that is where I would compare the two numbers. 4.NBT.3 This standard refers to place value understanding, which extends beyond an algorithm or procedure for rounding. The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. Students should have numerous experiences using a number line and a hundreds chart as tools to support their work with rounding. Example: Your class is collecting bottled water for a service project. The goal is to collect 300 bottles of water. On the first day, Max brings in 3 packs with 6 bottles in each container. Sarah wheels in 6 packs with 6 bottles in each container. About how many bottles of water still need to be collected?

Student 1 First, I multiplied 3 and 6 which equals 18. Then I multiplied 6 and 6 which is 36. I know 18 plus 36 is about 50. I’m trying to get to 300. 50 plus another 50 is 100. Then I need 2 more hundreds. So we still need 250 bottles. Student 2 First, I multiplied 3 and 6 which equals 18. Then I multiplied 6 and 6 which is 36. I know 18 is about 20 and 36 is about 40. 40+20=60. 300- 60 = 240, so we need about 240 more bottles.

I can...

I can identify the location of a digit in a number. I can determine the value of a digit in a number. I can explain the relationship between the location of a digit and its value. I can demonstrate the value of a number using a variety of tools. I can read and write multi digit whole numbers. I can compare multi digit whole numbers. I can round multi digit whole numbers. I can explain how a multi digit number is rounded to a specific place value.

Essential Vocabulary

place value, digit, ones, tens, hundreds, thousands, million, ten times, expanded form, standard form, written form, compare, inequality, >, <, =, symbols, comparisons, round, about, approximately

Sample Assessments

On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. How many total miles did they travel? Round 368 to the nearest hundred. This will either be 300 or 400, since those are the two hundreds before and after 368. Draw a number line, subdivide it as much as necessary, and determine whether 368 is closer to 300 or 400. Since 368 is closer to 400, this number should be rounded to 400 Example or reasoning: Round 76,398 to the nearest 1000. Step 1: Since I need to round to the nearest 1000, then the answer is either 76,000 or 77,000. Step 2: I know that the halfway point between these two numbers is 76,500. Step 3: I see that 76,398 is between 76,000 and 76,500. Step 4: Therefore, the rounded number would be 76,000.

Differentiation

Intervention:

Students will make a place value chart using paper and highlighters.

Have students make checkbooks with a beginning balance and allow them to earn additional deposits. Students write checks to rent desks, use pencil sharpeners, purchase construction paper and etc. Use balance scales to compare numbers (found in Foss kit) Use a deck of cards to practice place value, making biggest/smallest number, etc.

Enrichment:

Students create and solve real world word problems.

Bring in guests from local business community (banker, grocery store manager, etc.) to explain how they use rational numbers. Given story problems work with a partner to create flash cards breaking multi-step problems down into each step.

## Common Core Standards

Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place.

## Anchor Standard/Mathematical Practice(s)

MP.2. Reason abstractly and quantitatively.MP.4. Model with mathematics.

MP.6. Attend to precision.

MP.7. Look for and make use of structure.

## Information Technology Standard

Use technology tools and skills to reinforce classroom concepts and activities.## Revised Bloom's Level of thinking

UnderstandingAnalyzing

## Learning Target/Task Analysis

4.NBT.1 This standard calls for students to extend their understanding of place value related to multiplyingand dividing by multiples of 10. In this standard, students should reason about the magnitude of

digits in a number. Students should be given opportunities to reason and analyze the

relationships of numbers that they are working with.

Example:

How is the 2 in the number 582 similar to and different from the 2 in the number 528?

Students should be familiar with and use place value as they work with numbers. Some activities

that will help students develop understanding of this standard are:

Investigate the product of 10 and any number, then justify why the number now has a 0 at

the end. (7 x 10 = 70 because 70 represents 7 tens and no ones, 10 x 35 = 350 because

the 3 in 350 represents 3 hundreds, which is 10 times as much as 3 tens, and the 5

represents 5 tens, which is 10 times as much as 5 ones.) While students can easily see the

pattern of adding a 0 at the end of a number when multiplying by 10, they need to be able

to justify why this works.

Investigate the pattern, 6, 60, 600, 6,000, 60,000, 600,000 by dividing each number by

the previous number.

Misconceptions

There are several misconceptions students may have about writing numerals from verbal

descriptions. Number4s like one thousand do not cause a problem; however a number like one

thousand two causes problems for students. Many students will understand the 1000 and the 2

but then instead of placing the 2 in the ones place, students will write the numbers as they hear

them, 10002 (ten thousand two). There are multiple strategies that can be used to assist with this

concept, including place-value boxes and vertical-addition method.

Students often assume that the first digit of a multi-digit number indicates the "greatness" of a

number. The assumption is made that 954 is greater than 1002 because students are focusing on

the first digit instead of the number as a whole.

4.NBT.2

This standard refers to various ways to write numbers. Students should have flexibility with the

different number forms. Traditional expanded form is 285 = 200 + 80 + 5. Written form is two

hundred eighty-five. However, students should have opportunities to explore the idea that 285

could also be 28 tens plus 5 ones or 1 hundred, 18 tens, and 5 ones.

Students should also be able to compare two multi-digit whole numbers using appropriate

symbols.

The expanded form of 275 is 200 + 70 + 5. Students use place value to compare numbers. For

example, in comparing 34,570 and 34,192, a student might say, both numbers have the same

value of 10,000s and the same value of 1000s however, the value in the 100s place is different so

that is where I would compare the two numbers.

4.NBT.3

This standard refers to place value understanding, which extends beyond an algorithm or

procedure for rounding. The expectation is that students have a deep understanding of place

value and number sense and can explain and reason about the answers they get when they

round. Students should have numerous experiences using a number line and a hundreds chart as

tools to support their work with rounding.

Example:

Your class is collecting bottled water for a service project. The goal is to collect 300 bottles of

water. On the first day, Max brings in 3 packs with 6 bottles in each container. Sarah wheels in 6

packs with 6 bottles in each container. About how many bottles of water still need to be collected?

Student 1

First, I multiplied 3 and 6 which

equals 18. Then I multiplied 6 and 6

which is 36. I know 18 plus 36 is

about 50. I’m trying to get to 300. 50

plus another 50 is 100. Then I need 2

more hundreds.

So we still need 250 bottles.

Student 2

First, I multiplied 3 and 6 which

equals 18. Then I multiplied 6 and

6 which is 36. I know 18 is about

20 and 36 is about 40.

40+20=60. 300- 60 = 240, so we

need about 240 more bottles.

## I can...

I can identify the location of a digit in a number.I can determine the value of a digit in a number.

I can explain the relationship between the location of a digit and its value.

I can demonstrate the value of a number using a variety of tools.

I can read and write multi digit whole numbers.

I can compare multi digit whole numbers.

I can round multi digit whole numbers.

I can explain how a multi digit number is rounded to a specific place value.

Essential Vocabulary

## place value, digit, ones, tens, hundreds, thousands, million, ten times, expanded form, standard form, written form, compare, inequality, >, <, =, symbols, comparisons, round, about, approximately

## Sample Assessments

On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34miles on the third day. How many total miles did they travel?

Round 368 to the nearest hundred.

This will either be 300 or 400, since those are the two hundreds before and after 368.

Draw a number line, subdivide it as much as necessary, and determine whether 368 is closer to

300 or 400. Since 368 is closer to 400, this number should be rounded to 400

Example or reasoning: Round 76,398 to the nearest 1000.

Step 1: Since I need to round to the nearest 1000, then the answer is either 76,000 or

77,000.

Step 2: I know that the halfway point between these two numbers is 76,500.

Step 3: I see that 76,398 is between 76,000 and 76,500.

Step 4: Therefore, the rounded number would be 76,000.

## Differentiation

## Intervention:

Students will make a place value chart using paper and highlighters.Have students make checkbooks with a beginning balance and allow them to earn additional deposits. Students write checks to rent desks, use pencil sharpeners, purchase construction paper and etc.

Use balance scales to compare numbers (found in Foss kit)

Use a deck of cards to practice place value, making biggest/smallest number, etc.

## Enrichment:

Students create and solve real world word problems.Bring in guests from local business community (banker, grocery store manager, etc.) to explain how they use rational numbers.

Given story problems work with a partner to create flash cards breaking multi-step problems down into each step.

## Instructional Resources

## Notes and Additional Information