Mathematics Success – Level D T101ntnmath.kemsmath.com/Level D Teacher Notes/Level D... · Mathematics Success – Level D T101 ... T104 Mathematics Success – Level D Step 2:

Mathematics Success – Level D T101

LESSON 5: Multi–Digit Expanded Form

[OBJECTIVE]The student will be able to read, write, and compare multi–digit whole numbers using base–ten numerals, number names, and expanded form.

[PREREQUISITE SKILLS]

basic understanding of place value

[MATERIALS]

Student pages S39–S49Transparencies T114, T116, T118, T120, T122, T124, T126, and T128Centimeter cubes (35 per student pair)

[ESSENTIAL QUESTIONS]

1. How do tens compare to ones? How do hundreds compare to tens?2. What is expanded form?3. How do we compare two numbers to see which one is larger or smaller?

[WORDS FOR WORD WALL]

place value, ones, tens, hundreds, compare, expanded form

[GROUPING]

Cooperative Pairs (CP), Whole Group (WG), Individual (I)*For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to students. This allows each student to be responsible for designated tasks within the lesson.

[LEVELS OF TEACHER SUPPORT]

Modeling (M), Guided Practice (GP), Independent Practice (IP)

[MULTIPLE REPRESENTATIONS]

SOLVE, Verbal Description, Graphic Organizer, Pictorial Representation, Concrete Representation

[WARM-UP] (5 minutes – IP, I, WG) S39 (Answers on T113.)

• Have students turn to S39 in their books to begin the Warm–Up. Students will round whole numbers to the nearest hundred or thousand. Monitor students to see if any of them need help during the Warm–Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Verbal Description}

Mathematics Success – Level DT102

[HOMEWORK] (5 minutes)

Take time to go over the homework from the previous night.

[LESSON] (60 minutes – M, GP, IP, WG, CP)

SOLVE Problem (3 minutes – WG, GP) T114, S40 (Answers on T115.)

Have students turn to S40 in their books, and place T114 on the overhead. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to read, write, and compare multi–digit numbers. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer}

Understanding Place Value - Concrete (10 minutes – M, WG, GP, CP) T114, S40 (Answers on T115.)

10 minutes – M, GP, WG, CP: Have students work in partners. Distribute 35 centimeter cubes to each pair of students. Have students turn to S40, and place T114 on the overhead, as this will be their place value mat to reference during the modeling portion. (*Teacher note: Ask students to leave cubes as individual units until they are asked to connect them together). {Concrete Representation, Verbal Description, Graphic Organizer}



MODELING

Understanding Place Value - Concrete

Step 1: Have students take 27 centimeter cubes and place them under the “Ones” column on their place value mats. Ask the following questions:

• What are the headings of the columns on the place value mat? (hundreds, tens, ones)

• Is it possible to move the centimeter cubes so that we are using more than the “Ones” column? (Yes.) How? (Students can connect the cubes together to create groups of ten.)

Model how to use ten of the ones and connect them together. This creates a group of ten that can be moved to the “Tens” column. You will be able to create 2 tens with 7 ones left over.

Hundre

ds

Tens

Ones


Hundre

ds

Tens

Ones


Step 2: Next, have partners model the following problem.

• Partner A will place 35 centimeter cubes in the “Ones” column.

• Ask how the students can rearrange the ones so they represent 35 using another column. (by connecting cubes into groups of ten)

• Partner B will count groups of ten to move to the “Tens” column, and Partner A will initial the chart if he/she agrees with Partner B’s fi nal answer.

Hundre

ds

Tens

Ones

Hundre

ds

Tens

Ones

Understanding Place Value - Pictorial (10 minutes – M, WG, GP, CP, IP) T116, T118, S41, S42 (Answers on T117, T119.)

4 minutes – M, CP, WG, GP: Have students work in partners. Assign the roles of Partner A and Partner B for specifi ed tasks. Have students turn to S41, and place T116 on the overhead. {Concrete Representation, Pictorial Representation, Verbal Description, Graphic Organizer}



MODELING

Understanding Place Value - Pictorial

Step 1: Students will transition their understanding of numbers with place value by drawing pictorial representations of centimeter cubes in the chart. Have students recreate the model of 27 with centimeter cubes.

Step 2: Model Question 1 for students by drawing two groups of ten and seven ones while having them draw the representation of the number 27 in their books.

Numeral Draw the Centimeter Cubes.

27 Hundre

ds

Tens

Ones

Step 3: Have students turn to page S42.

• What is different about the two numbers on S42 from the numbers on S41? (These numbers, 149 and 238, have values in the hundreds.)

• Explain to students that the procedure will be the same for hundreds as for tens.

• How can students represent a group of 100? (a square divided into 100 sections)

• Model for students how to draw the hundreds square, the four groups of tens, and nine individual cubes.



4 minutes – IP, CP: Have students work as partners to complete the pictorial representation of 35 on S41 and the pictorial representation of 238 on S42.{Graphic Organizer, Pictorial Representation, Verbal Description}

2 minutes – WG: Review the pictorial models for 35 and 238. {Graphic Organizer, Pictorial Representation, Verbal Description}

Expanded Form (17 minutes – M, WG, GP, CP, IP) T120, T122, S43, S44(Answers on T121, T123.)

8 minutes – M, CP, WG, GP: Have students turn to S43, and place T120 on the overhead. {Pictorial Representation, Graphic Organizer, Verbal Description}

MODELING

Expanded Form

Step 1: Explain to students that they will be using the graphic organizer on S43 to help identify different ways to represent a number

• What type of representation is in Column 1 ? (Pictorial)

• Have students identify the representation for Column 2. (expanded form)

Step 2: Explain to students that in expanded form a number is written as the sum of the place value of each digit.

• Have Partner A identify the value of the hundreds place. (3 groups of 100 or 300)

• Model how to write the expanded form of 300. (3 • 100) Have students write the expanded form in Column 2.

• Have Partner B identify the value of the tens place. (5 groups of 10 or 50)

• Model how to write the expanded form of 50 (5 • 10), adding that to the expanded form of 300.

• Have Partner A identify the value of the ones place. (7 groups of 1 or 7)

• Model how to write the expanded form of 7 (7 • 1), adding that to the expanded form of 50.



Pictorial Expanded Form Numeral Written

(3 • 100)+(5 • 10) + (7 • 1)

Step 3: Have students look at Column 3. (Numeral) Tell students that in this column the number will be written in the form that they usually see, as a numeral.

• Have Partner A identify the hundreds from the expanded form. (3 groups of 100)

• Have Partner B identify the hundreds digit (3) and circle it in the expanded form column.

• Have Partner A identify the tens digit (5) and circle it in the expanded form column.

• Have Partner B identify the ones digit (7) and circle it in the expanded form column.

• Have students write the numeral in Column 3. (357)

Pictorial Expanded Form Numeral Written

(3 • 100)+(5 • 10) + (7 • 1) 357

three hundred

fi fty–seven



Step 4: Have students look at Column 4. (Written) Tell students that in this column the number will be written in word form.

• Explain to students that when writing the numeral in words, you start at the left and move to the right identifying each place value.

• Have Partner A identify the hundreds. (3 hundreds or 300)

• Model for students how to write 3 hundred in words. (three hundred)

• Have Partner B identify the tens. (5 tens or 50)

• Model for students how to write 5 tens in words. (fi fty)

• Explain to students that when writing the ones column there is always a hyphen between the tens and ones places.

• Have Partner A identify the ones. (7 ones or 7)

• Model for students how to write the 7 ones in words. (seven)

The fi nal written number is three hundred fi fty-seven.

*Teacher note: Make sure that students are not adding “and” in between the hundred and fi fty. Explain to them that adding “and” is a signal that we are going to speak about a decimal. In this case, we are only working with whole numbers, so the word “and” should never be used when speaking or writing the numeral.

Correct: “three hundred fi fty–seven”

Incorrect: “three hundred AND fi fty-seven”

7 minutes – IP, CP: On S43 and S44, have partners complete Problems 2 - 4. Monitor closely to make sure students are using the appropriate vocabulary. {Graphic Organizer, Pictorial Representation, Verbal Description}

2 minutes – WG: Have students come back together as a class and share their results. {Graphic Organizer, Pictorial Representation, Verbal Description }

Comparing Multi-Digit Numbers (13 minutes – M, WG, GP, CP) T124, T126, S45, S46 (Answers on T125, T127.)

6 minutes – M, WG, GP, CP: Have students turn to page S45, and place T124on the overhead. Use the modeling boxes below to help students understand the process for comparing numbers. {Graphic Organizer, Verbal Description}



MODELING

Comparing Multi-Digit Numbers

Step 1: Have students look at Problem 1. Explain that they will be learning how to use symbols to explain the relationship between the two numbers.

• Have Partner A identify the fi rst numeral. (147)

• Have Partner B identify the value of the hundreds. (1) Have students write the 1 in the hundreds column of the fi rst row of the place value chart.

• Have Partner A identify the value of the tens. (4) Have students write the 4 in the tens column of the fi rst row of the place value chart.

• Have Partner B identify the value of the ones. (7) Have students write the 7 in the ones column of the fi rst row of the place value chart.

Have students write the numeral 258 in the second row of the place value chart.

Step 2: Explain to students that when comparing numerals, start at the place value that is the furthest to the left.

• What place value are we looking at to compare the numerals? (hundreds)

• Have Partner A identify the value of the hundreds in 147. (1)

• Have Partner B identify the value of the hundreds in 258. (2)

• Which value is greater? (2)

Explain to students that they know 258 is greater than 147 because a value with 2 hundreds is greater than a value with 1 hundred.

Step 3: Model for students how to write the “less than” symbol in the circle.

Read the statement: One hundred forty-seven is less than two hundred fi fty-eight.

147 < 258 Hundre

ds

Tens

Ones

1 4 7

2 5 8



Step 4: Have students look at Problem 2.

• Ask students how this comparison differs from Problem 1. (Both numerals have a 1 in the hundreds place.)

Have students write both numerals in the place value chart.

Step 5: What place value are we looking at to compare the numerals? (hundreds)

• Have Partner A identify the value of the hundreds in 139. (1)

• Have Partner B identify the value of the hundreds in 109. (1)

Explain to students that because both numerals have the same value in the hundreds place, they will have to move to the next place value (tens) to compare.

• Have Partner A identify the value of the tens in 139. (3)

• Have Partner B identify the value of the tens in 109. (0)

• Which numeral is greater? (139)

Step 6: Model for students how to write the “greater than” symbol in the circle.

Read the statement: One hundred thirty-nine is greater than one hundred nine.

139 > 109 Hundre

ds

Tens

Ones

1 3 9

1 0 9

Step 7: Have students look at Problem 7 on S46. Explain that they can compare numbers without a place value chart by writing the numbers vertically and lining up the place values.

• Which value is greater? (100)

10

100

• Explain your thinking. (The value of the hundred is zero in the number 10 and 1 in the number 100, so 10 is less than 100.)




5 minutes – IP, CP: Have partners complete Problems 3 and 4 on S45 and Problems 5, 6, and 8 - 12 on S46. Partner A will complete the odd problems, and Partner B will complete the even problems. Each partner will then switch books and initial next to the answers if he/she agrees with the original answer. Students should be able to explain their reasoning for the comparisons. {Graphic Organizer, Verbal Description}

2 minutes – WG: Review the answers for Problems 3 - 6 and 8 - 12 on S45 and S46. {Graphic Organizer, Verbal Description}

SOLVE Problem (5 minutes – GP, WG) T128, S47 (Answers on T129).

Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (Since students are not choosing an operation, focus on the strategy that students should use in the “L” step. Guide students to use the place value chart to line up the digits. Show students that they do not necessarily need to create a large chart like the one provided in the solution to the SOLVE problem, but that they can simply line up the digits and draw vertical lines as a quick visual.) {SOLVE, Graphic Organizer, Verbal Description}



If time permits… (10 minutes – IP, CP) S48 (Answers on T130).

Have students complete Problems 1 - 10 on page S48.

[CLOSURE] (2 minutes)

To wrap up the lesson, go back to the essential questions and discuss them with students.

• How do tens compare to ones? How do hundreds compare to tens? (One ten is made up of 10 ones. One hundred is made up of 10 tens.)

• What is expanded form? (Expanded form allows us to break a number apart and represent it as an addition statement based on each separate place value.)

• How do we compare two numbers to see which one is larger or smaller? (First, line up the numerals so that the place value matches for both numbers. Start at the place value that is furthest to the left and compare to see which number is larger. If the numbers are the same, move to the next column to the right and continue comparing until one number is different.)

[HOMEWORK] Assign S49 for homework. (Answers on T131.)

[QUIZ ANSWERS] T132 - T133

The quiz can be used at anytime as extra homework or to assess how students progress on understanding multi–digit expanded form.

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Mathematics Success – Level D T101ntnmath.kemsmath.com/Level D Teacher Notes/Level D... · Mathematics Success – Level D T101 ... T104 Mathematics Success – Level D Step 2: