SECOND GRADE - Pearson Assessmentsstorage.schoolnet.com/cfisd/MATH_2_A_4 OF 4 PV NUMB… · Web...

Second Grade Place Value to 1,200

Section 4: Number Lines

Table of Contents

Topic Suggested Number of Days

Page No.

Part 1 Number Lines Increments of One Hundreds Chart Increments of One – Number Lines for Partner Practice Increments of Ten Increments of Ten – Number Lines for Partner Practice Increments of One Hundred Increments of Tens or Hundreds – Number Lines for Partner Practice

Part 2 Open Number Lines Locating 2-Digit Numbers on an Open Number Line Partner Practice 1A Partner Practice 1B Locating 3-Digit Numbers on an Open Number Line Partner Practice 2 Locating 4-Digit Numbers on an Open Number Line

2 days (9/17 ‒ 9/18)

3 days (9/21 – 9/23)

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Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016

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SECOND GRADEPLACE VALUE TO 1,200

Part 1 Number Lines

TEK 2.2E The student is expected to locate the position of a given whole number on an open number line.

TEK 2.2F The student is expected to name the whole number that corresponds to a specific point on a number line.

TEK 2.1D The student is expected to communicate mathematical ideas, reasoning and their implications using multiple representations, including symbols, diagrams , graphs, and language as appropriate.

Student BackgroundIn first grade students used number lines to compare numbers and found the missing number on a number line.

Essential Question: How does a number line help you understand how numbers work?

Vocabulary: before, between, digit, less, greater, after, pattern, increasing, decreasing, ones, tens, hundreds, thousands, place value

Materials: hundreds chart (pg. 6), scissors, tape, Increments of One ‒ Number Lines for Partner Work (pg. 7)base ten blocksSmartBoard Number Lines to use with Teacher NotesMATH_2_A_2 NUMBER LINES SMARTBOARD 2015_RESMATH_2_A_3 NUMBER LINE APRIL IMN QUESTION 2015_RESstudent copies of Practice 1MATH_2_A_4 NUMBER LINE PRACTICE 2015_RES

MATH_2_A_5 NUMBER LINE IMN QUESTION BY TENS 2015_RES MATH_2_A_6 NUMBER LINE IMN QUESTION BY 100 2015 _RES

student copies of Practice 2MATH_2_A_7 NUMBER LINE PRACTICE 2 2015 _RES

student copies of IMN Number LinesMATH_2_A_8 IMN NUMBER LINES 2015_RESstudent copies of Independent Practice ProblemsMATH_2_A_9 NUMBER LINE IP 2015_RESStudent copies of Mixed Practice Problems

Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016 1

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MATH_2_A_10 PV MIXED PRACTICE 2015_RES Number Lines in Increments of One

A SmartBoard with all the number lines used in the following lessons can be found in the resources (MATH_2_A_2 NUMBER LINES SMARTBOARD 2015_RES)

****The following is very important to help kids make the necessary connections.*****

1. Demonstrate the connection between a hundreds chart and a number line by cutting apart a hundreds chart (pg. 6) and tape it together into a number line. Compare the similarities and the differences between the two.

2. Display slide 2 of the SmartBoard. Explain to students that a number line goes on forever in both directions, like space. Say, “Let’s look at this partial number line.” Display the partial number line or cut apart another hundreds chart and select the section with the numbers 41-50. Be sure to cover-up the number 47 before showing the number line to the class.

Point to the partial number line. What happens to the numbers as you read them from left to right? they get biggerWhich is getting bigger, the digit in the ones place or the digit in the tens place? the digit in the ones place This means the numbers are increasing by one.

Build the first 3 numbers using base ten blocks in the Teacher SmartBoard (MATH_2_A_2 NUMBER LINES SMARTBOARD 2015_RES) to demonstrate the ones digit is increasing by 1, when reading the numbers from left to right.

If you read the numbers in the opposite direction (from right to left) what happens to the numbers? they decrease by oneThis means that you are subtracting 1.

Refer to the blocks again to show how the numbers decrease by 1 unit when reading them from right to left.

When numbers are missing on a number line you can figure out what they are by looking at the numbers before and/or after the missing the number(s).


41 42 43 44 45 46 48 49 50

41 42 43 44 45 46 48 49 50

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Point to the space where the number is missing.

What number comes before the missing number? 46How many ones does this number have? 6 onesSince the missing number is to the right of 46, the number increases.If we add 1 more to the number of ones, how many would we have now? 7 onesDid the number of tens change? no When we change the 6 ones to 7 ones in the number 46 what number do we get? 47What number is one more than 46? 47

Once again point to the space where the number is missing.

We can also find our missing number by looking at the number that comes after it. What number comes after the missing number? 48What is the value of the ones digit? 8Since our missing number is to the left of 48, the number decreases.If we subtract 1 from the number of ones, how many would we have now? 7 ones Did the number of tens change? noWhen we change 8 ones to 7 ones in the number 48 what is our new number? 47What number is one less than 48? 47

(Uncover the number to show students the missing number 47).

We can also say that 47 is between 46 and 48What strategy helped us find the missing number? looking at the numbers before and after the missing number

3. Now draw/display (slide 3) a number line with 3-digit numbers such as the one below:

How is this number line different from the one before? the numbers are bigger; 3-digit; there are 2 missing numbers

What is happening to the numbers on the number line as you read them from left to right? they are increasing by 1

Just like in the number line before, this means that you are adding 1 to the number in the ones place. And if you read the numbers in the opposite direction (from right to left) you are subtracting 1 from the number in the ones place.

What number comes before the first question mark? 639What digit is in the ones place? 9What number do you get if you add 1 more to the digit in the ones place? 10


645644642638 ? 643639 ?637636

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Since we made a group of ten, we need to add it to the tens place. How many groups of ten in 639? 3If we add 1 group of ten how many tens do we have now? 4

Use base ten blocks to demonstrate adding 1 more to the 9 units in the number 639. Then trading the 1 group of 10 for a rod and placing it in the tens place to make 4 groups of ten and the number 640.

Do we have any ones left? No, we used them all to make a group of ten.So our new number has 6 groups of a hundred, 4 groups of ten and 0 ones. What number does that make? 640

Now let’s look at the other question mark (point to it). What number comes after it? 642What digit is in the ones place? 2Since we are looking for the number that comes before this question mark, we need to find the number that is one less than 642. What number do you get if you take 1 away from the digit in the ones place?

641 Write the missing numbers on the number line.

4. Draw/display (slide 4) a number line with 4-digit numbers (see below).

What do you notice about this number line? the numbers have 4-digits, etcWhich digit is changing? the digit in the ones place

Continue the same questioning to find the missing numbers.

Use base ten blocks to demonstrate adding 1 more to the 9 units in the number 1,149. Then trading the 1 group of ten for a rod and placing it in the tens place to make 5 groups of ten and the number 1,150.

5. Partner Practice

The students will practice identifying points on the number line using Increments of One ‒ Number Lines for Partner Practice (pg. 7)

6. IMN

Review steps for using a number line that counts by one.Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016

4

1,148 1,149 ? 1,152 ?1,151 1,154 1,155

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Students should then respond to the question:

April doesn’t know what number is between 345 and 347. What would you say to April to help her figure out how to find numbers that are between two others?

(MATH_2_A_3 NUMBER LINE APRIL IMN QUESTION 2015_RES)

This question is written multiple time so that the teacher can cut and have the students glue it to their IMN.

7. Independent Practice

The student will do “Number Line ‒ Practice 1” (MATH_2_A_4 NUMBER LINE PRACTICE 2015_RES).


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Hundreds Chart

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100


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67 68 ? ? 71

138?136135134

?772771?769

??411410409

103102??99

Increments of One ‒ Number Lines for Partner Practice

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Number Line in Increments of Ten

1. Display (slide 5) a number line like the one shown below. Point out that this number line has a box instead of a question mark in the place of the missing number.

What happens to the numbers on the number line as you read them from left to right? they get bigger

Which digit is getting bigger, the digit in the ones place, or the digit in the tens place? the tens place

Use base ten blocks to help students see that the digit in the tens place is the one increasing. You can also display the hundreds chart, along with the blocks, to show the pattern of numbers increasing by ten.

This means the numbers are increasing by 10. The steps to finding the missing number on this number line is the same as finding the missing number for numbers increasing by 1, except this time we need to look at the digit in the tens place.

Why do you think we need to look at the digit in the tens place? because the numbers are increasing by ten

2. Point to the space where the number is missing.

What number comes before the missing numbers? 64 How many groups of ten does this number have? 6 groups of ten

If we add 1 group of ten, how many groups of ten will we have now? 7 groups of ten Did the number of ones change? noWhat number does 7 groups of ten and 4 ones make? 74So we can say that 74 is ten more than 64

Point to the space where the number is missing one more time.

Now let’s try it going the other way. What number comes after the missing space? 84How many groups of ten does this number have? 8


948454 64443424

948454 64443424

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Since we are reading the numbers from right to left, we have to subtract 1 group of ten from the 8 groups of ten because the numbers are decreasing. If we take 1 group of ten away, how many groups of tens will we have now? 7Did the number of ones change? NoWhat number do we have now? 74We can also say that 74 is ten less than 84

Use base ten blocks to demonstrate how you get 74 when you add a group of ten to 64 or remove a group of ten from 84.

3. Display slide 6.

How is this number line different from the one before? it has 3-digit numbersHow is it the same? the digit in the tens place is changing

Point to the space where the number is missing.

What number comes before the missing number? 122 How many groups of ten does this number have? 2 groups of ten

Since we are reading the numbers from left to right, we have to add 1group of ten because the numbers are increasingIf we add 1 group of ten to the 2 groups of ten how many groups of ten will we have now? 3 tens Did the number of ones change? noDid the number of hundreds change? noWhat number does 1 group of a hundred, 3 groups of ten, and 2 ones make? 132So we can say that 132 is ten more than 122

Once again point to the space where the number is missing.

Now let’s try it going the other way. What number comes after the missing space? 142How many groups of ten does this number have? 4 groups of tenSince we are reading the numbers from right to left, we have to subtract 1 group of ten because the numbers are decreasing. If we take 1 group of ten away, how many groups of ten will we have now? 3 groups of tenDid the number of ones change? noDid the number of hundreds change? noWhat number does 1 group of a hundred, 3 groups of ten and 2 ones make? 132We can also say that 132 is ten less than 142

Use base ten blocks to demonstrate how you get 132 when you add a ten to 122 or remove a ten from 142.


182172152 162142122112

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4. Now display (slide 7) this number line with 4-digit numbers. Continue the same questioning as before to find the missing number. Use base ten blocks to model the regrouping of 10 groups of ten to make another group of a hundred.

5. Partner Practice

The students will practice identifying points on the number line usingIncrements of Ten ‒ Number Lines for Partner Practice (pg. 11)


1,150 1,9001,170 1,1801,1601,1401,300

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??151141131

??329319309

?244?224214

Increments of Ten ‒ Number Lines for Partner Practice

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Number Line in Increments of One Hundred

1. Display (slide 8) the following number line.

What happens to the numbers when you read them from left to right? they get bigger

The digit is changing in what place value? the hundreds placeThis means that the numbers are increasing by hundreds.Point to the space where the number is missing.

What number comes before the missing number? 900 How many groups of a hundred does this number have? 9 groups of a hundred

Since we are reading the numbers from left to right, we have to add 1 group of a hundred because the numbers are increasing.If we add 1 group of a hundred, how many hundreds will we have now? 10 groups of a hundred

Use base ten blocks to model the regrouping of 10 groups of a hundred to make 1 group of a thousand.

Did the number of ones change? noDid the number of tens change? noDid the number of hundreds change? YesHow many group of a hundred do we have now? none, we used them all to make a thousandWhat number does 1 group of a thousand, 0 groups of a hundred, 0 groups of ten, and 0 ones make? 1,000So we can say that 1,000 is a hundred more than 900

2. Point to the space where the number is missing once again.

Now let’s try it going the other way. What number comes after the missing space? 1,100How many group of a hundred does this number have? 1 group of a hundredSince we are reading the numbers from right to left, we have to subtract 1 group of a hundred because the numbers are decreasing. If we take 1 group of a hundred away, how many do we have left? 0Did the number of ones change? noDid the number of tens change? noDid the number of thousands change? no


700 1,100900 1,200800600500

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What number does 1 group of a thousand, 0 groups of a hundred, 0 groups of ten and 0 ones make? 1,000We can also say that 1,000 is a hundred less than 1,100

3. Partner Practice

Working with partners the students will find the missing numbers on various number lines, “Increments of Tens or Hundreds ~ Number Lines for Partner Practice” (pg. 14).

4. IMN ‒

How can you quickly tell if a pattern is increasing by ten?

How can you quickly tell if a pattern is decreasing by ten?

How can you quickly tell if a pattern is increasing by a hundred?

How can you quickly tell if a pattern is decreasing by a hundred?

For preprinted questions go to: MATH_2_A_5 NUMBER LINE IMN QUESTION BY TENS 2015_RES and/or MATH_2_A_6 NUMBER LINE IMN QUESTION BY 100 2015 _RES


Students will do “Number Lines - Practice 2” (MATH_2_A_7 NUMBER LINE PRACTICE 2 2015 _RES)


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Increments of Tens or Hundreds ‒ Number Lines for Partner Practice

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? 563 663363263

? 166156146 176

? 567367267167

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Part 2 Open Number Lines

Locating 2-Digit Numbers on an Open Number Line

The process of estimating the location of numbers on an open number line draws upon knowledge and understanding of numbers and their relation to each other, which increases number sense. Therefore, the emphasis of the following lesson is on number sense and approximation rather than on precision.

Display a number line (slide 9) with the numbers 20, 30 and 40 like the one below: (Remember these number lines can be found on the SmartBoard.)

What numbers do you see on this number line? 20, 30 and 40It seems that the numbers that come between 20 and 30, 30 and 40 are not shown

Can you tell me what numbers are not shown between 20 and 30? (Have students count and point to where each number might be located on the number line. 21, 22, 23…29)

Can you tell me what numbers are not shown between 30 and 40? (Have students count and again point to where each number might be located on the number line.31, 32, 33…39)

Hold up a card with the number 32. Tell students that you need help in finding were this number is located on the number line.

Let’s figure out where to begin. 32 comes between which two numbers on the number line? 30 and 40

(If necessary, have students go back and recite the numbers that are not shown between the numbers 30 and 40.)

Okay, so now I know what area my number belongs, but where on the number line should I place it? Should I put 32 closer to 30 or 40? 30

How do you know? (At this time evaluate students’ responses to indicate their level of number sense and understanding. If necessary, show them the number line from the previous lesson.)

Now hold up the number 36. Tell students you need their help to find where to place this number.Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2015-2016

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403020

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Let’s figure out where to begin. 36 comes between which two numbers on the number line? 30 and 40

Okay, now we know what area our number can be found, but where on the number line should I put it? Should I put it closer to 30 or 40? (accept all answers)

Because the number 36 is not very close to 30 or 40, it is hard to tell. However, knowing the number that is halfway between 30 and 40 will give us a better idea of where to put this number on the number line.

Use a hundreds chart or a number line to help students find the number that is halfway between 30 and 40 (35). (This may be a good time to review the numbers that come halfway between other numbers that end in zero.)

Let’s put a dot on the number line to indicate the halfway mark which also represents the number 35.

Now who can tell me where to put the number 36? after the halfway mark; after 35How do you know? (Answers will vary.)Have a student label 36 on the number line.

Let’s try another one.

Display (slide 10) the following number line.

Now I need your help in figuring out where to put the numbers 92, 82, and 89 on this number line.

It may be helpful to find the number that is at the halfway point. Does anyone know what number is at the halfway point of the numbers 80 and 100? 90

Give students time to discuss and give answers. Then tell them you want to show them a quick way to find the halfway point.

Since both numbers end in 0 you can count by ten. Let’s skip count by ten starting with 80 (write the numbers on the board as students say them): 80, 90, 100


10080

403020 35

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What number did we say between 80 and 100. 90Let’s place a dot to remind us where the number 90 is located.

Allow a student to write the numbers on the number line. As they do, ask how they know the number goes in that location.

Remember, the focus is on number sense rather than on precision.

Partner Practice

Cut up the number cards Partner Practice 1A (pg. 18) and place them face down between two students. Have each student take turns picking a card and drawing a point and labeling it where the number should be on a number line (Partner Practice 1B (pg. 19). They continue until all cards are picked.


10080 90

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Partner Practice 1A

71 72 7374 75 7677 78 7981 82 8384 85 86


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87 88 89Partner Practice 1B

Name____________________________


9070

9070

9070

9070

9070

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1. Display (slide 11) the following number line along with the following numbers: 451, 495, and 447

Ask students to place the numbers on the number line. Ask students to explain how they justify where the placement of each number (Give time for discussion. Encourage students to come up with multiple strategies.)

If necessary, guide students through questioning to order the numbers from least to greatest (447, 451, 495).

You may also help them find the number that is at the halfway point of 400 and 500.

What are we counting by when we count 300, 400, 500, 600… ? by 100

Use a number line or hundreds chart to show students what number is halfway to 100 (50). Point out that when you move from a hundred to the next hundred the halfway point is 50. Therefore, the halfway point from 400 to 500 is 450. Place a mark on the number line to show the halfway point.

Allow students to discuss the placement of the numbers 451, 495, and 447. If necessary, ask questions such as the following to guide the students along.

Is 451 greater or less than 450? greaterOn a number line would 451 be closer to 450 or 500? 450

Continue similar questioning for the other numbers until all the numbers have been placed on the number line.

2. Display (slide 12) the following number line and ask students to label or draw a line to show where each number should go on the number line.


450 500400

500400

9070

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859 905 895

Give students time to discuss and have a “healthy struggle” before offering any suggestions. As students identify the points, ask for a reason for their answer.

If students have a hard time getting started, help them find the number that goes at the halfway point:

Let’s find the number that goes at the halfway point.What digit is changing? 8What place is the 8 in? hundreds placeWe have learned that the halfway point of a hundred is 50. But that won’t work here because both numbers already have 50.We also learned that if the numbers both end a 0 we can count by 10s to find the number that is halfway. Let’s count by ten starting with 850 (as students count, ask them to point to where the number would fall on the number line).

It may be helpful to write the numbers on the board as students count so they can see the number that is halfway. 850, 860, 870, 880, 890, 900, 910, 920, 930, 940, 950

What number is halfway between 850 and 950? 900

If students don’t know what comes after 890, use base ten blocks to illustrate the regrouping of 10 groups of ten to make a group of a hundred.

Let’s place a mark on the halfway point to remind us where 900 is located (you may write the number 900 as well). Now we can draw a line to show were the numbers belong.

3. Partner Practice

On Partner Practice 2 (pg. 22), students write 3-digit numbers in their correct location on a number line, then compare their number line with their partner’s. Students should also


950850

900 950850

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compare and share their strategies. Remember the focus is on number sense rather than precision.

Partner Practice 2

1. Write the numbers 420, 590, and 510 in their correct place on the number line.

Compare your number line with your partner’s number line.

Tell your partner how you decided where to put each number.

2. Write the numbers 150, 165, and 144 in their correct place on the number line.


600 400

17575

135

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Compare your number line with your partner’s number line.

Tell your partner how you decided where to put each number.


1. Display (slide 13) the number line along with the following numbers; 1,147; 1,115; 1,185

What do you notice about the numbers on this number line? numbers are bigger, numbers have thousands, etc.Which digits are changing? 1 and 2Look at the numbers carefully. What place value are these digits in? hundreds placeSince the numbers that are changing are in the hundreds place, we know that we are counting by 100s.Who remembers what number is halfway to 100? 50Since the number in the thousands remains the same, our halfway number is 1,150. Let’s mark it on the number line so it can help us place our numbers.

Once the halfway point has been established, allow students to locate the position for the numbers.

2. Now let’s try another one. Display slide 14. Who can figure out where the number 1,136

might go on this number line?

Allow students to discuss with a partner or at table groups. Do not offer any assistance unless the whole class is at a loss. Once someone is ready to share, have them locate the spot with a dot and justify their answer. Remember the focus is on number sense rather than precision.

3. IMN Activity

Students will complete the number lines and then paste them into their IMNs.MATH_2_A_8 IMN NUMBER LINES 2015_RES



1,2001,1000

1,1411,13100

1,150 1,2001,1000

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Students will complete “Number Lines Independent Practice Problems” (MATH_2_A_9 NUMBEER LINE IP 2015_RES).

5. Mixed Practice

Students will work the set of problems “Place Value – Mixed Practice Problems”(MATH_2_A_10 PV MIXED PRACTICE 2015_RES).


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