SECOND GRADE - Pearson Schoolstorage.schoolnet.com/cfisd/MATH_2_A_P… · Web view · 2015-07-31... word, and expanded form to represent numbers up to 1,200. Vocabulary: standard

Second Grade Place Value to 1,200

Table of ContentsTopic Page

No.Warm-up

Place Value

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Place Value

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Place Value

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Place Value

Warm-up

Place Value

Addition and Subtraction Facts Sums to 20 Making Groups of Ten StrategyPart 1 Number Sense – Odd and Even Numbers Guided Practice Part 2 Composing and Decomposing 2-Digit Numbers 2-Digit Number Cards for Partner Work Addition and Subtraction Facts Sums to 20 A Group of Ten + ExtrasPart 3 The Value of One HundredPart 4 Composing and Decomposing 3-Digit Numbers Matching Cards for Reviewing Composing and Decomp. 2-Digit NumbersAddition and Subtraction Facts Sums to 20 Count on 1, 2, or 3 Count back 1, 2, or 3Part 5 The Value of 1,000Part 6 Composing and Decomposing 4-Digit Numbers to 1,200Addition and Subtraction Facts Sums to 20 Doubles Doubles PicturesPart 7 Read, Write and Describe the Value of Numbers to 99 SpinnersPart 8 Read, Write and Describe the Value of Numbers to 999 Word Name Flash Cards Guided PracticeAddition and Subtraction Facts Sums to 20 Doubles +1Part 9 Read, Write and Describe the Value of Numbers to 1,200 Guided PracticePart 10 Exploring Place ValueAddition and Subtraction Facts Sums to 20 Fact Families (Additive Property)Part 11 Comparing Whole Numbers (through 1,200) Comparing 2-Digit Numbers Partner Practice Comparing 3-Digit Numbers Comparing 4-digit Numbers Part 12 Ordering Numbers Ordering 2-Digit Numbers Guided Practice Problems Ordering 3-Digit Numbers Guided Practice Problems Ordering 4-Digit Numbers Guided Practice Problems

126710

11121417

18192022

24252731333638

39394243

46474850515255565961646670

Property of Cy-Fair ISD Elementary Math Dept. 2014-2015

Part 13 Number Lines Increments of One Hundreds Chart Increments of One – Number Lines for Partner Work Increments of Ten Increments of Ten– Number Lines for Partner Work Increments of One Hundred Increments of Tens or Hundreds~ Number Lines for Partner Practice Part 14 Open Number Lines Locating 2-Digit Numbers on an Open Number Line Partner Practice 1 Locating 3-Digit Numbers on an Open Number Line Partner Practice 2 Locating 4-Digit Numbers on an Open Number Line

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86

889091

SECOND GRADEPLACE VALUE TO 1,200

TEKS 2.2A, 2.2B, 2.2C, 2.2D, 2.2E, 2.2F, 2.4A, 2.7A, 2.7B

Warm-up (5 minutes)Addition and Subtraction Facts - Making Groups of Ten Strategy

This strategy will be very useful for helping students with composing and decomposing numbers. Students need to understand what 10 represents and how to make groups of 10. It is essential for developing mental math strategies. It is suggested that the teacher focus on one strategy at a time and use no more than 10 minutes of instructional time. Once the strategy is introduced it should be practiced frequently for short periods of time.

Tens Facts

Materials: ten-frames (MATH_2_A_FACT STRATEGIES 5_RES-2014) and 2-color counters

Tell students that today they will be finding combinations that make groups of 10. Give each student a ten-frame and 10 counters. Before you begin, you may want to ask students to count the number of squares in the frame. Tell students to place a red counter on one of the squares in their frame. Ask students, “If you have 1, how many more do you need to make a group of 10?” Write 1 + = 10 then put yellow counters on the remaining squares. Ask, “How many more counters were needed to fill the frame?” 9

Property of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 1

Addition and Subtraction Fact Strategies will be incorporated throughout the Place Value Notes. This is in aid of both Composing and Decomposing numbers, as well as, getting students ready for 2-Digit Addition and Subtraction.

Write 1 + 9 = 10.

Guide students once again, this time starting with 7 counters.Ask, “If you have 7, how many more do you need to make a group of 10?” Once again tell students to put 7 red counters on their frame and count how many yellow counters are needed to fill the frame.

Once students solve, write 7 + 3 = 10.Allow students time to explore other ways to make groups of 10.When the students are finished, write all the facts that make groups of ten on the board.Ask students, “What do you notice about these facts?” Through discussion students should notice the related facts, ie., 1 + 9 = 10, 9 + 1 = 10, so 1 + 9 = 9 + 1.

Part 1 Odd and Even Numbers

TEK 2.7 A The student is expected to determine whether a number up to 40 is even or odd using pairings of objects to represent the number.

Vocabulary: odd numbers, even numbers, pairs, partners, even, equal, left over

Materials: bags of 55 color tiles or two-color counters (1 set of 55 for each pair of students)Guided Practice Problem (p. 6) 1 copy per studentInteractive Math Notebook (IMN) (MATH_2_A_ODD OR EVEN NUMBERS IMN ACTIVITY_RES-2014)Practice Problems (MATH_2_A_ODD OR EVEN NUMBERS_RES-2014)

1. InstructionMake a T-chart and leave it untitled, then pass out the bags of 55 manipulatives. Tell each student to pull out 1 tile/counter.Record the number 1 along with a pictorial representation on the left-hand side of the T-chart, (see picture). Have students copy this onto a half sheet of paper. 1


*Note: This strategy should be practiced as a warm-up for about 5 minutes for the next few days.

1 2

1 2 3 4

5 6

1 2 3 4

5 6

Now have the students pull out 2 tiles/counters. Say, “I’m going to put the number two on the other side and draw picture of my counters.” Have students copy this.Continue pulling counters, recording the number and drawing a pictorial representation. (Make sure to draw the chips in pairs when possible.) The T-chart should look like this:

.

When you finish 10, ask students what they notice about the chips on the right-hand side? Explain that when a number of objects are grouped in pairs (2) with no leftovers, that number is an even number. So 2 is an even number. When you had 4 tiles/counters, there are two groups of two, so 4 is also an even number.

What do you notice on the other side? There is always one left over.“That’s correct, when they don’t have a pair they are called odd numbers.Label your table as shown below.

Have your students title their charts and paste them onto the right side of the IMN. Continue having students fill out their chart until they get to 20. (To have enough manipulatives for this activity, have students pull out 11, record and draw it on the chart then return them to the bag.)


Odd Numbers Even Numbers

Once the chart is complete, ask the students what they notice about the numbers. Some students may notice that the even numbers count by two’s. Others may notice that the ones place in the even numbers is 2, 4, 6, 8, or 0. The number in the ones place for the odd numbers is 1, 3, 5, 7, or 9.

2. Interactive Math Notebook (IMN) (MATH_2_A_ODD OR EVEN NUMBERS IMN ACTIVITY_RES-2014)

On the left side of their IMN, opposite their list of odd and even numbers, students should explain why some numbers are odd and others are even. They should illustrate their explanation as proof.

3. Guided Practice

The teacher will guide the students through the problems using the 4-step process.

How many rectangles are shown below? ________Is the number of rectangles even or odd? Why?

Main Idea : even or odd

Details/Known: Picture (Students should count the number of boxes in the picture) 35

Strategy: Students should use two-color counters or color tiles and count out 35 of them and then pair them.

Circle the boxes in groups of 2.

How/Why: 35 is odd because there is one box left over.

The student’s work should look similar to this:


4. Independent Work

Students will use color tiles or two color counters to build the numbers in the pictures and then pair them in “Odd or Even Numbers (MATH_2_A_ODD OR EVEN_RES-2014).Make sure students use the 4-step process on each problem.


Even or odd? Picture35

Even or odd? 35 is odd because there is one box without a partner.

Guided Practice Problem

How many rectangles are shown below? ________Is the number of rectangles even or odd? Why?

Part 2 Composing and Decomposing 2-Digit Numbers


TEK 2.2 A The student is expected to use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens and ones.

Vocabulary: compose, decompose, represent, unit, groups, digit, tens, ones, equal, regroup, label, base ten blocks, representation, tens facts, ten frame, digit, strategy

Materials: base ten blocks or virtual blocks, teacher made place value mats,2-digit number cards (pg 10)Interactive Math Notebook (IMN) (MATH_2_A_COMPOSING OR

DECOMPOSING 2-DIGIT IMN ACTIVITY-2014)Practice Problems ~

MATH_2_A_COMPOSING AND DECOMPOSING 2-DIGIT NUMBERS_RES-2014

1. Instruction

The teacher will place 7 units in the ones place on a teacher made place value mat.Units will be added one at a time and the value recorded. When 10 units are on the mat, the teacher will discuss how these can be regrouped into 1 group of ten or a tens rod.

10 = 10 ones = 1 group of ten (Now the number is no longer a single digit)

One additional unit will be placed on the mat. At this point the teacher will point out how this amount can be expressed two different ways as eleven ones, or as one ten and one.

11 = 11 ones = 1 group of ten + 1 one

Continue placing units on the mat until there are a total of 10 unit cubes. This is 1 group of 10. Regroup for another tens rod.

20 = 1 group of ten and 10 ones = 2 groups of ten = 20 onesPlace 5 more units on the mat. Write the representations:

25 = 2 groups of ten and 5 ones = 25 ones

Could it be represented another way? (Show these equivalencies with the blocks.)

25 = 2 groups of ten + 5 ones = 1 group of ten + 15 ones = 25 ones = 1 group of ten + 1 group of ten + 5 ones

Add 5 more units cubes to get a total of 30.Together write the representations, i.e.

30 = 3 groups of ten = 2 groups of ten + 10 ones = 1 group of ten + 20 ones = 30 ones = 2 groups of ten + 1 group of ten


Continue to add cubes and write representations until students are ready for partner work. Continue modeling with the blocks as long as necessary.

2. Partner Work

Students will select a card with a 2-digit number written in standard form. They will take turns building different representations with the blocks and recording them on a dry erase board. Use the “2-Digit Number Cards for Partner Work” on page 10.

3. Independent Work

Students will use base ten blocks to compose and decompose 2-digit numbers, “Making and Taking Apart Numbers (MATH_2_A_Composing and Decomposing 2-Digit Numbers_RES-2014).”The 4-step process should be used on every problem. On problem #1 the work may look like this:

6 groups of ten + 7 ones = _____ ones

4. Interactive Math Notebook (IMN) Activity (MATH_2_A COMPOSING AND DECOMPOSING 2-DIGIT IMN ACTIVITY_RES-2014):


number of ones

6 groups of ten + 7 ones

7

605040302010

6

I counted and labeled the blocks.

67

Note: Since the student has done their work on the picture, nothing need appear in this quadrant.

picture

If you had the number 26, which way would you rather show it –26 ones, one group of ten and 16 ones, or two groups of ten and 6 ones? Why?

\


2-Digit Number Cards for Partner Work

64 64

35 35

26 26

52 52Warm-up (5 minutes)Property of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 10

Addition and Subtraction Facts ~ A Group of Ten + Extras

Materials: ten-frame (MATH_2_A_FACT STRATEGIES 5_RES-2014) and 2-colored counters

Give each student a ten-frame and counters.

Tell students that since they know how to make a group of ten, they can use the strategy to solve the fact 9 + 4.

9 + 4 10 + 3

Put 9 chips on the frame. How many more do we need to make a group of 10? (1). Take 1 from the 4 and place it in the frame. Now write and the new addition fact, (10 + 3 = 13).

Follow the same procedure with the fact, 8 + 5.

8 + 5 10 + 3Property of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 11

In preparation for A Group of Ten + Extras strategy, it is recommended that students learn their tens facts, and do the “Add 10” activity.

Add 10

Materials: paper bag, number cards 1 - 9

Label the bag with the words “Add 10.” The number cards are placed in the bag and all students sit in a circle around the bag. Students take turns pulling a card from the bag and adding that digit to 10. The teacher writes these facts on the board as the students generate them. After about five students have given a fact, stop the class and examine the facts. Students should detect the pattern, i.e. the making of the “teens” numbers. Let the rest of the students have a turn in order to practice the pattern.

Once students get the connection, use teacher made flashcards to help them practice this process mentally.

Part 3 The Value of One Hundred

TEK 2.2A use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens and ones.

TEK 2.2B use standard, word and expanded forms to represent numbers up to 1,200

Vocabulary: Hundred, units, regroup, pattern, place value mat,base ten blocks, represent, representation

Materials: base ten blocks or virtual blocks, teacher made place value mat, Interactive Math Notebook (IMN) (MATH_2_A_VALUE OF 100 IMN ACTIVITY_RES-2014)games ~ MATH_2_A_VALUE OF ONE HUNDRED 1_RES-2014

MATH_2_A_VALUE OF ONE HUNDRED 2_RES-2014

1. Show the students a 3-part place value mat. Review what goes in the right-hand column (ones), and in the adjacent column (tens). See if students know what goes in the left-hand column (hundreds). Label a class chart.

The students will place ten units in the ones column. They will then regroup these ten ones (units) into one group of ten (rod).

10 = 1 group of ten = 10 ones

In their Interactive Math Notebook (IMN)s, on the left-hand side, students will then record what they did (regrouped ten ones into a group of ten) and share it with a partner or group. Students may also draw a visual of the action. You may wish to copy and use the Hundreds PV Charts in MATH_2_A_VALUE OF 100 IMN ACTIVITY_RES-2014.


*Note: This strategy, as well as the Make Ten strategy, should be practiced as a warm-up for about 5 minutes for the next few days.

Put together 10 onesto make 1 group of ten.

Hundreds Tens Ones

The teacher will label a class drawing, “Put together ten ones to make 1 group of ten.”

2. Exploration

The teacher will then give each student a group of one hundred or a flat. Allow studentsto predict what will be equal to the hundred (flat).

The students should come to the conclusion that ten groups of ten are equal to one group of 100.

The teacher will model this relationship for the class. Each student will trade ten groups of ten or rods for one group of a hundred or a flat. The teacher should then count by tens to show that this also equals 100 ones. As the teacher counts by tens, lay the rods on the flat to show that:

10 groups of ten = 1 group of a hundred = 100 ones

Using their IMN the students will write about this action and draw a picture of it. You may wish to copy and use the Hundreds PV Charts in MATH_2_A_VALUE OF 100 IMN ACTIVITY_RES-2014. Students will share their entries with each other.

An example of what the students’ work should look like is shown on the next page.


Hundreds

Tens Ones

3. Discuss the pattern - If we group ten ones that gives us a group of ten. If we group ten groups of ten, that gives us a group of a hundred. So if we group ten in one place that gives us the value of the next place. That’s how our numbers work – by grouping ten and moving them to the next place.

Show students a thousands block and inform them that the next place is the thousands place. “Who can figure out how we would get to one thousand with our blocks?” (put together 10 groups of one hundred)

If time permits, students can practice regrouping up to the 100s place by playing “Win a Flat” (MATH_2_A_Value of One Hundred 1_RES). After this game students can play a more challenging version, “Give Away a Flat” (MATH_2_A_Value of One Hundred 2_RES).

4. Partner Exploration

With a partner students will determine how many groups of tens and ones are in 200, 300, 400, 500, 600, 700, 800, and 900. They will write the equivalencies:

3 groups of a hundred = 30 groups of ten = 300 ones

5. Independent Practice – Interactive Math Notebook (IMN) Entry (Left-side)

Write down everything you know about 600.

Part 4 Compose and Decompose 3-Digit Numbers


Vocabulary: standard number, regroup, hundreds, tens, ones, placevalue mat, base ten blocks, represent, representations,equal

Materials: base ten blocks or virtual blocks, place value mats, Matching Cards for Reviewing Composing and

Decomposing of 2-Digit Numbers (page 17)Partner Work ~ MATH_2_A_Composing and Decomposing 3-Digit Numbers 1_RES -2014


Put together 10 groups of ten to make 1 group of hundred.

Practice Problems ~ MATH_2_A_Composing and Decomposing 3-Digit Numbers 2_RES-2014

1. Review

To review composing and decomposing 2-digit numbers, the student will match the number cards (page 17).

2. Instruction

Have students place blocks representing 85 on the place value mat. Together write a few equivalencies:

85 = 8 groups of ten + 5 ones = 7 groups of ten + 15 ones =

1 group of ten + 75 ones = 85 ones = 5 groups of ten + 3 groups of ten + 5 ones

Add 5 unit cubes, one at a time, i.e. 85 is 8 groups of ten + 5 ones → 86 is 8 groups of ten + 6 ones → 87 is 8 groups of ten + 7 ones → 88 is 8 groups of ten + 8 ones → 89 is 8 groups of tens + 9 ones → 90 is 9 tens.

(Students may not be able to build all the representations, for example you probably don’t have 85 ones for each student or pair of students to build it, so have them

do the ones they can, and tell you about any others they can think of).

Continue adding cubes until 99 is reached. Regroup for a ten, and then regroup ten tens for the hundred.

Review the representations of 100, i.e. 1 group of a hundred = 10 groups of ten = 100 ones.

3. Have students show 217 with blocks. Together manipulate the blocks to show different representations.

2 groups of a hundred + 1 group of ten + 7 ones = 1 groups of a hundred + 11 groups of ten + 7 ones = 217

also,

2 groups of a hundred + 17 ones = 217 ones = 1 group of a hundred + 1 group of a hundred + 17 ones = 217

4. On the board write the representation 8 groups of a hundred + 52 ones. The students will build the number and find the standard form.

Continue working together to compose and decompose hundreds numbers until students are able to proceed to the partner work. Make sure to have students decompose a number in at least 3 ways. Have the students demonstrate to each other the ways they were able to decompose and compose numbers and explain why these methods are equivalent.

5. Partner Work


Working together with the base ten blocks, students will compose and decompose numbers. (MATH_2_A_Composing and Decomposing 3-Digit Numbers 1_RES-2014)

6. Independent Practice

Using base ten blocks, the students will do independent practice problems, “Making and Taking Apart 3-Digit Numbers” (MATH_2_A_Composing and Decomposing 3-Digit Numbers 2_RES-2014)To practice the 4-step process, the teacher may guide students through #1.


1. Draw blocks to show the number 425.

show 425

= hundred

= ten

= one

I made it with blocks.I drew my blocks.

373 groups of ten +

7 ones

2 groups of ten + 4 ones

1 group of ten + 14 ones

7 groups of ten + 18 ones 88

5 groups of ten 3 groups of ten + 20 ones


Matching Cards for Reviewing Composing and Decomposingof 2-Digit Numbers

7 +

8 9 108

Warm-up (5 minutes)Addition and Subtraction Facts - Count On 1, 2, or 3

Materials: paper cups or containers each labeled with a number from 3 – 10 followed by a plus sign (see below); popsicle sticks, straws or other type of counter, poster MATH_2_A_FACT

STRATEGIES 1_RES)

1. Tell students that the number on the cup represents how many objects are already in the container. (You may want to have the objects in container when you first demonstrate).

Write the addition fact 7 + 3 on the board.

Tell students there is no need to count what is already in the cup. “Count on” starting from 7, e.g. 7 – 8 – 9 – 10. (Put a stick in the cup each time you say a number, 8- 9- 10).

Do a few more examples using cups with different numbers and varying the number of sticks you add (1, 2 or 3).

2. Remind students that they should always “count on” from the big number. You may wish to print the poster found in the material section.

Write the addition fact 3 + 6. For this fact, what cup do we need to get? 6Why 6? Because it is the big number Count: 6 - 7 - 8 – 9

Do a few more examples mixing the order of the numbers, sometimes the larger number comes second in the number sentence, for example: 5 + 3, 2 + 8, 1 + 6, 5 + 2, but you still start adding onto the larger number,.


Note: The count on strategy is not recommended for use beyond adding on 3.

Don’t count everything.Don’t count it all.

Start with the Large number,

Count on the small.

11 –

10 9 8

3. Write the addition fact 9 + 2.

Tell students that they can think of their head as the cup and imagine adding the sticks. For example, think of 9 being in your head (cup) and mentally put in 2 sticks. If students are having trouble with mental math, have them tap their head and say 9. Then clap 10 – 11. (Remind students that they can also use the making groups of ten strategy.)

Practice the “count on” strategy using flashcards. Have students identify the “count on” facts from the flashcard stack. Then practice these facts.

Additional Practice Resources ~“Count on Wheels” (MATH_2_A_FACTSTRATEGIES 2_RES) The wheels are bradded together. The inner wheel is given a turn and the numbers added.

Warm-up (5 minutes)Addition and Subtraction Facts - Count Back 1, 2, or 3

***In preparation for this strategy, have students practice counting backwards from 18. Use a number line for students having difficulty.

Materials: paper cups or containers each labeled with a number from 3 – 18 followed by a minus sign; popsicle sticks, straws or other counters.

Write the subtraction fact 11 – 3.

Tell students that the number on the cup represents how many objects are in the cup. (You may want to have the objects in the cup when you first demonstrate).

When you want to find what is left after subtracting 3 from the cup, you can count backwards. Demonstrate this by counting backwards from 11, i.e. 11 - 10 – 9 – 8.Remove a straw on when you say 10, when you say 9, and when you say 8.

Do a few more examples using cups with different numbers and varying the number of sticks you subtract (1, 2 or 3).


objects

The “Empty Wheel” (MATH_2_A_FACT STRATEGIES 4_RES-2014) can be used for practice. A subtrahend is written in the center of the circle and is subtracted from the number on the outer circle. This wheel can also be used for addition.

Part 5 The Value of 1,000


TEK 2.2B use standard, word and expanded forms to represent numbers up to 1,200

Vocabulary: Thousands, cube, thousands block, hundred, flat, units, rods, regroup, pattern, place value mat (with 4 parts), base ten blocks, represent, representation

Materials:

1. InstructionShow students a 4-part place value mat. Review what goes in the right-hand column (ones), the adjacent column (tens), and the column to the left of the tens (hundreds). See if students know what goes in the left-hand column (thousands).Label a class chart.

Review with students how many ones (units) it took to make a group of ten (rod). Have students regroup 10 units and trade it for a rod.

Ask students how many groups of ten (rods) did we need to make a group of a hundred (flat). Students should trade 10 rods for a flat.

2. Exploration

The teacher will then give each table a group of a thousand (a cube). Allow students to predict and discuss what will be equal to the cube.

Students should justify their responses and come to the conclusion that ten groups of a hundred are equal to 1,000.

The teacher will model this relationship for the class by grouping the ten flats to show they are equal to the thousands cube. Each table will trade ten groups of a hundred (flats) for a group of a thousand (cube). The teacher should then count by hundreds to show that this also equals 1,000 ones.10 groups of a hundred = 1 group of a thousand = 1,000 ones


*Note: The Count on and Count Back strategies, as well as previously taught fact strategies, should be practiced as a warm-up for about 5 minute for the next few days. You may alternate reviewing the previous strategies, while focusing on the new ones.

Using their Interactive Math Notebooks, the students will write about this action and draw a picture of it. Students will share their IMN entries with each other.

Since this is the first time 2nd graders will be ask to draw a thousands block, the teacher may want to give students a quick tutorial:

Have students draw 2 overlapping squares as such:

Then draw lines to connect the corners.

3. Ask the students what they notice. Do they see a pattern when going from one place to another? Students should be able to explain that if they group ten ones they get a group of ten. If they group ten tens that gives us a group of a hundred. If we group ten hundreds that gives us a thousand. So if we group ten in one place it gives us the value of the next place. That’s how our numbers work; we group ten and move to the next place.

4. Independent Practice – IMN

Write down everything you know about 1,000.Property of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 21

Thousands Hundreds Tens Ones

Part 6 Compose and Decompose 4-Digit Numbers to 1,200


Vocabulary: standard number, regroup, thousands, hundreds, tens, ones, placevalue mat, base ten blocks, represent, representations,equal

Materials: base ten blocks or virtual blocks, 4-part place value mats, (MATH_2_A_COMPOSING AND DECOMPOSING 4-DIGIT NUMBERS

1_RES-2014)Making and Taking Apart 4-Digit Numbers” (MATH_2_A_COMPOSING AND

DECOMPOSING 4-DIGIT NUMBERS 2_RES-2014).

1. Review

To review composing and decomposing 3-digit numbers, have students build the number 259 with place value blocks in 3 different ways. Have them draw the three representations in their IMN’s.

2. Instruction

Have students place blocks representing 989 on the place value mat.Together write a few equivalencies.

989 = 9 groups of a hundred + 8 groups of ten + 9 ones = 8 groups of a hundred + 18 groups of ten + 9 ones = 8 groups of a hundred + 17 groups of ten + 19 ones = 5 groups of a hundred + 4 groups of a hundred + 5 groups of ten + 3 groups of ten + 9 ones, etc.

Rebuild the number as 9 groups of a hundred + 8 groups of ten + 9 ones and add 1 unit cube. Now you have 9 groups of a hundred + 8 groups of ten + 10 ones, regroup the 10 ones for one groups of ten (rod), 990 is 9 groups of a hundred + 9 groups of ten. Continue adding units cubes one at a time, i.e..991 is 9 groups of a hundred + 9 groups of ten + 1 ones 992 is 9 groups of a hundred + 9 groups of ten + 2 ones 993 is 9 groups of a hundred + 9 groups of ten + 3 ones 994 is 9 groups of a hundred + 9 groups of ten + 4 ones.

Continue adding cubes until 999 is reached. Regroup for a ten, then regroup ten groups of ten for a groups of a hundred, then regroup for a group of a thousand.

Review the representation of 1,000, i.e. 1 thousand = 10 groups of a hundred = 1,000 ones.

3. Have students show 1,134 with blocks. Together manipulate the blocks to show different representations.

1 group of a thousand + 1 group of a hundred + 3 groups of ten + 4 ones = 1 groups of a thousand + 1 group of a hundred + 2 groups of ten + 14 ones = 1,134

Also, 5 groups of a hundred + 5 groups of a hundred + 1 group of a hundred + 3 groups of ten + 4 ones = 11 groups of a hundred + 34 ones = 1,134. You can do as many different representations as the students can think of and build with the blocks they have.


4. On the board write the representation 1 group of a thousand + 12 groups of ten + 4 ones. The students will build the number and find the standard form.Continue working together to compose and decompose numbers up to 1,200 until students are able to proceed to partner work.

5. Partner Work

Working together with the base ten blocks, students will compose and decompose numbers. (MATH_2_A_COMPOSING AND DECOMPOSING 4-DIGIT NUMBERS 1_RES-2014)


Using base ten blocks, the students will do independent practice problems “Making and Taking Apart 4-Digit Numbers” (MATH_2_A_COMPOSING AND DECOMPOSING 4-DIGIT NUMBERS 2_RES-2014). To practice the 4-step process, the teacher may guide the students through #1.

= 1,000 = 100 = 10

= 1

Work is shown above, so nothing is needed here.


1. Draw blocks to show the number 1,034 in 3 different ways.

Way 1

Way 2

Way 3

Draw 1,034 in 3 ways

I made it with blocks.I drew the picture and 10 hundreds = 1,000 oand 10 ones = 1 ten.

There are numerous solutions that students can create. This is just an example of how they may decompose the 1,034.

Warm-up (5 minutes)Addition and Subtraction Facts - Doubles

Materials: doubles items or pictures, pgs 25 and 26

1) Bring doubles items or pictures of doubles items (see pgs 25 and 26) to class and discuss. Write the related addition facts. Ask, “What do you notice about the facts?” Through questioning, lead students to realize that the same numbers are added twice.

Possible Doubles Itemseyes 1 + 1 = 2

wheels on a car 2 + 2 = 4 six-pack of coke 3 + 3 = 6 legs on a spider 4 + 4 = 8 fingers on hands 5 + 5 = 10 egg carton 6 + 6 = 12

days in 2 weeks on a calendar 7 + 7 = 14box of new crayons (16 count) 8 + 8 = 16

wheels on an 18-wheeler 9 + 9 = 18


Note: This strategy should be practiced as a warm-up for about 5 minutes for the next few days. Remember to review the previously taught strategies as well.

1 + 1 = ☐ 2 Eyes

2 + 2 = ☐ 4 Wheels on a Car

3 + 3 = ☐ 6-pack of Cola

4 + 4 = ☐ 8 Legs on a Spider

Doubles Pictures


5 + 5 = ☐ 10 Fingers

7 + 7 = ☐ 14 days

16 Crayons8 + 8 = ☐

9 + 9 = ☐ 18-Wheeler

6 + 6 = ☐ 12 Eggs(1 dozen)


Part 7 Read, Write and Describe the Value of Numbers to 99

TEK 2.2 B The student is expected to use standard, word, and expanded form to represent numbers up to 1,200.

Vocabulary: standard number, standard form, digit, value, expanded form, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, hundred, eleven, twelve, thirteen, fourteen, fifteen,

sixteen, seventeen, eighteen, nineteen, place value

Materials: 3-part mat, base ten blocks or virtual blocks, markers, valuespinners (pages 31, 32), Naming Chart, student copy of Naming Chart (MATH_2_A_Read Write and Describe 2-Digit 1_RES-2014),

practice problems (MATH_2_A_ Read Write and Describe 2-Digit 2_RES-2014)

1. Review

Count by 1s to 100.Count by 100s to 900.Have the class look at the 100s numbers on cards and say them aloud.

etc.

2. As a class begin filling in the “naming” chart which shows different ways to represent a number. Write the standard form of 45 and identify it as such.

Explain to students that this standard number, 45, is written with two digits. What do you think a digit is? (A symbol used to write numbers.) What digits do we have here?

a 4 and a 5(Refer back to the chart.) Why do you think we call 45 a 2-digit number? There are 2-digits -

the 4 and the 5(Write 28 on the board.) In the number 28 what digits do we have? a 2 and an 8. So, we would call 28 a 2-digit number, as well.(Write 167 on board.) What digits do we have? a 1, a 6, and a 7


300 800

places label

standard form

Tens Ones

4 5

What would we call 167? a 3-digit number(Write 1,005 on the board.) What would we call this? a 4-digit number Is the zero a digit? yes(Write 325,682 on the board.) What would we call this? a 6-digit numberAll these numbers (28; 167; 1,005; and 25,682) are called standard numbers. They are written using digits – the way we usually see numbers.

3. Return to the chart and include the base ten drawing and the base ten words.

Tens Ones

4 5

o o o o o

4 tens 5 ones

4. Expanded Form.

Referring back to the base ten words, write the number in expanded form.

Tens Ones

4 5


places label

standard form

base ten (build with blocks)

base ten (with words)

places label

standard form



expanded form (values)

o o o o o

4 tens 5 ones40 5

We call a number that is written like this, 40 + 5, expandedform. Expanded form shows the values for all the digitsin the number.

Point out the connection between the digit 4 and the value 40. Do the same with the 5. Show that the value of a digit depends on it’s place. Give the following example:

Let’s look at 26 and 62. (Write these two numbers and underline the digit 6 in each.)In 26 what is the value of the 6? 6 because it is in the ones placeIn 62 what is the value of the 6? 60 because it is in the tens place, and 6 groups of ten are 60.(Write some 2-digit numbers on the board and have students discuss the value of different digits.)

5. Partner Work

Using the two spinners (pgs. 31-32), the students will find the value of various digits. Students will first spin a 2-digit number. They will then spin the second spinner to identify the place value. They should state the value to their partner in a complete sentence. “The value of the 6 in 67 is 60, 6 groups of ten.”

6. Return back to the naming chart for 45. Review the various representations that are listed so far.

There is only one more form of this number which we need to write. We now need to write it in words.If we look at the value of the 4 (point to 40), what is it? 40So let’s write that down in words. (Write forty.) What is the value of the 5? 5Let’s write that as well. What do we have? 45 in words, forty-five

Tens Ones

4 5


+

places label

standard form




value of 9 in 94 94

T O

9 tens 4 ones90 + 4

I made a naming chart.9 4

o o o o o

4 tens 5 ones40 5

forty five

Have students copy the above into their IMN.Students should fill in similar charts for other 2-digit numbers. They may use the form, “Representing 2-Digit Numbers” (MATH_2_A_Read Write and Describe 2-Digit 1_RES-2014).

7. Independent PracticeThe students will work the set of problems, “Read, Write, and Describe 2-Digit Numbers” (MATH_2_A_Read Write and Describe 2-Digit 2_RES-2014). The teacher may do #1 with students for model the 4 steps.


places label

standard form




+

-

What is the valueof the 9 in 94?

Intervention: The teacher may need for students to draw blocks in the naming chart, as well.

78 30

92 67

Spin your number …..



ones placetens place

Find the value of the digit in the …..


Part 8 Read, Write and Describe the Value of Numbers to 999

TEK 2.2B The student is expected to use standard, word and expanded for to represent numbers up to 1,200.

Vocabulary: standard number, standard form, digit, value, expanded form, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, hundred, eleven, twelve, thirteen, fourteen, fifteen,

sixteen, seventeen, eighteen, nineteen, place value

Materials: 3-part mat or place value mat, base ten blocks or virtual blocks, markers, value spinners, Word Name Flash Cards

(pages 37,38), Naming Chart, student copy of the Naming Chart (MATH_2_A_Read Write and Describe 3-Digit 1_RES-2014), practice problems (MATH_2_A_Read Write and Describe 3-Digit 2_RES-2014)IMN Activity(MATH_2_A_READ WRITE REPRESENT 3-DIGIT IMN ACTIVITY_RES-2014)

1. Represent 3-digit numbers using a Naming Chart similar to that used for 2-digit numbers.

Build the number 245 with the base ten blocks. The class can refer to these blocks as the class completes the chart.

2. The students should practice filling in the chart with other 3-digit numbers. The practice can be done either as a class or with a partner.


places label

standard form

base ten (pictures)



words

Hundreds Tens Ones

2 4 5

o o o o o

2 hundreds 4 tens 5 ones200 40 5two

hundred forty five

++

When students have had some practice beginning with the standardform, have them begin with another form of the number and complete the chart. For example, they should complete the chart when given only the words. Form “Representing 3-Digit Numbers” (MATH_2_A_Read Write and Describe 3-Digit 1_RES-2014) may be used.

3. Partner Work

Using the Word Name Flash Cards (pg. 36, 37), the students will practice saying hundreds numbers. The standard form will be shown to the student by his partner. The student will then say the number in words. The partner checks how the number is said by checking the word form on the back of the card. Switch roles.

4. Guided Practice

The teacher will guide the students through the problem usingthe 4-step process.

Main idea: 349 in words

Details/Known: 349

Strategy:

[Intervention ~ The teacher may wish to have the students draw the picture of the base ten blocks, as well.]

How: I made a naming chart.


Joel wrote the number 349 in words. How would this number be written?

A. three four nineB. three hundred fourteen nineC. three forty-nineD. three hundred forty-nine

You may show the students that they can label their chart with H, T and O to represent Hundreds, Tens and Ones.

H T O3 4 9

300 40 9three hundred forty nine

+ +

LOST!

239 is lost! Help us find it!

Represent 239 in all the ways you can.

5. Independent PracticeThe student will complete the problem set, “Read, Write, Represent 3-Digit Numbers” (MATH_2_A_Read Write and Describe 3-Digit 2_RES-2014).

6. IMN Entry (MATH_2_A_READ WRITE AND DESCRIBE 3-DIGIT NUMBERS IMN ACTIVITY)



361 408

829 770

502 214

390 685

Word Name Flash Cards


three hundred sixty-one

eight hundred twenty-nine

five hundred two

three hundred ninety

four hundred eight

seven hundred seventy

two hundred fourteen

six hundred eighty-five

Guided Practice

Joel wrote the number 349 in words. How would this number be written?

A. three four nine

B. three hundred fourteen nine

C. three forty-nine

D. three hundred forty-nine


Warm-up (5 minutes)Addition and Subtraction Facts - Doubles +1***Students are most successful with this strategy after they have mastered their doubles.

Materials: unifix cubes

Write the problem 8 + 7.

Tell students that if they know their doubles facts, they can quickly solve a problem like this one.(They can still use making groups of ten as well.)

Point to the problem and ask, “Which digit is smaller?” 7 Make 2 rows of 7 with the unifix cubes.

The smaller number is then doubled, (7 + 7 = 14). Since 8 is one more than 7, add one more cube to one of the trains. The fact 8 + 7 now becomes 7 + 7 + 1 = 15.

Point out that these numbers, 8 and 7, are “neighbors.” They are next to each other on a number line. (Put up a number line so students can easily see their proximity.) The doubles plus 1 is only used when numbers are “neighbors.”

Part 9 Read, Write and Describe the Value of Numbers to 1,200

TEK 2.2B The student is expected to use standard, word and expanded form to represent numbers up to 1,200.

Vocabulary: standard number, standard form, digit, value, expanded form, hundred, thousand, place value

Materials: 4-part mat or place value mat, base ten blocks or virtual blocks,

1. Represent 4-digit numbers using a Naming Chart similar to that used for 3-digit numbers.Property of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 40


Build the number 1,152 with the base ten blocks. The class can refer to these blocks as the class completes the chart.

T housands Hundreds Tens Ones1, 1 5 2

o o

1 thousand 1 hundred 5 tens 2 ones

1,000 100 50 5one

thousand,one

hundred fifty two

2. The students should practice filling in the chart with other 4-digit numbers. The practice can be done either as a class or with a partner.

When students have had some practice beginning with the standard form, have them begin with another form of the number and complete the chart. For example, they should complete the chart when given only the words. Form “Representing 4-Digit Numbers” (MATH_2_A_READ WRITE AND DESCRIBE 4-DIGIT 1.RES-2014)

3. Partner Work

Using the naming chart or the form, students should challenge each other by filling out one of the representations and then having their partner complete the other ways to represent their number.

4. Guided Practice (pg 42)

The teacher will guide the students through the problem using the 4-step process.


places labelstandard form

base ten (pictures)

base ten (with words)expanded form (values)

words++ +

Alice wrote the number 1,200 in words. How would this number be written?

A. one two zero zeroB. one thousand, twentyC. one thousand two hundred

Main idea: 1,200 in words

Details/Known: 1,200

Strategy:TH H T O1, 2 0 0

1,000 200 0 0one thousand, two hundred

(Students should label the thousands place with TH so as not to confuse it with the tens place.)

How/Why: I made a naming chart.


The student will complete the problem set, Read, Write, and Represent 4-Digit numbers(MATH_2_A_READ WRITE AND DESCRIBE 4-DIGIT 2_RES-2014)

Guided Practice Problem Property of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 42


A. one two zero zeroB. one thousand, twentyC. one thousand two hundred


A. one two zero zeroB. one thousand, twentyC. one thousand two hundredD. two hundred one

Part 10 Exploring Place Value


TEK 2.2C The student is expected to generate a number that is greater than or less than a given whole number up to 1,200.

TEK 2.2D The students is expected to use place value to compare and order whole numbers up to 1,200 using comparative language, numbers and symbols (<, >, =).

Vocabulary: thousands, hundreds, tens, ones, place, value, units, greatest,value, least, smallest, largest

Materials: paper with 3 lines (see next page), bundles of base ten blockswhich are taped together (1 bundle of each ~ 3 ones, 3 tens,3 hundreds, 4 ones, 4 tens, 4 hundreds, 6 ones, 6 tens, 6 hundreds, i.e. a total of 9 bundles of blocks), digit cards(MATH_2_A_Exploring Place Value 1_RES-2014),a “Do Not Use” box, practice problems(MATH_2_A_Exploring Place Value 2_RES-2014)

1. Present the following problem to the students.

Start the 4-step problem solving process.

Main Idea: largest number he madeDetails: largest 3-digit number

digit cards 3 4 6use a digit one time

2. Strategy:

Show the students the piece of paper with the 3 lines on it (see following page). Havestudents name the places, i.e. ones, tens, and hundreds. Teacher label.


Juan has these three digit cards.

Juan made the largest 3-digit number he could with these digits. He only used each digit one time. What number did he make?

3 4 6

____ ____ ____

H T O

____ ____ ____6

3. Hold up the digit card 3.

If we have the digit 3, it can be 3 ones (show studentsthe bundle of 3 units cubes). What else could thedigit 3 stand for? 3 groups of ten (show bundle of 3 rods)What else? 3 groups of a hundred (show bundle of 3 flats)

Off to the side line up these “possibilities” for the digit 3 as shown below.

Do the same with the digits 4 and 6.

4. If Juan is making the largest number he can, which ofthese groups of blocks has the greatest value? the 6 groups of a hundred (Put the blocks above

the hundreds place on the paper and the “6” card on the line.) Through questioning, make sure students understand the hundreds place has the largest value.


3 4 6

H T O

____ ____ ____6 4

H T O

____ ____ ____6 4

H T O

The problem said that ‘he only used each digit one time.’ Since we have already used the digit “6,” we need to remove the 6 tens and the 6 ones bundles. (Place the unused blocks in the “Do Not Use” box.)

We also need to remove the four groups of a hundred block bundle and the three groups of a hundred block bundle. Why do you think that is? We have already used the hundreds place.

5. Now from the blocks that are left, what should we use next? Which bundle is now the biggest? the 4 groups of ten. (Put the blocks above the tens

place on the paper and the “4” card on the line.)

Since we have used the digit “4,” we must remove the 4 ones. What else must we remove? the 3 groups of ten, because the tens place is now used (Put these in the “Do Not Use” box.)

All that remains is the 3 ones in the ones place. (Put the blocks above the ones place on the paper and the “3” card on the line.)

(Write the number 643 as the largest number that could be created.)


3

6. Complete the 4-step process by writing the “How/Why:”

We used the 6 groups of a hundred blocks, the 4 groups of ten blocks, and the 3 ones blocks.We used the largest bundle of blocks in the biggest valued place.

7. Partner work:

Give students 3 digit cards and have them make the largest number they can.To assess understanding, students can be asked to write an Interactive Math Notebook (IMN) entry in which they are given 3 digits, and they explain how to make the largest number.

8. Using the same technique described above, make the smallest possiblenumber. This may be followed by more partner practice and an additional Interactive Math Notebook (IMN) entry.

9. Repeat the process using 4 digits.

Independent Practice

The student will complete the independent practice, “Exploring Numbers” (MATH_2_A_Exploring Place Value 2_RES-2014).

Warm-up (5 minutes)Addition and Subtraction Facts Sums to 20 ~Fact Families (Additive Property)

Materials: unifix cubes

Using unifix cubes, select 3 cubes of one color and connect them to two cubes of another color. Now write the fact 3 + 2 = 5 on the board.

With the same set of cubes, flip the cubes and write the number sentence to show the additive property: 2 + 3 = 5.

Beginning with the same digit of 5, remove the 3 cubes and write down the corresponding number sentence, 5 - 3 = 2.


Now do the reverse to get the last member of the fact family. Starting with the 5, the 2 cubes are removed. This leaves a difference of 3. 5 - 2 = 3

2 + 3 = 53 + 2 = 55 – 3 = 25 – 2 = 3

Concretely model this process a few more times with different numbers.

Additional Resource

Two additional fact practice sheets are included in the Resources(MATH_2_A_FACTSTRATEGIES6_RES-2014). The sum or difference iswritten in the center circle, and facts which can generate that answerare paired in the outer circles. In other words, opposite circles willyield the answer in the center.

Part 11 Comparing Whole Numbers (through 1,200)

TEK 2.2D The student is expected to use place value to compare and order whole numbers to 1,200 using comparative language, numbers, and symbol (< , > , or = ).

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.

Vocabulary: thousands block, units, ones, tens, hundreds, greater than, less than, equal, relationship, digit, 2-digit number, 3-digit number, 4-digit number

Materials: sticker dots or circles to represent dots, base ten blocks (ones, tens, hundreds, and thousands), 2 sets of crowns (made using multi-colored sentence strips—shown below),MATH_2_A_COMPARING NUMBERS 1_RES-2014MATH_2_A_IMN COMPARING NUMBERS 2_RES-2014 MATH_2_A_IMN COMPARING NUMBERS 3_RES-2014 MATH_2_A_COMPARING NUMBERS 4_RES-2014



hundreds tens onesthousands

Comparing 2-digit Numbers

To ensure students’ understanding of the meaning of “greater than” and “less than” you may want to demonstrate using the following activity:

Have two students each grab a handful of counters. Have each student count his/her counters and record the numbers on the board. Discuss which number is greater and draw a dot by the smaller number. Next draw two dots by the larger number. Then connect the dots, i.e.:

9 13Reverse the numbers, with the larger number first, and again place 2 dots by the larger number and one dot by the smaller number. Connect the dots making a greater than symbol this time. Have students practice reading aloud the inequalities with both “greater than” and “less than.”

1. Invite 2 students to the front of the room. Place a tens crown on the first student, and a ones crown on the second student.

Place the number 47 on one side of the floor. Seat the two children behind the number (see diagram on page 49).

How many groups of tens does the tens place (child) need? 4How do you know? Because the 4 is in the tens place (Give that child 4 rods.)

How many unit cubes does the ones place (child) need. 7(Give that child 7 unit cubes.)

Place the number 64 on the other side of the floor and crown two more children. Have the class help in deciding how many blocks to give each student using the same questioning as above.

Now let’s figure out which of these numbers is larger. Which one of our places is the largest, the tens or the ones? The tens.

Will the “tens place children” please stand. (Have these students show how many groups of ten they have.) Who has more? 6 tensSo which number is greater? 64How do you know? Because 64 has more groups of ten than 47How many more groups of ten? 2What about the children holding the ones? Do we need to count how many they have? No, since there are more groups of tens in the number 64, it is the biggest number. (Show that the number of ones does not matter by placing the 7 unit cubes on one of the 2 more groups of ten [rods].)


10schild

1schild

4 7

10schild

1schild

64

Less than

1schild

10schild

64

10schild

1schild

4 7

Greater than

(Place a sheet of paper between the 47 and the 64.)

I am going to mark the smaller number with 1 dot. Will you remind me which number is smaller? 47 (Place sticker or circle on the side nearest the 47).

Now I’m going to mark the larger number with 2 dots, (place 2 stickers or circles on the side nearest 64).

(Take a marker and connect the dots like the diagram below.)

This symbol “<” stands for less than. (Write the words less than above the symbol.)

First model, then have students repeat how this relationship is read. “47 is less than 64.”

2) Flip the numbers and tell the students that you will again put 1 dot beside the smaller number and 2 dots beside the larger number. Draw a line to connect the dots as shown below. Ask students what they think this symbol might mean. Tell students that the symbol “>” stands for greater than. Together state this relationship, “64 is greater than 47.”

Write 47 < 64 and 64 > 47, so that students can see it written both ways. Then have them practice reading it both ways.

3) Partner Practice

Students practice using the greater than and less than symbols on the partner practice (page 50). They should label the symbols correctly with “Greater Than” and “Less Than”.

Intervention: Students experiencing difficulty can continue to use base ten blocks.


24 46

38 35

62 29

16 61

77 66

Partner Practice

Write > or < to make the relationships true.

Comparing Numbers ~ 3-Digit

1. Invite 3 different students to the front of the room.


100schild

10schild

1schild

3 4 2

100schild

10schild

1schild

2 4 8 >

If 3 students are coming up to the front, what kind of number are we going to make? A number that has hundreds; a 3-digit number

Place a hundreds crown on the first student, a tens crown on the second student, and a ones crown on the third student.

Place the number 342 on one side of the floor. Seat the children behind the number in order.

How many groups of one hundred does the hundreds place (child) need? 3 (Give that child 3 groups of a hundred [3 flats].)How many groups of ten does the tens place (child) need? 4 (Give that child 4 groups of ten [4 rods].)How many ones does the ones place (child) need? 2 (Give that child 2 ones [2 unit cubes].)

Place the number 248 on the other side of the floor and crown three more children. Have the class help in deciding how many blocks to give each student using the same questioning as above.

Have two other students sitting off to the side holding the “>“and “< “ signs. The teacher can either make the signs again using dots, use signs from the previous lesson, or print the signs from Resources (MATH_2_A_COMPARING NUMBERS 1_RES-2014).

Now let’s see which of these numbers is larger. Which set or group of blocks has the greatest value—the ones, the tens or the hundreds? The hundreds Will the hundreds place children please stand. Who has the most? The one holding 3 hundreds So which number is the largest? 342

What about the children holding the tens and the ones? Do we need to count what they have in their hands? No, since 343 has more hundreds, it is the bigger number. (Have the tens and ones children from the number 248 place their rods and units on the extra hundred from 342 to prove that the extra hundred is much bigger than the 48.)

Have the two students holding the greater than (>) and less than (<) signs stand up. Determine as a class which sign needs to go between the two numbers. Have that child move in between and have the whole class say the number relationship together. 342 is greater than 248When comparing the numbers 342 and 248, which place was most important in helping us make our decision? The hundreds place


So we could say that when comparing 342 and 248 the number in the hundreds place determines which number is greater.

Write 342 > 248 and 248 > 342, so that students can see it written both ways. Then have them practice reading it both ways.

2. Repeat using different students. Show relationships in which the hundreds place is the determining place because it has the largest value in the number. Then do some examples in which the tens place is the determining place because the hundreds place has the same value in both numbers. Continue comparing numbers in which the ones place is the determining place, and some in which the numbers are equal.

Suggested numbers: 391 and 411; 411 and 391

548 and 552; 552 and 548 423 and 421; 421 and 423 214 and 214

Have students justify their decisions.

3. Partner Practice

Give students a pair of numbers to evaluate. The students will determine the relationship and circle the determining digits.

Comparing 4-digit Numbers

1. Once again invite 4 different students to the front of the room.

If 4 students are coming up to the front, what kind of number are we going to make? a 4-digit number

Place a thousands crown on the first student, a hundreds crown on the second student, a tens crown on the third student, and a ones crown on the fourth student.

Place the number 1,023 on one side of the floor. Seat the children behind the number in order.

How many groups of a thousand does the thousands place (child) need? 1 (Give that child 1 group of a thousand [1 thousand block].)How many groups of a hundred does the hundreds (child) need? 0 (we don’t give any hundreds [flats] to that child.)How many groups of ten does the tens (child) need? 2 (Give that child 2 groups of ten


>100schild

10schild

1schild

1,121 4 2

100schild

10schild

1schild1,0231000s

child

1000schild

[2 rods]).How many ones does the ones (child) need? 3 (Give that child 3 ones [3unit cubes]).

Place the number 1,121 on the other side of the floor and crown four more children. Have the class help in deciding how many blocks to give each student using the same questioning as above. Have two other students sitting off to the side holding the “>“ and “< “ signs.

Now let’s see which of these numbers is larger. Which group of blocks has the greatest value—the ones, the tens, the hundreds, or thousands? The thousands Will the thousands place children please stand. Who has the most? They both have the same number. Since they both have the same number, we have to look at the place with the next greatest value. Which place should we look at next? Look at the hundreds place.Will the hundreds place children please stand. Who had the most? The one holding 1group of hundred

What about the children holding the tens and the ones? Do we need to count what they have in their hands? No, since 1,121 has more groups of a hundred, it is the bigger number. (Again you can prove that the extra hundred in the number 1,121 is much bigger than the 23 in the number 1,023.)

Have the two students holding the greater than (>) and less than (<) signs stand up. Determine as a class which sign needs to go between the two numbers. Have that child move in between and have the whole class say the number relationship together. 1,121 is greater than 1,023When comparing the numbers 1,121 and 1,023, which place value was most important in helping us make our decision? The hundreds place

So we could say that when comparing 1,121 and 1,023 the 1 in the hundreds place determined which number was greater.

Write 1,121 > 1,023 and 1,023 < 1,121, so that students can see it written both ways. Then have them practice reading it both ways.


Draw the blocks.

2 hundreds 3 tens 4 ones 2 hundreds 2 tens 6 ones

Which symbol correctly compares the number?

A. >B. <C.. =

2. Repeat using different students. Show relationships in which the thousands place is the determining place, some in which the hundreds place is the determining place, some in which the tens place is the determining place, some in which the ones place is the determining place, and some that are equal.

Suggested numbers: 1,164 and 978; 978 and 1,164

1,156 and 1,156 1,034 and 1,262; 1,262 and 1,034

1,025 and 1,024; 1024 and 1,025

3. Partner Practice

Give students a pair of numbers to evaluate (the numbers can be 2-digit, 3-digit or 4-digit numbers less than 1,200). The students will decide the relationship and circle the digits that determine the place to compare with.

Possible numbers: 25 and 29; 727 and 772, 1,012 and 1,200

4. IMN (Math Interactive Notebook)

The teacher may want to review comparing numbers using symbols withMATH_2_A_IMN COMPARING NUMBERS 2_RES-2014 (right side of IMN) and MATH_2_A_IMN COMPARING NUMBERS 3_RES-2014 (left side of IMN) .


The students will work the practice problems, “Comparing Numbers”(MATH_2_A_COMPARING NUMBERS 1_RES-2014)

The following page shows a model of the 4-step process for the first problem.

symbol correctly compares numbers


Notice: Discuss with students how there are no + signs between the place value. The + is understood. .

2 hundreds 3 tens 4 ones

2 hundreds 2 tens 6 ones

Intervention: Students experiencing difficulty can continue to use blocks as they solve these problems.

Part 12 Ordering Numbers

TEK 2.2D The student is expected to use place value to compare and order whole numbers to 1,200 using comparative language, numbers, and symbol (< , > , or = ).


Vocabulary: order, greatest, least, fewest, most, largest, biggest, smallest, between, place value chart, hundreds, tens, ones, thousands, digits, relationships, symbol, equal

Materials: base ten blocks, place value mats, Guided Problems, student copies of Guided Practice Problems (pages 62, 63, 67 and 68)

MATH_2_A_IMN ORDERING NUMBERS 1_RES-2014MATH_2_A_IMN ORDERING NUMBERS 2_RES-2014MATH_2_A_ORDERING 2-DIGIT NUMBERS_RES-2014MATH_2_A_ORDERING 3-DIGIT NUMBERS_RES-2014MATH_2_A_ORDERING NUMBERS_RES-2014

Ordering 2-Digit Numbers


Drew blocksCircled number determining the largest value place2 hundreds 3 tens 4 ones gets 2 dots, because it has more groups of ten

Students draw pictures of the blocks, or circle place on the numbers that determine the largest value.

possible answers

Ana - 60 gumballs

Joe - 84 gumballs

Ron - 48 gumballs

Ana - 60 gumballs

Joe - 84 gumballs

Ron - 48 gumballs

1. Display Guided Practice Problem #1 and give each student a copy to work along with the teacher (page 59). The teacher will read the problem, stopping at each speed bump (/) and model how to solve the problem using the 4-step process.

list gumballs from greatest to least

2. The teacher and students build each number from the story problem with base 10 blocks on different place value mats. Students may work as table groups or with partners, so that each student builds at least one number. Have the students draw pictures to represent the numbers in the “detail/known” section of their guided practice page.


3. Table groups will discuss how to arrange the blocks from greatest to least. Students will move the mats with the blocks so they are in order from greatest to least. Then as a whole class, discuss what order they put the blocks in and their reasoning.


Ana, Joe, and Ron all counted gumballs. Ana counted 60 gumballs, Joe counted 84, and Ron counted 48. List the numbers of gumballs from greatest to least.

Main Idea Details/Known

How/ WhyStrategy

1

2

3

4. The teacher should model how to make a place value chart (see following page) to assist in ordering numbers.

We don’t always have place value blocks when we are putting numbers in order. Another way we can order numbers is to use a place value chart. (Students copy the chart which the teacher has made in the “strategy” section on their papers.)How were we going to order these numbers? from greatest to least So which place has the greatest value? the tensLet’s look there first.We have a 6, an 8, and a 4 in the tens place.What is the value of the 6? 60What is the value of the 8? 80What is the value of the 4? 40So which one has the greatest value? the 8If 8 tens has the largest value, which number is greatest? 84 Label 84 with a 1 to indicate it is first in order. (Model.)


strategy:

So, what number in the tens place is second? (6) Why? (6 tens are greater than 4 tens) Which number is the smallest (4)Let’s finish labeling our place value chart.


G → L

place value chart

Ana - 60 gumballs

Joe - 84 gumballs

Ron - 48 gumballs

Tens Ones

6 0

8 4

4 8

21

3

Label the 60 with a (2) and the 48 with a (3) because it is the smallest.

The students should then write the numbers in order from greatest to least.

84, 60, 48

Now have students rewrite the numbers using the symbols, and practice reading it to a partner:

84 > 60 > 48

5. Discuss how they decided which number would go first, second and third. Through guided questions, come up with a statement(s) to use for the “how” section of the 4-step process.


6. Do the guided practice problem #2 (page 60) using base 10 blocks for more concrete practice. Have students draw representations of the blocks in the “detail/known” step of their 4-step process.

7. Independent WorkStudents will do “Ordering 2-Digit Numbers” (MATH_2_A_ORDERING 2-DIGIT NUMBERS _RES-2014). Students may use place value blocks to solve these problems. However, students should progress to the stage of solely using place value charts.

Guided Practice ProblemsProperty of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 59

Ana - 60 gumballs

Joe - 84 gumballs

Ron - 48 gumballs

possible answers

I built the numbers ORI used place value chart ORI looked at the digits in tens place because they have the greatest value. OR8 tens is bigger

84, 60, 46

84 > 60 > 46

Tens Ones6 08 44 8

1. Ana, Joe, and Ron all counted gumballs. Ana counted 60 gumballs, Joe counted 84, and Ron counted 48. List the numbers of gumballs from greatest to least.

2. Mrs. Tatum bought candy. The table below shows the number of pieces of candy.


Write the numbers in order from least to greatest.


1. The teacher will demonstrate ordering 3-digit numbers. Model solving problem #1 (page 64) using the 4-step process as before.


Candy Number of Pieces

Jolly Ranchers 42Skittles 43Dum Dum Pops 32

1

2

3

Main Idea: list girls’ scores least to greatest

Details/Known: M - 322 points

L - 223 points

S - 232 points

2. The teacher and student table groups build each number from the story problem with base 10 blocks on mats. Have students draw a picture to represent each number beside the corresponding “detail.”

Details: M 322 points

L 223 points

S 232 points

3. As before, students discuss how to arrange the mats from least to greatest. Then they place the mats in order.

Ask the students, “How did you decide which number would go first, second, and third?” (Have several students explain their thinking.)

4. This time, demonstrate making a chart which should be used when ordering 3-digit numbers.

Strategy:


In the game, Marcy scored 322 points, Lily scored 223, and Sara scored 232. List the girls’ scores from least to greatest.

L → GH T O

3

2

2

2

2

3

2

3

2

First we focus on the hundreds place, since those numbers have the greatest value.What do you see? a 3, and 2 twosSince we are looking for the smallest number, we will disregard the 3 groups of a hundreds for now. But we have two 2 groups of a hundred. So we have to look where? the tens placeThe first number with a 2 in the hundreds place (2 groups of a hundred) has a 2 in the tens place

or 2 groups of ten.The second number with a 2 in the hundreds place has a 3 in the tens place.Which is less, 2 groups of ten or 3 groups of ten? 2 groups of tenSo which number is the smallest? (223)Mark it with a 1. Mark the other 2 hundred number with a 2.And what do we mark the 3 hundred number with? (3)Why? (because it is the largest, so it comes last) Write the numbers from least to greatest.

223, 232, 322

How could this relationship be written using < symbols?

(223 < 232 < 322)

Which number comes between the smallest and the largest number? (232)

Have students read inequalities to a partner.

As a class, come up with a statement to explain how they got the answer.

An example of what the completed 4-step process may look like can be found on the following page.

M 322 points


list girls’ scores least to greatest L 223 points

S 232 points

223, 232, 322 (223 < 232 < 322)

5. Do Guided Practice Problem #2 (page 65) with the students.

6. Partner Practice

Give each student a card with a different 3-digit number on it. Have the students work together to put themselves in order from greatest to least or least to greatest. You may wish to start with table groups working together to order their numbers, and then progress towards having the whole class line up in order.

7. Extra Practice :SMARTBOARD

MATH_2_A_ORDERING 3-DIGIT NUMBERS _RES-2014

Intervention: Students who are having difficulty may use place value blocks or draw pictures to represent the numbers.

Guided Practice Problems


I built the numbers. ORI used place value chart. ORI looked at the hundreds place first then I looked at the digits in the tens place because there were 2 numbers with 2 hundreds.

Possible answers

H T O

3

2

2

2

2

3

2

3

2

1. In the game, Marcy scored 322 points, Lily scored 223, and Sara scored 232. List the girls’ scores from least to greatest.

2. Mark, Adrian, and Seth counted their bugs. The table below shows the numbers of bugs each boy has. List the numbers of bugs from greatest to least.

Name Number of Property of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 65

BugsMark 206Adrian 273Seth 266



1. Use Guided Practice problem #1 (page 70) to demonstrate ordering 4-digit numbers following the same procedure as before using the 4-step process.

Main Idea: pennies collected G L (greatest to least)

Details/Known: S – 1,022 pennies

R – 1,103 pennies

M – 1,200 pennies

2. The teacher and student table groups build each number from the story problem with base 10 blocks on mats. Have students draw a picture to represent each number beside the corresponding “detail.”

Details/ S – 1,022 penniesKnown:

R – 1,103 pennies

M – 1,200 pennies

3. As before, students discuss how to arrange the mats from least to greatest. Then they place the mats in

order.

Ask the students, “How did you decide which number would go first, second, and third?” (Have several students explain their thinking.)

4. Demonstrate making the chart below which should be used when ordering numbers. Point out that this time we have to add a place for the thousands and we will label it with a Th so as not to get confused with the T for the tens place.


The second graders were collecting pennies. Sam’s class collected 1,022 pennies, Ron’s class collected 1,103 pennies, and Max’s class collected 1,200 pennies. List the pennies collected in order from greatest to least.

3

2

1

Strategy:

First we focus on the thousands place, since those numbers have the greatest value.What do you see? all the numbers are 1sBecause all the numbers in the thousands place have the same value, we have to look at the

numbers with the next highest value. So which place do we look at now? the hundreds placeSince we are looking for the greatest number, we can already determine that the number with the 0 hundreds is the smallest.Mark it with a 3. Now let’s compare the other 2 numbers. One number has 1 hundred and the other has 2 hundreds. Which is more, 1 hundred or 2 hundreds? 2 hundredsWrite a 1 by the number with 2 hundreds. Mark the other number with a 2. Write the numbers from greatest to least.

1,200, 1,103, 1,022

How could this relationship be written using < symbols?

(1,200 > 1,103 >1,022)

Which number comes between the smallest and the largest number? (1,103)

As a class decide what to write in the How section of the 4-step process.

Example of what a complete 4-step process is on the next page.


G → LTh H T O

1

1

1

0

1

2

2

0

0

2

3

0

pennies collected G L S – 1,022 pennies

R – 1,103 pennies

M – 1,200 pennies

1,200, 1,103, 1,022

(1,200 > 1,103 >1,022)

5. Do Guided Practice Problem #2 (page70) with the students.

6. Partner Practice

Give each student a card with a different 4-digit number on it (up to 1,200). Have the students work together to put themselves in order from greatest to least or least to greatest. As before, you may wish to start with table groups working together to order their numbers, and then progress towards having the whole class line up in order.

7. Independent Work

Students will do “Ordering Numbers” (MATH_2_A_ORDERING NUMBERS _RES-2014). Students should progress to the stage of solely using place value charts.

Intervention: Students who are having difficulty may use place value blocks or draw pictures to represent the numbers.


I built the numbers ORI used place value chart. ORI looked at the thousands place first then I looked at the digits in the hundreds place to find the numbers greatest to least

Possible answersTh H T O1

1

1

0

1

2

2

0

0

2

3

0

8. IMN

The teacher should use the following for the right side of the Interactive Math Notebook:

MATH_2_A_IMN ORDERING NUMBERS _RES-2014 MATH_2_A_IMN ORDERING NUMBERS _RES-2014

Use the following question on the left side:

Ben ordered the following numbers from greatest to least. He put themin this order.

864, 873, 722

Is Ben correct or incorrect? Why?

A copy of this question can be found at MATH_2_A_IMN QUESTION _RES-2014

(This question is written multiple times so that the teacher can cut and have the students glue it to their IMN)


Guided Practice Problems

1. The second graders were collecting pennies. Sam’s class collected 1,022 pennies, Ron’s class collected 1,103 pennies and Max’s class collected 1,200 pennies. List the pennies collected in order from greatest to least.

Part 13 Number LinesProperty of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 71

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.


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

Materials: hundreds chart (page75), scissors, tape, Increments of One~ Number Lines for Partner Work (page 76)base ten blocksMATH_2_A_TN NUMBER LINES_RES-2014MATH_2_A_IMN NUMBER LINE QUESTION 1_RES-2014MATH_2_A_NUMBER LINE PRACTICE 1_RES-2014

MATH_2_A_IMN NUMBER LINE QUESTION 2_RES-2014 MATH_2_A_IMN NUMBER LINE QUESTION 3_RES-2014 MATH_2_A_NUMBER LINE PRACTICE 2_RES-2014 MATH_2_A_IMN NUMBER LINES_RES-2014

MATH_2_A_NUMBEER LINE IP PRACTICE_RES-2014 MATH_2_A_MIXED PRACTICE_RES-2014

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_TN NUMBER LINES_RES-2014)

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

1. Demonstrate the connection between a hundreds chart and a number line but cutting apart a hundreds chart and tape it together into a number line. Compare the similarities and the differences between the two.

2. 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.


41 42 43 44 45 46 48 49 50

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.

Use base ten blocks 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 1unit 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).

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? 7onesDid 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 48


41 42 43 44 45 46 48 49 50

636 637 ?639 643?638 642 644 645

What strategy helped us find the missing number? looking at the numbers before and after the missing number

3. Now draw/display 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? 10Since 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 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 Work

The students will practice identifying points on the number line usingIncrements of One ~ Number Lines for Partner Work (page 62)

6. IMN Right side: Review steps

Left side 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?

(This question is written multiple time so that the teacher can cut and have the students glue it to their IMN) MATH_2_A_IMN NUMBER LINE QUESTION 1_RES-2014


The student will do “Number line- Practice 1” (MATH_2_A_NUMBER LINE PRACTICE 1_RES-2014).


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

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


134 135 136 ? 138

769 ? 771 772 ?

409 410 411 ? ?

99 ? ? 102 103

Number Line in Increments of TenProperty of Cy-Fair Elementary Math Dept. (2nd Grade) 2014-2015 77

67 68 ? ? 71

Increments of One ~ Number Lines for Partner Work

24 34 44 6454 84 94

24 34 44 6454 84 94

1. Display 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? 8Since 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 groups of ten away, how many groups 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


112 122 142 162152 172 182

1,1302 1,140 1,160 1,1801,170 1,19021,150

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. 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 numbers? 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 increasing

If 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 group 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.

4. Now display 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.


760 770 780 790 ?

131 141 151 ? ?

309 319 329 ? ?

214 224 ? 244 ?


Increments of Ten ~ Number Lines for Partner Work

500 600 800 1,200900 1,100700

Number Line in Increments of Hundreds

1. Display the following number line.

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

What place value is the digit that is changing in? 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 numbers? 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? noWhat 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 Work

Working with partners the students will find the missing numbers on various number lines, “Increments of Ten or Hundred ~ Number Lines for Partner Work” (pages 86).

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_IMN NUMBER LINE QUESTION 2_RES-2014)

(MATH_2_A_IMN NUMBER LINE QUESTION 3_RES-2014)


Students will do “Number Line -Practice 2” (MATH_2_A_NUMBER LINE PRACTICE 2_RES-2014)


67 77 87 ? 107

360 370 380 390 ?

263 363 663563?

176146 156 166?

167 267 367 567?


Increments of Tens or Hundreds~ Number Lines for Partner Practice

20 30 40

Part 14 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 with the numbers 20, 30 and 40 like the one below:

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 the 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.

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)


3520 30 40

80 100

80 100

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 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 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 so 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

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

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


90

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

Partner Practice

Cut up the number cards on page 86 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 (page 87). They continue picking a card until all cards are picked.


Partner Practice 1A


71 72 7374 75 7677 78 7981 82 8384 85 8687 88 89

70 90

70 90

70 90

70 90

70 90

70 90

Partner Practice 1B

Name____________________________


400 500

400 500450

850 950


1. Display 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 decided/justify where they place 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 the following number line and ask students to label or draw a line to show where each number should go on the number line.

859 905 895

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


850 950900

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, 950What 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

Partner Practice 2, page 90: 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 compare and share their strategies. Remember the focus is on number sense rather than precision.


400 600

13513 17575

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.

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

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


1,1000 1,200

1,1000 1,2001,150

1,13100 1,141


1. Display 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 2 Look 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. 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. Partner Practice

Students practice identifying numbers that go on number lines using Partner Practice 3. Encourage students to share with their partner how they figured out an answer.

4. IMN: MATH_2_A_IMN NUMBER LINES_RES-2014

5. Independent Practice: MATH_2_A_NUMBEER LINE IP PRACTICE_RES-2014

6. Mixed Practice: MATH_2_A_MIXED PRACTICE_RES-2014


Documents

SECOND GRADE - Pearson Schoolstorage.schoolnet.com/cfisd/MATH_2_A_P… · Web view · 2015-07-31... word, and expanded form to represent numbers up to 1,200. Vocabulary: standard