Second Grade - NJCTLcontent.njctl.org/courses/math/2nd-grade/place-value/place-value... · Second...

Second GradePlace Value

20151124

www.njctl.org

Table of Contents

Digits and Units

Comparing Numbers

Skip Counting

Click on the topic to go to that section.

Making Models of Two Digit Numbers

Drawing Models of NumbersCounting within 1000

Reading & Writing Numbers in Different Forms

Writing Numbers in Expanded Form

Let's Count

Abacus Primer

Give and Take

Modeling Word Problems

Making 3 Digit Numbers and Using Expanded Form

Standards for Mathematical Practices

MP8 Look for and express regularity in repeated reasoning.

MP1 Make sense of problems and persevere in solving them.

MP2 Reason abstractly and quantitatively.

MP3 Construct viable arguments and critique the reasoning of others.

MP4 Model with mathematics.

MP5 Use appropriate tools strategically.

MP6 Attend to precision.

MP7 Look for and make use of structure.

Click on each standard to bring you to an example of how to meet this standard within the unit.

Digits and Units

Click to return to Table of Contents

The Digits of Our Number System

Think of a number, any number!

Teacher N

The Digits of Our Number System

0 1 2 3 4 5 6 7 8 9

Any number that we can think of is based on ten symbols. These ten symbols are called digits.

You already know them.

We can make any number at all by using these 10 digits. Each digit in a number will represent a

certain number of units.

Digits

Circle the digits in each number separately.

1048 1

Math Practice

MP 6 Attend to precision

Ask students to explain the difference between a digit and a number. After they circle the digits in each number, ask them how many digits are in

each number.

Count the balloon. How do we write that number?

Count these balloons. How do we write that number?

The digit one is the same but it is in a different place so it represents a different unit.

What is a Unit?

Base ten blocks are useful to understand units.

This one cube is worth 1.

Teacher N

To help the students understand this concretely, have the students use base ten blocks or cubes which snap together to make a

unit of ten out of ten units of one. Note: You may

substitute popsicle sticks and rubber bands to group

them for this activity.

Ten ones make one unit of ten.

What is a Unit?

If we put 10 cubes together, we have ten units of one and, it can make one unit of ten.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Ten units of ten make one unit of one hundred

If we put ten units of ten together we make... 100!

What is a Unit?

Teacher N

So, a unit is a single thing.

Small units can be put together to make bigger units.

Bigger units can be broken apart to make smaller units.

The digits in a number tell us how many different units we have in the number.

What is a Unit?

These cubes represent the ones unit.

These longs represent the tens unit because they are a group of ten stuck together.

This flat represents the hundreds unit because it is a group of 100 stuck together.

1 Of the choices below, what is the largest unit?

A hundredsB tensC thousandsD ones

2 Which shows the order of the units from the greatest to the smallest?

A tens, ones, hundred's

B hundreds, tens, ones

C hundreds, ones, tens

3 How many digits does the number 8 have?

A 1 digit

B 2 digits

C 3 digits

4 The value of the 5 digit in 56 is worth

C 5000

5 In the number 138, which digit shows the units of tens?

6 The value of the 2 in 237 is how much?

A 2B 20C 200D 2000

7 How many digits does the number 54 have?

Lab: Let's Count!

Teacher N

Students will sit in a large circle or U shape for this activity. Students will bundle units of one, tens, hundreds to 1,000.

See directions posted under the labs section of the website:

https://njctl.org/courses/math/2ndgrade/placevalue/

Making Models of Two Digit Numbers

Tens Ones

Hundreds

One cube equals one unit of ones.

Tens Ones

Hundreds

Ten cubes equals 10 units of ones.

Making Models We can make models of numbers by using cubes, longs, and flats. Models help us understand the digits in a number.

What can we do when we get ten units of ones?

Teacher N

Use a place value chart (see teacher resources section of web site) with base ten blocks to practice making numbers. It

is helpful if the chart is laminated and students use

dryerase markers for continual use.

Tens Ones

Hundreds We use the 0 in the ones place to show that there are no units of ones.

We can put them together to make one unit of ten!

Making Models

Tens Ones

1 3Hundreds

1 ten + 3 ones = 13

Make the number 13 using only cubes. When you can, trade 10 ones for one unit of ten.

Write the number you made by placing the digits in the correct place on your chart.

Practice Making and Writing Numbers

This shows

Tens OnesHundreds

Make the number 34. Use cubes (units of one) and longs (units of ten) for this number. Write the digits in the correct

place on your place value chart.

______ tens + _______ ones = 34This shows

Tens OnesHundreds

______ tens + _______ ones = 67This shows

Make the number 67. Write the digits in the correct place on your place value chart.

Tens OnesHundreds

___ tens + ___ ones = ___This shows

Pick your own number. Pull the baseten blocks onto the chart to show the number. Then write the digits in the

correct place under the blocks.

Math Practice

8 Which shows the number?

Answer

9 Which number is shown?

A 83B 43

Answer

10 Which shows this number?

A 90B 9C 19

Answer

A 4B 44C 40D 14

Answer

Lab: Abacus Primer

The abacus is an ancient tool for doing calculations. This activity uses a simplified abacus to teach place value. Each bead represents 1 in the given place, and students can use it to get a visual understanding that 10 beads in a given place can be represented by a single bead in the place to

its left.

Click here for complete directions

Writing Numbers in Expanded Form

Teacher N

How would you show 36 with base 10 blocks?

Teacher N

Expanded Form

How many blocks are there in all?

_____________

Math Practice

MP 2 Reason Abstractly and Quantitatively

After students have answered how many blocks there are in all, ask them to identify what the 3 represents and what the

6 represents.

Tens OnesWhich number does

this show?

Expanded Form

50 + 2 = 52 5 tens and 2 ones = 52

Expanded Form

Tens Ones

To expand means to stretch out.

s t r e t c h

Put the palms of your hands together, then pull them apart. This is expanding.

In math, expanding a number means to pull it apart to show the value of each digit.

Writing numbers in expanded form helps us to understand the value of a digit in a number.

Expanded Form

Let's see what expanded form looks like with the number 13.

10 + 3 = 13expanded form

Tens Ones

1 3Hundreds

Where did the 10 come from?

The 1 digit is in the tens place and so it represents or shows one unit of ten. The one digit has a value of 10.Discuss the question, then click here.

Expanded Form

Practice making two digit numbers and writing them in expanded form.

Use these types of base ten blocks and a place value chart.

Tens OnesHundreds

The format for expanded form is this:

_____ + _____ = _____the value

of the tens digit

the value of

the ones digit

the number you made

Teacher N

Use a variety of two digit numbers for this activity. Students enjoy making up number for the class to try. Also, it may help to keep this page visible while the students

*Base Ten Blocks are infinitely cloned.

12 What would this number be in expanded form?

B 20 + 4 = 24

C 2 + 4 = 24

13 This number in expand form is:

A 80 + 1 = 81

B 80 + 10 = 81C 8 + 1 = 81

14 The number 39 in expanded form would look like:

A 30 + 10 = 39

B 30 + 90 = 39

C 30 + 9 = 39

15 What number is missing in the expanded form for the number 58?

50 + ____ = 58

16 What is the number missing from the expanded form of 93?

____ + 3 = 93

Making Three Digit Numbers and

Using Expanded Form

What number do the blocks show?

99clickclick

Tens Ones

Base Ten Blocks

Tens Ones

What happens if we add one more cube?

Base Ten Blocks

Tens Ones

This chart shows: 10 tens and 0 ones

10 tens = 100

Now we have ten longs and instead of saying 10 tens, we are going to use another, higher place value.

Base Ten Blocks

You can now trade 10 tens for a hundred.

10 tens = 100

Trading

Tens OnesHundreds

Place Value Chart

1 Hundred 0 Tens 0 Ones

Let's look at expanded form with numbers in the 100s.

To make the number 128 number we need to use a new block. This block is called a flat. Each flat is worth 100.

Tens Ones

2Hundreds

The expanded form for this number looks like this:

100 + 20 + 8 = 128

What do you think the expanded form will look like? Discuss.

Discuss the question, then click here.

Expanded Form

Tens OnesHundreds

2 hundreds + 4 tens + 7 ones = 247This shows

______ + ______ + ______ = 247

expanded form

Make the number 247. Use cubes (units of one) and longs (units of ten) and flats (units of 100). Write the digits in the correct place on your place value chart. Then, try to show

the expanded form too!

Reveal the answer below.

Expanded Form

Math Practice

MP 1 Make sense of problems and persevere in solving them.

Ask students how they should start to solve this problem. Then have them talk out each step as

they solve it.

4 hundreds + 6 tens + 5 ones = 465 This shows

expanded form

Make the number 465. Write the digits in the correct place on your place value chart. Can you write the expanded form

Reveal the answer below.

Expanded Form

Tens OnesHundreds

______ + ______ + ______ = 465

400 20 7+ +

+ +600 0 9

Drag each digit left to see the expanded form.

500903

800100

Drag the place value digits to the right to make a 3 digit number.Expanded Form

Tens OnesHundreds

3 units of hundreds + 5 units of tens + 7 units of ones = 357

What would this number be?

How many hundreds? How many tens? How many ones?

Expanded form is: 300 + 50 + 7 = 357

Note: It is best to make numbers with the units in order from largest to smallest. However, the units are still the same

even if they are not in the "correct" order.

Expanded Form

Practice Making More Numbers and Using Expanded Form Game

Use your place value charts to make more two and three digit numbers. Also, practice writing them in expanded form.This game is like the other one you played with two digit number but it adds expanded form.

1) Partner A goes first and makes a number with the blocks.

2) Partner B guesses the number and writes it on the place value chart. Then, the expanded form is written.

One point is given for writing the correct number accurately. Another point is given for writing the expanded form correctly.

3) Partner B makes a number while partner A guesses it. Points are scored as above.

Continue this way as time allows.

17 These blocks show 6 tens and 4 ones

18 These blocks show 1 hundred, 9 tens, and 2 ones.

A 390B 309C 319

A 483B 384C 834D 843

22 What is the number for this expanded form?

100 + 40 + 9

23 Fill in the blank.

800 + 20 + 1 = _____

24 Which answer shows the correct expanded form for 85?

A 8 + 5 = 85

B 80 + 5 = 85

C 8 + 50 = 85

25 Which number is missing?

300 + ____ + 2 = 362

26 Fill in the blank.

800 + 20 + 1 = _____

Reading and Writing Numbers in Different Forms

Number Form

There are a few ways that we learn to read and write numbers.

We learn to write them in number form using digits to show different amounts of things.

10 fingers 25 cookies 24 hours

365 days 1,400 people

Expanded Forms

We also learn to write them in expanded form to show the value of each digit.

20 + 5 = 25 300 + 60 + 5 = 365 1,000 + 400 = 1,400

Word Form

Another way to write number is in word form.

six or thirteen or twentyeight or seventy

or even one billion

or a combination of words and numbers like

2 tens + 5 ones

2 tens and 3 ones

20 + 3

These are 3 ways we can write the number 23.

Numbers can also be written as words.

twentythree

Word Form

Each number can be written as a word.

onetwothreefour fivesixseveneightnine ten

12345678910

eleventwelvethirteenfourteenfifteensixteenseventeeneighteennineteen

111213141516171819

Word Form

twentythirtyfortyfiftysixtyseventyeightyninety

2030405060708090

Use number words as you count up from the tens, placing a hyphen in between the words.

sixtyonesixtytwosixtythreesixtyfoursixtyfive

sixtysixsixtysevensixtyeightsixtynine

6162636465

66676869

27 Which shows the number seventy?

A 7B 17C 70D 30

Answer

28 Which shows the number fifteen?

Answer

29 Which shows the number twelve?

Answer

30 Show the number eight.

Answer

31 Show the number sixtysix.

Answer

32 Show the number twentynine.

Answer

33 Which is another way to write 83?

A 80 + 3

B fiftythree

C 30 + 8

D eight tens and 8 ones

Answer

A 72B 2 tens and 7 onesC 70 + 2D seven

Answer

A 11 + 11

B 1 one

D eleven

Answer

Drawing Models of Numbers

Drawing Models We used base ten blocks or sticks to show units of

hundreds, tens, and ones. Now, let's draw models of these units and label them too. Use H for the hundreds unit, T for

the tens unit, O for the ones unit. Underneath put the number of units.

One unit of 100 one unit of 10 one unit of 1

Teacher N

More Practice Drawing Models

Draw and label two units of one hundred.Click shape to reveal answer.

Draw and label four units of ten.Click shape to reveal answer.

Teacher N

Have students practice drawing different numbers of hundreds, tens, and ones. Ask

them to label them too.For example, "Draw 3 units of ten." or "Draw 7 units of one

hundred." Ask also, "How much is it

worth?"

More Practice Drawing Models

Draw and label seven units of one.Click shape to reveal answer.

Teacher N

When we draw cubes, it helps to always draw no more than 5 on the top row and 5 on the bottom row. This helps with

counting and consistency of representation.

By putting our drawing models together and in order from the greatest unit to the smallest, we

can model numbers.

Modeling Numbers

This model shows 2 hundreds, 4 tens, and 7 ones. We write the number 247.

36 What number is this a model for?

37 What is the number this is modeling?

38 A student drew the model below but forgot to label it. What number do you think it shows?

A 260B 261C 214D 216

39 Another student forgot to label this drawing. What number does it show?

40 This student made a model but didn't put the units in order. What number do you think he or she was trying to make?

A 234B 432C 324D 423

Counting within 1000

Counting up to 100

This time we will use a different tool for counting. We will use straws or sticks and rubber bands.

Teacher N

There are many reasons we would need to count numbers of things that are greater than 100.

What are some reasons you can think of?

Click on the objects to reveal some ideas.

Counting Beyond 100

Number of days before a special event.

How much money it might cost to buy something.

How many cupcakes we would need to make for everyone at school.

What are some other reasons you can think of?

Counting by Ones beyond 100

Here is 100 sticks. when we add one more, what do we have? 101?

Continue adding one more until we get to 110.

102, 103, 104, 105, 106, 107, 108, 109, 110!

What can we do with these 10 sticks?

We can make a unit of 10.

Regrouping

Now we have 110. Count with me as we count up by 10s.

110...

120 130 140 150 160 170 180 190 200What can we do with these 10 units of ten?

Skip Counting by 10s beyond 100.

Teacher N

Yes, we can bundle them into a unit of 100!

Expanded Form

Now we have 200. Let's count by 100s from 200 to 1000.

200 300 400 500

600 700 800 900 1000

Skip Counting by 100s to 1000

Counting to 129 Student Practice

Each pair needs: A place value mat, 129 straws or sticks, rubber bands to bundle.

Practice counting from zero to 129 by ones. Each time you get ten units of one, exchange it for a unit of ten. Take turns bundling the units of ten.

What will happen when you get ten units of ten? What will you do?

Teacher N

Practice Counting Up and Down

count up

count down

starting at _____

Teacher N

41 When we count, what number comes after 100?

42 If we are counting by 10s, what number comes after 130?

43 Counting by 100s what would come next?

100, 200, 300, 400, 500, ____

44 We need 9 units of tens to make 100.

45 Counting by ones, what number comes after 125?

46 Counting by ones, what number comes after 109?

Counting to 50 Game Each partner needs:

12 ones

5 tens

1 hundred

one die

Each pair need:

The goal of the game is to make 50.

Partner A rolls the die. Take that number of ones and line

them up in a row on your hundred flat on the first row. Say your total the unit form way. For example, "I have 5 units of one."

Partner B takes a turn.

Partner A's turn again. Roll the die. Add that many one

units. Start a new row if you need to.

If you have completed a row of 10, exchange it with a ten

Now it is partner B's turn again.

Remember each time to say your total the unit form way.

For example, "I have 1 unit of ten and 3 units of one."

Continue until one person reaches 50.

Teacher N

This game will reinforce the idea of changing units after reaching 9.

A more challenging game to 150 can be

played with two flats and two dice.

Skip Counting

Counting by 10s

Counting by 100s

Counting by 5s

Advanced Skip Counting by 10s

Practice Counting Within 1000

Skip Counting by Fives

click to return to Skip Counting

How long do you think it would take to count by ones to 1000? Learning how to skip count by 5s, 10s, and 100s will help us count within 1000 much faster.

You already know some about skip counting but let's learn some more!

5 10 15

10 20 30 40.

100 200 300 400...

Skip Counting

+5 +5 +5 +5

Skip Counting by 5s

How can skip counting by 5s help us?

Well, suppose we wanted to know how many fingers we had in this class. Everyone could hold up their

hands. Each hand would be one group of five fingers and we could count by fives. This would be much quicker than counting every finger! We will try this

Skip Counting by 5s

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

When you count by 5s you make FIVE jumps at once.

1 2 3 4 5

What do the numbers we land on end in?

0 and 5click to reveal answer

Skip Counting

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99100

Let's continue counting by 5s.Skip Counting

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 65, 70, 75, 80, 85, 90, 95, 100

Count by 5s

What number do you think comes next?

105Move boxfor answer

What patterns do you notice about

the blue numbers?the green numbers?

Teacher N

105, 110, 115, 120, 125, 130, 135, 140, 145, 150,

155, 160, 165, 170, 175, 180, 185, 190, 195, 200

As you keep counting by 5s, the pattern continues.

What patterns do you notice about

the red numbers?

Count by 5s

Okay, are you ready to count how many fingers we have in our class? Everybody raise both of your hands!

How many fingers are in our class?

5 1510 20 30 40 5025 35 45

Practice Counting by 5s from Any Number You can count by fives from any number simply by using your fingers. You can find 5 more than and 5

less than a number in this way. Let's try it!

If you are counting by 5s...

What number would come after 265?

What number would come before 265?

What number would come before 420?

If we count by 5s:

Count by 5s

Move boxfor answer

If we count by 5s:

Move boxfor answer

Count by 5s

Practice Counting by 5s

count up by 5s

count down by 5s

starting at _____

Teacher N

This is a great and short activity that can be done at any time. 1) Tell the students the number

to start at.2) Hold your thumb up to signal

they need to count up.3) Hold your thumb down to

signal they need to count down.4) You may also choose to use

a stop signal.

Try this problem!

Diego wanted to know how many fingers were in his class. He asked everyone to raise their hands. He counted 16 hands. How many fingers were there?

Teacher N

Try another!

Ana bought many packs of gum. Each pack had 5 pieces of gum in it. If she bought 12 packs of gum,

how many pieces did she have altogether?

Math Practice

MP 3 Construct viable arguments and critique the reasoning of others.

Allow students time to work through the answer on their own. Then have students discuss their answer with a partner and then ask a few students to defend their thoughts with the entire class before explaining the

correct answer.

47 Is this number pattern counting by 5s?30, 35, 45, 50, 55

No Answ

48 Is this number pattern counting by 5s?185, 190, 195, 200, 205

49 What is the next number in the pattern?

65, 70, 75, 80, ?

310, 315, 320, 325, ?

580, 585, 590, 595, ?

630, 635, 640, 645, ?

53 Omar put his marbles into groups of 5. Then he counted the number of groups he had. He had 8 groups. How many marbles did he have in total?

Skip Counting by Tens

How can knowing how to skip count help us?

After discussing, click below.

Many times we may skip count when numbers we are counting are really large. Skip counting can be much faster and we can keep track of our counting easier!

Teacher N

Ask the class to count by tens. Observe students to gain insight as to who is comfortable with this. How high can they count up? Up to 120 for now is fine, later they will learn to count to

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

1 2 3 4 5 6 7 8 109

When you count by 10s you make TEN jumps at once.

Look at the yellow boxes. What digit is in the ones place?

Use a Number Line Skip Count by Tens

Teacher N

We can use a number line to practice.

We can also use 100s charts to practice. We can start at zero as we have done before.

Use a 100s Chart to Skip Count by Tens

Teacher N

Explain that when counting by tens on a 100s chart, we can start at zero (not on the chart) and count up ten. Doing this one more time will get the students to 20.

However, one can count by tens starting at any number. Try starting at 32 and counting up ten more. Students should land on the square directly under 32. They may notice that on a chart like this, any time ten more is added, the square directly below is reached. This also shows that the tens

place is what changes when ten is added. You are adding one more unit of ten.

We can use meter strips to practice.

Use a Meter Strip to Count by Tens

Teacher N

10, 20, 30, 40, 50, 60, 70, 80, 90

What place in the number (the tens place or ones place) is changing as you count?

To find what comes after 90, think...what is ten more than 90?

100click

The tens place is changing because we are adding one unit of tens each time!

Math Practice

MP 7 Look for and make use of structure

Ask students what pattern they see in the tens place. Allow them time to explain their answer to a partner before discussing it as a class.

Ten units of ten make one unit of one hundred

When we count by tens, we always write or say 10, 20, 30, 40, 50, 60, 70, 80, 90 and then, we go to a

new unit.

Counting by 10s

320, 330, 340, 350, 360

760, 7_0, 7_0, ___, ___, ___

Just as we saw patterns when we counted by 5s, there are patterns when we count by tens. What pattern do you notice about the digits in the ones

place Tens place? Hundreds place?

Let's try these.

When does the digit in the hundreds place change?

Counting by 10s

Teacher N

count up by 10s

count down by 10s

starting at _____

Teacher N

This is similar to the counting by 5s activity and can be done

at any time. 1) Tell the students the number

to start at.2) Hold your thumb up to signal

they need to count up.3) Hold your thumb down to

signal they need to count down.4) You may also choose to use

a stop signal.

Try this problem!

Karla has 100 stickers. Jeremy has 60 stickers. He wants the same amount of stickers as Karla.

How many more does he need?

Hint: Use a number line, meter strip, or other tool to help.

Teacher N

You may wish to ask the students to solve this using

pictures and numbers. Ask for students to show and explain their answers. Later they will need to write their answers in

words.

He needs 40 more stickers.

Try another!

Tyler read 20 pages in his book. He has 30 more pages to read before he finishes it. How many pages will he have

read in this book?

Math Practice

54 Which number comes next?

30, 40, 50, ____

55 What number comes next?

140, 150, 160, ____

56 Count by tens. What number comes after 340?

57 Count by 5s. What number comes next?

210, 215, 220, ____

58 Count by 10s. What number comes after 630?

Answer

59 Count by tens. What is the next number?

36, 46, 56, 66, ?

60 Tam was counting the number of kids at his school. There were 140 of them. His teacher said that 10 students were moving away. How many students would there be after the 10 moved?

32, 42, 52, 62, 72, 82, ? ?

We can also start at a number not ending in zero like 32. Notice that when we count up ten more, the number is

directly underneath the one you started at.

32, 42, 52, 62, 72, 82, ? ?

What place value or digit is NOT changing as you count?

The ones place is not changing because we are adding one unit of ten each time!

Even if the ones place is not a zero, you can still skip count by tens. Noticing some patterns will help you see

how it works.

Look carefully at these numbers that are skip counting by ten.

What do you notice about the digit in the ones place?What do you notice about the digit in the tens place?

What do you notice about the digit in the hundreds place?

528, 538, 548, 558, 568, 578

Teacher N

673, 683, 693, 703, 713, 723

In this group you will see some of the same patterns with the digits in the ones place.

Wait! What is happening with the digits in the tens place? Why is it doing that?

What happens with the digit in the 100s place?

Remember when we got 10 units of ten, we bundled them into one unit of 100. Those tens are now in the 100s place so there are no tens until we count more.

click for the answer

Teacher N

The digits in the ones place still stays the same. In this group the digit in the tens place goes up one until it gets to 9, then it starts at zero again. The digit in the 100s place

stays the same until it gets into the 100s.

849, 859, 8_9, 8__, 8__, ___, ___

Count by 10s

267, 277, 2_7, 2__, ___, ___, ___

10 less 10 more

435425 445971 981961

807523

797513

61 Is this number pattern counting by 10s?

142, 152, 162, 172

No *Hint: Look at the ones place. Then, look at the tens and 100s place.

62 Is this number pattern counting by 10s?

564, 575, 586, 597

63 What number comes next in this pattern?

348, 358, 368, ?

64 What comes next in the number pattern?

677, 687, 697, ?

65 Which number is 10 more than 71?

66 Which number is 10 less than 46?

67 Which number is 10 more than 92?

68 Which number is 10 less than 308?

Skip Counting by Hundreds

Earlier we skip counted by 100s. Let's review and practice again.

Take ten longs, or ten "tens"...

Put them together and you get ...

a flat or 100!

When we count by hundreds we always go 100, 200, 300, 400, 500, 600, 700, 800, 900 and then, we go to a new

Ten units of 100 make one unit of one thousand

A bundle of ten longs is the same as a flat, it shows 100. Use bundles to help you count by 100s.

100 200 300 400

Notice how ONLY the hundreds place changes as you count by 100s.

100 200 300 400?What number would come next?

500click for answer

When we count by hundreds we always go 100, 200, 300, 400, 500, 600, 700, 800, 900 and then, we go to a new

Ten units of 100 make one unit of one thousand

What comes after 900?

Advanced Skip Counting by 100sWe can easily skip count by 100s starting at any

number too!Just like we saw patterns skip counting by tens, we see other patterns when we skip count

by 100s.

What patterns do you see? What stays the same? What changes?

Even as the pattern continues....

What stays the same? What changes?

127, 227, 327, 427, 527

627, 727, 827, 927, 1,027

You try!

148, 24_, 3__, ___, ___, ___,___, ___,

948, 1,048

Remember, when we have ten units of 100, we can make one unit of 1000!

69 What number would come after?

300, 400, 500, 600, ____

70 What is the next number in this pattern?

800, 700, 600, 500, ?

71 Skip count by 100s. What would come next?

123, 223, 323, ____

A 433B 324C 423D 400

72 Skip count by 100s. What would come next?

342, 442, 542, ____

73 What number comes after 999?

Practice Counting within 1000

We can use what we learned with skip counting to help us count within 1000.

Counting Up Using Different Units

Suppose we wanted to count from 358 to 500?

How many flats, longs, and cubes would we start with?

We may start like this:

We'll put a box around it to show where we are starting.

Counting 358 to 500

Next, we could add ones 359, 360

370, 380, 390, 400

And, what do we do when we have ten ones?

From 360 we continue counting by tens.

Counting 358 to 500

358 359, 360, 370, 380, 390, 400, 500

This is how we did it. We can underline the places to show

where we changed to larger units.

Try This

Practice counting from 126 to 220 with a partner. Model with your sticks or blocks as you count.

Next, count down. Can you count all the way back to 126?

After using the sticks or blocks, try it without them. Later, you may wish to try it as fast as you can. Te

acher N

This activity will help them practice counting with concrete materials. Supply students with enough materials to practice a variety of counting such as:

207 to 310

375 to 441

Counting within 1000

As we counted with sticks or blocks, we can also show our counting by drawing models.

Try it!

Draw and label the number 98 using pictures. Put a box around it. Show how you would count from 98 to 140.

Teacher N

Have students share how they counted. Not all

students may have counted in the same way. Seeing differences will enhance their understanding of

counting.

Modeling with pictures and Numbers

We can model counting from 98 to 140 with numbers as well.

98, 99, 100, 110, 120, 130, 140

You Try!

Draw and label the number 56 using pictures. Put a box around it. Show how you would count from 56 to

400. Try showing with numbers too.

Teacher N

Practice Counting within 1000 and Skip Counting

Can you count up and down?

Teacher N

Each of the next slides will reinforce previous lessons. The ability to count up and

down supports the understanding of number

sense.

Skip Counting by 10s and 100s

Let play a game to practice skip counting by 10s and 100s!

When I hold up a bundle of ten, I want you to skip count by tens. When I hold up a bundle of 100, I want you to count

by 100s.

Lets go!

Go from 0 to 160 by tens.

Go from 80 to 220 by tens.

Make up some of your own!

Teacher N

You will need a bundle of 10 sticks and a bundle of 100 sticks rubber banded.

Write the numbers on the board while they count.

Skip Counting by 10s and 100sWhen I hold up a bundle of ten, I want you to skip count by tens. When I hold up a bundle of 100, I want you to

count by 100s.

Next, lets count by 100s!

Go from 0 to 700 counting by 100s

Go from 200 to 1000 by 100s.

Try 20 to 820 by 100s.

Make up some of your own!

More PracticeSkip Counting by 1s, 10s and 100s

Now, let's mix it up!

Count from 0 to 140 by tens.

Count from 140 to 640 by hundreds.

Count from 640 to 648 by ones.

If I count up ten from 648, what will the number be?

If I count up 100 from that number, what will it be.

Teacher N

otes You will also need a single

stick as well as the ten and hundred bundle. Add your

own for more practice. Spend only about 5 minutes on this.

We can also use drawings to solve word problems.

Mr. Conrad's class collected 17 cans for the canned food drive at school. They had a goal of collecting 70

cans. How many more cans did they need?

How might you use counting as we have done in the last slides to solve this problem?

Teacher N

Lead them to drawing and putting a box around 17. Count up to 70 drawing ones and tens as before. When they have reached 70, they will need to just count the ones and tens outside the box for their

answer.

Use drawing again to solve this problem.

Mr. Conrad's class collected 86 cans for the canned food drive at school. They had a new goal of

collecting 120 cans. How many more cans did they need?

Comparing Numbers

Marisa has 34 cards. Robert has 43 cards. Who has more cards?

Use base 10 blocks to show each number.34 43

_____ tens _____ ones

_________ has more cards.

Compare Numbers

Teacher N

otes Base 10 blocks are infinitely

cloned.Have students make each number using the

base 10 blocks.

_____ tens _____ ones3 4

_____ tens _____ ones

How do we know that Robert has more cards?

Compare Numbers

When we compare numbers, we are looking at the relationship between the numbers.

We use words:

less thangreater thanequal to

We use symbols:

To compare numbers:

Compare Numbers

To compare 2 digit numbers, look at the tens place. When the 10s are the same, look at the ones place. We can draw pictures or use base 10 blocks to help us.

22 25Which number is greater?

Since the 10s are the same, we have to look at the ones to see which number has more.

Compare Numbers

22 is less than 25

We use our symbols to show less than and greater than.

Read the number sentence from left to right, like you read a word sentence.

< <Compare Numbers

22 < 25

To help remember which symbol to use think of the symbol having dots on each end.

The small, closed end with one dot faces the smaller number.The larger, open end with two dots faces the larger number.

Compare Numbers

18 14< <

Which symbol should we use?

18 is greater than 14move box fornumber sentence

Teacher N

Compare Numbers

< <Which symbol should we use?

32 is less than 48move box fornumber sentence

Teacher N

Compare Numbers

If the numbers are exactly the same, we say they are equal.

45 45=45 is equal to 45

Comparing Tens

Tens Ones Tens Ones

Teacher N

Two students will roll the dice, one at a time. Drag the correct symbol into the box to make the statement true. Have one student read the statement; roll

again and have the other student read the statement.

Comparing Three Digit Numbers

Amy has 127 buttons. Jimmy has 113 buttons.

Who has more buttons?

Amy Jimmy

We can use base 10 blocks to help us see which number is bigger.

127 113

When comparing 3 digit numbers look at the hundreds place first.

127 113<Since both numbers have a 1 in the hundreds place,

look at the tens place to compare the numbers.

2 is larger than 1 so:127 is greater than 113

149 163

149 is less than 163move box fornumber sentence

Teacher N

136 118

Math Practice

MP 8 Look for express regularity in repeated

reasoning

What tricks do you know to help remember which sign to

What happens when the hundreds and tens place have the same number?

174 176

Look at the ones place. 4 is less than 6 so:174 is less than 176

174 < 176

Teacher N

otes Encourage students to come

to the conclusion that you have to look at the

ones place to see which number is greater.

356 324

Teacher N

244 is less than 247move box for

number sentence

Teacher N

Which symbol should we use?

431 is equal to 431

=move box for

number sentence

Comparing Hundreds

H T O H T O

Teacher N

Two students will roll the dice, one at a time. Drag the correct symbol into the box to make the statement true. Have one student read the statement; roll

again and have the other student read the statement.

74 Is this number sentence correct?85 < 58

Answer

75 Is this number sentence correct?

67 > 62

No Answer

76 345 is greater than 354

Answer

77 440 is less than 441

Answer

78 Which makes this statement correct? 678 is __________ 578

A greater than

B less than

C equal to

Answer

79 Which makes this statement correct?

234 is __________ 257

A greater than

B less than

C equal to

Answer

80 Which makes this statement correct?

418 is ___________ 415

A greater than

B less than

C equal to

Answer

81 Which symbol is correct?

A <B >C =

Answer

A <B >C =

Answer

Lab: Give and Take

Children develop understanding and reasoning through exploration, interaction, and feedback. When students are learning about trading tens and ones, math manipulatives help to make the concepts

concrete. This game provides students an excellent opportunity practice addition, subtraction, and

regrouping/trading tens. The students also learn about the ideas behind place value and Base 10.

Click here for complete directions

Second Grade - NJCTLcontent.njctl.org/courses/math/2nd-grade/place-value/place-value... · Second...

Documents

Grade 2: Understand Place Value - School …mdk12.msde.maryland.gov/.../M_2_NBT_A_1_4_U_PlaceValu.docx · Web viewGrade 2: Unit 2.NBT.A.1-4, Understand Place Value DRAFT Maryland

d3jc3ahdjad7x7.cloudfront.net...© Harcourt † Grade 5 UNIT 1: USE WHOLE NUMBERS Chapter 1: Place Value, Addition, and Subtraction 1.1 Place Value Through Millions ............PW1

Grade Level: 6 Course Title: Math Place Value: Addition ...storage.cloversites.com/mercerareaschooldistrict... · Grade Level: 6 Course Title: Math Topic/Concept: Place Value: Addition

Grade 1 Unit 4: Place Value, Comparison, Addition and ... · Grade 1 Unit 4: Place Value, Comparison, Addition and Subtraction of Numbers to 40 (7 Weeks) Stage 1 – Desired Results

GRADE 3 • MODULE 23 GRADE Mathematics Curriculum GRADE 3 • MODULE 2 Module 2: Place Value and Problem Solving with Units of Measure ommon, . Answer Key GRADE 3 • MODULE 2 Place

GRADE 4 MATHS SYLLABUS - FIRST TERM INSTAMATHS … · 4 3. PLACE VALUE AND VALUE PLACE VALUE Place Value Instamaths 11 Total 20 Your mark: Place value is the idea that a figure has

Second Edition€¦ · place value. Indeed, only half of them master it by the end of the fourth grade. On the other hand, Asian children master place value in the first grade. Asian

Grade Five Mathematics Curriculum Map Module 1 - Place ... · Grade 5 Math Modules – Page 1 Module 1 - Place Value/Base Ten (Approximately 3 weeks) Mathematical Practices Florida

Unit 3 Grade 8 From Powers to Circles Grade 8: Unit 3 – From Powers to Circles 3 Unit 3: Day 1: Value of the Place Grade 8 Math Learning Goals • Review value of the place and correct

Learning Place Value in First Grade Through Language and

Mrs. Russell’s Third Grade Place Value Jeopardy

Miss Bowen 4 th Grade Math PLACE VALUE. Write the place value of the underlined number. 4, 685, 712 PLACE VALUE

Grade 5 EnVision Math Lessons Aligned to IXL€¦ · Grade 5 EnVision Math Lessons Aligned to IXL Topic 1: Place Value Topic - Lesson IXL Skill 4A.1 1-1 Place Value IXL Skill: Place

3 rd – 5 th grade Subtraction Place Value and Negative Numbers

Place Value - Center For Teaching & Learningcontent.njctl.org/courses/math/3rd-grade-math/place-value/unit-1... · Slide 3 / 268 - Place Value ... It tells you that there are 7 ones

· Web viewiPad Apps for 2nd Grade Math Slide (Place Value) + and –

Grade 3, Module 2: Place Value and Problem Solving with

A Place Value Study Guide for Grade 5s

3 rd Grade Math SOL Powerpoint By ____________. Place Value

€¦ · Web viewiPad Apps for 2nd Grade . Math Slide (Place Value) + and –