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Second GradePlace Value
20151124
www.njctl.org
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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
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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.
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Digits and Units
Click to return to Table of Contents
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The Digits of Our Number System
Think of a number, any number!
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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.
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Digits
Circle the digits in each number separately.
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128
2982
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.
9
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.
10
one
What is a Unit?
Base ten blocks are useful to understand units.
This one cube is worth 1.
Teacher N
otes
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.
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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.
12
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?
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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?
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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.
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1 Of the choices below, what is the largest unit?
Answ
er
A hundredsB tensC thousandsD ones
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2 Which shows the order of the units from the greatest to the smallest?
Answ
er
A tens, ones, hundred's
B hundreds, tens, ones
C hundreds, ones, tens
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3 How many digits does the number 8 have?
Answ
er
A 1 digit
B 2 digits
C 3 digits
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4 The value of the 5 digit in 56 is worth
Answ
er
A 500
B 50
C 5000
D 5
19
5 In the number 138, which digit shows the units of tens?
Answ
er
20
6 The value of the 2 in 237 is how much?
Answ
er
A 2B 20C 200D 2000
21
7 How many digits does the number 54 have?
Answ
er
22
Lab: Let's Count!
Teacher N
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Teacher N
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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/
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Making Models of Two Digit Numbers
Click to return to Table of Contents
26
Tens Ones
1
Hundreds
One cube equals one unit of ones.
Tens Ones
10
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?
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otes
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.
27
Tens Ones
1 0
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
28
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
29
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.
Practice Making and Writing Numbers
______ tens + _______ ones = 34This shows
30
Tens OnesHundreds
______ tens + _______ ones = 67This shows
Make the number 67. Write the digits in the correct place on your place value chart.
Practice Making and Writing Numbers
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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.
Practice Making and Writing Numbers
Math Practice
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8 Which shows the number?
A 52
B 22
C 25
D 28
Answer
33
9 Which number is shown?
A 83B 43
C 38
D 82
Answer
34
10 Which shows this number?
A 90B 9C 19
D 91
Answer
35
11 Which shows this number?
A 4B 44C 40D 14
Answer
Quiz
36
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
Click to return to Table of Contents
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Writing Numbers in Expanded Form
Click to return to Table of Contents
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How would you show 36 with base 10 blocks?
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Expanded Form
43
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.
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Tens OnesWhich number does
this show?
Expanded Form
45
50 + 2 = 52 5 tens and 2 ones = 52
Expanded Form
Tens Ones
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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
47
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
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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
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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
work.
*Base Ten Blocks are infinitely cloned.
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12 What would this number be in expanded form?
Answ
er
A 24
B 20 + 4 = 24
C 2 + 4 = 24
50
13 This number in expand form is:
Answ
er
A 80 + 1 = 81
B 80 + 10 = 81C 8 + 1 = 81
51
14 The number 39 in expanded form would look like:
Answ
er
A 30 + 10 = 39
B 30 + 90 = 39
C 30 + 9 = 39
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15 What number is missing in the expanded form for the number 58?
50 + ____ = 58
Answ
er
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16 What is the number missing from the expanded form of 93?
____ + 3 = 93
Answ
er
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55
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Making Three Digit Numbers and
Using Expanded Form
Click to return to Table of Contents
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What number do the blocks show?
99clickclick
Tens Ones
Base Ten Blocks
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Tens Ones
What happens if we add one more cube?
Base Ten Blocks
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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
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You can now trade 10 tens for a hundred.
=
10 tens = 100
Trading
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Tens OnesHundreds
Place Value Chart
1 Hundred 0 Tens 0 Ones
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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
1 8
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
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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.
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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
too?
Reveal the answer below.
Expanded Form
Tens OnesHundreds
______ + ______ + ______ = 465
65
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
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Tens OnesHundreds
5
3 units of hundreds + 5 units of tens + 7 units of ones = 357
7
What would this number be?
How many hundreds? How many tens? How many ones?
3
Expanded form is: 300 + 50 + 7 = 357
Hint
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
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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.
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17 These blocks show 6 tens and 4 ones
Yes
No
Answ
er
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18 These blocks show 1 hundred, 9 tens, and 2 ones.
Yes
No
Answ
er
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19 Which shows this number?
Answ
er
A 390B 309C 319
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20 Which shows this number?
Answ
er
A 24
B 204
C 240
D 6
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21 Which shows this number?
Answ
er
A 483B 384C 834D 843
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22 What is the number for this expanded form?
100 + 40 + 9
Answ
er
A 14
B 941
C 149
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23 Fill in the blank.
800 + 20 + 1 = _____
Answ
er
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24 Which answer shows the correct expanded form for 85?
Answ
er
A 8 + 5 = 85
B 80 + 5 = 85
C 8 + 50 = 85
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25 Which number is missing?
300 + ____ + 2 = 362
Answ
er
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26 Fill in the blank.
800 + 20 + 1 = _____
Answ
er
Quiz
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79
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Reading and Writing Numbers in Different Forms
Click to return to Table of Contents
81
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
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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
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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
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23
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
85
Each number can be written as a word.
onetwothreefour fivesixseveneightnine ten
12345678910
eleventwelvethirteenfourteenfifteensixteenseventeeneighteennineteen
111213141516171819
Word Form
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twentythirtyfortyfiftysixtyseventyeightyninety
2030405060708090
Use number words as you count up from the tens, placing a hyphen in between the words.
sixtyonesixtytwosixtythreesixtyfoursixtyfive
sixtysixsixtysevensixtyeightsixtynine
6162636465
66676869
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88
27 Which shows the number seventy?
A 7B 17C 70D 30
Answer
89
28 Which shows the number fifteen?
A 15
B 50
C 14
D 5
Answer
90
29 Which shows the number twelve?
A 20
B 12
C 2
D 18
Answer
91
30 Show the number eight.
Answer
92
31 Show the number sixtysix.
Answer
93
32 Show the number twentynine.
Answer
94
33 Which is another way to write 83?
A 80 + 3
B fiftythree
C 30 + 8
D eight tens and 8 ones
Answer
95
34 Which is another way to write 27?
A 72B 2 tens and 7 onesC 70 + 2D seven
Answer
96
35 Which is another way to write 11?
A 11 + 11
B 1 one
C 12
D eleven
Answer
97
98
99
Drawing Models of Numbers
Click to return to Table of Contents
100
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
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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.
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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?"
102
More Practice Drawing Models
Draw and label seven units of one.Click shape to reveal answer.
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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.
103
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.
104
36 What number is this a model for?
Answ
er
105
37 What is the number this is modeling?
Answ
er
106
38 A student drew the model below but forgot to label it. What number do you think it shows?
Answ
er
A 260B 261C 214D 216
107
39 Another student forgot to label this drawing. What number does it show?
Answ
er
A 502
B 52
C 520
D 250
108
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?
Answ
er
A 234B 432C 324D 423
Quiz
109
110
111
Counting within 1000
Click to return to Table of Contents
112
Counting up to 100
This time we will use a different tool for counting. We will use straws or sticks and rubber bands.
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113
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?
114
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!
115
What can we do with these 10 sticks?
We can make a unit of 10.
Regrouping
116
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.
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117
Yes, we can bundle them into a unit of 100!
Expanded Form
118
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
119
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?
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120
Practice Counting Up and Down
count up
count down
starting at _____
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121
41 When we count, what number comes after 100?
Answ
er
A 99
B 110
C 101
D 111
122
42 If we are counting by 10s, what number comes after 130?
Answ
er
A 140
B 200
C 131
D 120
123
43 Counting by 100s what would come next?
100, 200, 300, 400, 500, ____
Answ
er
124
44 We need 9 units of tens to make 100.
True
False
Answ
er
125
45 Counting by ones, what number comes after 125?
Answ
er
126
46 Counting by ones, what number comes after 109?
Answ
er
127
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
unit.
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
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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.
128
129
130
131
132
Skip Counting
Click to return to Table of Contents
Counting by 10s
Counting by 100s
Counting by 5s
Advanced Skip Counting by 10s
Practice Counting Within 1000
133
Skip Counting by Fives
click to return to Skip Counting
134
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
20...
10 20 30 40.
..
100 200 300 400...
Skip Counting
135
+5 +5 +5 +5
Skip Counting by 5s
136
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
soon.
Skip Counting by 5s
137
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.
20
1 2 3 4 5
What do the numbers we land on end in?
0 and 5click to reveal answer
Skip Counting
138
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
139
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?
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140
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
141
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
142
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?
143
What number would come after 255?
260Move boxfor answer
What number would come before 420?
If we count by 5s:
415
Count by 5s
Move boxfor answer
144
What number would come after 385?
390
What number would come after 595?
If we count by 5s:
600Move boxfor answer
Move boxfor answer
Count by 5s
145
Practice Counting by 5s
count up by 5s
count down by 5s
starting at _____
Teacher N
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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.
146
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
otes
147
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.
148
47 Is this number pattern counting by 5s?30, 35, 45, 50, 55
Yes
No Answ
er
149
48 Is this number pattern counting by 5s?185, 190, 195, 200, 205
Yes
No
Answ
er
150
49 What is the next number in the pattern?
65, 70, 75, 80, ?
Answ
er
151
50 What is the next number in the pattern?
310, 315, 320, 325, ?
Answ
er
152
51 What is the next number in the pattern?
580, 585, 590, 595, ?
Answ
er
153
52 What is the next number in the pattern?
630, 635, 640, 645, ?
Answ
er
154
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?
Answ
er
155
156
157
Skip Counting by Tens
click to return to Skip Counting
158
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
otes
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
1000.
159
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
20
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
otes
We can use a number line to practice.
160
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
otes
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.
161
We can use meter strips to practice.
Use a Meter Strip to Count by Tens
Teacher N
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162
10, 20, 30, 40, 50, 60, 70, 80, 90
Practice Counting by 10s
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!
click
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.
163
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
164
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
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165
Practice Counting by 10s
count up by 10s
count down by 10s
starting at _____
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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.
166
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.
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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.
167
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
168
54 Which number comes next?
30, 40, 50, ____
Answ
er
A 51
B 70
C 60
D 55
169
55 What number comes next?
140, 150, 160, ____
Answ
er
A 171
B 175
C 170
D 180
170
56 Count by tens. What number comes after 340?
Answ
er
A 350
B 341
C 345
D 400
171
57 Count by 5s. What number comes next?
210, 215, 220, ____
Answ
er
A 230
B 221
C 300
D 225
172
58 Count by 10s. What number comes after 630?
Answer
173
59 Count by tens. What is the next number?
36, 46, 56, 66, ?
Answ
er
174
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?
Answ
er
175
176
177
Advanced Skip Counting by 10s
click to return to Skip Counting
178
32, 42, 52, 62, 72, 82, ? ?
Advanced Skip Counting by 10s
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.
179
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!
click
Advanced Skip Counting by 10s
180
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
Advanced Skip Counting by 10s
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181
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
Advanced Skip Counting by 10s
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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.
182
849, 859, 8_9, 8__, 8__, ___, ___
Count by 10s
267, 277, 2_7, 2__, ___, ___, ___
183
10 less 10 more
435425 445971 981961
807523
797513
274
??
??
184
61 Is this number pattern counting by 10s?
142, 152, 162, 172
Yes
No *Hint: Look at the ones place. Then, look at the tens and 100s place.
Answ
er
Hint
185
62 Is this number pattern counting by 10s?
564, 575, 586, 597
Yes
No
Answ
er
186
63 What number comes next in this pattern?
348, 358, 368, ?
Answ
er
187
64 What comes next in the number pattern?
677, 687, 697, ?
Answ
er
188
65 Which number is 10 more than 71?
Answ
er
A 61
B 81
C 72
189
66 Which number is 10 less than 46?
Answ
er
A 36
B 56
C 45
190
67 Which number is 10 more than 92?
Answ
er
A 12
B 82
C 102
191
68 Which number is 10 less than 308?
Answ
er
A 298
B 307
C 318
192
193
194
Skip Counting by Hundreds
click to return to Skip Counting
195
Skip Counting by Hundreds
Earlier we skip counted by 100s. Let's review and practice again.
196
Take ten longs, or ten "tens"...
Put them together and you get ...
a flat or 100!
Skip Counting by Hundreds
197
When we count by hundreds we always go 100, 200, 300, 400, 500, 600, 700, 800, 900 and then, we go to a new
unit.
Ten units of 100 make one unit of one thousand
Skip Counting by Hundreds
198
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.
Skip Counting by Hundreds
199
100 200 300 400?What number would come next?
500click for answer
Skip Counting by Hundreds
200
When we count by hundreds we always go 100, 200, 300, 400, 500, 600, 700, 800, 900 and then, we go to a new
unit.
Ten units of 100 make one unit of one thousand
What comes after 900?
1,000
201
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
202
You try!
148, 24_, 3__, ___, ___, ___,___, ___,
948, 1,048
Remember, when we have ten units of 100, we can make one unit of 1000!
Advanced Skip Counting by 100s
203
69 What number would come after?
300, 400, 500, 600, ____
Answ
er
204
70 What is the next number in this pattern?
800, 700, 600, 500, ?
Answ
er
205
71 Skip count by 100s. What would come next?
123, 223, 323, ____
Answ
er
A 433B 324C 423D 400
206
72 Skip count by 100s. What would come next?
342, 442, 542, ____
Answ
er
207
73 What number comes after 999?
Answ
er
208
209
210
Practice Counting within 1000
click to return to Skip Counting
211
Practice Counting within 1000
We can use what we learned with skip counting to help us count within 1000.
212
Counting Up Using Different Units
Suppose we wanted to count from 358 to 500?
How many flats, longs, and cubes would we start with?
213
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.
358
214
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.
215
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
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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
216
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.
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Have students share how they counted. Not all
students may have counted in the same way. Seeing differences will enhance their understanding of
counting.
217
Modeling with pictures and Numbers
We can model counting from 98 to 140 with numbers as well.
98, 99, 100, 110, 120, 130, 140
218
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.
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219
Practice Counting within 1000 and Skip Counting
Can you count up and down?
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Each of the next slides will reinforce previous lessons. The ability to count up and
down supports the understanding of number
sense.
220
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!
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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.
221
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!
222
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.
223
224
225
Modeling Word Problems
Click to return to Table of Contents
226
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?
Modeling Word Problems
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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.
227
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?
Modeling Word Problems
Quiz
228
229
230
Comparing Numbers
Click to return to Table of Contents
231
Marisa has 34 cards. Robert has 43 cards. Who has more cards?
Use base 10 blocks to show each number.34 43
_____ tens _____ ones
_____ tens _____ ones
_________ has more cards.
Compare Numbers
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otes Base 10 blocks are infinitely
cloned.Have students make each number using the
base 10 blocks.
232
34
_____ tens _____ ones3 4
43
_____ tens _____ ones
34
How do we know that Robert has more cards?
Compare Numbers
233
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:
and
Compare Numbers
234
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
235
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
236
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
237
18 14< <
Which symbol should we use?
18 is greater than 14move box fornumber sentence
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Compare Numbers
238
32 48
< <Which symbol should we use?
32 is less than 48move box fornumber sentence
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Compare Numbers
239
If the numbers are exactly the same, we say they are equal.
45 45=45 is equal to 45
Equal
240
Comparing Tens
< < =
Tens Ones Tens Ones
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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.
241
Comparing Three Digit Numbers
Amy has 127 buttons. Jimmy has 113 buttons.
Who has more buttons?
242
Amy Jimmy
We can use base 10 blocks to help us see which number is bigger.
127 113
Comparing Three Digit Numbers
243
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
Comparing Three Digit Numbers
244
149 163
< <Which symbol should we use?
149 is less than 163move box fornumber sentence
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Comparing Three Digit Numbers
245
136 118
< <Which symbol should we use?
136 is greater than 118move box fornumber sentence
Comparing Three Digit Numbers
Math Practice
MP 8 Look for express regularity in repeated
reasoning
What tricks do you know to help remember which sign to
use?
246
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.
Comparing Three Digit Numbers
247
356 324
< <Which symbol should we use?
356 is greater than 324move box fornumber sentence
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Comparing Three Digit Numbers
248
< <Which symbol should we use?
244 is less than 247move box for
number sentence
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Comparing Three Digit Numbers
249
Which symbol should we use?
431 is equal to 431
=move box for
number sentence
Comparing Three Digit Numbers
250
Comparing Hundreds
< < =
H T O H T O
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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.
251
74 Is this number sentence correct?85 < 58
Yes
No
Answer
252
75 Is this number sentence correct?
67 > 62
Yes
No Answer
253
76 345 is greater than 354
True
False
Answer
254
77 440 is less than 441
Yes
No
Answer
255
78 Which makes this statement correct? 678 is __________ 578
A greater than
B less than
C equal to
Answer
256
79 Which makes this statement correct?
234 is __________ 257
A greater than
B less than
C equal to
Answer
257
80 Which makes this statement correct?
418 is ___________ 415
A greater than
B less than
C equal to
Answer
258
81 Which symbol is correct?
_____
A <B >C =
Answer
259
82 Which symbol is correct?
_____
A <
B >
C =
Answer
260
83 Which symbol is correct?
_____
A <B >C =
Answer
261
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
Click to return to Table of Contents
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