Lessons
Lesson 1: Count by 2's
Duration:
45 minutes
 
Materials:
Lessons 1 - 4 Hundred Chart, the
number strips used are from Kim Sutton. Use a red crayon or marker. A
variation of this step is to color the even numbers red on a hundreds chart.
Activities
-
At the end of the lesson, ask students to respond to the following statement
in their math journal:
Starting with the
number 46, explain how to count on by twos.
Today, you
will listen to the book, Pie for Piglets; Counting by Two's by
Michael Dahl. As you are listening, pay close attention to the patterns you
hear in the book.
-
Did you
notice any patterns in the book?
-
What did
these patterns have in common?
-
Is there
another way you could count by 2's?
-
Using a
hundreds chart and chips, count by 2's starting at two.
When finished
placing chips on chart, begin with two and touch each chip while saying the
number underneath.
-
Listen to the
2's song on the Skip Counting, Intellitunes CD, by Ron Brown.
-
On individual
number line strips and a red crayon or marker, begin with the number two and
color a red dot above each number as you count on by 2's up to 100. Follow
teacher instructions to count forward or backward by two when given a
certain number. Ask students if
there are any other ways to count by 2's. (i.e. odd numbers also)
Teacher model this on overhead or hundreds pocket chart.
-
Call out
random numbers on the hundreds chart and have students count forward and
backward by 2's to practice counting by 2's from any number.
-
Play the 2's
song on the Skip Counting, Intellitunes, CD by Ron Brown.
-
Using the hundreds chart
or the number strip, call out a number and ask the students to either count
forward by 2's or backward by 2's from that number. Repeat as needed.
Part A-Explain how to count by 2's.
Part B-Teacher
dictates an even or odd number and asks the students to write the next five
numbers counting by 2's.
Part C-Teacher dictates an even or odd number and asks the
students to write the five previous numbers counting backward by 2's.
Differentiation
Support:
Hundreds
chart, chips, number strips, song, and book are used to support all
kinds of learners.
Small
group instruction lessons could include using flashcards that count by
2's and have missing numbers.
Extension: While
reading the book, point out patterns for 2's.
Remember to point out that counting by 2's isn’t always 0, 2,
4, 6, 8, with even numbers.
Lesson 2:
Count by 2’s Problem Solving
Duration:
45
minutes
Materials:
Lessons 1 - 4 Hundred Chart
Activities
-
Display a word problem.
Read and understand the word problem.
Ask the question: What is the problem asking you to find out?
Underline the question or statement that explains what you are looking
for.
-
Circle key words.
(This will usually tell you what operation to use.)
-
Reread the problem sentence by sentence.
-
Circle names and
information (numbers and words attached to them) that is needed to
solve the problem.
-
Write a number sentence.
Draw a picture to illustrate the number sentence.
Solve the problem.
Explain your thinking in words.
-
One day Alice decided she wanted to count all of her earrings. She
thought it would be quicker to count each pair of earrings rather than
each individual earring. Alice knew she had 13 pairs of earrings.
Counting by 2’s, determine how many earrings Alice had altogether.
-
Michael’s friends invited him to go outside and play catch with a
baseball. However, his mom told him that because it was raining, he
would have to find his old pair of blue tennis shoes. Michael knew he
had 23 shoes. Are there enough shoes to make 12 pairs? Justify your
answer.
-
After playing in the snow all day long, the 18 children had worn out
their gloves. How many gloves needed to be bought for the next day?
-
Maria has a collection of sand dollars. She has eleven stacks of sand
dollars. Each stack has 2 sand dollars in it. How many sand dollars
does she have in all?
Differentiation
Extension:
Strategies for Higher Order Thinking
Support:
SIOP
Strategies: Eight Components of Sheltered Instruction Observation Protocol
Lesson 3:
Count by 10's
Duration:
45 minutes
Activities
-
While reading the book,
point out patterns for 10. Remember to point out that counting by 10s isn’t always 10,
20, 30, 40, and 50.
Ask students if there are any other ways to count by 10's.
(i.e. It can also be 23, 33, 43, 53, etc.
-
Teacher, model
this on overhead or hundreds pocket chart.
Call out random numbers on
the hundreds chart and have students count forward and backward by 10's to
practice counting by 10s from any number.
-
Play the
10's song on the Skip Counting, Intellitunes, CD by Ron Brown.
-
Use a green crayon or a
marker. Using the hundreds
chart or the number strip, call out a number and ask the students to either
count forward by 10's or backward by 10s from that number. Repeat as needed. At the end of the lesson,
ask students to respond to the following question in their math journal:
How does being
able to count by ten help you?
-
Today you will listen to the book,
Bunches of Buttons, by
Michael Dahl. As you are
listening pay close attention to the patterns you hear in the book?
-
Did you
notice any patterns in the book?
-
What did
these patterns have in common?
-
Is there
another way you could count by 10's?
-
Using a
hundreds chart and chips, count by 10's starting at ten.
Listen to the
10's song on the Skip Counting Intellitunes CD, by Ron Brown
-
When finished
placing chips on chart, begin with ten and touch each chip while saying
the
number underneath. Using a
number line strip and a green crayon or marker, begin with the number ten
and
place a green dot above each number as you count on by 10's up to 100.
Part A-Explain how to count by 10's.
Part B-Teacher dictates a
number and asks the students to write the next five numbers counting by 10's.
Part C-Teacher dictates a number and asks the students to
write the five previous numbers counting backward by 10's.
Differentiation
Extension:
Strategies for Higher Order Thinking
Support:
SIOP
Strategies: Eight Components of Sheltered Instruction Observation Protocol
Hundreds
chart, chips, number strips, song, and book are used to meet all kinds of
learners. Small group
instruction lessons could include using flashcards that count by 10s and
have missing numbers.
Lesson 4:
Count by 10's
Problem Solving
Duration:
45 minutes
Materials:
Lessons 1 - 4 Hundred Chart
Activities
-
Display word problem.
Read and
understand word problem. Ask the
question: What is the problem asking you to find out?
Underline the
question or statement that explains what you are looking for. Circle key
words. (This will usually tell you what operation to use.) Reread the
problem sentence by sentence.
Circle names
and information (numbers and words attached to them) that is needed to solve
the problem.
Write a
number sentence. Draw a
picture to illustrate the number sentence. Solve the
problem.
Explain your
thinking in words.
-
Jill wanted to see how
much money she had in her piggy bank. After dumping it out, she grouped
the pennies into piles with ten pennies in each pile. When all the
pennies were sorted, Jill had 13 piles. How many pennies did Jill have
altogether?
-
Challenge-How would
you write this number using the dollar ($) sign and a decimal?
-
After counting all the
pennies, Jill wanted to count all the dimes. If she had 18 dimes, how
much money did she have in all? Joe lives near the
beach and this summer he collected 132 seashells.
-
Joe decided to put
the seashells in baggies to give to his friends. If each baggie holds
10 seashells, how many baggies will Joe need?
-
You have 5 dogs and
they all are 7 and all weigh 10 pounds. How much do they weigh
altogether?
-
On the playground,
Jamie found one black rock every 10 minutes. How many black
rocks did he find in 80 minutes? How many did he
find in 120 minutes?
Differentiation
Extension:
Strategies for Higher Order Thinking
Support:
SIOP
Strategies: Eight Components of Sheltered Instruction Observation Protocol
Lesson 5:
Count by 100's
Duration:
45
minutes
Materials:
Lesson 5 Hundreds Wheel
Assessment:
Part
A-Explain how to count by 100's, Part B-Teacher dictates a number
and asks the students to write the next five numbers counting by 100's, Part C-Teacher dictates a number and asks the students to
write the five previous numbers counting backward by 100's.
Use
numbers that aren’t too obvious (i.e. 3,492 rather than 1,200).
Activities
-
Ask students to count
by 100s starting with 100 until they reach 1,000.
Remember to point out that counting by 100s isn’t always
100, 200, 300, 400, and 500.
-
Ask
students if there are any other ways to count by 100s. (i.e. It can also be
123, 223, 323, 423, etc.)
Teacher model
this on overhead or hundreds pocket chart.
Call out random three digit numbers and have students
count forward and backward by 100 to practice counting by 100s from any
number.
-
Play the song “Counting by
100” on the Intellitunes Math! Math! Math! CD by Ron Brown.
-
Use your overhead base
ten blocks to make a three digit number. Model how to add and subtract
100.
Note how the
tens and ones remain the same, but the hundreds change.
Model how to add 100 to a number with a 9 in the hundreds
place (i.e. change the thousands place as well as the hundreds place). Use
the term “regrouping” to explain this process.
-
Distribute base ten
blocks to each student. Give them a three digit number and ask them to
model it with their blocks. Ask them to either add or subtract 100. Once
they have shown the number using their blocks, have them write the sum or
difference on their white boards.
Continue
having them practice with blocks as needed.
-
Assemble
Lesson 5 Hundreds Wheel
Make a copy for each
student on cardstock and laminate.
Have each
student cut out their pieces.
Use a brad to assemble the two pieces. Place the wheel on
the bottom and the rectangular piece on the top.
Students practice adding
and subtracting 100 using their Hundreds Wheel.
Dictate
numbers to the thousands place.
Use numbers
that have a nine in the hundreds place requiring the students to regroup.
At the end of the lesson,
ask students to respond to the following questions in their math journal:
Explain what
happens to a number when you add 100?
Explain what
happens to a number when you subtract 100?
Explain what happens
to the number 2,953 when you add 100?
Count by 100's
starting with 100 until you reach 1,000.
Is there another way you could count by 100s?
Listen and sing along to
the song, Counting by 100, on the Intellitunes Math! Math! Math!
CD by Ron
Brown.
When you have a number
such as 2,350, and you want to add 100 to it, all you have to do is find
the digit in the hundreds place and add one to change the number to
2,450. If you subtract 100, find the digit in the hundreds place and
subtract one to change the number to 2,250.
Use base ten blocks to
model the numbers your teacher dictates. Practice adding and
subtracting 100 from the given numbers using your base ten blocks.
Write the sums and differences on your white board.
Assemble Hundreds
Wheel. Follow your teacher’s instructions.
Practice adding and
subtracting 100 using your Hundreds Wheel.
Differentiation
Extension:
Strategies for Higher Order Thinking
Support:
SIOP
Strategies: Eight Components of Sheltered Instruction Observation Protocol
Use
Lesson 5 Hundreds Wheel
to assist with assignments.
Lesson 6:
Count by 100's
Problem Solving
Duration: 45
minutes
Activities
-
There are 837 books in
our school library. The librarian wants to order 100 more. How many
books will there be altogether?
-
The mailman left the
post office with 1,732 envelopes. By 1:00, he had delivered 500
envelopes. How many more envelopes did he still need to deliver?
Teacher Notes:
1. Display word problem.
2. Read and understand word problem.
3. Ask the question: What
is the problem asking you to find out?
4. Underline the question
or statement that explains what you are looking for.
a. Circle key words.
(This will usually tell you what operation to use.)
5. Reread the problem
sentence by sentence.
a. Circle names and
information (numbers and words attached to them) that is needed to
solve the problem.
6. Write a number
sentence.
7. Draw a picture to
illustrate the number sentence.
8. Solve the problem.
9. Explain your thinking
in words.
Lesson 7:
Even or Odd
Duration: 45
minutes
At the end of the lesson,
ask students to respond to the following statement in their math journal:
Assessment:
Students respond to the
prompt, "What the different outcomes when we add even numbers and when we
add odd numbers?
Activities
-
Justify (or explain) why 35 is not an even number.
What is the outcome when you roll two even numbers?
What is the outcome when you roll two odd numbers?
What is the
outcome when you roll an even and an odd number?
Describe the
similarities of the numbers on the left side.
What is
another 2-digit number that would fit the pattern on the left side?
-
Describe the
similarities of the numbers on the right side.
What is
another 2-digit number that would fit the pattern on the right side?
-
Use the book,
Even Steven and Odd Todd by Kathryn Cristaoldi, to help you give a
name to each set of numbers on the board.
-
Say chant: 0,
2, 4, 6, 8 who do we appreciate? EVEN NUMBERS EVEN NUMBERS ALRIGHT EVEN
NUMBERS!
Listen to the
songs “Even or Odd” and “Add ‘em Up!” on the Math Concepts I & II
Intellitunes CD by Ron Brown.
Play Even/Odd game.
Using a 10-sided
double die and the Even/Odd Outcome sheet, roll the die and find the sum of
the two digits. Write the equation in the correct section on the sheet.
After about five minutes, analyze your results. What do you notice about the
sums of the equations in each section? Do you notice any patterns? How can
this information help you when you add numbers.
-
Assessment Prompt:
Give each student 1 index card. Ask students to write “even”
on one side of the index card and “odd” on the other side. Teacher calls
out numbers and students hold up either the odd or even side of the index
card depending on the number given. (Teacher, use assessment checklist that
is attached.) Have students explain what the different outcomes are when
they add even numbers and when they add odd numbers.
On a separate sheet of
paper, explain what the outcomes are when you add:
even + even
odd + odd
even + odd
What outcome
occurs most often?
Differentiation
Support: Use hundreds chart as a reference. Using calculator tape, students
create their own number line (at least to 20) color coding the odd and even
numbers. (i.e. odd numbers are all red and even numbers are all blue)
**Hint-odd and red both have three letters, blue and even both have four
letters.
Extended Learning:
Write random
2-digit odd numbers on the left side of the board and random 2-digit even
numbers on the right side of the board. Ask students what the left side/odd
numbers have in common (i.e. digits in the ones place). Do the same with
the right side/even numbers. Show
students that the digit in the ones place determines whether or not a number
is even or odd.
Tell the students that
since they can now determine even and odd numbers you want them to notice
something else about even and odd numbers. Give the students the Even/Odd
Outcome sheet and one 10-sided double die. Have them roll the die and add
the two numbers. The students will write the equation in the correct section
on their sheet. After doing this activity for about 5 minutes, ask the
students to analyze their results. What do they notice about the sums of the
equations in each section? Are there any patterns? How can this information
help you when you are adding numbers?
Resources
Lesson 7 Assessment Checklist
Lesson 7 Even-Odd Outcome Sheet
Lesson 7 Even-Odd Sheet
Lesson 8:
Even and Odd
Numbers Problem Solving
Duration:
45
minutes
Activities
-
Even numbers are numbers that can be split in half
evenly.
For example half of four is
two.
Four stars-- **** Split in
half-- ** **
If even numbers are numbers that can be split in half, why
isn’t 9 an even number?
Nine stars-- ********* Split in half--* * * * * * * * *
-
When you add even
numbers, your sum is always even.
-
If I added 124 and
136, would my sum be odd or even? Justify your answer.
-
When you add two odd
numbers your sum is always even.
-
If I added 213 and
352 would my sum be odd or even? Justify your answer.
-
I am a three digit
number. I am less than 300. I am greater than 100. All my digits are
odd. If you take each of my three digits and add them together, they
equal 9. What number am I?
-
I am a four digit whole
number. Each digit is an even number. All the digits are different. I am
the greatest number that can be described that way. What am I?
-
Billy’s address is 2456
Fun Lane, Sally’s address is 328 Fun Lane, and Johnny’s address is 8202
Fun Lane. What do all of these numbers have in common?
Teacher Notes:
1. Display word problem.
2. Read and understand word problem.
3. Ask the question: What is the problem asking you to find
out?
4. Underline the question or statement that explains what you
are looking for.
-
Circle key words.
(This will usually tell you what operation to use.)
5. Reread the problem sentence by sentence.
-
Circle names and
information (numbers and words attached to them) that is needed to
solve the problem.
6. Write a number sentence.
7. Draw a picture to illustrate the number sentence.
8. Solve the problem.
9. Explain your thinking in words.
Lesson 9:
Names for
Numbers
Duration:
45
minutes
Assessment:
At
the beginning of the lesson, ask students to write all the ways they can
think of to write the number 25 in their math journal. At the end of the
lesson, ask students to add to their list all the ways they can think of to
write the number 25.
Activities
-
Read the book 12
Ways to Get 11 by Eve Merriam. As you read the book, have the students
write down all the ways to make eleven. Do this as a whole group. Some
students may need assistance thinking beyond addition and
subtraction.Other forms of numbers are tally marks, expanded notation,
fractions, number form, word form, multiplication, division, multi-step
process, etc. Continue with other numbers as needed. Give assistance
where needed.
-
For transition into
step five, use student errors to show non-examples. Show students cards
that have examples and non-examples of the given number. Model and
explain how to differentiate between what is an example and what is a
non-example.
-
Place 4-5 stations
around the room with a 2-digit number on each paper. Draw a horizontal
line in the middle of the paper. Students will write examples on the top
half and non-examples on the bottom half. Divide the students into 4-5
groups and have them rotate around the room adding an example and
non-example to each station. When finished, do a gallery walk and
discuss the students’ work.
-
Play the song
“Number Game” on the Intellitunes Mighty Math Songs CD by Ron Brown.
-
Assessment:
Give students a 2-digit
number (avoid multiples of 10 and 25, 50, and 75) and an index card. Each
student will write at least three examples on the front (label this side as examples) and
at least two non-examples on the back (label this side as non-examples).
Differentiation
Tier 2 and 3 Interventions:
During step two, pull a
small group to the table and use counters and the hundreds chart to
assist with creating names for numbers.
Lesson 10 and 11:
Place Value
Duration:
Two 45
minute lessons
Assessment: At
the end of lesson 6, ask students to respond to the following statement in
their math journal:
Why do you need to know
place value?
Activities
-
Assemble place value
pocket charts and cut out digit cards. You learned place value to the
thousands place in second grade. Using your digit cards and pocket chart
to the thousands place, let’s review. Let’s learn place value to the ten
thousands place.
-
Practice identifying
digits to the ten thousands place and naming the place of given digits.
Use the songs “Place Value” song and “Place Value Rap” CD Math Concepts
I and II by Ron Brown to help you learn your place value. Using your
pocket chart and your digit cards, display numbers to the ten thousands
place.
Identify digits in different places. Identify the digit in the place
your teacher states.
-
Use your white board,
math journal, or discuss your responses with a partner.
Play
Lessons 10-11 Place Value Bingo
-
Assessment Prompt—Make
enough copies of the attached assessment for each student. (Two
assessments per page)
-
Administering the
Lessons 10-11 Assessment
-
Read the following to the students:
On question number 1, put a square around the digit in the thousands
place and a circle around the digit in the tens place.
On question number 2, underline the digit in the ten thousands place and
put a triangle around the digit in the ones place.
On question number 3, circle the digit in the hundreds place and put a
square around the digit in the ten thousands place.
On question number 4, put a 2 in the ones place, put a 3 in the hundreds
place, put a 0 in the thousands place,
put an 8 in the tens place, and put a 6 in the ten thousands place.
On question number 5, put a 9 in the ones place, put a 5 in the hundreds
place, put a 1 in the thousands place, put a 7 in the tens place,
and put a 4 in the ten thousands place.
Notes for the Teachers:
Assemble place value pocket charts and cut out
Digit Cards (1)
Digit Cards.
Number Sense Unit Word Problems
Place Value Chart-HTO
Place Value Chart-HTTTT
Using your place value pocket chart, review ones, tens, hundreds, and
thousands places.
Display a four digit number in the place value pocket chart. Ask students to
find what digit is in the ones place, tens place, etc.
Tell the students one digit from the number and ask them to state the
place value of that digit.
Continue review as needed.
Using your place value pocket chart, introduce the ten thousands place
value.
Show the relationship between the ones and thousands on the place value
chart.
Ask the students if they can find any other similarities among the tens and
hundreds and thousands and ten thousands.
Use the following analogy to help students see the relationships between the
different places. Put a big comma in between the thousands and the hundreds
place value.
Practice place value to the ten thousands place.
Display a five digit number and ask them to identify digits in different
places.
State the place and have students identify the digit in that place.
Students may use white boards, math journals, or discuss oral responses with
a partner.
Use the songs “Place Value” song and “Place Value Rap” CD Math Concepts I
and II by Ron Brown to help students learn their place value.
Using the pocket chart students created and their digit cards, dictate
numbers to the ten thousands place. Students will then use their digit cards
to create the dictated number in their pocket charts.
Display a five digit number and ask them to identify digits in different
places.
State the place and have students identify the digit in that place.
Students may use white boards, math journals, or discuss oral responses with
a partner.
Play Place Value Bingo. Each student receives a copy of the game board and
they write any digit 0-9 in each blank until the card is full. Either roll
the die to make 5-digit numbers or dictate 5-digit numbers. If a digit from
the number matches one of the place values, the students have on their Bingo
card, they get to cover that square. Only one space may be covered for each
5-digit number. Ask the students to write the 5-digit number in the box for
easier checking.
Lesson 12:
Place Value
Problem Solving
Duration: 45
minutes
Activities
-
This mystery number has 4 digits. Every digit is an odd number. None of
the digits is a 7. Every digit in the number is different. The greatest
digit is in the thousands place. The smallest digit is in the ones
place. The digit in the hundreds place is smaller than the digit in the
tens place. What is the mystery number?
-
This mystery number has 4 digits. If you add one to this number it will
be a 5 digit number. What is the mystery number?
-
I
am a four digit number. I have a one in my thousands place, and a two in
my hundreds place. I am a palindrome. (A palindrome reads the same,
forwards and backwards. The words “pop” and “level” are palindromes. The
numbers “747" and “842248" are palindromes.) What number am I?
-
I’m a five digit number. Four of my digits are zeros. I am the greatest
number possible with those characteristics. What number am I?
Teacher Notes:
1. Display word problem.
2. Read and understand word problem.
3. Ask the question: What is the problem asking you to find
out?
4. Underline the question or statement that explains what you
are looking for.
-
Circle key words.
(This will usually tell you what operation to use.)
5. Reread the problem sentence by sentence.
-
Circle names and
information (numbers and words attached to them) that is needed to
solve the problem.
6. Write a number
sentence.
7. Draw a picture to
illustrate the number sentence.
8. Solve the problem.
9. Explain your thinking
in words.
Lesson 13:
Read and
Write Numbers from 0-99,999
Duration:
45 minute
lesson
Assessment: At the
end of the lesson, ask students to respond to the following question in
their math journal.
Activities
-
Why do you need to know how
to read numbers in word form and standard notation?
Open your
reading book to any page and begin reading. Where on the
page did you begin reading? (the top)
Why did you
begin there?
When reading,
what direction do you read? (left to right)
-
When you read
words, you read them the same way you read numbers. Begin with the digit on
the left and read the
remaining digits to the right. Remember the
apartment buildings showing us that numbers are read in groups of
three?
Who remembers
what punctuation mark is used to separate each group of three digits?
(comma)
The comma
cues you to name the apartment building you are leaving.
For example:
If you have the number 32,893 the comma is where you say the word thousand.
-
Read aloud
the numbers your teacher posts on her pocket chart. Every time you see a
comma, say the word thousand and use your hand to make a comma.
-
Now that you
know how to read numbers, we are going to learn how to write numbers in word
form. Use white
boards to practice writing numbers in word form and standard notation.
-
Play the
matching game. Match the
standard notation with the word form.
http://www.funbrain.com/numwords/index.html (On this website in Method
1, the student is asked to type the number in word form that is written on a check. In Method two the student is shown a number spelled out on a check
and the students need to enter the digits to form that number. Options are
0 and 10, 0 and 100, 0 and 1,000, 0 and 10,000 for both methods.)
-
Assessment
Prompt: Use the
lesson thirteen assessment that is attached. In numbers one through five,
the students write the numbers in word form. Six through ten needs to be
changed to standard notation.
Tier 2 and 3
Interventions: Students who have
writing difficulties can be partnered.
Extended Learning:
1. Have students open their
reading book to any page and begin reading
2. Ask them the following
questions:
b.
Where on the
page did you begin reading? (the top)
c.
Why did you
begin there?
d.
When reading,
what direction do you read? (left to right)
3. When you read words, you
read them the same way you read numbers. Begin with the digit on the left
and read the remaining digits to the right.
4. Remember the apartment
buildings showing us that numbers are read in groups of three?
a. Who remembers what punctuation mark is used to separate
each group of three digits? (comma)
b. The comma cues you to name the apartment building you are
leaving.
c. For example: If you have the number 32,893 the comma is
where you say the word thousand.
5. Using your pocket chart,
display some 3, 4, and 5-digit numbers that you read aloud with the class.
You will need to model how to read the four and five digit numbers.
a. To make this activity kinesthetic, have the students make
a big comma with their hand every time they say the word thousand.
6. Tell students they are
going to learn how to write numbers in word form.
7. Post four and five digit
numbers in the place value pocket chart and ask the students to read the
number.
a. Show on the board/overhead how this number is written in
words. Model numbers as needed.
b. Ask students
to write the numbers in word form on their white boards.
c. Show numbers in word form and ask students to write the
standard notation of the number. Model numbers as needed.
d. Ask students to write the numbers in standard notation on
their white boards.
8. Distribute materials for
matching game and explain the rules. Match the standard notation with the
word form.
Resources
Lesson 13 Assessment
Lesson 14:
Value
Duration:
45
minute lesson
Assessment: At
the end of the lesson, ask students to respond to the following statement in
their math journal:
Compare the value of the
9 in the following numbers 9,832 and 3,491. In which number does
nine have the greater value? Explain your thinking.
Activities
-
Learn how to find the
value of digits in a number by observing the teacher’s demonstration.
-
Explore the base 10
blocks for three minutes.
-
Use your base 10 blocks
to represent each number your teacher gives you. Write the value of
each digit on your white board.
-
Put away base 10
blocks.
-
Take out your place
value pocket chart and create the same number as your teacher. Then use
your white board to write the value of the digit your teacher calls out.
-
Play the game Value
Concentration with a partner.
Assessment Prompt:
Use the attached assessment.
Tier
2 and 3 Interventions:
Use the place value
pocket chart throughout the entire lesson
and assessment.
Extended Learning:
-
Using overhead base 10
blocks, display a 3-digit number
-
Then show how the
base ten blocks tell the value of the digits. (For example, if you
have 3 tens, the value is 30.) Continue modeling until most
students grasp the concept.
-
Distribute the base 10
blocks and allow the students to explore them.
-
State a number and ask
the students to represent that number with their blocks.
-
Call out a digit in
the number and have students write the value of that digit on their
white boards.
-
Put away base 10
blocks.
-
Using your place value
pocket chart, display various 3-digit numbers and have the students
write the value of a given digit on their white boards.
-
Gradually increase the
numbers to five digits.
-
Rather than displaying
numbers, you could give them orally
-
Play the game Value
Concentration with a partner. (See attachment)
Resources
Lesson 14 Assessment
Lesson 14-Value Concentration
Lesson 15 and 16:
Standard
Notation and Expanded Notation
Duration: Two 45
minute lessons
Assessments: At
the end of the lesson, ask students to respond to the following statement in
their math journal:
Use words and pictures
to explain the place value of the digits in the number 837.
In Math today, we are going to begin by discussing what happens to something
after it dies. Does it remain the same or
does it change in some manner?
If you said it changes in some manner, you are correct. When something
dies, its form changes and it breaks down or decomposes. This same idea
applies to numbers! Today you aren’t going to see numbers dying, instead
you are going to be decomposing, or breaking down, numbers.
Activities
-
Grab the students’ attention by telling them you are going to talk
about something really gross and gruesome. Ask them what happens to
something (you can be more specific by discussing a bug or a body) after it
dies. Does it remain the same or does it change in some manner? The
students should come to the conclusion that when something dies, its form
changes and it breaks down or decomposes. Transition into how the same can
be applied to numbers. In this lesson, they will be decomposing, or
breaking down, numbers. Remember how we learned to write different names for
numbers? If I give the number 24, who can give me some different names
for that number? We are going to focus on one specific way to write 24
differently using value.
What is the value of 2? 20 What is the value of 4? 4
What is the sum of 20 and 4? 24; 20+4 is another way to write 24! We
call this expanded notation because that is the value of each digit in
the number 24.
-
Continue giving numbers
and build up to the ten thousands place. Some activities to practice
expanded notation are:
Write three, four, and five digit numbers on a beach ball. In a large
circle, toss the ball around. The student who is holding the ball is the
only one who can speak. When the student catches the ball, they need to
state the number that their right thumb is on in expanded notation.
-
In partners, have one
student give their partner a three, four, or five digit number. Their
partner then has to state that number in expanded notation. Then switch
and take turns giving each other numbers and expanding them.
Ask students, what are things that come in standard sizes? (i.e. ruler,
pencil, notebook) What are things that don’t come in standard sizes?
(i.e. cars, necklaces, clothes, shoes, desks)
The number 24 written as 2, 4 is considered standard notation in math
because it is the most common way numbers are written. Name other
numbers in standard notation, and ask the students to orally state
numbers in standard notation.
-
Play the song ”Expanded
Notation” on the Intellitunes Math Beats CD by Ron Brown.
-
In a large circle, toss
a ball or bat a balloon around. The student who is holding the ball or
the balloon is the only one who can speak. Your goal is to have each
student say a number in standard notation. Once every student has had
one or two turns, you may have them state a non-example (i.e. 3 tens and
4 ones or 300+20+5).
Some activities to
practice standard and expanded notation are:
Have the students
create their own matching game with expanded and standard notation.
Play with a partner. (They may create their own or you may use the
attached document.)
Using the website,
http://208.183.128.3/tutorials/gameboard.htm, create a board
game for expanded and standard notations.
Use the website
www.aaamath.com.
Place Value
Aerobics by Kim Sutton.
Resources
Lessons 15-16 Assessment
Lessons 15-16 Number Forms Matching
Lessons 15-16 Number Sort
Lessons 15-16 Number Notation Sort
Differentiation
Tier
2 and 3 Interventions: Use the place
value pocket chart to recognize the places of each digit in a number.
Lesson 17 and 18:
Comparing
Numbers 0-99,999
Duration:
Two 45
minute lessons
Assessment:
Using the attached worksheet, have students roll a 10-sided die and fill in
the blanks to create a number. Using greater than, less than, or equal
symbols compare the two numbers.
Activities
-
Choose two students
(it’s best to choose different sizes or heights) to stand in front of
the classroom. Ask students to determine how the two students are alike
and different.
-
People are alike
and different in many ways, and so are numbers! Some numbers can be
small like 1 or 25. Some numbers can be large like 23,532.
-
Why might it be
important to determine whether one number is larger or smaller than
another number? (Example: If you can’t swim and you go to a pool,
it is important to know where the deep end is and where the shallow
end is. The depths of pools are marked using numbers.)
-
Prepare ahead of time
several three, four, and five digit numbers on construction paper. You
will also need two hula hoops. Begin by asking the students to make a
3-digit number in their place value pocket charts. After all numbers
have been created, place one of your 3-digit numbers on the floor
between the two hula hoops. Ask the students to determine if their
number is larger or smaller than the number between the two hula hoops.
If their number is larger, they need to put one leg inside the hula hoop
to the right of the number. If their number is smaller, they need to
put one leg inside the hula hoop to the left of the number. You can
also reverse the sides (larger numbers on left and smaller numbers on
right).
-
This activity could
be done outside with sidewalk chalk.
-
Using a transparency or
place value pocket chart, display the following sets of numbers one at a
time:
-
392
398
-
4,923 4,939
-
10,271 10,276
-
3,452 32,945
-
6,018
618
-
83,291 8,294
-
7,629 7,629
-
Display the sets of
numbers so they are vertical (one above the other, lining up the
place value of each digit.)
-
Using the numbers
392 and 398, compare the digits with the highest place value (i.e.
each number has a 3 in the hundreds place). Since they are the
same, go to the next highest place (tens) and compare those digits
(i.e. each number has a 9 in the tens place). Since they are the
same again, move to the ones place and compare those digits. The
digits in the ones place are different, so now you can determine
which number is larger and which one is smaller. Start using the
terminology “greater than”, “less than”, and “equal” in this step.
-
Continue modeling
this concept using the remaining sets of numbers. Make additional
sets of numbers if needed.
-
Using the sets of
numbers from number three, explain the greater than and less than
symbols. Teach the chant: The alligator eats the larger number.
(As you say the chant, make your hand in the shape of an alligator’s
mouth.) The alligator’s mouth is always open to the larger number
because he wants to eat the largest number there is!
-
Listen and sing
along to the song “Number Eating Alligator” on the Intellitunes
Math! Math! Math! CD by Ron Brown.
-
Using the numbers
392 and 398 teach the “dots”. Rewrite the numbers so they are
beside each other horizontally with a space in the middle. Ask
students which number is greater, and then put two dots next to the
three in the number 398. Since 392 is the smaller number, put one
dot next to the two. Now connect the dots to make a less than
symbol.
392
:398
392.
:398
c. Continue modeling the numbers on your transparency using
the dots. Show as many examples as you need. You may also have the
students write this on their white boards.
-
Set up the
following activities in your classroom to practice comparing
numbers:
-
Put the
students in pairs and give each pair numbers to compare. Have
the students use a string or jump rope to make the greater than
or less than symbol between the two numbers on the floor.
-
Using a deck of
cards, change all the aces to ones and the kings to zeros
(remove all the 10’s, jacks, and queens). In partners, have the
students draw five cards and lay them down in the order they
drew them left to right on their place value mat. Taking turns,
each student may switch the places of two digits. They can do
this a total of four times. The objective is to create the
largest number. Whoever has the largest number receives all ten
cards. Once the whole deck has been used, the person with the
most cards wins and the game is over.
-
Use the website
www.aaamath.com to practice comparing numbers.
-
Write four and
five digit numbers on a beach ball. Within their small groups,
have the students toss the ball back and forth. When the ball
is caught with both hands, the student compares the numbers
their thumbs are touching. Read the numbers left to right.
Resources
Lessons 17-18 Assessment
Lesson 19:
Comparing
Numbers/Writing Numbers Word Problems
Duration:
45
minutes
Activities
1.
Jordan went
to the grocery store and spent $32.00. Laura went to the grocery store on
the same day and spent $48.00.
a.
Who spent the
most money at the grocery store?
b.
Write
Jordan’s total in word form.
c.
Write Laura’s
total in word form.
2.
The Big Rider
bike store is open year-round. During the summer they sold 516 bicycles.
In the winter they sold 283 bicycles.
a.
Which season
did they sell more bicycles?
b.
Why do you
think they sold more bicycles during this season?
c.
Write the
number of bicycles they sold during the winter in word form.
3.
Holly and
Tracy love hiking. In June, they decided to hike Pike’s Peak which is
14,110 feet high. In July, they hiked Cheyenne Mountain which is 12,895
feet high.
a.
Which
mountain is the highest? Explain how you know it is the highest.
b.
Write 14,110
in word form.
Teacher Notes:
1. Display word problem.
2. Read and understand word problem.
3. Ask the question: What is the problem asking you to find
out?
4. Underline the question or statement that explains what you
are looking for.
a. Circle key words. (This will usually tell you what
operation to use.)
5. Reread the problem sentence by sentence.
b. Circle names and information (numbers and words attached
to them) that is needed to solve the problem.
6. Write a number
sentence.
7. Draw a picture to
illustrate the number sentence.
8. Solve the problem.
9. Explain your thinking
in words.
Lesson 20 and 21:
Ordering
Numbers 0-99,999
Duration: Two 45
minute lessons
Equip
the student with necessary supports to explore the subject.
Rethink and revise opportunities should be provided for students: At
the end of the lesson, ask students to respond to the following statement in
their math journal:
Explain how you know the
number 13,982 is larger than 13,980.
1. Take out your
place value pocket charts and digit cards. Place all your digit cards face
down and mix them up. Choose five cards and put them in your pocket chart
to make a 5-digit number.
2. Put numbers
in order from least to greatest.
3. Put numbers
in order from greatest to least.
4. Explain how
to put three numbers in order from least to greatest and greatest to least.
5. Put away
place value pocket charts and digit cards.
6.
Take out
white boards, markers, and erasers.
7.
Listen to the
teacher explain how to use the place value chart to order four numbers
8.
Use your
white board to put four numbers in order from least to greatest or greatest
to least.
9.
Using your
cube pattern, write 5-digit numbers on each face of the cube (don’t forget
to put your name on one face). Assemble your cube.
a.
Get in a
group of four or five.
b.
Each person
in the group rolls their cube.
c.
Put your
cubes in order from least to greatest.
d.
After five
minutes, put your cubes in order from greatest to least.
e.
You can also
switch to different groups.
Assessment Prompt-
Copy and paste the following assessment into a word document.
Put the set of numbers in
order from least to greatest by cutting them out and gluing them onto
construction paper.
Tier 2 and 3
Interventions:
Extended Learning:
Notes for the Teacher
Page
1. After every student has made a 5-digit number in their
pocket chart, ask two students to come to the front of the room and hold up
their numbers so the class can see them. When the students come up, tell
them that the student with the smallest number should stand on the left and
the student with the largest number should stand on the right. Once the
students have arranged themselves, ask the rest of the class if they are
correct.
a. How would we read this
using greater than and less than?
b.
Using what you learned yesterday about numbers, how do you
know that one number is larger than another number?
2. “Challenge” the students as to whether they can put three
numbers in order from least to greatest. Ask another student to come to the
front. Have the students put their numbers in order from least to greatest.
a. What strategy did you use to order your numbers?
3. Ask three different students to come up and put their
numbers in order from greatest to least.
a. What strategy did you use to order your numbers?
b. For more practice, have different students come to the
front and order their numbers.
4. Ask three different students to come up, but don’t have
them stand in numerical order.
a. Are they standing in order
from least to greatest?
b. How do you know they are not in
order from least to greatest?
c. Are they standing in
order from greatest to least?
d. How do you know they are not in
order from greatest to least?
e. What
strategy can we use to put them in order from least to greatest? (look at
the place value of the digits in each number)
5. Prepare ahead of time graph paper with large squares.
Label the top of the paper ones through ten thousands. Make a copy for
every student and one transparency for modeling.
a. Call on 4 different
students to give you a four or five digit number. Write the numbers on the
place value transparency as they are dictated to you. As you write each
number, explain to the students how to write them on the place value
transparency.
b. Using a piece of paper, cover up
all the digits except for the highest place value. Begin by comparing all
the digits in the highest place value. Once you have determined the
greatest number, label it with a 1.
c.
Continue
moving the paper one place at a time to the right until all numbers have
been ordered, numbering them from greatest to least.
d. Continue practicing until
students understand this concept.
6. Write four 4-5 digit numbers on the board in any order.
Have the students complete step 7 independently on their white boards.
Continue practicing until they can successfully order five 4-5 digit
numbers, greatest to least and least to greatest.
7. Using a cube pattern (copy the pattern on cardstock) ask
students to write 5-digit numbers on each face of the cube. Then assemble
the cube.
a. Put students in groups of
four or five.
b. Have each student in the group
roll their cube and then put their cubes in order from least to greatest.
c. Have each student in the
group roll their cube and then put their cubes in order from greatest to
least.
d. You can also switch students in
groups to add in new numbers.
Resources
Lessons 20-21 Cube Pattern
Lesson 22:
Ordering
Numbers Problem Solving
Duration:
45 minutes
-
It was a close finish
in the Annual Toaster Throwing Championship. Sally Musclesworth threw
the toaster 1,414 inches. Paula Pernicious threw 70 inches farther than
Sally. Bonnie Bigenough’s best throw was 1,408 inches. Who was the
winner?
-
In the cookie bake off,
Betty Crocker made 2,941 cookies. Joan Pillsbury made 4,853 cookies,
and Rachel Ray made 495 cookies. Put the cooks in order from greatest
to least based on the number of cookies they baked.
-
Who made the most
cookies?
-
Who made the least
cookies?
Teacher Notes:
1. Display word problem.
2. Read and understand word problem.
3. Ask the question: What is the problem asking you to find
out?
4. Underline the question
or statement that explains what you are looking for.
a. Circle key words.
(This will usually tell you what operation to use.)
5. Reread the problem
sentence by sentence.
a. Circle names and
information (numbers and words attached to them) that is needed to
solve the problem.
6. Write a number
sentence.
7. Draw a picture to
illustrate the number sentence.
8. Solve the problem.
9. Explain your thinking
in words.
Lesson 23:
Smallest/Largest Numbers
Duration:
45
minute lesson
Assessment: At
the end of the lesson, ask students to respond to the following statement in
their math journal:
Apply what you know about
digits and place value to make the:
a.
largest five
digit number
b.
smallest five
digit number
Activities
-
Take out your
digit cards and choose your favorite digit.
-
When grouped
with three other students, make the smallest number possible with each
student’s digit card.
-
When grouped
with three other students, make the largest number possible with each
student’s digit card.
-
Play the
following games.
-
In a group of
three to four students, use a deck of cards (digits 0-9 only) to practice
making the largest and smallest numbers possible. Each student draws five
cards and creates the largest number possible. The student with the largest
number gets to keep all the cards from that round. Once you have used the
entire deck of cards, shuffle them and play again. This time make the
smallest number possible.
-
In groups of three to four students, use a 10-sided die to roll a digit.
Put that digit in one of the places (ones through ten thousands) on the
worksheet. Take turns rolling the die and continue rolling until all blanks
have been filled. You may only roll the die one time when it is your turn
and then pass it to the person on your right. Once all blanks have been
filled with a digit, determine who has the largest number. The person with
the largest number circles their number. Continue playing until the time is
up. The person with the most circles wins. (You may also play this game
trying to make the smallest number.)
Assessment Prompt-Give
each student an index card. On the board write the following digits: 8,
6, 3, 7, 1
Ask students to use the
five digits to make the smallest number and the largest number possible.
(On one side of the card, ask the students to write the word “smallest” and
on the other side of the card, ask them to write the word “largest.”)
Tier 2 and 3
Interventions:
Extended Learning:
-
Ask students to take
out their digit cards and choose their favorite digit.
-
Ask four or five
students to come to the front of the room and put themselves in order so
that they make the smallest number possible.
-
What strategy did you use to make your number?
-
How do you know it’s the smallest number?
-
Ask four or five more
students to come up to the front of the room and put themselves in order
so that they make the largest number possible.
-
What strategy did you use to make your number?
-
How do you know it’s the largest number?
-
Continue steps two
and three until every student has had a chance to participate.
**Make sure you practice 5-digit numbers!
4. Play the following
games.
a. In a group of three to four students, use a deck of cards
(digits 0-9 only) to practice making the largest and smallest numbers
possible. Each student draws five cards and creates the largest number
possible. The student with the largest number gets to keep all the cards
from that round. Once the students have used the entire deck of cards,
shuffle them and play again. This time make the smallest number possible.
b. In groups of three to
four students, use a 10-sided die to roll a digit. Put that digit in one of
the places (ones through ten thousands) on the worksheet. (See attached)
Take turns rolling the die and continue rolling until all blanks have been
filled. The students may only roll the die one time when it is their turn
and then pass it to the person on their right. Once all blanks have been
filled with a digit, determine who has the largest number. The person with
the largest number circles their number. Continue playing until the time is
up. The person with the most circles wins. (Remind the students they
may also play this game trying to make the smallest number)
Resources
Lesson 23 Smallest-Largest Numbers
Lesson 24:
Smallest/Largest Numbers Problem Solving
Duration:
45 minutes
-
This mystery number has
5 digits. There is a 6 in the ten thousands place. None of the other
digits is a 6. What is the smallest number that this mystery number can
be?
-
This mystery number has
5 digits. There is a 6 in the ten thousands place. None of the other
digits is a 6. What is the largest number that this mystery number can
be?
Teacher Notes:
1. Display word problem.
2. Read and understand word problem.
3. Ask the question: What is the problem asking you to find
out?
4. Underline the question
or statement that explains what you are looking for.
a. Circle key words.
(This will usually tell you what operation to use.)
5. Reread the problem
sentence by sentence.
a. Circle names and
information (numbers and words attached to them) that is needed to
solve the problem.
6. Write a number
sentence.
7. Draw a picture to
illustrate the number sentence.
8. Solve the problem.
9. Explain your thinking
in words.
Lesson 25:
Number Line
Duration: 45 minute
lesson
Equip
the student with necessary supports to explore the subject.
Rethink and revise opportunities should be provided for students: At
the end of the lesson, ask students to respond to the following statement in
their math journal:
You are at the park
playing and you get really hungry. If you leave now, it will take you 34
minutes to get home. About how many minutes will it take you to get
home?
1. a. Determine
what two tens 23 is between.
b. What is halfway between 20 and 30?
c. Would you place 23 before or after 25?
d. Is 23 closer to 20 or 30.
2. Tape your number line to the bottom of your white board.
3. Using the number your teacher gives you:
a. Plot the two tens the number comes between.
b. Plot the halfway point.
c. Plot the 2-digit number.
4. Using the number your teacher gives you:
a. Plot the two hundreds the number comes between.
b. Plot the halfway point.
c. Plot the 3-digit number.
Assessment
Prompt: Administer
the attached assessment.
Differentiation
Extended Learning:
Prepare blank
number lines for each student. Copy them on cardstock and laminate.
1. Either draw a number line on your board using a Vis a Vis or create a
blank number line (laminated) and tape it on your board. Display the number
23 on your board.
a. Ask students to discuss what two tens 23 is between.
b. Write 20 on the far left of your number line and 30 on the
far right.
c. Ask students where the half way point is. (25)
d. Students should then determine whether 23 would be to the
left or right
of 25.
e. Plot 23 on the number line.
f. Ask students if 23 is closer to 20 or 30.
A variation of step 3 is
to use a monkey stuffed animal and 2 bananas (real or pictures). Place one
banana on each end of the number line. The monkey is the number 23. Tell
the students the monkey is hungry and ask them which way on the number line
he would go to get to the closest banana.
2. Pass out student number
lines and have them tape their number lines onto the bottom of their white
boards.
3. Give students two digit
numbers. Ask them to:
a. Plot the two
tens the number comes between.
b. Plot the
halfway point.
c. Plot the
2-digit number.
d. Repeat as
needed.
4. Repeat step 2 using
three digit numbers.
Give students
three digit numbers. Ask them to:
a.
Plot the two hundreds the number comes between.
b.
Plot the halfway point.
c.
Plot the 3-digit number.
d.
Repeat as needed.
Resources
Lesson 25 Assessment
Lesson 26:
Skaters on
Mountains (Rounding)
Duration:
45
minutes
Equip
the student with necessary supports to explore the subject.
Rethink and revise opportunities should be provided for students: At
the end of the lesson, ask students to respond to the following statement in
their math journal:
Explain how you would
round 72 to the nearest ten.
1. Yesterday you
used a number line to plot numbers and determine which number it would be
closer to.
2. Now you are going to use
a larger number line to help you round numbers.
3. Observe the teacher’s
mountain number line as it is being drawn. Notice the number pattern.
4. Using a large piece of
butcher paper, make your own mountain number line. You may also draw and
color a
skateboarder.
5. Plot the 2-digit number
your teacher gives you on your mountain number line. Will your number stay
the same
or round up?
6. Sing the following song to the tune of Twinkle, Twinkle
Little Star
Rounding up and down is
fun,
We will do it 'till we're done.
If a number's 1-4,
Round it down right through the floor.
If a number's 5-9,
Round it up it is just fine.
7. Round the 2-digit numbers your teacher dictates. Write
your answers on your white boards.
8. Using the number 134, you will be rounding this number to
the nearest ten. What digit is in the tens place?
9. Continue to practice with more 3-digit numbers. Use your
number line to round three digit numbers to the tens
place.
Assessment Prompt-
This assessment
should be conducted using student white boards and a teacher checklist.
Give the students the
following numbers and have them round them to the nearest ten.
78, 39, 21
Give the students the
following numbers and have them round them to the nearest hundred.
283, 104, 657
Tier 2 and 3
Interventions:
Have some mountain number
lines already prepared and laminated. This way students can use a Vis a Vis
to write on the number line. This will help them to accurately round
numbers.
Extended Learning:
Notes for the Teacher
Page
1. Yesterday you used a
number line to plot numbers and determine which number it would be closer
to.
2. Today you are going to
use a larger number line to help you round numbers. This number line looks
like a mountain.
3. Begin drawing the
mountain number line on the board and ask students if they recognize the
pattern. Once they do, have them state the next number. Tell the students
they are all skateboarders today and they will be skateboarding up and down
the mountains. However, they will need to take stops along the way.
a. Point to a place on the mountain (not the peak or valley)
and ask the students what would happen if you stopped right here on your
skate board? The students should respond that they would slide down to the
lowest point or the bottom.
4.
Using a large piece of butcher paper, have the students make a mountain
number line. The students can also draw and color a skateboarder.
5. Give students two digit numbers to plot on their mountain number line.
Ask the students if their number will stay the same or round up.
6. Teach students the following song to the tune of Twinkle,
Twinkle Little Star
Rounding up and down is
fun,
We will do it 'till we're done.
If a number's 1-4,
Round it down right through the floor.
If a number's 5-9,
Round it up it is just fine.
7. Continue giving the students 2-digit numbers. Have them
write their answers on their white boards.
8. Write the number 134 on the board. Tell students that they will be
rounding this number to the nearest ten. Ask them what digit is in the tens
place and underline it. Put a box around the three and the digit to the
right, which is a four. Have a student plot the number 34 on your number
line. Ask them what 34 would round to. Since 34 rounds to 30, 134 rounds
to 130. If the original number has three digits, the rounded number must
have at least three digits also.
a. When
teaching 3-digit numbers, you can adjust the number line so it has 3-digit
numbers instead of 2-digit numbers.
9. Continue to practice with more 3-digit numbers. Have the
students use their number lines to round 3-digit numbers to the tens place.
Resources
Lesson 26 Assessment Checklist
Lesson 27:
Rounding
Duration:
45 minutes
At
the end of the lesson, ask students to respond to the following statement in
their math journal.
Using the idea of kings,
princes, and servants, explain how to round the number 48.
Activities
1.
Review how to use the mountain number line to round two and three digit
numbers.
2. What do you know about
kings and princes?
3. Use the following
process to round the number 83.
a. You are
going to round the number 83 to the nearest ten.
b. What digit
is in the tens place? Then underline that digit.
c. The bossy king is right next door to the right. Since he
is a king, he needs a crown. Draw a crown above the digit three.
d. Draw a “roller coaster” (similar to the first mountain on
the number line) and label 0-4 on the left side going up and 5-9 on the
right side going down. Include the words “stay the same” on the left side
and “go up” on the right side. If the crowned number stays on the left
side, the number has to stay the same and remain a lowly servant in the
king’s castle. But if the crowned number is on the right side, the number
moves up to a prince and gets all of the king’s riches!
e. What side of the roller coaster is the king on? Since he
is on the left side, the digit in the tens spot has to stay the same and be
a servant for the rest of his life.
f. The three becomes a zero. You can also say that “all of
the king’s men become zeros.”
g. Check that your rounded number has at least the same
number of digits as your original number (83).
4. Practice this strategy numerous times using two and three
digit numbers. Use your white board to practice.
Assessment Prompt-
Round the number 86 to the
nearest ten.
Tier 2 and 3
Interventions:
Extended Learning:
Notes for the Teacher
Page
1.
Review how to use the mountain number line to round two and three digit
numbers.
2. Ask students to tell you
what they know about kings and princes.
3. Explain to the students
the following process using the number 83.
a. Tell
students that they are going to round the number 83 to the nearest ten.
b. Ask them
what digit is in the tens place. Then underline that digit.
c. The bossy king is right next door to the right. Since he
is a king, he needs a crown. Draw a crown above the digit three.
d. Draw a “roller coaster” (similar to the first mountain on
the number line) and label 0-4 on the left side going up and 5-9 on the
right side going down. Include the words “stay the same” on the left side
and “go up” on the right side. After completing the diagram, explain to the
students that if they stay on the left side, the number has to stay the same
and remain a lowly servant in the king’s castle. But if they are on the
right side, the number moves up to a prince and gets all of the king’s
riches!
e. Ask the students what side of the roller coaster the king
is on. Since he is on the left side, the digit in the tens spot has to stay
the same and be a servant for the rest of his life.
f. The three becomes a zero. You can also say that “all of
the king’s men become zeros.”
g. Check that your rounded number has at least the same
number of digits as your original number (83).
4. Practice this strategy numerous times using 2-digit
numbers. The students should use their white boards to practice.
Lesson 28:
Rounding Word
Problems
Duration:
45 minutes
Activities
1.
Bill
and his family were going on a camping trip to the mountains. From their
home in Colorado Springs to their campsite is 213 miles. About how many
miles will it take them to get there?
2. Julie
weighs 149 pounds and Bobby weighs 174 pounds. Round Julie and Bobby’s
weights to the nearest ten pounds.
a.
About
how much does Bobby weigh?
b.
About
how much does Julie weigh?
3. At
the Boston Marathon, Joe Runsalot finished in 289 minutes. His competitor,
Billy Speeds, ran the same race in 242 minutes. Steve Slowpants had to walk
part of the race and finished in 351 minutes. Round the athletes’ times to
the nearest hundred.
a.
About
how many minutes did it take Joe Runsalot to finish the race?
b.
About
how many minutes did it take Billy Speeds to finish the race?
c.
About
how many minutes did it take Steve Slowpants to finish the race?
d.
CHALLENGE-Put the athletes in the order they finished the race.
Teacher
Notes:
Display the word problem.
Read and understand the word problem.
Ask the question: What is the problem asking you to find out?
Underline the question or statement that explains what you
are looking for.
Circle key words. (This will usually tell you what operation to use.)
Reread the problem sentence by sentence.
Circle names and information (numbers and words attached to them) that is
needed to solve the problem.
Write a number sentence.
Draw a picture to illustrate the number sentence.
Solve the problem.
Explain your thinking in
words.
Lesson 29:
Estimation
(three and four digit numbers and finding sums and differences)
Duration:
45 minutes
Rethink and revise opportunities should be provided for students: At
the end of the lesson, ask students to respond to the following statement in
their math journal:
Using the
idea of kings, princes, and servants, explain how to round the number 784.
Activities
1.
Review how to use the king, prince, and servant strategy to round numbers.
2. Use this same strategy
to round three and four digit numbers.
3. Practice rounding three
and four digit numbers on your white board.
4. Repeat step three for
4-digit numbers.
5. Look at the following
example to learn how to estimate sums and differences.
a. Find the sum of the two estimates.
b. Find the actual sum.
c. Compare the actual sum to the estimate to determine if the
actual answer is in the ball park.
d. Continue to practice with 2-digit numbers and progress to
4-digit numbers.
e. Practice both addition and subtraction problems.
6. Whiteboard Exchange: In pairs, students will write a two,
three, or four digit addition or subtraction problem on their white boards.
The students will exchange white boards with their partner. Find the
estimated and actual sums or differences. Return the white boards to their
partners to check.
Assessment Prompt:
Lesson 29 Estimation Assessment
Differentiation
Extended Learning:
1. Review how to use the
king, prince, and servant strategy to round numbers.
2. Use this same strategy
to introduce rounding with three and four digit numbers.
3. Give students 3-digit
numbers and have them practice rounding. The students will write their
answers on their white boards.
4. Repeat step three for
4-digit numbers.
5. Write 23+ 38 vertically
on the board. Ask the students what 23 would round to and write 20 to the
right of 23. Do the same with the number 38.
a.
Find
the sum of the two estimates.
b.
Find
the actual sum.
c.
Compare the actual sum to the estimate to determine if the actual answer is
in the ball park.
d.
Continue to practice with 2-digit numbers and progress to 4-digit numbers.
e.
Practice both addition and subtraction problems.
6. Whiteboard Exchange: In
pairs, students will write a two, three, or four digit addition or
subtraction problem on their white boards. The students will exchange white
boards with their partner. Find the estimated and actual sums or
differences. Return the white boards to their partners to check.
a.
If
students need more practice with estimation, you may have them “Round the
Room.” Place numbers on the floor, or around the room, face down in a pile.
The students will select a number and then round it to the nearest hundred.
They will then move to the desk with that hundred on it. For example, if I
drew the number 720, I would move to the table or desk with 700 on it and
then sit down.
Lesson 30:
Estimation
Problem Solving
Duration:
45 minutes
-
Ellen was planning a
trip to Timbuktu. If the trip was more than 200 miles she figured she
would take the train. Anything less, she decided she would use her
scooter. She looked at a map and saw that it was about 56 miles to
Windy Town. From Windy Town to Timbuktu was another 163 miles.
Estimate the mileage. Should Ellen take the train or her scooter?
-
Carol had 611 marbles
ready for the marble show. She had a hole in her pocket and lost 291 of
them. She needs 300 marbles to enter the show. Does she still have
enough to enter?
-
I am an amount of
money. I am the cost of five $ .88 hamburgers rounded to the nearest
dollar. About how much money am I?
Teacher
Notes:
1. Display word problem.
2. Read and understand word problem.
3. Ask the question: What is the problem asking you to find
out?
4. Underline the question or statement that explains what you
are looking for.
-
Circle key words.
(This will usually tell you what operation to use.)
5. Reread the problem sentence by sentence.
-
Circle names and
information (numbers and words attached to them) that is needed to
solve the problem.
6. Write a number sentence.
7. Draw a picture to illustrate the number sentence.
8. Solve the problem.
9. Explain your thinking in words.
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Highest Frequency
High
Frequency
Other
Standards and E-Skills
Reads, writes, and orders numbers to 10,000 (written
form, standard form, expanded form)
Tell time to nearest 5 minutes (digital and analog).