June 26, 2009
Number Sense and Operations
(Developmentally Appropriate Lessons for K-5 Students)
Amanda Anderson
Title I Teacher
Lincoln Elementary
[email protected]
1
June 26, 2009
Executive Summary
This 15 day unit plan is constructed in a format that best fits my Title I teaching
schedule. I have, on average, a total of 14 classes a day. Each class fits in a 25 minute time slot.
Within these classes are students who range in age from kindergarten to fifth grade, and
developmentally from struggling to advance. This unit plan teaches the concepts of number
sense and operations on a third grade level in 20 minute intervals. After each lesson is a
category called “Adaptations,” which contains the alterations necessary to quickly adapt this unit
for any other elementary grade K-5. The Minnesota state standards that this unit will address,
for each grade level, can be found after the “Unit Plan Outline and Overview” section located
below. This unit plan starts with a pre-assessment on the first day to find out the students'
prior knowledge to the following concepts which came from the third edition of the Everyday
Math series: fact families, what's my rule, parts and total, changing number stories, number
comparisons, and partial sums algorithms. Each concept will be addressed over two days and on
Fridays the students will be receiving post assessments over the two new concepts they learned
that week. This will be done through activities, formal and informal assessments, and through
the use of technology.
Standard Based Unit Plan Outline and Overview
Day 1
Pre-Assessment over all concepts.
Launch, Explore, Share, and Summarize: Fact Families
Day 2
Launch, Explore, Share, and Summarize Fact Families
Day 3
Launch and Explore: What's my rule?
Day 4
Continued Exploration, Share, and Summarize: What's my rule?
Day 5
Activities and Post Assessment: Fact Families and What's my rule?
Day 6
Launch, Explore, Share, and Summarize: Parts and Total (stories)
Day 7
Launch, Explore, Share, and Summarize: Parts and Total (stories)
Day 8
Launch, Explore, Share, and Summarize: Changing Number Stories
Day 9
Continued Exploration, Share, and Summarize: Changing Number Stories
Day 10
Activities and Post Assessment: Parts and Total and Changing Number
Stories
Day 11
Launch, Explore, Share, and Summarize: Number Comparisons
Day 12
Launch, Explore, Share, and Summarize: Number Comparisons
Day 13
Launch, Explore, Share, and Summarize: Partial Sums Algorithms
Day 14
Launch, Explore, Share, and Summarize: Partial Sums Algorithms
Day 15
Activities and Post Assessment: Number Comparisons and Algorithms
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June 26, 2009
Standards Addressed in this Unit
Kindergarten:
Number and Operation: Use objects and pictures to represent situations involved in combining and
separating.
K.1.2.1. Use objects and draw pictures to find the sums and differences of
numbers between 0 and 10.
First Grade:
Number and Operation: Use a variety of models and strategies to solve addition and subtraction problems in
real-world and mathematical contexts.
1.1.2.1. Use words, pictures, objects, length-based models (connecting
cubes), numerals and number lines to model and solve addition and
subtraction problems in part-part-total, adding to, taking away from
and comparing situations.
Second Grade:
Number and Operation: Demonstrate mastery of addition and subtraction basic facts; add and subtract oneand two-digit numbers in real-world and mathematical problems.
2.1.2.2. Demonstrate fluency with basic addition facts and related
subtraction facts.
Third Grade:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Fourth Grade:
Number and Operation: Represent and compare fractions and decimals in real-world and mathematical
situations; use place value to understand how decimals represent quantities.
4.1.1.5. Solve multi-step real-world and mathematical problems requiring the use
of addition, subtraction and multiplication of multi-digit whole numbers.
Use various strategies, including the relationship between operations, the
use of technology, and the context of the problem to assess the
reasonableness of results.
Fifth Grade:
Number and Operation: Divide multi-digit numbers; solve real-world and mathematical problems using
arithmetic.
5.1.1.3. Estimate solutions to arithmetic problems in order to assess the
reasonableness of results.
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June 26, 2009
Table of Contents
Page
1. Third Grade Pre-Assessment........................................ 5
2. Day 1: Fact Families................................................. 9
3. Day 2: Fact Families................................................. 13
4. Adaptations for Fact Families....................................... 15
5. Day 3: What's My Rule?............................................ 28
6. Day 4: What's My Rule?............................................ 32
7. Adaptations for What's My Rule?.................................. 34
8. Day 5: Post Assessment for Fact Families......................... 42
and What's My Rule?
9. Day 6: Parts and Total............................................. 45
10. Day 7: Parts and Total............................................. 49
11. Adaptations for Parts and Total................................... 52
12. Day 8: Changing Number Stories...................................60
13. Day 9: Changing Number Stories.................................. 63
14. Adaptations for Changing Number Stories........................ 65
15. Day 10: Post Assessment for Parts and Total.................... 72
and Changing Number Stories
16. Day 11: Number Comparisons...................................... 76
17. Day 12: Number Comparisons...................................... 80
18. Adaptations for Number Comparisons.............................. 83
19. Day 13: Partial-Sums Algorithms................................... 88
20. Day 14: Partial-Sums Algorithms.................................. 91
21. Adaptations for Partial-Sums Algorithms.......................... 93
22. Day 15: Post-Assessment for Number Comparisons............... 98
and Partial-Sums
23. Resource Citations.................................................. 102
4
June 26, 2009
Name_______________
Date:________
What Do You Know?
(Grade 2-3)
1. Can you show me what 8 + 9 equals?
2. Do you know what a fact family is? (Circle one.)
Yes!
No.
Maybe?
3. Can you show me a fact family triangle
using these numbers? (8, 9, and 17)
4. Can you double the number of smiley faces
by drawing them?
5
June 26, 2009
5. Can you tell me the rule that should go in the box?
in
Rule
out
in
out
7
12
10
15
21
26
45
30
16
21
3
8
6. Can you answer this story question?
Miss Anderson wanted to make some cookies for her students for their first day of
school. Yesterday she made 20 cookies, and today she made 16 cookies.
How many cookies in all did she make?
Total
Answer:________________
Can you fill out the table
using the numbers
from the story?
Part
Part
7. Can you fill in the blanks on these change number stories?
Change
Start
27
End
+ 7
6
June 26, 2009
Change
End
Start
- 9
10
8. Can you answer this story question?
In Florida today, the temperature is 82 degrees.
In Minnesota, the temperature is 71 degrees.
What is the difference?
Quantity
Answer:________________
Can you fill out the table
using the numbers
from the story?
Quantity
Difference
9. Can you add these together? How much do you have?
+
+
+
=
7
+
June 26, 2009
10. Can you subtract these? How much is left?
_
=
_
You're Done!
Thank you for your hard work!
8
June 26, 2009
Day 1
Pre-Assessment and Introduction
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:




The students will complete a written pre-assessment which covers the concepts they will
be learning over a period of fifteen days.
The students will complete an MCA sample question based on fact families.
The students will develop an understanding of fact families as measured by oral
responses through group and guided discussion and participation.
The students will create fact family houses with a partner for numbers 11-20.
Materials (located at the end of each continued lesson):







What Do You Know? Pre-Assessment Activity Sheet
Visualizer to display MCA Sample question
MCA Sample question
Dry Erase Markers
Fact Family House Activity Sheet (#'s 11-20)
Blue paper to use to Photocopy Fact Family House Activity Sheets
Pencils
Procedure:
Launch (4 min.):
The students will first come to class and complete a short 10 question pre-assessment
that contains the concepts they will be learning over the next 15 days (5 min.). After the preassessments are completed and turned in, the students will see a sample MCA question displayed
on the white board through the use of a visualizer. The sample question is as followed:
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June 26, 2009
The teacher will then ask, “How can we figure out this problem? How can we solve it?”
(Possible student responses: We need to figure out which answer is right, by guessing, by
subtracting, etc.) “Let's come up with a way to solve the problem together.” Through volunteer
sticks, one student will be selected to read the problem. As one student is reading the problem,
another student will write down any numbers on the board beside that he or she hears as the
problem is being read. An example of what should be written on the board is the following:
15
7
The teacher will then ask, “To find out an answer, do we need to add the two numbers
together and get a sum? Or should we take away or subtract the 7 from the 15 to find a
difference?” Through group discussion and teacher guidance the teacher and students will come
up with the difference (a difference of 8).
Explore (11 min):
“Did you know that 7, 8, and 15 are a fact family? Does anyone know what a fact family
is?” It will be explained to the students that a fact family is a group of different addition and
subtraction problems that can be created by using the same three numbers. It will be explained
that with addition, the turn around fact can be used where 7 + 8 has the same answer as 8 + 7.
The teacher will then present an example of a fact family triangle on the visualizer that will be
displayed on the white board. This fact family triangle will be completed as a whole group using
the same numbers 7, 8, and 15.
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June 26, 2009
Here is an example of what will be completed as a group on the board together. This will remain
on the board for the duration of class.
15
+,7
8
7+8=15
8+7= 15
15-7=8
15-8+7
The students, through the guidance of the teacher, will be working in pairs (six to eight
students =three to four pairs) to work together and practice making fact family houses. The
students will take turns writing each of the fact family house equations for numbers 11 to 20 (1
through 10 will be completed the next day. At the end, they will cut out and fold the houses
together so that they create an accordion of math facts that they can use as a reference during
this 15 day unit. A sample of the fact family houses can be seen below.
11
+,5
...
12
+,6
5+6=11
6+5=11
11-6=5
11-5=5
6
13
+,6
6
6+6=12
12-6=6
14
+,7
6+7=13
7+6=13
13-6=7
13-7=6
Turn around
is the same.
11
7
7
7+7=14
14-7=7
Turn around
is the same.
...
June 26, 2009
Share (3 min.):
While the students are working on their family fact houses, the teacher will be asking
questions to inspire a mathematical discussion. These questions will be based on having the
students share different ideas on how they are use their detective skills to solve to find the
missing numbers on each of the fact family triangles. “How are you coming up with the different
answers for the missing numbers?” (Possible student responses: I counted up from 6 to 12 to
find out that my answer was 6, I knew that 15 take away 6 was 9, and 14 is only one less, so I
knew that 14 take away 6 was 8, etc.) By having the students share their ideas, it will give
others new ways to solve and comprehend different fact family equations. The teacher will also
be asking the students for different ways they can use these fact family houses in the future.
Summarize (2 min.):
Towards the end of class, the teacher will get the group's attention and ask, “So, what
did we learn about or try today?” Based on the students' responses, the teacher will be able to
conclude whether or not the students truly comprehended today's activities. “So, not only did
we learn how to solve a MCA math problem by using fact family ideas, but we also were able to
create fact family houses in order to help us remember different fact family math problems in
the future. Excellent! Wonderful detective work!”
12
June 26, 2009
Day 2
Continuing with Fact Families
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will demonstrate their prior knowledge of fact families by completing fact
family houses (#1-10).
The students will further their comprehension of fact families as measured by their oral
responses while playing Fact Family Top It.
The students will expand upon their mathematical vocabulary through group discussion
during the summary portion of this lesson.
Materials:





Fact Family House Activity Sheet (#1-10)
The students should still have their Fact Family House Activity Sheet (#'s 11-20)
Yellow paper to use to Photocopy Fact Family House Activity Sheets for 1-10
Fact Family Top-It Cards
Pencils
Launch (4 min.):
When the students first come to class, the teacher will say, “Remember how we learned
about the idea of fact families yesterday for numbers 11-20? Why do you think it's important
that learn about fact families?” (Possible student responses: to learn more about fact families,
to know that each fact family has a different answer, etc.) “Excellent! Today I would like to see
how much you remember by working with your partner and coming up with the fact families for
the numbers 1-10).” These fact family houses will be on yellow paper to show as a visual
reminder the difference between the sums and differences between the numbers 1-10, and
11-20.
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June 26, 2009
Explore (11 min.):
After completing the fact family houses, the students will play a game of Top-It with
their partner using the fact family flash cards. They will first shuffle up the flash cards and
divide the cards so that each partner receives 10 cards. They will then each flip a card over.
Whoever has the larger card wins and gets the other opponents flash card. The person with the
higher number fact family flash card must first say the number on their flash card and read one
of the math problems on the card that would create that number. Example: “I win, 13 is bigger
than 7. 6 plus 7 equals 13.” The person with the most cards at the end of the time allowed, or if
they receive all of the cards, wins.
Share (3 min.):
The teacher will get the group's attention and ask, “What did we learn about fact
families? How did we solve them?” (Possible student responses: We created fact family houses,
we played Top-It, we worked with a partner to figure out the problems and came up with the
right answers, etc.) “Who can give me an example of one way you solved a fact family math
problem.” (Possible student responses: I counted up from 7 to 13 to find out the number was 6,
I knew that 2 plus 2 was four and three is only one more so I knew that 2 plus 3 is five, etc.)”
Summarize (3 min):
The teacher will ask, “So, what was one main idea or big picture we've learned about over
the last two days?” (Goal response: fact families). From the students' responses, the teacher
will be able to summarize this two day concept, while also showing the importance in recognizing
that the students truly do comprehend the concept of fact families. “So, from what you are
telling me, not only did we learn about fact families, but we played a game on fact families, we
practiced our addition and subtraction skills, and we got to work with a partner and show the
many different ways we can learn and solve our math problems with fact families. Wonderful!
Give yourselves a pat on the back for all of your fact family hard work!” If time allows, they can
play an additional game of fact family Top-It.
Lesson's Materials and Resources
1.
2.
3.
4.
5.
6.
7.
8.
9.
Pre-Assessment: Found Above before the start of the lesson (pages 5-8)
MCA Sample Question (page 23)
Large Fact Family Triangle (page 24)
Fact Family Triangles #11-10 (page 25)
Fact Family Triangles #1-10 (page 26)
Fact Family Top-It Cards (page 27)
Alternate Pre-Assessment for K-1 (pages 16-18)
Alternate Pre-Assessment for 4-5 (pages 19-22)
Lesson Adaptations (page 15)
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June 26, 2009
Fact Family Lesson Adaptations for K, 1, 2, 4, 5
K




1



In order to make this lesson developmentally appropriate for kindergarten
students, and to meet the requirements of the suggested Minnesota standard,
simply use only the fact family triangles that work with the numbers 1-10.
Explain how the number 0 does not have a fact family card and explain the
different mathematical equations when 0 is added or subtracted to itself it is still
0.
Using pictures to represent the fact family equations is another way to help the
students visually solve the different math equations.
Also, use the alternative pre-assessment version that is suitable for students in
grades K-1. This pre-assessment alternative can be found on page 16.
In order to make this lesson developmentally appropriate for first grade students,
and to meet the requirements of the suggested Minnesota standard, simply use
only the fact family triangles that work with the numbers 1-15.
Using pictures to represent the fact family equations is another way to help the
students visually solve the different math equations.
Also, use the alternative pre-assessment version that is suitable for students in
grades K-1. This pre-assessment alternative can be found on page 16.
2

These two days of lessons are completely appropriate for students to work on in
second grade and meet the Minnesota standard selected.
4

In order to make this lesson developmentally appropriate for fourth grade
students, and to meet the requirements of the suggested Minnesota standard,
simply change the fact family triangles to represent multiplication, the addition
and subtraction of decimals, and fraction equations.
Also, the sample MCA questions should be changed to focus more on a higher level
of thinking involving a fraction equation where the fact family triangles can be
used. .
Use the alternative pre-assessment version that is suitable for students in grades
4-5. This pre-assessment alternative can be found on page 19.


5



In order to make this lesson developmentally appropriate for fifth grade students,
and to meet the requirements of the suggested Minnesota standard, simply change
the fact family triangles to represent multiplication and division equations using
multi-digit numbers.
Also, the sample MCA questions should be changed to focus more on a higher level
of thinking involving a division equation using multi-digit numbers where the fact
family triangles can be used. .
Use the alternative pre-assessment version that is suitable for students in grades
4-5. This pre-assessment alternative can be found on page 19.
15
June 26, 2009
Name_______________
Date:________
What Do You Know?
(Grade K-1: Should be read to the students)
1. How many flowers do I have?
+
=
2. Do you know what a fact family is? (Circle one.)
3. Can you use tally marks to show 8+2=10
4. Can you finish drawing the pattern?
5. Can you draw 3 squares, 4 triangles, and 2 circles below?
How many shapes to I have?
16
June 26, 2009
6. Can you answer this story question?
Miss Anderson wanted to buy some bags of candy for her students for their first day of
school. Yesterday she bought 6 bags of candy, and today she bought 1 bag of candy.
How many bags of candy does she have? Can you draw those bags of candy?
7. Can you fill in the blanks on these change number stories?
Change
Start
2
End
+ 1
Change
End
Start
9
-4
8. Can you make your own pattern below?
You can draw any shapes you would like.
17
June 26, 2009
9. Can you add these together? How much do you have?
+
=
+
10. Can you subtract 8 cubes? How many are left?
=
_
You're Done!
Thank you for your hard work!
18
June 26, 2009
Name_______________
Date:________
What Do You Know?
(Grade 4-5)
1. Can you show me three ways to make ½?
2. Solve the following problem:
½ + ¾ + 1 =
3. Can you show me a fact family triangle
using multiplication, division, or fractions?
4. Can you draw a picture of a fraction that is equal to .75?
19
June 26, 2009
5. Can you tell me the rule that should go in the box?
in
Rule
out
in
out
7
84
12
144
2
24
10
120
5
60
0
0
6. Can you answer this story question?
Miss Anderson wanted to make some cookies for her students for their first day of
school. Yesterday she made 4 batches of cookies. Each batch has 28 cookies. She then
wanted to divide up these batches for each of her small classes. She has 14 classes.
How many cookies does each class get? Show your work.
7. Can you fill in the blanks on these change number stories?
Change
Start
End
72
9
20
June 26, 2009
Change
Start
End
240
480
8. Can you answer this story question?
In Florida today, the temperature is 99 degrees.
In Minnesota, the temperature is 62 degrees.
What is the difference?
Quantity
Answer:________________
Can you fill out the table
using the numbers
from the story?
Quantity
Difference
9. Can you multiply these together? How much do you have?
X
x
=
21
June 26, 2009
10. Can you solve this division problem?
Answer:
You're Done!
Thank you for your hard work!
22
June 26, 2009
MCA Sample Question
23
June 26, 2009
Fact Family Triangle
+, +
+
-
=
=
=
=
24
6
6
__
+,6
6
13
+,__
__
14
+,7
__
15
+,7
25
8
8
17
+,__
__
18
+,9
___+___=___ ___+___=___ ___+___=___
___+___=___
___-___=___ ___-___=___ ___-___=___
___-___=___
8
__
+,-
__
___+___=___
___+___=___
___-___=___
___-___=___
9
19
+,-
__
___+___=___
___+___=___
___-___=___
___-___=___
9
20
+,-
___+___=___ ___+___=___ ___+___=___ ___+___=___ ___+___=___
___+___=___
___+___=___
___+___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
5
__
+,-
June 26, 2009
0
1
__
+,1
1
3
+,__
2
4
+,2
__
5
+,3
26
3
3
7
+,__
__
8
+,4
___+___=___ ___+___=___ ___+___=___
___+___=___
___-___=___ ___-___=___ ___-___=___
___-___=___
3
__
+,-
__
___+___=___
___+___=___
___-___=___
___-___=___
4
9
+,-
__
___+___=___
___+___=___
___-___=___
___-___=___
9
10
+,-
___+___=___ ___+___=___ ___+___=___ ___+___=___ ___+___=___
___+___=___
___+___=___
___+___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
___-___=___
1
__
+,-
June 26, 2009
27
8
5
3
1
16
+,-
11
+,-
6
+,-
1
+,-
8
6
3
0
8
6
3
1
17
+,-
12
+,-
7
+,-
2
+,-
3
6
4
1
9
6
4
1
18
+,-
13
+,-
8
+,-
3
+,-
9
7
4
2
9
7
4
2
19
+,-
14
+,-
9
+,-
4
+,-
10
7
5
2
9
8
9
2
20
+,-
15
+,-
10
+,-
5
+,-
11
7
1
3
June 26, 2009
June 26, 2009
Day 3
Introduction to What's My Rule?
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will complete an MCA sample question based on the What's My Rule
concept.
The students will develop an understanding of What's My Rule as measured by oral
responses through group and guided discussion and participation.
The students will be creating What's My Rule examples with a partner as measured by
written assessments.
Materials:




Visualizer to display MCA Sample question
MCA Sample Question
Dry Erase Markers
What's My Rule Partner Activity Sheet
Procedure:
Launch (4 min.):
The students will first come to class and see a sample MCA question displayed on the
white board through the use of a visualizer. The sample question is as followed:
28
June 26, 2009
29
June 26, 2009
The teacher will then ask, “How can we solve this problem? What is it asking us to do?”
(Possible student responses: We need to figure out a pattern? We need to know the next
number? We need a rule? etc.) “Let's come up with a way to solve the problem together. We
have been working with fact families and about finding the sum through addition and the
difference through subtraction. Do we need to add or subtract here?” (Goal Answer: Subtract)
What is the difference between each of the numbers. What is the difference between 1 and 4,
between 4 and 7, between 7 and 10?” (Answer: Three.) So, if three is our difference, then we
know our next number will need to be three more than the last number. What number is three
more than 10?” (Answer: 13) “Exactly, we've found our rule to the pattern. We've discovered
that each time the number gets bigger by three so our rule is +3. Excellent!” Through volunteer
sticks, one student will be selected to write the answer on the line. As one student is writing
the answer, another student will be drawing the 13 dots in the box, and a third volunteer will be
writing the rule on the lines at the bottom of the page.
Explore (10min.):
The teacher will then say, “You have been such wonderful detectives so far in finding out
the rule in a number story. Can you find the rule to the problem below? It's not a story, it is
called an in-and-out box. This means that a certain number goes in, changes inside the box due
to a certain rule, and comes out as a different number. Here is a list of numbers that went in
the box, and how they changed after coming out of the number box. What is my rule?” The
students and teacher will then discuss the strategies they could use to figure out the rule in the
box (Possible student responses: counting up from the original number to the new number to find
the difference, subtracting the old number from the new number, etc.). “So, now that we have
worked together, what is the rule that should go in this box?” (Possible student responses: Add
5) “Wonderful! So we need to write +5 in the rule box.” Through volunteer sticks one student
will write the rule +5 in the box.
(Here is an example of the rule that the teacher will place on the visualizer
in
for the students to see.)
Rule
out
30
in
out
5
10
12
17
26
31
55
60
June 26, 2009
Then, the teacher will say, “Now that we have a better understanding about in-and-out
boxes, being wonderful detectives and finding out the missing rule and using addition and
subtraction skills to find out what the rule in the box should be, I am going to have you work
with your partner and solve these missing rule boxes. Remember to try your best and use your
number detective skills that we have just talked about. Good luck!” The format of these in and
out rule boxes will be almost identical to the problem located on page 22. The teacher will be
walking around to provide guidance, modeling, and to answer any questions the students may
have.
What's My Rule Lesson's Materials
1.
2.
3.
4.
5.
6.
7.
MCA Sample Question (page 29)
What's My Rule Partner Activity Sheet for Day 3 (page 35, 36)
What's My Rule In-and-Out Box Icon for Larger Box (page 37)
What's My Rule In-and-Out box Icon for Smaller Boxes (page 38)
What's My Rule Partner Activity Sheet for Day 4 (page 39, 40, 41)
Post-Assessment on Fact Families and What's My Rule (page 42, 43, 44)
Lesson Adaptations (page 34)
31
June 26, 2009
Day 4
Continuing with What's My Rule?
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:




The students will further explore the concept of “what's my rule” by working with hand
made function boxes and demonstrating the different rules with a partner.
The students will be practicing the relationship between addition and subtraction by using
different math number rules of their choice and ability level.
The students will be assessing the reasonableness of their results by discussing, as a
class and with their partners, how the different number rules work and how to check to
make sure they are correct in their answers.
The students will use their prior knowledge when using a calculator in terms of how to
find the next number in a series of addition and subtraction problems (using the equals
sign to find the next number that follows the number rule involved).
Materials:








Larger Cardboard Box (without a lid)
Smaller Empty Puff Kleenex Boxes (four a group of eight you will need four boxes)
Small Counters (color does not matter but they need to be small enough to easily get in
and out of the box)
In-and-Out Box Icon (to tape on the large box)
In-and-Out Box Icon (to tape on the smaller Kleenex boxes)
In-and-Out Partner Activity Sheet
Pencils
Calculators for the Students Use
32
June 26, 2009
Procedure:
Continued Exploration (14 min.):
The students will first come to class and see a medium-sized cardboard box with a
picture of a blank in and out box taped to the side of it. The teacher will then begin by saying,
“Do you remember how we worked with in and out boxes yesterday and became detectives to try
and figure out what the pattern and rule was for each box? Well, today I have my own in and
out box with counters in it. I am going to be pulling a certain number of counters in the box and
a certain number of counters out of the box. I would like you to count with me.” The teacher
will then work with putting the following counters in and out of of the box: put three in and take
six out, put four counters in and take eight out, place five counters into the box and take ten
out, etc.) “Does anyone have an idea of what rule I am thinking of in my head? (Possible student
responses: the rule is double, twice as much, your taking out the same number you put in and
adding more of the same number, etc.) The teacher will then try this two more times with the
group using the following rules: +4, and -2. The teacher will then split the group into pairs and
give each group an empty Kleenex box filled with counters. A smaller version of the in and out
box is taped to the side of each box. Each student will also receive an activity sheet and a
calculator so that they can record the different rules they make as a group. The purpose of
using the calculator is to use the equal button to find out what the next series of numbers. This
concept should be previously taught before this in and out box activity and will fall under prior
knowledge. The teacher will be walking around for guidance.
Share (3 min):
“What did we learn about What's My Rule and number rules? How did we solve them?”
(Possible student responses: We worked on an MCA math problem, we worked with in and out
boxes, we worked with a partner to figure out the problems and solve the answers, played with
an actual in and out box, etc.) “Who can give me an example of one way you solved a What's My
Rule math problem?” (Possible student responses: I counted up from 4 to 8 and saw a pattern
so I new the rule was to double, I was able to use a calculator to find the next number, I was
able to see a pattern so it helped me fill in the missing numbers on one of the in and out boxes,
etc.)
Summarize (3 min.):
The teacher will focus the group's attention and ask, “So, what was one main idea or big
picture we've learned about over the last two days?” (Goal response: What's My Rule?).
Students responses may very but the goal of their responses is to see whether or not they truly
understand the concept of what's my rule and if they would be able to recognize and solve these
types of problems in the future. “So not only did we learn about What's My Rule, but we
actually played with in and out boxes, worked with a partner to be detectives and solve the
missing number rules, worked as a group to figure out patterns, practiced our addition and
33
June 26, 2009
subtraction skills, and we got to work with a partner and show the many different ways we can
learn and solve math rule problems. What wonderful ideas! You are all becoming great math
detectives!” If time allows, they can come up with additional rules using the in and out math box
manipulatives.
What's My Rule? Lesson Adaptations for K, 1, 2, 4, 5
K


1


In order to make this lesson developmentally appropriate for kindergarten
students, and to meet the requirements of the suggested Minnesota standard,
simply use the basic addition and subtraction equations using numbers 1-10 for the
What's My Rule activities.
Using pictures instead of dots would be another alternative when using an example
of the MCA math sample question.
In order to make this lesson developmentally appropriate for first grade students,
and to meet the requirements of the suggested Minnesota standard, simply use the
basic addition and subtraction equations using numbers 1-15 for the What's My
Rule activities.
Using pictures instead of dots would be another alternative when using an example
of the MCA math sample question.
2

These two days of lessons are completely appropriate for students to work on in
Second Grade and meet the Minnesota standard selected.
4

In order to make this lesson developmentally appropriate for fourth grade
students, and to meet the requirements of the suggested Minnesota standard,
simply change the What's My Rule activities to rules that follow the addition and
subtraction of decimals, fractions, and multiplication.
Also, the sample MCA questions should be changed to focus more on a higher level
of thinking involving fraction rule equations.

5


In order to make this lesson developmentally appropriate for fifth grade students,
and to meet the needs of the suggested Minnesota standard, What's My Rule
activities should follow and focus on multiplication, arithmetic, and estimation
equations.
Also, the sample MCA question should be changed to focus more on a higher level
of thinking involving a division and estimation rule equation.
34
June 26, 2009
Names:__________________
__________________
in
Date: ____________
What's My Rule?
1.
Rule
out
in
out
6
2
10
6
4
0
15
11
9
5
22
18
in
out
15
23
7
15
3
11
9
17
8
16
30
38
in
2.
Rule
out
35
June 26, 2009
3.
in
Fill in the missing numbers.
Rule
in
out
4
2
22
20
32
5
1
50
out
4. Make up your own rule with your partner.
in
Rule
in
out
36
out
in
Rule
out
June 26, 2009
37
June 26, 2009
in
Rule
out
in
Rule
out
38
June 26, 2009
Names:__________________
__________________
in
Date: ____________
What's My Rule?
1.
Rule
in
out
in
out
out
in
2.
Rule
out
39
June 26, 2009
What's My Rule?
in
3.
Rule
in
out
in
out
out
in
4.
Rule
out
40
June 26, 2009
What's My Rule?
in
5.
Rule
in
out
in
out
out
in
6.
Rule
out
41
June 26, 2009
Day 5
Post-Assessment on Fact Families and What's My Rule?
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:




The students will be using prior knowledge of fact families as measured by their
responses while playing Fact Family Top-It.
The students will be using their prior knowledge of fact families as measured by their
responses while quizzing each other on their fact family triangles.
The students will be using their prior knowledge of “what's my rule” as measured by their
responses while taking turns creating rules using the in and out box manipulatives.
The students will be using their prior knowledge of What's My Rule by completing a
written assessment where they will record the different rules they create while working
with a partner.
Materials:






Fact Family House Accordion Cards (the students worked on these already)
Fact Family Top-It Cards (these have already been cut out, extras are on page 27)
In-and-Out Kleenex Boxes (these are already made, extras are on pages 37, 38)
In-and-Out Partner Activity Sheets (pages 39, 40, 41)
Pencils
Post-Assessment Checklist (page 44)
Procedure:
1. The students will be working at three learning stations (A station that focuses on Fact
Family Top-It, a station that focuses on “what's my rule” and creating new rules using the
in-and-out box manipulatives, and a station that focuses on quizzing each other on the
fact family triangles). They will be rotating among these three stations approximately
42
June 26, 2009
every six minutes. This way every group has a chance to explore every station. With
there being 6-8 students at a time, there will be approximately 2-3 students in each
group.
2. While the students are working at the different learning stations, the teacher will be
walking around with a checklist to informally and formally assess the students on their
comprehension of fact families and number rules. This form of assessment takes about 5
minutes to complete for each student.
43
June 26, 2009
Name of Student
Date:
Classroom Teacher
Assessment Questions
Regarding Fact Families
and “What's My Rule”
Grade Level:
Mastery Level
Yes, fully
mastered!
Understands the
majority of this
concept.
1. Is the student able to use
the fact family houses
correctly?
2. Is the student able to
name examples of different
fact family equations?
3. Is the student able to help
others solve fact family
equations?
4. Can the student provide
reasoning in how to solve
different fact family
equations?
5. Does the child use
different strategies to solve
fact family equations?
6. Is the student able to
work with a partner to come
up with different number
rule examples?
7. Is the student able to
provide reasoning on how to
solve those different number
rule examples?
8. Does the child use
different strategies to solve
“what's my rule” equations?
9. Would the student be able
to explain the concept of
fact families to another
person?
10. Would the student be
able to explain the concept
of “what's my rule” to
another person?
44
Additional
Comments
Needs Additional
Help and Guidance
Provide Example:
June 26, 2009
Day 6
Introduction to Parts and Total
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will complete an MCA sample question based on the concept of Parts and
Total number stories.
The students will be working with pictures, and manipulatives when learning about the
concept of Parts and Total number stories.
The students will be completing a written assessment in order to show their
comprehension of how to locate the parts and total in number stories.
Materials:







MCA sample question
Visualizer to display the MCA sample question
Dry erase markers
Dice (at least 8: four groups of two, or six: three groups of two)
Part and Total blank template for the visualizer
Part and Total blank student activity sheet
Pencils
Procedure:
Launch (3 min.):
The students will first come to class and see a sample MCA question displayed on the
white board through the use of a visualizer. The sample question is as followed:
45
June 26, 2009
46
June 26, 2009
The teacher will then ask, “How can we solve this problem? What is it asking us to do?”
(Possible student responses: We need to look at the graph and see how many lemonades they
sold on Sunday, we need to add up the number of lemonades they sold, etc.) “Let's come up with
a way to solve the problem together. We have been working with fact families and number rules
to find out the sum through addition and the difference through subtraction. Do we need to add
or subtract here?” (Goal Answer: Add) “What do we need to add? How do you know?” (Goal
Answer: we need to add up the number of lemonades sold on Sunday in order to answer the
question) “What would my answer be?” (Goal: Twenty-Five) “Exactly, great detective work!”
Explore (11 min.)
Then teacher will then say, “Tell me, what would we need to do if the question had said
“How many glasses of lemonade did they sell in all?” (Possible student responses: you would need
to add all the numbers up, I don't know, you could count the number of lemonades there are,
etc.) “Let's think of it this way, are there three parts in this number story?” (Answer: Yes)
Through volunteer sticks, one students will read the question while another student circles the
days to show the different number parts that need to be added together. “Let's think of
another way to organize the information in the number problem so that it is easier to see what
our parts are that we need to add to come up with our total, our answer. The teacher puts the
following Parts and Total graphic organizer on the visualizer to display it on the white board:
Total
Part
Part
Part
“What are our three parts to this story?” (Possible student responses: the number of lemonades
they sold on Friday, Saturday, and Sunday). “Let's fill in this table together. How many
lemonades did they sell of Friday? (Fifteen) On Saturday? (Thirty) On Sunday? (Twenty-Five)
Very good! Now, that we know our three parts to the story, and we know that we need to add
these three parts to find our total number of lemonades sold, what number should I write in the
total box? (Seventy) Excellent work, detectives!”
“Now the we have a better understanding of how different parts of a problem can give us
a total, you will be working with partners to play with dice to make your own number story. Don't
worry about spelling, just try your best. You and your partner are going to each roll to dice, you
are going to write each of the numbers you roll into the parts portion of the part and total table.
You are then going to add the two numbers and find out your total. After you have filled in the
47
June 26, 2009
table you are going to write short number stories using the numbers you came up with when you
rolled your dice and added the numbers together.” The teacher will provide an example up on
the visualizer that will stay displayed for the remainder of the lesson for the students to use as
a guide. If the students finish early, they can practice taking turns rolling the dice and adding
up the two numbers they roll.
Share (3 min.):
While the students are working on the Parts and Total dice activity, the teacher will be
asking questions to inspire a mathematical discussion. These questions will be based on having
the students share different ideas on how they are use their detective skills to solve to find the
missing numbers on each of the fact family triangles. “How are you coming up with the different
answers for the parts and total?” (Possible student responses: I am using my fact family houses
for hints, I am counting the dots on the dice, I knew that 6 plus 2 makes 8 and the number 3 is
only one more, etc.) By having the students share their ideas, it will give others new ways to
solve and comprehend different parts-and-total equations. The teacher will also be asking the
students for different ways they can use these parts-and-total problems in the future.
Summarize (3 min.):
Towards the end of class, the teacher will get the group's attention and ask, “So, what
did we learn about or try today?” Based on the students' responses, the teacher will be able to
conclude whether or not the students truly comprehended today's activities. “So, not only did
we learn how about parts and totals, but we were able to try an activity with dice to make our
own parts and total math problems. You worked very hard! Bravo, detectives!”
48
June 26, 2009
Day 7
Continuing with Parts and Total
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will be using their prior knowledge of Parts and Total by completing a Candy
Shop Activity Sheet
The students will expand upon their mathematical vocabulary through group discussion
during the summary portion of this lesson.
The students will be working with partners to check their answers as they work on
strengthening their addition, subtraction, fact family, and number rule skills.
Materials:




Sweet Shop Items Activity Sheet
Parts and Total Tables Student Activity Sheet
Dice
Pencils
Procedure:
Launch: (4 min.):
The students will first come to class and be given an activity packet with a picture of a
candy shop and all of it's items. The teacher will then begin by saying, “Do you remember how
we worked with parts and totals yesterday and became detectives to try and figure out how to
find the different parts in the number stories? How did we find those parts of the story?
What detective skills did we use?”
49
June 26, 2009
Explore: (10 min.):
“Well, today we are going to pretend you are going to this candy shop. There are a few
number model stories that I would like you to find the parts and total of, the rest of the stories
are your own. Pretend you have as much money as you want to buy some of the items from this
candy shop. At the end, you will talk with your partner about what you bought, and how your
organized your number stories. I will be walking around and helping however I can. Please let me
know if you have any questions.” The teacher will be available for guidance and assistance. The
students are allowed to help each other in their groups decide what they want to buy, how to
organize their number stories, how to identify the parts of the number story and total, etc.
Share (3 min.):
While the students are working on the candy shop activity, the teacher will be asking
questions to inspire a mathematical discussion. These questions will be based on having the
students share different ideas on how they are use their detective skills to create and solve
Parts and Total equations. “What did we learn about parts and total? How did we solve them?”
(Possible student responses: We worked on an MCA math problem and figured out the parts, we
worked with dice and created parts and total math problems from the numbers we rolled, we
worked on candy shop number stories, we made our own number stories, etc.) “Who can give me
an example of one way you solved a parts and total number story?” (Possible student response
example: I spent eight dollars on licorice, and two dollars on cotton candy which are my two
parts. So, I added my parts together and my total for sweets was 10 dollars.) The teacher will
also be asking the students for different ways they can use these parts-and-total problems in
the future.
Summarizing (3 min.):
The teacher will then get the group's attention and ask, “So, what was one main idea or
big picture we've learned about over the last two days?” (Goal response: Parts and Total).
Based on the students' responses, the teacher will be able to conclude whether or not the
students truly comprehended today's activities. “Not only did we learn about Parts and Total
number stories, but we actually played with dice to make our number stories, explored a candy
shop to find out the parts and total, discussed different ways to solve these number stories,
practiced our addition and subtraction skills, and we got to work with a partner and show the
many different ways we can learn and solve parts and total number stories. I can see how hard
you all have worked at become math detectives! You should be proud!” If time allows, the
students can practice taking turns rolling the dice and adding up the two numbers they roll.
50
June 26, 2009
Parts and Total Number Stories Lesson's Materials
1.
2.
3.
4.
5.
6.
MCA Sample Question (page 46)
Parts and Total blank template for visualizer (page 53)
Parts and Total student activity sheet with dice (pages 53, 54)
Sweet Shop Items Activity Sheet (pages 55, 56)
Sweet Shop Parts and Total Student Activity Sheet (pages 57, 58 )
Lesson Adaptations (page 52)
51
June 26, 2009
Parts and Total Lesson Adaptations for K, 1, 2, 4, 5
K




1




In order to make this lesson developmentally appropriate for kindergarten students, and to meet the
requirements of the suggested Minnesota standard, have the students create parts and total
equations with the numbers 1-12.
Change the MCA questions so that instead of one glass of lemonade representing five glasses of
lemonade, have each glass of lemonade just represent one glass.
Using pictures to represent the parts and total equations equations instead of having them write
lengthy number stories is another way to help the students can visually solve the different math
equations.
For the Candy Shop activity, have each candy be worth anything from 1-10 dollars. Have the students
circle the candies they want to buy. Multiple copies of this shop will need to be made. They can then
add the dollar amounts together to show how much money they spent at the candy shop.
In order to make this lesson developmentally appropriate for first grade students, and to meet the
requirements of the suggested Minnesota standard, have the students create parts and total
equations using addition skills with the numbers 1-12.
Change the MCA questions so that instead of one glass of lemonade representing five glasses of
lemonade, have each glass of lemonade just represent one glass.
Using pictures to represent the parts and total equations equations instead of having them write
lengthy number stories is another way to help the students can visually solve the different math
equations.
For the Candy Shop activity, have each candy be worth anything from 1-10 dollars. Have the students
circle the candies they want to buy. Multiple copies of this shop will need to be made. They can then
add the dollar amounts together to show how much money they spent at the candy shop.
2

These two days of lessons are completely appropriate for students to work on in Second Grade and
meet the Minnesota standard selected.
4

In order to make this lesson developmentally appropriate for fourth grade students, and to meet the
requirements of the suggested Minnesota standard, simply change the dice Parts and Total activity
so that each student rolls twice. With each roll they will be rolling the two dice and multiplying the
two numbers together so that each product is a part of the equation. Then have the students add
the two products together to make a total.
Also, the sample MCA question should be changed to focus more on a higher level of thinking involving
a fraction equation where the fact family triangles can be used. So, instead of each glass
representing five glasses of lemonade, have each glass be worth 5 ½ glasses .
Pick a different shopping activity sheet than a candy shop so that the students are challenged at
their level. Have them pick items from a catalog, magazine, or menu they enjoy. There is a menu
located at the end of the “partial sums” lesson in this unit plan.


5



In order to make this lesson developmentally appropriate for fifth grade students, and to meet the
requirements of the suggested Minnesota standard, simply change the dice Parts and Total activity
so that each student rolls twice. With each roll they will be rolling the two dice and multiplying the
two numbers together so that each product was one part of the equation. Then have the students
add the two products together to make a total.
Also, the sample MCA questions should be changed to focus more on a higher level of thinking
involving a division equation using multi-digit numbers where the fact family triangles can be used.
Pick a different shopping activity sheet than a candy shop so that the students are challenged at
their level. Have them pick items from a catalog or magazine they enjoy.
52
Part
Part
Total
Part
June 26, 2009
53
June 26, 2009
Name:__________________
Date:___________
Parts and Total with Dice
1.
Number Story
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
Total
Part
Part
2.
Number Story
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
Total
Part
Part
54
June 26, 2009
3.
Number Story
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
Total
Part
Part
5.
Number Story
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
Total
Part
Part
6.
Number Story
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
Total
Part
Part
55
June 26, 2009
Let's see what we can buy inside!
56
June 26, 2009
Here, each
candy is 5
dollars.
The box of
chocolates
is 8 dollars.
Each candy
is 3
dollars.
The gum is
1 dollar a
piece.
Here, each
candy is 3
dollars. The
candy house
is 35 dollars.
Here, each
candy is 2
dollars.
57
June 26, 2009
Name:__________________
Date:___________
Parts and Total with Candy
1.
Number Story
Total
Part
How much would one candy
house and one box of
chocolates cost?
Part
2.
Number Story
Total
Part
How much would one piece
of gum and one candy cane
cost?
Part
58
June 26, 2009
3.
Number Story
Total
Part
How much would one of the
$3 chocolates, and one of
the $2 dollar chocolates
cost?
Part
5.
Your Own Number Story
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
Total
Part
Part
6.
Your Own Number Story
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
_____________________
Total
Part
Part
59
June 26, 2009
Day 8
Introduction to Changing Number Stories
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will complete an MCA sample question based on the concept of Change
Number Stories.
The students will be completing a written assessment which shows their comprehension of
today's lesson on Change Number Stories.
The students will be practicing their addition and subtraction skills by using real-world
mathematical problems when working with Change Number Stories.
Materials:





MCA Sample Question
Visualizer
Number Change Blank Graphic Organizer
Miss Anderson's Rose Story
Everyday math Student Worksheet page 40
Procedure:
Launch (4 min.):
The students will first come to class and see a sample MCA question displayed on the
white board through the use of a visualizer. The sample question is as followed:
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June 26, 2009
61
June 26, 2009
The teacher will then ask, “How can we solve this problem? What is it asking us to do?”
(Possible student responses: We need to find the missing number that will give us 8, we need to
find out what we can take away from 17 that will give us 8, we need to find out how much Lin
needs, etc.) “Let's come up with a way to solve the problem together. We have been working
with fact families, number rules, sum which means to add, and difference when means to
subtract. Do we need to add or subtract here?” (Goal Answer: Subtract) “What do we need to
subtract? How do you know?” (Goal Answer: we need to subtract a number from 17 to get 8
because it gives us that clue in the directions and number story) “What would my answer be?”
(Goal: Nine). “Exactly, great work detectives!”
Explore (10 min.):
Then the teacher will say, “Tell me, is there another way we could have organized the
parts in this same math problem? What is changing in this math problem? In other words, what
happens to the number 17 so that it changes into 8?” (Possible Student responses: 9 is taken
away from 17, etc.) “Could our fact families fit in here somewhere? How?” (Goal Answer: We
can use our fact family accordions to solve this answer, because it's important to know our fact
families when figuring out the different math problems, it's the same numbers just put in a
different way.) “Exactly. This is exactly what we are going to be focusing on today: finding out
the changes in different math problems. Let me show you another way we could have organized
this math problem.”
(The teacher puts the following Number Change graphic organizer on the visualizer to
display it on the white board.)
Change
Start
17
End
(-9)
?
8
The teacher says, “As you can see, it's the same numbers and the same information, but
we organized the numbers in a way to show the change that makes 17 end as an 8, which is why
we put a question mark in the middle space because that is the number we are trying to find.
Once we find that number we are going to put it on top of the question mark to remind us what
the number change needed to be. So, if we start with 17 and our change is to take away 9, then
we end up with 8. Who can tell me what is missing from this change number story?”
The teacher then puts the following story and graphic organizer up on the visualizer to
display it on the white board (the students and teacher will work together to fill in the
missing information so that, in the end, the story and and change number boxes look like
the following):
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June 26, 2009
Miss Anderson bought flowers to put in her vase. She bought 6 yellow roses and a certain
number of pink roses. She ended up with 20 roses. How many pink roses did she buy?
Start
6
(+14)
?
End
20
Answer: Miss Anderson bought 14 pink roses.
“Now that you have a better understanding of how to complete change number stories,
and since you already know how to locate the parts and total in number stories, I am going to
have you work on a change number activity sheet with your partner. Remember to read the
stories carefully so that you know where the right numbers go.” The teacher will pass out a
Student Journal activity sheet (page 40) from out of the Everyday Math Series. The teacher
will also walk around and provide guidance, role modeling, and assistance.
Share (3 min.):
While the teacher and students are working on the Student Journal activity sheet, the
teacher will be asking the students to share how the different change number stories could be
solved. “How many parts are there in the number change stories? How do you know? How are
you coming up with the different answers for the number change?” (Possible student responses:
I am reading the stories and finding the numbers I need to use in my number change problems, I
am using my fact family folding book, I already knew it, I was able to find out the answer by
subtracting/adding, etc.) By having the students share their ideas, it will give others new ways
to solve and comprehend different change number stories.
Summarize (3 min.):
Towards the end of class, the teacher will get the group's attention and ask, “So, what
did we learn about or try today?” Based on the students' responses, the teacher will be able to
conclude whether or not the students truly comprehended today's activities. “Not only did we
learn how about change number stories, but how we can use our fact family knowledge to solve
them, and how to locate the different parts in a change number story in order to find the
correct answer. Wow! Great detective work! I'm impressed!”
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June 26, 2009
Day 9
Continuing with Changing Number Stories
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will be using their prior knowledge of Change Number Stories by playing a
dice game that focuses on this concept.
The students will expand upon their mathematical vocabulary through group discussion
during the summary portion of this lesson.
The students will be working with partners to check their answers as they work on
strengthening their addition, subtraction, and change number stories.
Materials:



Dice (at least 8: four groups of two, or six: three groups of two)
Change Number Stories Blank Template for Students
Pencils
Procedure:
Continued Exploration (14 min.):
The students will first come to class and be placed into groups of two before being given
a blank Change Number activity packet. Each group will also receive two dice. The teacher will
place these materials at the end of each table so it is out of the way of the students' hands
while the teacher is talking. The teacher will then begin by saying, “Do you remember how we
worked with Change Number stories yesterday and became detectives to try and figure out how
to find the changing part of each number story as well as the different parts in the number
stories? Well, today you get to decide how your change number stories will go. You will take
turns with your partner rolling two dice. You will then fill in two out of the three Change
Number sections in the story. Then, through what we've learned over the last two days, you
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June 26, 2009
need to find out how to solve the last missing number.”
The teacher will provide the following example:
Change
Start
2
(+3)
?
End
5
“You will be working with partners. Feel free to help each other.” The teacher will be
walking around to provide guidance, assistance, and role modeling.
Share (3 min.):
“What did we learn about Change Number Stories? How did we solve them?” (Possible
student responses: We worked on an MCA math problem and figured out the parts and the
change, we worked with dice and created our own change number stories, we worked on finding
out the missing numbers in the change number stories, we worked as a group and in partners with
math change number problems, etc.) “Who can give me an example of one way you solved a
change number story?” (Possible student response example: I used addition to figure out the
missing number, I used subtraction to figure out a missing number, I remember this answer from
another problem and was able to figure out the problem that way, etc.)
Summarize (3 min.):
The teacher will then get the group's attention and ask, “So, what was one main idea or
big picture we've learned about over the last two days?” (Goal response: Change Number
Stories). Based on the students' responses, the teacher will be able to conclude whether or
not the students truly comprehended today's activities. “So, your telling me that we learned
about Change Number stories, we used addition and subtraction, we tried and solved different
types of Change Number stories, and we played a game to help us better understand Change
Number stories. Wow! Way to use your math detective skills!” If time allows, the students can
continue playing the dice number change game.
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June 26, 2009
Change Number Stories Lesson's Materials
1.
2.
3.
4.
5.
6.
MCA Sample Question (page 61)
Number Change Blank Graphic Organizer (page 67)
Miss Anderson's Rose Story (page 68)
Everyday Math Student Worksheet page 40 (page 71)
Change Number Stories Blank Template for Students (pages 69, 70)
Lesson Adaptations (page 66)
Parts and Total Lesson Adaptations for K, 1, 2, 4, 5
K



1



In order to make this lesson developmentally appropriate for Kindergarten students, and to meet the
needs of the suggested Minnesota standard, have the students create changing number equations
with the numbers 1-12.
When working on the MCA question have the students make circles that they can cross out to find
out the difference.
Using pictures to represent the changing number equations equations instead of having them write
lengthy number stories is another way to help the students can visually solve the different math
equations.
In order to make this lesson developmentally appropriate for first grade students, and to meet the
needs of the suggested Minnesota standard, have the students create changing number equations
with the numbers 1-12.
When working on the MCA question have the students make tally marks that they can cross out to
find out the difference.
Using pictures to represent the changing number equations equations instead of having them write
lengthy number stories is another way to help the students can visually solve the different math
equations.
2

These two days of lessons are completely appropriate for students to work on in Second Grade and
meet the Minnesota standard selected.
4

In order to make this lesson developmentally appropriate for fourth grade students, and to meet the
needs of the suggested Minnesota standard, simply change the dice Changing Number activity so that
each student rolls twice. With each roll they will be rolling the two dice and multiplying the two
numbers together so that each product was one part of the equation. Then have the students add
the two products together to make a total. They can either do products or use the two number to
make two, two-digit numbers..
Also, the sample MCA questions should be changed to focus more on a higher level of thinking
involving a fraction equation, addition/subtraction with two and three digit numbers, or multiplication.

5


In order to make this lesson developmentally appropriate for fifth grade students, and to meet the
needs of the suggested Minnesota standard, simply change the dice Changing Number activity so that
each student rolls twice. With each roll they will be rolling the two dice and multiplying the two
numbers together so that each product was one part of the equation. Then have the students add
the two products together to make a total. Division could be easily integrated into this dice activity
as well.
Also, the sample MCA questions should be changed to focus more on a higher level of thinking
involving a division equation using multi-digit numbers where the fact family triangles can be used.
66
Change
Change Number Model
June 26, 2009
67
June 26, 2009
Change Number Story
Miss Anderson bought flowers to put in her vase.
She bought 6 yellow roses and a certain number of pink roses.
She ended up with 20 roses. How many pink roses did she buy?
Change
Start
End
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June 26, 2009
Name___________________
Date:____________
Change
1.
Start
End
Change
2.
Start
3.
End
Change
End
Start
4.
Change
Start
End
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June 26, 2009
5.
Start
Change
End
Change
6.
End
Start
Change
7.
End
Start
Change
8.
End
Start
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June 26, 2009
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June 26, 2009
Day 10
Post-Assessment on Parts/Total and Changing Number Stories
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:




The students will be using prior knowledge of Parts and Totals as measured by their
responses while playing with dice to creating new number stories.
The students will be using their prior knowledge of Change Number stories while working
with dice to create new Change Number problems and and solve for the missing numbers.
The students will be using their prior knowledge on Parts and Totals and Change Number
stories by creating and illustrating their own number story.
The students will be assessed through an informal assessment on the concepts of
Parts/Total and Change Number stories.
Materials:






Parts and Total Student Activity Sheets (pages 54, 55)
Parts and Total Candy Shop (pages 56-58) (Have both parts and total activity sheets be
at the same station so the students can choose which version they want to play.)
Number Change Student Activity Sheet (pages 69, 70)
Blank Number Story Activity Sheet (page 74)
Pencils
Post-Assessment Checklist (page 75)
Procedure:
1. The students will be working at three learning stations. (One station will be focusing on
Parts and Total, a second station will be focusing on Number Change stories, and a third
station will be focusing on creating several number stories of their choice complete with
illustration). They will be rotating among these three stations approximately every six
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June 26, 2009
minutes. This way every group has a chance to explore every station. With there being
6-8 students at a time, there will be approximately 2-3 students in each group.
2. While the students are working at the different learning stations, the teacher will be
walking around with a checklist to informally and formally assess the students on their
comprehension of Parts/Total and Change Number stories. This form of assessment
takes about 5 minutes to complete for each student.
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June 26, 2009
Name:_______________________
Date:___________
A Number Story
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
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June 26, 2009
Name of Student
Date:
Classroom Teacher
Assessment Questions
Regarding Parts/Total and
Change Number Stories
Grade Level:
Mastery Level
Yes, fully
mastered!
Understands the Needs Additional
majority of this Help and Guidance
concept.
Provide Example:
1. Is the student able to
complete a parts-and-total math
equation correctly?
2. Is the student able to use the
dice to come up with correct and
different parts-and-total
equations?
3. Is the student able to help
others solve parts-and-total
equations?
4. Can the student provide
reasoning in how to solve
different parts-and-total
equations?
5. Does the child use different
strategies to solve parts-and-total
equations?
6. Is the student able to work
with a partner to come up with
different change number stories?
7. Is the student able to provide
reasoning on how to solve those
different change number stories?
8. Does the child use different
strategies to solve change
number stories?
9. Would the student be able to
explain the concept of parts and
total equations to another
person?
10. Would the student be able to
explain the concept of change
number stories to another
person?
75
Additional
Comments
June 26, 2009
Day 11
Introduction to Number Comparisons
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will be completing a written assessment on comparison number stories with
a partner.
The students will complete an MCA sample question based on comparison number stories.
The students will be practicing their addition and subtraction skills by using real-world
mathematical problems when working with comparison number stories.
Materials:






MCA Sample Question
Visualizer
Dry Erase Markers
Temperature Sample Question
Number Stories Page Continued page 160.
Pencils
Procedure:
Launch (3 min.):
The students will first come to class and see a sample MCA question displayed on the
white board through the use of a visualizer. The sample question is as followed:
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June 26, 2009
The teacher will then ask, “How can we solve this problem? What is it asking us to do?”
(Possible student responses: We need to find the missing number that will give us the right
answer, we need to subtract 466 from 513, we need to find the difference, we need to look at
how these two numbers will give us an answer, etc.) “Let's come up with a way to solve the
problem together. We have been working with fact families, number rules, sum which means to
add, and difference when means to subtract. We have also learned about parts and total
stories, and change number stories. So, let's take what we know and apply it to what we don't.
Do we need to add or subtract here?” (Goal Answer: Subtract) “What do we need to subtract?
How do you know?” (Goal Answer: we need to subtract 466 from 513 to get our answer because
if we were to add the two numbers it would not tell us the number of points the basketball
player needs to make the same number of points as he did last year.) “What would my answer
be?” (Goal: 47). “Perfect! I can tell you are using the skills we have learned over the last two
weeks to solve this math problem. What great detective work!”
Explore (11 min.):
The teacher will then put the following math problem up on the visualizer
so that it is displayed on the white board:
The temperature in Hawaii today is 86 degrees. In Bemidji, the temperature was 67 degrees.
How many more degrees was Hawaii's temperature today than Bemidji's temperature?
After the question has been displayed, the teacher will say “Here is a question I am
wanting to solve. What can we do to find out the answer? (Possible student responses: You can
subtract 67 from 86, I don't know, try adding them, etc.) Is there another way we can organize
the information to make it easier to see what I need to do? I know that, sometimes, the words
'how many more' tells me that I am trying to find a difference. So, I think I am going to create
a subtraction problem where I take away 67 from 86. But, I think I am going to organize it this
way.”
This is what the teacher draws under the word problem already located on the visualizer:
Quantity
86
Quantity
67
?
Difference
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June 26, 2009
“This tells me my two numbers that I am comparing and what I need to find, which is the
difference between the two. So, if I subtract 67 from 86 I will find my difference and if I
show my work I will see that my difference is 19 degrees. So my number model is:
86-67=19
OR
19+67=86
(This shows another fact family.)”
The students will then work as a group with the teacher to complete Student Journal
page 160 on to deepen their comprehension on comparison number stories.
Share (3 min.):
While the teacher and students are working on Student Journal “What did we learn about
Number Comparison Stories? How did we solve them?” (Possible student responses: We worked
on an MCA math problem and figured out the parts and the change, we worked on an activity
sheet that helped us practice the steps in how to solve them, we did a class question together,
we worked as a group to learn about these problems, etc.) “Who can give me an example of at
least one way you solved a number comparison story?” (Possible student response examples: I
used what I knew about fact families to answer the questions, I used addition and subtraction to
figure out the missing number, I listened while we worked on them in class to look for a pattern,
etc.)
Summarize (3 min.):
The teacher will then focus the group's attention and ask, “So, what was one main idea or
big picture we've learned about over the last two days?” (Goal response: Number Comparison
Stories). Based on the students' responses, the teacher will be able to conclude whether or
not the students truly comprehended today's activities. “So, your telling me that we learned
about Number Comparison stories, the steps we need to take to solve them, how to look for the
different parts in the story, and how we can use what we've already learned about fact families
to find the answers. Each day you are all becoming powerful math detectives! Keep up the great
work!”
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June 26, 2009
Day 12
Continuing with Number Comparisons
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will be using their prior knowledge to individually work on a Comparison
Number story activity using M&M's.
The students will be strengthening their basic addition and subtraction skills to help
check each other's M&M's number stories in order to make sure that their comparison
number stories were solved correctly.
The students will expand upon their mathematical vocabulary through group discussion
during the summary portion of this lesson.
Materials:




Individual packets of M&M's
MM Comparison Student Activity Sheet Blank Template
Pencils
Visualizer
Procedure:
Launch:
When the students will first come to class they will have an assigned seat. They will be
working individually today through the guidance of the teacher. The students will see a blank
MM Comparison Activity sheet already displayed on the white board through the use of a
visualizer. The teacher will hand out one activity sheet to each student before he/she begins
the lesson. Then the teacher will start by saying, “Do you remember how we worked with
Comparison Number stories yesterday and became detectives to try and figure out how to find
the two quantities and their difference? What steps did we take? How do you know when
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June 26, 2009
you've found the answer? How could we write and find our difference using the following
numbers? (52 and 17)” The students will discuss how they would put these two answers into a
number comparison chart and how they would find the difference (Answer: The difference is
35.)
Explore (11 min.):
“Today you get to fill in the numbers of your own comparison number stories using
M&M's. Everyone will be working on their own today, because every MM pack is slightly
different. You may have a different number of M&M's than someone else, and they might have a
different number of green M&M's than you. So, it's okay if your numbers are different as long
as your answers match up to your own comparison number stories.” The teacher will then model
how to fill out the activity sheet by using his/her own packet of M&M's to answer a couple of
comparison number stories. Then, the students will be free to try the comparison number
stories on their own. The teacher will be walking around for guidance, number modeling, and
assistance. The students will be allowed to eat their small packet of M&M's once their activity
sheets are complete and corrected by a partner and then the teacher.
Share (3 min.):
“What did we learn about Change Number Stories? How did we solve them?” (Possible
student responses: We worked on an MCA math problem and figured out the parts or quantities
and the difference, we worked on a Home Link activity sheet with Comparison Number stories on
it, we played an MM game that had Comparing Number stories on it, we worked with our partner
to check our answers, we worked as a group, etc.) “Who can give me an example of one way you
solved a comparison number story?” (Possible student response example: By counting my M&M's
and finding the difference, by putting the numbers in the story in the right spot, by remember
what we did on other comparing number stories, by knowing my fact family rules, etc.) By having
the students share their ideas, it will give others new ways to solve and comprehend different
number comparison stories so that they will be prepared if ever they need to solve this type of
problem in the future.
Summarize (3 min.):
The teacher will then get the group's attention and ask, “So, what was one main idea or
big picture we've learned about over the last two days?” (Goal response: Comparison Number
Stories). Based on the students' responses, the teacher will be able to conclude whether or not
the students truly comprehended today's activities. “So, your telling me that we learned about
Comparison Number stories, we used subtraction to solve them, we tried and different types of
Comparison Number stories together, and we played an MM game to help us better understand
Comparison Number stories. Wow! We've worked a lot of Comparison Number stories. I can
tell you were using your detective skills and followed directions very well. Wonderful, job!”
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June 26, 2009
Comparison Number Stories Lesson's Materials
1.
2.
3.
4.
5.
MCA Sample Question (page 77)
Hawaii and Bemidji Comparison Number Story (page 84)
Everyday Math Student Journal page 160 (page 85)
MM Comparison Student Activity Sheet (page 86, 87)
Lesson Adaptations (page 83)
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June 26, 2009
Parts and Total Lesson Adaptations for K, 1, 2, 4, 5
K




1




In order to make this lesson developmentally appropriate for kindergarten students, and to meet the
requirements of the suggested Minnesota standard, have the students create number comparison
equations with the numbers 1-12.
Change the MCA question so that it includes number comparisons with single digit numbers. The MCA
example provided in the third grade would cause the kindergarten students to become too
overwhelmed.
Using pictures to represent the number comparison equations instead of having them write lengthy
number stories is another way to help the students visually solve the different math equations.
Create visuals to work on number comparison models instead of the Everyday Math Student Journal
page. The journal page will be too advanced for them.
For the MM activity, it would be better to create a table where the students can clearly write the
number of M&M's there are for each color or have them draw the total number of M&M's on their
paper. This way their muscle coordination helps them to further understand the difference between
their total number of M&M's and the number of a specific color M&M.
In order to make this lesson developmentally appropriate for first grade students, and to meet the
requirements of the suggested Minnesota standard, have the students create number comparison
equations with the numbers 1-12.
Change the MCA question so that it includes number comparisons with single digit numbers. The MCA
example provided in the third grade would cause the kindergarten students to become too
overwhelmed.
Using pictures to represent the number comparison equations instead of having them write lengthy
number stories is another way to help the students visually solve the different math equations.
Create visuals to work on number comparison models instead of the Everyday Math Student Journal
page. The journal page will be too advanced for them.
For the MM activity, it would be better to create a table where the students can clearly write the
number of M&M's there are for each color or have them draw the total number of M&M's on their
paper. This way their muscle coordination helps them to further understand the difference between
their total number of M&M's and the number of a specific color M&M.
2

These two days of lessons are completely appropriate for students to work on in second grade and
meet the Minnesota standard selected.
4

In order to make this lesson developmentally appropriate for fourth grade students, and to meet the
requirements of the suggested Minnesota standard, simply change the M&M's activity slightly when
working with number comparisons so that after they find the difference, they can also try to find
the percentage, decimal, and fraction of each MM color in comparison to the whole number (total).
Also, the sample MCA question should be changed to focus more on a higher level of thinking involving
a fraction equation where the fact family triangles can be used.

5


In order to make this lesson developmentally appropriate for fifth grade students, and to meet the
requirements of the suggested Minnesota standard, simply change the M&M's activity slightly when
working with number comparisons so that after they find the difference, they can also try to find
out the percentage, decimal, and fraction of each MM color in comparison to the whole number
(total). They will then also show how division plays into finding the MM color percentages.
Also, the sample MCA questions should be changed to focus more on a higher level of thinking
involving a division equation using multi-digit numbers where the fact family triangles can be used.
83
June 26, 2009
Comparison Number Story
The temperature in Hawaii today is 86 degrees.
In Bemidji, the temperature was 67 degrees.
How many more degrees was Hawaii's temperature
today than Bemidji's?
84
June 26, 2009
85
June 26, 2009
Name:____________________
1. In your M&M packet you have a
total of _____ M&M's. Out of your
total number of M&M's, ______
of your M&M's are red. What is the
difference between the number
of red M&M's and your total number
of M&M's?
Date:__________
Quantity
Quantity
Difference
2. In your M&M packet you have
_____ green M&M's. In your M&M
packet you also have _____ brown
M&M's. What is the difference
between the number of green M&M's
and brown M&M's?
Quantity
Quantity
Difference
3. In your M&M packet you have
Quantity
_____ blue M&M's. In your M&M
packet you also have _____ yellow
M&M's. What is the difference
between the number of blue M&M's
and yellow M&M's?
Quantity
Difference
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June 26, 2009
Name:____________________
4. In your M&M packet you have a
total of _____ M&M's. Out of your
total number of M&M's, ______
of your M&M's are orange. What is
the difference between the number
of orange M&M's and your total
number of M&M's?
Date:__________
Quantity
Quantity
Difference
5. In your M&M packet you have
_____ red M&M's. In your M&M
packet you also have _____ green
M&M's. What is the difference
between the number of red M&M's
and green M&M's?
Quantity
Quantity
Difference
6. In your M&M packet you have
Quantity
_____ blue M&M's. In your M&M
packet you also have _____ orange
M&M's. What is the difference
between the number of blue M&M's
and orange M&M's?
Quantity
Difference
87
June 26, 2009
Day 13
Introduction to Partial-Sums Algorithms
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will be completing a written assessment on partial-sums algorithms as a
small group.
The students will complete a math discussion question based on the concept of partialsums algorithms.
The students will be practicing their addition and subtraction skills by using real-world
mathematical problems when working with partial-sums algorithms.
Materials:




Math Addition Question/Partial-Sums Algorithm to be displayed on the white board
Visualizer
Dry Erase markers
Partial-Sums Group Activity Sheet
Procedure:
Launch (4 min.):
The students will first come to class and see a math question displayed on the white
board through the use of a visualizer. The sample question is as followed:
456
+ 232
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June 26, 2009
The teacher will then ask, “How can we solve this problem? What are the steps we should
take when adding these two numbers together?” (Possible student responses: start with the
ones, then add the tens, then add the hundreds, I don't know, estimate, etc.) “We will solve this
problem together. Let's try a new way of organizing these two numbers before we add them.
Have any of you heard of partial-sums algorithms?” (Possible Student responses: yes, no) “Well,
let's look at this term, the word 'partial' means 'part of,' and the word 'sum' means 'to add,' so,
using my detective skills, that tells me we are going to be adding parts of the numbers to get an
answer. You may be used to adding the ones first, then the tens, then the hundreds together.
With partial sums we will be adding the other way by adding the hundreds together, then the
ten, and, finally, the ones. Let's use the problem on the visualizer as our example.” The teacher
then writes the partial-sums format using the two three-digit numbers displayed on the
visualizer. Here is what the teacher should write:
100s 10s
1s
456
+2 3 2
600
80
8
688
Explore (10 min.):
After the problem has been written, presented, and discussed with the students, the
teacher will hand out a partial sums activity sheet which focused on three-digit partial-sums
addition which uses the visuals of flats, longs, and cubes. The teacher and students will be
working on this activity sheet as a small group in order to make sure that everyone fully
comprehends the concept of partial-sums so that they will be ready and prepared for
tomorrow's activity on partial sums.
Share (3 min.):
“What did we learn about Partial-Sums equations? How did we solve them?” (Possible
student responses: We worked on an MCA math problem and figured out the way we need to add
the two numbers together, by adding the hundreds place first, by grouping the numbers into
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June 26, 2009
three different parts to make it easier to add, we worked with our partner to check our
answers, we worked as a group, etc.) “Who can give me an example of one way you solved a
partial-sums problem?.” (Possible student response example: I knew that a flat was equal to 100
so I knew I needed to added that part first, I remember some of the rules from the fact family
houses so that helped me with the adding part, I made sure to keep my numbers neat so that
they all lined up the right way before adding them, etc.) By having the students share their
ideas, it will give others new strategies when they come across partial-sums equations in the
future.
Summarize (3 min.):
The teacher will then get the group's attention and ask, “So, what did we learn about
today? (Goal response: Partial-Sums). Based on the students' responses, the teacher will be
able to conclude whether or not the students truly comprehended today's activities. “So, your
telling me that we learned about Partial-Sums, how to set them up to be solved, how to add the
different place-values together, and what we would need to do if we ever saw these types of
problems in the future. Awesome! What great math detectives! Nothing seems to stump you!”
90
June 26, 2009
Day 14
Continuing with Partial-Sums Algorithms
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:



The students will be using their prior knowledge to work with a partner on a Partial-Sums
activity using a Restaurant Menu.
The students will be strengthening their basic addition and subtraction skills to help
check each other's work when adding the prices of different menu items together in
order to make sure that their partial-sums were solved correctly.
The students will expand upon their mathematical vocabulary through group discussion
during the summary portion of this lesson.
Materials:




Mock Restaurant Menu
Blank Menu Prices Recording Template
Pencils
Partial Sums Math Worksheet
Procedure:
Launch (3 min):
When the students will first come to class they will be put into pairs for they will be
working with a partner during today's activities. “Do you remember how we worked with partialsums yesterday and became detectives to try and figure out the best way to organize the two
three digit numbers we needed to add together? Tell me how I could solve the following
equation using the Partial-Sums method: 321+ 446 = ?” The students will then guide the teacher
in how this problem would be correctly solved using partial-sums.
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June 26, 2009
Explore (11 min.):
“Today you get to create your own partial-sums math problems. We are going to pretend
to go to a fancy restaurant where you and your partner are going to receive a menu. I will be
paying so you won't need to worry about how much the food costs. But, you do need to order one
appetizer, one main course dish, and one desert. I don't want any of you to be hungry at the end
of our meal. You are then going to add the prices of the three food items you picked together
using the partial-sums method.” The teacher will first model what he/she expects the students
to do in terms of modeling and will write a partial-sums algorithm up on the visualizer using three
items from the menu list. This example will remain up on the board for the duration of class so
that the students can use it as a model if they get stuck.
Share (3 min.):
When most of the students have filled out one example of the three food items of their
choice, and have checked their work with their partner, the teacher will ask for a few volunteers
to share what they “bought” and, as a class, they will go over how these different partial-sums
algorithms were solved. The teacher will then ask, “What did we learn about Partial-Sums
Algorithms? How did we solve them?” (Possible student responses: We worked on an math
problem and figured out how to add the hundreds, tens, and ones together, we worked on an
activity sheet that used partial-sums algorithms using flats, longs, and cubes, we worked with
our partner to check our answers, and used partial-sums when pretending to order from a fancy
restaurant menu, etc.) “Who can give me an example of one way you solved a partial-sums
algorithm problem?” (Possible student response example: By adding up the hundreds, tens, and
ones I was able to add 123 and 224 and get 347, etc.) By having the students share their ideas,
it will give others new strategies when they come across partial-sums equations in the future.
Summarize (3 min.):
The teacher will then get the group's attention and ask, “So, what was one main idea or
big picture we've learned about over the last two days?” (Goal response: Partial-Sums
algorithms). Based on the students' responses, the teacher will be able to conclude whether or
not the students truly comprehended today's activities. “So, your telling me that we learned
about partial-sums algorithms, we used them to add different numbers together, we used
partial-sums with flats, longs, and cubes, and we practiced partial-sums when pretending to
order food from a restaurant. Wow! What a lot of great examples! You are becoming better
math detectives every day. Give yourselves a round of applause!” If there is time, the students
can continue to order from the fancy restaurant menu and come up with more partial-sums
equations.
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June 26, 2009
Partial-Sums Algorithms Lesson's Materials
1.
2.
3.
4.
5.
Math Question/Partial-Sums Algorithm (page 94)
Partial Sums Group Activity Sheet (page 97)
Mock Restaurant Menu (page 95)
Blank Menu Prices Recording Template (page 96)
Lesson Adaptations (page 93)
Parts and Total Lesson Adaptations for K, 1, 2, 4, 5
K



1



In order to make this lesson developmentally appropriate for kindergarten students, and to meet the
requirements of the suggested Minnesota standard, have the students create partial-sums number
equations using the tens and ones place.
Modify the MCA question so that the students are working with the tens and ones place. If you
would like to include the hundreds place, try to stay within the numbers of 1-10.
The restaurant menu would need to be altered so that it was pictures of food with the price next to
the pictures. Stay away from decimals and just stick with whole dollar amounts for right now.
In order to make this lesson developmentally appropriate for first grade students, and to meet the
requirements of the suggested Minnesota standard, have the students create partial-sums number
equations using the tens and ones place.
Modify the MCA question so that the students are working with the tens and ones place. If you
would like to include the hundreds place, try to stay within the numbers of 1-10.
The restaurant menu would need to be altered so that it was pictures of food with the price next to
the pictures. Stay away from decimals and just stick with whole dollar amounts for right now.
2

These two days of lessons are completely appropriate for students to work on in second grade and
meet the Minnesota standard selected.
4

In order to make this lesson developmentally appropriate for fourth grade students, and to meet the
requirements of the suggested Minnesota standard, simply change the partial-sums to higher place
values. Also, increase the number of food items they select from the menu in order to help
strengthen their addition skills with multi-digit numbers.
5

In order to make this lesson developmentally appropriate for fifth grade students, and to meet the
requirements of the suggested Minnesota standard, simply change the directions of the restaurant
menu activity. Have them pretend that they are splitting the price of their food items with a partner
so that not only will they need to total the prices of the items they select, but then they need to
take that total and divide it equally among the other members in their group.
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June 26, 2009
Math Question
456
+ 232
94
June 26, 2009
Miss Anderson's Marvelous Meals Restaurant
Appetizers
Oysters
Shrimp
Scallops
Lobsters
Lobster Cakes
Apple Smoked Bacon
Tenderloin
Ribs
12.00
15.00
20.00
25.00
7.00
6.00
17.00
15.00
Main Dishes
New York Steak
Porterhouse Steak
Filet Mignon
Salmon Steaks
Tuna Steaks
Shrimp Scampi
Deep Fried Shrimp
Pork Chops
Lamb Chops
Veal Loin Chops
Chicken Parmesan
Chicken Alfredo
100.00
100.00
110.00
100.00
100.00
25.00
27.00
25.00
45.00
100.00
50.00
50.00
Desserts
Hot Fudge Sundae
Key Lime Pie
The Famous Brownie Sundae
8.00
6.00
7.00
95
June 26, 2009
Miss Anderson's
Marvelous Meals Restaurant
Food
Items
Food Prices
Filet Mignon
$110.00
Shrimp
$15.00
Key Lime Pie
$6.00
Partial-Sums
+
96
$110.00
$ 15.00
$ 6.00
$100.00
$ 20.00
+ $ 11.00
June 26, 2009
97
June 26, 2009
Day 15
Post-Assessment on Number Comparisons
and Partial-Sums Algorithms
Standard:
Number and Operation: Add and subtract multi-digit whole numbers; represent multiplication and division in
various ways; solve real-world and mathematical problems using arithmetic.
3.1.2.2. Use addition and subtraction to solve real-world and mathematical
problems involving whole numbers. Use various strategies, including
the relationship between addition and subtraction, the use of
technology, and the context of the problem to assess the
reasonableness of results.
Objectives:




The students will be using prior knowledge of Number Comparisons as measured by their
responses when reviewing and working on a Number Story student activity sheet.
The students will be using their prior knowledge of Partial-Sums by working with flats,
longs, and cubes to make new partial-sums algorithm problems. .
The students will be creating their own number comparison or partial-sums algorithm
story and illustrating their own number story.
The students will be assessed through an informal post-assessment over the concepts of
Number Comparisons and Partial-Sums Algorithms.
Materials:




Partial Sums Table for Flats, Longs, and Cubes (page 99)
Number Story Student Activity Sheet (page 74)
Pencils
Post-Assessment Checklist (page 101)
Procedure:
1. The students will be working at three learning stations. (One station will be focusing on
Number Comparisons, a second station will be focusing on Partial-Sums, and a third
station will be focusing on creating several number stories of their choice complete with
illustration). They will be rotating among these three stations approximately every six
minutes. This way every group has a chance to explore every station. With there being
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June 26, 2009
6-8 students at a time, there will be approximately 2-3 students in each group.
2. While the students are working at the different learning stations, the teacher will be
walking around with a checklist to informally and formally assess the students on their
comprehension of Number Comparisons and Partial-Sums Algorithms. This form of
assessment takes about 5 minutes to complete for each student.
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June 26, 2009
Number of Units
How many cubes for
each?
Showing Partial Sums
Example:
1. Flats: 5
500
500+100=600
2. Longs: 12
120
20
3. Cubes: 7
7
7
Equals:
627
New Example:
1. Flats:
2. Longs:
3. Cubes:
Equals:
New Example:
1. Flats:
2. Longs:
3. Cubes:
Equals:
New Example:
1. Flats:
2. Longs:
3. Cubes:
Equals:
100
June 26, 2009
Name of Student
Date:
Classroom Teacher
Assessment Questions
Regarding Number
Comparisons and
Partial-Sums Algorithms
Grade Level:
Mastery Level
Yes, fully
mastered!
Understands the Needs Additional
majority of this Help and Guidance
concept.
Provide Example:
1. Is the student able to
complete a number comparison
equation correctly?
2. Is the student able to create
correct and different number
comparison equations?
3. Is the student able to help
others solve number comparison
equations?
4. Can the student provide
reasoning in how to solve
different number comparison
equations?
5. Does the child use different
strategies to solve number
comparison equations?
6. Is the student able to work
with a partner to come up with
different partial-sums
algorithms?
7. Is the student able to provide
reasoning on how to solve those
different partial-sums
algorithms?
8. Does the child use different
strategies to solve partial-sums
algorithms?
9. Would the student be able to
explain the concept of number
comparison equations to another
person?
10. Would the student be able to
explain the concept of partialsums algorithms to another
person?
101
Additional
Comments
June 26, 2009
Source Citations:
“Volume 1."Everyday Mathematics. 3rd ed. 2007. Print.
(100-140)
Harcourt Family Learning. Math Skills Grade 2. 2004.
Print. (41)
"Volume 1. Grade 3."Everyday Mathematics Student Math
Journal. 3rd ed.. 2007. Print. (40)
"Math Masters, Grade 2."Everyday Mathematics . 3rd ed..
2007. Print. (160)
102