Links Away

Jennifer Showalter
MAR 3
* What introductory information is necessary for children to have prior to starting this activity?
I would like to do this lesson with Kindergarten children. I used my son and did this lesson with him since he was in Kindergarten this year. For this lesson the introductory information necessary would be number recognition, able to count to ten, and also be good listeners and follow directions.
* What grade level/s is appropriate for this activity? Please use appropriate justification for your answers here.
This is a great math activity because it can be modified for students in grades K-2. This can be done using different concrete, pictorial, symbolic, and verbal representations of subtraction. For Kindergarteners this activity is appropriate because the objectives of the lesson are that students will be able to count to 10, model numbers to 10, count differences from numbers to 10, write and recognize numerals to 10, and record differences in vertical and in horizontal format.
* How will you engage students with different learning styles?
This is a great lesson because you can incorporate different concrete, pictorial, symbolic, and verbal representations of subtraction that can be modified to meet all the different learning styles. The students are also engaged by the story you choose to use with the lesson. I also think that modeling for the students engages them and draws them in, especially if you are excited and enthusiastic about the lesson. Modeling the lesson also makes them familiar with the concept and lets them know what they will be doing for the assignment. This manipulative is great for visual learners and thinkers. I am all for the constructivist learning theory and this goes hand in hand with that. It is broken up into segments that build upon each other if you complete the unit lessons. Thus, the students understand one concept before moving on to the next. Not only is this manipulative good for mainstream students but I feel it is also a great asset for Special Ed. Students and algebra tutors. It gives them different ways to explore the concepts while learning or teaching. I like the way that the teachers can model with the materials and lecture less. Teachers can use the manipulatives as a sense making device in math that represent abstract ideas with concrete materials.
* How does this activity connect to the real world for students? Be specific.
The students are learning to use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
The students are learning that counting and basic math facts are used in everyday life and that these numbers and facts are used in subtraction. This activity uses the students as an example and also stories that they can relate to. The book The Very Hungry Caterpillar and the M&M Counting Book are great because you can incorporate food and M&M’s and use the kids in the lesson to show what happens when one item is eaten. This helps scaffold their learning experience. This lesson also helps them work cooperatively together which is important in the real world.
* Why is this activity with its concepts important for student learning? Be specific.
According to the MN academic standards, students are to recognize, create, complete, and extend patterns, use rules to describe patterns, use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences and use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences. This particular activity gives students the activity to understand these concepts by using hands on manipulatives in a group setting with student and teacher interactions. Research shows that students develop mathematical understanding from a young age and need many opportunities to help them grow. They explore the relation between addition and subtraction and also write story problems in which subtraction is required and begin to memorize the subtraction facts.

* What are your comments on this activity? Would you use it in your classroom?
This lesson allows students to work in a fun environment while teaching a very important skill. It allows a student to work with hands on manipulatives, have a multitude of interactions with their peers as well as with their teacher, and allows for a constant practice exploring the five models of subtraction. I like this lesson and activity because it allows for a variety of extension activities to be acted upon in continuing on with their mathematical understanding. This lesson would be useful and support student learning as well as meet MN academic standards in mathematics for grade K-2, algebra. We know that young students need hands on learning and approaches; they need constant practice and reinforcement, and peer and teacher support. This lesson allows for all of those things and can support further understanding of mathematical concepts and I would love to use it in my classroom.











This is a Unit Plan I found where students explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using links. They also learn that the order property does not hold for subtraction and explore the relation between addition and subtraction. Students also write story problems in which subtraction is required and begin to memorize the subtraction facts. A brief bibliography of related books for children is provided. I chose to do my MAR on the first lesson which is laid out in depth, but I also included brief descriptions of the other unit lessons so you could see the whole picture of what the students are learning in the five models of subtraction.
Math Content
The sequence of lessons in this Unit Plan builds an understanding of the process and properties of subtraction. Students will build concrete, pictorial, symbolic, and verbal representations of subtraction.

Counting Back and Counting On
This lesson, which focuses on the counting model for subtraction, begins with reading a counting book. The students model the numbers as the book is read. Then they make a chain of links and write in vertical and horizontal format the differences suggested by adding and subtracting one link at a time from their chains. Finally, they draw a chain showing one link being taken away and write in two formats the difference it represents.

Learning Objectives


Students will be able to:
count to 10
model numbers to 10
count differences from numbers to 10
write and recognize numerals to 10
record differences in vertical and in horizontal format

Materials


Counting Book, from the Counting Books Resource Sheet Links in Two or More Colors (or Connecting Cubes or Large Paper Clips) Student Slates or Whiteboards Song Lyrics
Instructional Plan

To set the stage for learning, choose a counting back book to read from the Counting Books resource sheet, such as Ten Sly Piranhas, Ten Little Ladybugs, or Five Little Monkeys Sitting in a Tree. If no books are available, tell a story about counting back such as the following:
There were eight candies on a plate. Zack took one of them; then Yula took one; then Xavier took one, and Wilma took one, and so forth.
As the students listen to the story, have them model each number from the story with counters, links, or candies, then write the numeral and number word for each. Watching their responses will help you assess the students’ current level of understanding.
Next give each child 10‑12 links. Hold up a number and ask the children to make a chain with that many links, lay it flat on the desk and then record the number of links on their slates. Then ask them to add one link and record the addition they have just modeled using the equation (horizontal) format. Now show the same starting number and ask the children to make a chain with that many links. Have students record that number as before but this time to count away one link and then record the subtraction they have just modeled using the horizontal format.
Now ask the students to build a chain of six links and hold the chain vertically so that it hangs down. Lead them in singing Six Little Ducks, from the Song Lyrics resource sheet, as they remove the links one at a time. Ask them to record each subtraction in vertical format.
When the children are ready, ask them to share one of their differences and the counting process that was used to get it. Summarize how students can count back to subtract one.

Questions for Students


How many links are in this chain (show a chain with ten links)? On this chain (show a chain with nine links)? Which chain has more? How many more?
[The chain with none links has more. It has one more link than the chain with ten links.]
What number sentence would show that you started with 10 links and took one away?
[10 – 1 = 9]
What was alike between the two ways we recorded subtraction? What was different?
[The numbers we used were the same. We got the same answer. They look different because one is going across and one is going up and down.]
How could you help a younger child model this subtraction sentence (write 10 – 1)?
[Tell her to start with ten things and take one away.]
What does the minus sign mean?
[It means "take away."]
What two symbols did you use to mean equals?
[Two short lines and one long line. Students may point to the two symbols.]
When you count backwards, what comes after seven?
[Six comes after seven.]

Assessment Options


Document your observations during class discussions and student practice. Use the Class Notes recording sheet.
Ask students to choose one subtraction example and write it in both vertical and horizontal format for an entry in their portfolio. Have them draw a picture that illustrates the subtraction fact.

Extensions


Put several counting back books in a math center along with paper, crayons and links. This availability will encourage children to continue to read books with a subtraction theme and to practice recording subtraction examples.

Teacher Reflection


Which books were best received? What others might you use?
Were the materials used for counting back appropriate?
Which students met all the objectives of this lesson? What extension activities would be appropriate for those children?
Which students did not meet the objectives of this lesson? What instructional experiences do they need next?
Do students understand the symbols for subtract and equals?
What mathematical ideas need clarification?

NCTM Standards and Expectations


Algebra Pre-K-2
Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

MN Math Standards
Algebra Kindergarten Standard
1. Recognize, create, complete, and extend patterns.
Algebra First Grade Standard
1. Recognize and create patterns; use rules to describe patterns.
2. Use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
Algebra Second Grade Standards
1. Recognize, create, describe, and use patterns and rules to solve real-world and mathematical problems.
2. Use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.





This lesson prepared by Grace M. Burton.
Retrieved from:
http://illuminations.nctm.org/LessonDetail.aspx?id=U60




Individual Lessons
Lesson 1 - Counting Back and Counting On
This lesson, which focuses on the counting model for subtraction, begins with reading a counting book. The students model the numbers as the book is read. Then they make a chain of links and write in vertical and horizontal format the differences suggested by adding and subtracting one link at a time from their chains. Finally, they draw a chain showing one link being taken away and write in two formats the difference it represents.
Lesson 2 - Taking Away Sets
This lesson encourages students to explore another model for subtraction, the familiar set model. Reading one of the many books that feature subtraction set the stage for this lesson in which the students write story problems, find differences using sets, and present results in a table. In the discussion of the table, they focus on the effects of subtracting all and subtracting 0.
Lesson 3 - Hopping Backward on the Number Line
In this lesson, students generate differences using a number line model. Because this model highlights the measurement aspect of subtraction, it is a distinctly different representation from the models presented in the previous lessons of this unit. The order property for subtraction is investigated. At the end of the lesson, children are encouraged to predict differences and solve puzzles involving subtraction.
Lesson 4 - Finding the Balance
This lesson encourages students to explore another model of subtraction, the balance. Students will use real and virtual balances. Students also explore recording the modeled subtraction facts in equation form.
Lesson 5 - Finding Fact Families
In this lesson, students explore the relation of addition to subtraction with books and links. Then the children search for related addition and subtraction facts for a given number. They also investigate fact families, including those where one addend is 0 and where the addends are alike.
Lesson 6 - Practice Makes Perfect
During this lesson, students use what they know about fact families to play a concentration game. They will also identify subtraction facts they need to learn.
Lesson 7 - Looking Back and Moving Forward
This final lesson reviews the work of the previous lessons and suggests a framework for summative assessment. Students will self-select a solution strategy for subtraction from the models introduced in this unit. An extension activity is suggested in which students use the mathematical knowledge and skills developed in the previous lessons to demonstrate understanding and ability to apply that knowledge to playing a new game.





Counting Books
The following is a list of books that are relevant to the topics in this unit.
• Baker, Keith. Quack and Count. New York: Scholastic, 1999.
• Bang, Mollie. Ten, Nine, Eight. New York: Greenwillow, 1983.
• Carle, Eric. The Very Hungry Caterpillar. New York: Putnam , 1969.
• Christelow, Eileen. Five Little Monkeys Sitting in a Tree. New York: Scholastic, 1991.
• Gerth, Melanie. Ten Little Ladybugs. Santa Monica, Calif.: Piggy Toes Press, 2000.
• Giganti, Paul, Jr. How Many Snails? New York: Greenwillow, 1988.
• Grossman, Virginia. Ten Little Rabbits. New York: Scholastic, 1991.
• Irons, Rosemary and Calvin Irons. The Mean Machine. Crystal Lake, Ill.: Rigby, 1987.
• McGrath, Barbara Barbieri. The M&M’s Counting Book. New York: Scholastic, 1994.
• Morozumi, Atsuko. One Gorilla. New York: Trumpet Club, 1990.
• Peek, Merle. Roll Over. New York: Clarion, 1981.
• Rees, Mary. There Were Ten in the Bed. Boston: Little, Brown and Company, 1988.
• Wise, William. Ten Sly Piranhas. New York: Dial, 1993.


Song Lyrics
The following are lyrics for songs used in the Link Away unit.

Six Little Ducks
Six little ducks went out to play,
Over the meadow and far away.
Mother Duck called, “Quack, quack, quack, quack.”
Five little ducks came running back.
Five little ducks went out to play,
Over the meadow and far away.
Mother Duck called, “Quack, quack, quack, quack.”
Four little ducks came running back.
Continue counting back until no little ducks come running back. Then sing:
No little ducks went out to play,
Over the meadow and far away.
Mother Duck called, “Quack, quack, quack, quack!”
Six little ducks came running back!

Ten in the Bed
There were 10 in the bed and the little one said, “Roll over, roll over.”
So they all rolled over and one fell out.
There were 9 in the bed and the little one said, “Roll over, roll over.”
So they all rolled over and one fell out.
Continue until the last verse, which is…There was 1 in the bed and the little one