Description: Cookies are used initially since students are familiar with and are interested in who has more than, less than, and the same amount of cookies, juice, crackers, etc.
Purpose: to help students make meaningful connections between what they have experienced with sharing cookies and other food items and the concept of comparing groups of concrete objects.
* The following description is an example of how you might implement this instructional strategy for Learning Objective 1. A similar process can be used for the other learning objectives in this plan.
Learning Objective 1: Identify if a given group of objects has more than, less than or the same number of objects when compared to another group of objects.
Materials:
Teacher -
Plastic samples, or shellacked cookies
Two containers or plastic baggies with cookies
A "mystery bag" to use when introducing the lesson,
Three cookie sheets or other visual display for displaying groups of shellacked or magnetic cookies.
Description:
1.) L ink to students' prior knowledge of sharing cookies .
For Example:
Let's see, what do you think I have in my mystery bag today? (Elicit student responses) Well look, I have some bags of cookies. I have chocolate chip cookies in this bag, and I have sugar cookies in this bag. Who likes cookies? I like them too. I like to make cookies and share them with my friends. Do you ever eat cookies with your family? Do we ever eat cookies in here for snack?
2.) I dentify the skill students will learn: Using concrete objects to identify if a group has the same as, more than, or less than a given number of objects.
For Example:
Today we are going to use cookies and other objects to practice comparing two groups.
3.) P rovide rationale/meaning for comparing more than, less than, same.
For Example:
When we compare groups to see if they are the same, or if one group is bigger (has more objects) or smaller ( has less objects) than the other, it will help us when we count
Purpose: to provide students a clear teacher model of how to identify and make groups of concrete objects that are the same as, more than or less than a given group of objects.
Learning Objective 1: Identify if a given group of objects has more than, less than, or the same number of objects when compared to another group of objects.
Materials:
Teacher -
2 types of cookies (shellacked and magnetized cookies, flannel board cookies, plastic samples etc.)
Paper plates (real or drawn)
Puppets, (could also use dolls, stuffed animals, flannel board figures)
Flannel, magnetic or another type of display board,
Description:
A.Break down the skill of identifying if a given group of objects has more than, less than or the same number of objects when compared to another group of objects.
1.)Review story situation/context.
2.)Line up and count objects in first group.
3.)Match the second group of objects with the first group.
4.) Compare and label groups.
5.) Count objects in each group.
Learning Objective 2: . Identify if a given group of objects has more than, less than, or the same number of objects when compared to other groups of objects using a variety of unlike objects.
Materials:
Teacher -
Variety of concrete items (e.g counting bears, counting blocks)
Pipe cleaners, yarn, coffee stirrers
Display area
Description:
A. Break down the skill of identifying if a given group of objects has more than, less than or the same number of objects when compared to other groups of objects.
1.) Review story situation/context.
2.) Line up and count objects in first group.
3.) Match the second group of objects with the first group.
4.) Compare and label groups.
5.) Count objects in each group.
Learning Objective 3: Identify if a given group of objects has more than, less than, or the same number of objects when compared to another group objects using like objects.
Materials:
Teacher -
Variety of like, concrete items (e.g green and red counting bears, blue and red counting blocks)
Pipe cleaners, yarn, coffee stirrers
Display area
Description:
A. Break down the skill of identifying if a given group of objects has more than, less than or the same number of objects when compared to other group of objects using like objects:
1. Review story situation/context.
2. Line up and count objects in first group.
3. Match the second group of objects with the first group.
4. Compare and label groups.
5. Count objects in each group.
Learning Objective 4: Make a group with more than, less than, or the same number of objects than a given a group of objects.
Materials:
Teacher -
2 types of cookies (flannel board cookies, plastic samples, etc.)
Paper plates (real or drawn)
Flannel, magnetic, or another type of visual display board
Description:
A. Break down the skill of making a group with more than, less than, or the same number of objects than a given a group of objects.
1. Review story situation/context.
2. Line up and count objects in first group.
3. Make a second group of objects.
4. Count objects in both groups.
Purpose: to provide students an opportunity to build their initial understanding of how to identify and make groups that show the same as, more than, or less than a given group of objects and to evaluate your students' levels of understanding after you have initially modeled the skill
* The steps for scaffolding your instruction are the same for each concept that you have explicitly modeled. This teaching plan provides you a detailed example of scaffolding instruction for Learning Objective 1. A similar process can be used for the learning objectives in this plan. You should scaffold your instruction with each skill/concept you model.
Materials:
Teacher -
A paper plate with chocolate chip cookies (shellacked and magnetized cookies, flannel board cookies, plastic samples etc.)
Bag of sugar cookies.
Flannel, magnetic or another type of display board
Students -
Paper plates with chocolate chip (plastic, shellacked, laminated paper) cookies
Bags with sugar cookies in them for each student.
Description:
1.) Scaffold Using a High Level of Teacher Direction/Support
a. Choose one or two places in the problem-solving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction. (Examples of choices are shown in red.)
· Present the problem and review the steps to solving it.
o Let's review what we have learned. I have two groups of cookies. I have a group of chocolate chip cookies on this plate and a group of sugar cookies in this bag. I want to see if I have more sugar cookies than chocolate chip cookies, less sugar cookies than chocolate chip cookies or the same number of sugar cookies as chocolate chip cookies. There are four steps that I am going to do and I want you to help me when I need help. Let me review what I am going to need to do. First I am going to line up and count my chocolate chip cookies. Next I am going to match my group of sugar cookies with my group of chocolate chip cookies. Then I am going go compare my groups and see if I have more sugar cookies, less sugar cookies or the same number of sugar cookies as I do chocolate chip cookies. The last thing I am going to do is to count both my groups.
· Line up and count objects in first group.
o The first thing I need to do is to line up and count my chocolate chip cookies. Who can help me? Fantastic! You lined up all the chocolate chip cookies in a row. That will help up later when we compare our groups. Let's count these chocolate chip cookies again. (1,2,…7). We have how many chocolate chip cookies? Right, 7 chocolate chip cookies.
· Match second group with first group.
o Now that we've lined up all of our chocolate cookies, I need to match this group of sugar cookies with them. I'll match one sugar cookie with this chocolate chip cookie, and one sugar cookie with this chocolate chip cookie, and one here, and one here, and one here, and this is a match, and this is a match. But look I've run out of chocolate cookies to match. Do I have any more chocolate chip cookies? No, I don't. I have some sugar cookies that are not going to be matched with chocolate chip cookies.
· Compare groups and label.
o Well, I need to see if I have more sugar cookies, less sugar cookies or the same number of sugar cookies as I do chocolate chip cookies. I'm going to guess first. From looking at both groups, I guess I have more sugar cookies than I do chocolate chip cookies. What do you think? Well, let's find out. Have I matched up all of my sugar cookies with chocolate chip cookies? Yes, you are right, I have. Do I still have some sugar cookies that are not matched? Yes I do. Since I have sugar cookies that are not matched, I must have MORE sugar cookies than I do chocolate chip cookies.
· Count both groups
o I think that I have more sugar cookies than I do chocolate chip cookies. This group of cookies has more than this group. I am going to count each group. We already counted the chocolate chip cookies. How many chocolate chip cookies do I have? (12,,,7) 7 Right! I have 7 chocolate chip cookies. Now I am going to count the sugar cookies. (1,2,…9) 9. I have 9 sugar cookies. I have more sugar cookies than I do chocolate chip cookies. Which group has more? Right the sugar cookie group has more. I have more sugar cookies and less chocolate chip cookies.
* Repeat this sequence demonstrating how to identify a group with less sugar cookies and a group with an equal number of sugar cookies.
b. Maintain a high level of teacher direction/support for another example if students demonstrate mis../../../understanding/non-understanding; move to a medium level of teacher direction/support if students respond appropriately to the selected questions/prompts.
2.) Scaffold Using a Medium Level of Teacher Direction/Support
a. Choose several more places in the problem-solving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction.
· Present the problem and review the steps to solving it.
· You are doing such a great job that now we're going to match some more groups and I'm going to ask for even more of your help. Let's review what we have to do. I have two groups of cookies - a group of chocolate chip cookies and a group of sugar cookies. I want to see if there are more sugar cookies, less sugar cookies or the same number of sugar cookies as chocolate chip cookies. The first thing to do is to line up our chocolate chip cookies. Then we're going to match the group of sugar cookies with the chocolate chip cookies. After we make all the matches that we can, we're going to decide if we have more sugar cookies, less sugar cookies or the same number of sugar cookies as chocolate chip cookies. The last thing to do is to count both groups.
· Line up and count objects in first group.
o What do we start with first - our chocolate chip cookies or our sugar cookies? Right our chocolate chip cookies. And what do I need to do with my chocolate chip cookies? Right! _____ and ____ come and do this first step for me. Good, ______ and ____ have lined up our chocolate chip cookies and have counted them for us. We have 5 chocolate chip cookies.
· Match second group with first group.
o Now that we've lined up our cookies, what do we need to do next? Right! We need to match this group of sugar cookies with our chocolate chip cookies. I need some helpers to show us how to match the sugar cookies with the chocolate chip cookies.
o Great, _____, _______, and _____ have each matched up our sugar cookies to our chocolate chip cookies.
· Compare groups and label.
Well, I need to see if I have more sugar cookies, less sugar cookies or the same number of sugar cookies as I do chocolate chip cookies. What is your guess? How many of you think I have more sugar cookies? How many of you think I have less sugar cookies? How many of think I have the same number of sugar cookies as chocolate chip cookies? Well, I wonder how I can find out? Boys and girls, you are so smart, I'll check my matches. Have I matched up all of my sugar cookies with chocolate chip cookies? Yes, you are right, I have. Do I have enough sugar cookies to match with all the chocolate chip cookies? No, I don't. I have less sugar cookies because there are not enough sugar cookies to match up with all the chocolate chip cookies. Show me which group has less. Show me which group has more.
· Count both groups
o What is the last thing I need to do? Right! I need to count both groups. _____ and ____ , come help me count. I have 5 chocolate chip cookies and 3 sugar cookies. This groups of sugar cookies has less than this group of chocolate chip cookies. Which group has less? Which group has more?
* Repeat this sequence demonstrating how to identify a group with more sugar cookies and a group with an equal number of sugar cookies.
b. Maintain a medium level of teacher direction/support for another example if students demonstrate mis../../../understanding/non-understanding; move to a low level of teacher direction/support if students respond appropriately to the selected questions/prompts.
3.) Scaffold Using a Low Level of Teacher Direction/Support
a. When students demonstrate increased competence, do not model the process. Ask students questions and encourage them to provide all responses. Direct students to replicate the process as you work together.
· Present the problem and review the steps to solving it.
· Boys and girls, you are doing such a great job that I want you to show ME how to find out if a group of sugar cookies has more than, less than, or the same number as a group of chocolate chip cookies. I'm going to give you each a plate of chocolate chip cookies and a baggie with some sugar cookies in it. I want you to show me what to do to see if we have more sugar cookies, less sugar cookies or the same number of sugar cookies as chocolate chip cookies. You show me and then I'll copy what you do up here with my cookies. Does everybody have their plate of chocolate chip cookies? Now I want everyone to hold up your baggie of sugar cookies. Good! Let's get started!
· Line up and count objects in first group.
o What do we start with first - our chocolate chip cookies or our sugar cookies? Right! Show me what to do with the chocolate chip cookies. Great, everybody lined up their chocolate chip cookies. I heard many people counting their cookies. How many chocolate chip cookies do we have? Right! We have 5 chocolate chip cookies.
· Match second group with first group.
o What do we do next? Great! We are going to match our sugar cookies with our chocolate chip cookies.
· Compare groups and label.
Now we are going to see if we have more sugar cookies, less sugar cookies or the same number of sugar cookies as chocolate chip cookies. What is your guess? I see you checking your matches. What did you find out? You are right. We have the more sugar cookies than chocolate chip cookies. Point to the group that has more.
· Count both groups
o What is the last thing we need to do? Right! We need to count both groups. We have 5 chocolate chip cookies. How many sugar cookies do we have? 8 sugar cookies. Which group has more?
* Repeat this sequence demonstrating identifying a group with less sugar cookies and a group with an equal number of sugar cookies.
b. When you are confident students understand, ask individual students to direct the problem solving process or have the class direct you: Students ask questions and you and the students respond/perform the skill.
Purpose: To provide students with multiple practice opportunities to identify if a given group of objects has more than, less than, or the same number of objects when compared to another group of objects.
Learning Objective 1:
Identify if a given group of objects has more than, less than or the same number of objects when compared to another group of objects.
Structured Language Experience:
Materials:
Teacher -
Bell or timer to signal when to rotate containers at tables.
Students-
4-5 pre-made groups of two types of cookies (chocolate chip and sugar) in box lids or other container. The number of chocolate chip cookies would remain constant (e.g. 6), but each container would display a different amount of sugar cookies. Containers should be differentiated with a color or symbol, letter or number.
Description:
Activity:
Students will work at tables in groups of 4 or 5 children. Each child at a table would have a lid that showed a group of chocolate chip cookies and a group of sugar cookies. Each child would need to decide if there were more, less, or the same number of sugar cookies as chocolate chip cookies. After deciding, each child will tell the other children at his/her table if they have more, less, or the same number of sugar cookies as chocolate chip cookies. When the teacher rings the bell the children at each table are to take turns telling the others at their table about their decision. After each child at the table has shared his/her decision with his/her tablemates, the teacher will ask one child at each table to share his/her decisions with the entire class before signaling children to pass the lids around the table. Continue until every child has practiced with each container at the table.
Structured Language Experience Steps:
1. Review directions for completing structured language experiences and relevant classroom rules.
2. Model how to perform the skills(s) within the context of the activity before the students begin the activity. Prior to starting this activity, the teacher will introduce the activity and model how to :
a. Look at the container
b. Decide if there are more, less, or the same number of sugar cookies as chocolate chip cookies.
c. Wait for the teacher signal and then tell table mates
d. Take turns telling tablemates and provide feedback to tablemates
e. Signal teacher if there is a question about a tablemate's decision
f. Rotate the containers around the table when the teacher signals.
g. Listen while children are sharing their responses with the whole class.
3.) Provide time for student questions.
4.) Signal students to begin.
5.) Monitor students as they work:
a. Circulate around the table and check on children's responses throughout the activity.
b. Make sure that each child receives feedback on his/her decision.
c. Provide closed choice questions (point to the group that shows more, is this more or less cookies) to help students who have difficulty with verbal expression label their containers.
d. Ask each child in the class to share his/her decision at least once with the entire class.
Purpose: to provide students with multiple practice opportunities to make a group of objects that is less than, more than, or the same as a given group of objects.
Learning Objective 4:Making groups showing more than, less than, or the same number of objects as a given group.
Structured Language Experience:
Materials:
Teacher -
Recording form to record student responses
Students -
10 plates with chocolate chip cookies/pair of students;
10 baggies with sugar cookies
One egg carton that has been cut into thirds or another container with five small cups and five small objects (token, counting bear, beans, pebbles etc.)/pair
Description:
Activity:
The teacher will put the students in pairs and assign initial roles (maker; recorder/listener). Each pair will get a container/envelope with the plates of chocolate chip cookies and the baggies of sugar cookies. Students will be asked to create groups of sugar cookies that show less, more or the same number of sugar cookies as the plate of chocolate chip cookies that their partner will pick. They will also need to tell their partner how they know that they have made a group that is less, more, or the same as the group of chocolate chip cookies. Each child will have five opportunities to make and tell their partner about their groups. Each time a child makes a group his/her partner will put a token (bean, pebble, etc.) in a section of the egg carton. When the egg carton is filled (i.e. after five turns), the partners will switch roles.
Structured Language Experience Steps:
1. Review directions for completing structured language experiences and relevant classroom rules.
2. Model how to perform the skills within the context of the activity before students begin the activity. Prior to starting the activity, the teacher will introduce the activity and model how to:
a. Line up and count the chocolate chip cookies.
b. Match the sugar cookies with the chocolate chip cookies
c. Compare and label sugar cookies as less, more, or the same as the chocolate chip cookies.
d. Count the number of objects in each group.
e. Tell your partner about the matching groups.
f. Listen to your partner.
g. Put a token in the cup each time after your partner has finished making and telling you about a group.
h. Signal the teacher if there is a question about your partner's groups.
i. Signal the teacher when you are ready to switch roles.
3.) Provide time for student questions.
4.) Signal students to begin.
5.) Monitor students as they work:
a. Circulate and check on children's responses throughout the activity.
b. Make sure that each child receives feedback during the activity.
c.For those students who have difficulty with verbal expression, the teacher may need to have them make models for their partners but not require them to describe their groups without teacher prompting.
Purpose: to provide the teacher with continuous data for evaluating student learning and whether your instruction is effective. It also provides students a way to visualize their learning/progress.
Materials:
Teacher-
Goal sheet/Chart
Planned verbal prompts for task completion
Students:
Concrete materials (premade groups of objects).
Description:
Steps for Conducting Continuous Monitoring and Charting of Student Performance:
1.) Choose whether students should be evaluated at the receptive/recognition level, the expressive level, or both.
2.) Choose appropriate criteria to indicate mastery.
3.) Provide appropriate number of prompts in an appropriate format (receptive/recognition or expressive) so students can respond.
Suggestions:
Receptive/recognition level:
Student can correctly identify if a given group of objects has more than, less than or the same number of objects when compared to another group of objects. Create a group with more than, less than, or the same number of objects than a given a group of objects.
Expressive level:
Create a group with more than, less than, or the same number of objects than a given a group of objects
4.) Provide students with the materials to complete each task.
5.) Provide directions on how to complete each task.
6.) Conduct evaluation. Provide 3-5 trials on each task.
7.) Count corrects and incorrects (# of trials) for each task.
8.) You and the students will plot their responses on a suitable chart. A goal line that represents proficiency should be visible on each student's chart. . For concrete level of understanding this should be 100%, (3/3 or 5/5 trials) on each task.
9.) Talk with children about their progress as it relates to.the goal line and their previous performance. Prompt them to self evaluate.( Did you line up your sugar cookies with your chocolate chip cookies; Did you check to see if you had sugar cookies left over?)
10.) Determine whether you need to alter or modify your instruction based on student performance.
Flexible Math Interview
Purpose: to provide the teacher with additional diagnostic information in order to check student understanding and plan and/or modify instruction accordingly.
Materials:
Teacher -
Groups of concrete objects
Description:
With individual students or in small groups, the teacher will take the role of a student. The teacher will have the student "teach" him/her how to:
a. Show more by building a group of objects greater than a give group and verbalize that the group shows more.
b. Take objects away to create a group that is the same as a given group of objects.
c. Show less by building a group of objects with fewer objects than the given group. Although the teacher should note errors or misconceptions while the student is "teaching", the teacher should not stop the student for correction purposes. By having the student complete the entire explanation, the teacher will gain a better understanding of the student's thinking. The teacher will confer with the student afterward.
Purpose: to provide periodic student practice activities & teacher directed review of this skill after students have mastered it.
1. Balance Scale:
Materials:
Balance Scale- One side will have a cup velcroed on it. This cup will contain a group of concrete objects.
Three cups to measure out objects for other side of the scale
Container of objects
Description : Students will fill one of the empty cups in order to make a group that has more than, less than, or the same number of objects as in the cup that is velcroed to the other side of the scale
2. Problem of the Day:
Materials:
Tag board with groups of concrete items of varying sizes.
Description:As children line up on given days, touch a group of items and ask a student to touch another group with more, less or the same number of items
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