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Description: Bags of M & M’s and other food are used since children have experiences with counting out food to share.
Purpose: To help students make meaningful connections between what they have experienced when sharing food and the concept of grouping objects into groups of ten.
* 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: Given a set of concrete objects, make groups of ten.
Materials:
Teacher-
Bag of M & M’s
Description:
1.) L ink to students’ prior knowledge of counting out food to share
For Example:
Did you ever have a bag of candy and you wanted to share it with a friend? With two friends? Often we need to figure out how to share our things with others.
2.) I dentify the skill students will learn: grouping by tens
For Example:
Today we are going to learn how to make groups of tens.
3.) P rovide rationale/meaning for grouping by tens.
For Example:
When we group things by tens, it can help us when we share and count food like M & M’s.
Purpose: to provide students a clear teacher model of how to group objects by tens.
Learning Objective 1: Group by tens using concrete objects.
Materials:
Teacher –
Bag of 30 M & M’s,
Ten frame (manufactured, or made from paper, meat trays)
Description:
A. Break down the skill of grouping by tens with concrete objecs
1.) Identify number
2.) Count number of objects by ones
3.) Bundle objects in groups of ten. Count groups.
4.) Say number using tens and ones.
Learning Objective 2: Count a set of objects by making groups of ten.
Materials:
Teacher –
Bag of M & M’s
Snack bag of pretzels
Six ten frame trays
Bag of beans
Description:
A. Break down the skill of count a group of concrete objects by making groups of tens using concrete objects.
1.) Bundle objects into groups of ten. Count groups of ten.
2.) Count individual objects not bundled.
3.) Say number using tens and ones
Purpose: to provide students an opportunity to build their initial understanding of how to make groups of tens using concrete objects and to provide you the opportunity to evaluate your students’ level 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 other the learning objective in this plan. You should scaffold your instruction with each skill/concept you model.
Learning Objective 1: Given a set of concrete objects, make groups of ten.
Materials:
Teacher –
Unifix cubes
Counting bears
Ten frames
Students-
Bag of thirty beans/student
Ten frames
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 response. Have these choices in mind before you begin scaffolding instruction (Examples of choices are shown in red.)
Identify number
Boys and girls, let’s review what we have learned. I have a bag of Unifix cubes. I am going to give a bag of Unifix cubes to each pair of students. I want to make sure that each person in a pair gets ten Unifix cubes to use. How many children are in a pair? Right two. Each bag has twenty-two Unifix cubes and I want to count the Unifix cubes in this bag to make sure there are enough so that each person gets ten. How many will each person get? Right – ten. How many Unifix cubes do I have? Right twenty-two. So I want to see how many groups of ten I can make from this bag of twenty-two. Do you think we will have enough Unifix cubes to make two groups of ten? Hmm, I don’t know; let’s count our Unifix cubes.
Count number of objects by ones to correspond to number
The first thing we are going to do is to count each of these cubes. One, two…twenty-two. There, I have twenty-two unifix cubes.
Bundle objects in groups of ten. Count groups.
How many cubes do I want to give each person? Right, ten. What can we use to help us find out how many groups of ten I have in this bag? Right, a ten frame. How many cubes do I put in each box on this tray? Right, one. Each of these trays will hold ten cubes. I am going to put one cube in each box. When the boxes are filled up, I know that I have made a group to ten. Show me with your fingers how many groups of ten you think we will make? Let’s count and see how many trays we can fill up. Help me count and fill up the first ten frame. What are we going to count to? Right, ten. One, two, … ten (Fill up one tray.). There is one group of ten. I am going to see if I can get another group of ten. Do you think I can? Help me count again. (One, two, three…ten.) I have made another group of ten... How many groups of ten have I made so far? Right! One, two groups of ten. Do you think I can make any more groups of ten? Well, let’s see. One, two. Nope I can’t make any more groups of ten.
Say number using tens (and ones, if there are “left overs.”)
Let’s see. I have two groups of ten. I wonder how much is two groups of ten? Well, I am going to count by tens and see- ten, twenty. Two groups of ten is twenty, plus one, two, more is twenty-two. So, ten, twenty plus two more is twenty -one, and twenty-two. I had twenty-two cubes and made two groups of ten. Each person will be able to have ten cubes.
b. Maintain a high level of teacher direction/support for another example if students demonstrate misunderstanding/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. (Examples of choices are shown in red.)
Identify number
You are doing so well, that this time I want you to give me even more help. Let’s see, this time I have a bag of forty-five counting bears. I want to see how many groups of ten I can make from these forty-five bears. Tell me again, how many bears do I have? Right, forty-five. How many groups of ten do you think we can make? Well, let’s see.
Count number of objects by ones to correspond to number
The first thing we are going to do is to count the bears by ones. Help me while I count them. One, two…forty-five. Well, we know we have forty-five bears.
Bundle objects in groups of ten. Count groups.
I wonder what I can use to make groups of ten? Right, a ten frame. Show me how many cubes do I put in each box on this tray? Right, one. Show me how many bears in all will go in each ten tray? Right ten. ____ and _____, help me count and fill up the first ten frame. What are we going to count to? Right, ten. One, two, … ten (Fill up one tray.). There is one group of ten. I am going to see if we can get another group of ten. Do you think I can? _____ and _____, help me fill up this tray. (One, two, three…ten.) We have made another group of ten... How many groups of ten have we made so far? Right! One, two groups of ten. Do you think we can make any more groups of ten? Well, let’s see, ____ and _____ will you help me fill up another frame? Now how many ten frames do I have filled up? Right, three. Can I fill up anymore? I think so too. Yes, look, I filled up one more. We have filled up four ten frames.
Say number using tens (and ones, if there are “left overs.”
Let’s see. How many groups of ten do we have? Right four. How much is four groups of ten? _______. count by tens and see- ten, twenty, thirty, forty. Four groups of ten is forty. Plus one, two, three, four, five more is forty-five . So, ten, twenty, thirty, forty, plus one, two, three, four, five is forty five.
b. Maintain a medium level of teacher direction/support for another example if students demonstrate misunderstanding/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 at their desks as you work together.
Identify number
Now I am going to have each of you work some problems. Each of you has a bag of thirty beans. I want you to tell me how many groups of ten you will have in this bag of beans. Boys and girls, how many beans do you have? How many groups of ten do you think you can make? Well, let’s see.
Count number of objects by ones to correspond to number
What is the first thing you are going to do? Right, everyone needs to count the beans.
Bundle objects in groups of ten. Count groups.
Now what do you need to do? Right, use your ten frames to make groups of ten. How many trays did you fill up? Good, everyone filled up three trays.
Say number using tens (and ones, if there are “left overs.”)
Let’s see. How many groups of ten do you have? Right, three. How much is three groups of ten? You all are sharp today! Three groups of ten is thirty. You made three groups of ten from your thirty beans.
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 make groups of ten.
Learning Objective 1: Given a set of concrete objects, make groups of ten.
Structured Language Experience
Materials:
Teacher –
Bell or timer to signal when to switch bins
Students –
3 containers (e.g. box tops) with groups of concrete objects placed on place value mats. Containers should be differentiated with a color or symbol, letter or number. Some groups in the containers should show groups of ten, some groups should only show groups of ones.
Description:
Activity:
Students will work at tables in groups of 3 children. Each child is assigned a container. Each child should look at his container and decide whether it shows groups of tens or not. When the teacher rings the bell the children at each table are to take turns telling the others at their table if their container shows groups of ten, and if so how many groups of ten. 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 containers 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 skill(s) within the context of the activity before students begin the activity:
a. Look at the container
b. Decide if the objects are in groups of ten.
c. Wait for the teacher signal and then tell tablemates if the container shows groups of ten.
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. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate behavior.
b. Make sure that each child receives feedback on his/her decision. Provide corrective feedback and modeling as needed.
c. Provide closed choice questions (are these objects in groups of ten or not?) 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 count objects by making groups of ten.
Learning Objective 2: Count objects by making groups of ten.
Structured Cooperative Learning
Materials:
Teacher –
Bell or timer
Sample container and ten frames
Students –
Several containers or envelopes. Each container will have counting objects (e.g. beans)
Ten frames (can be made from index cards and then laminated).
Description:
Activity:
Students will work in teams of 4 students. Each team will count the items in each of their containers by grouping by tens. Because this activity requires space for the ten frames, it might be best to do this as a table or floor activity. The teacher will ring a bell to signal an end to the activity and at that time, ask individual students from each team to come to the front to show their solutions. Teams can get points for each correct answer.
Cooperative Learning Groups Steps:
1.) Provide explicit directions for the cooperative group activity including what you will do, what students will do, and reinforce any behavioral expectations for the game.
2.) Arrange students in cooperative groups. Groups should include students of varying skill levels.
3.) Assign roles to individual group members and explain them:
a. Materials manager (gets the materials)
b. Turn –taker (makes sure that each student at the table gets a turn)
c. Reporter (raises his/her hand to let the teacher know when the group has completed the task.)
d. Encourager(s) (encourages each person as they are deciding)
4.) Distribute materials.
5.) Model one example of skill(s).
a. Select a container.
b. Count objects using ten frames.
c. Say number using tens and ones (if needed).
d. Make sure that the team agrees with the decision before the next student has a turn.
6.) Review/model appropriate cooperative group behaviors and expectations.
a. Agree or disagree with a teammate’s decision
b. Listen while children are sharing their responses with the whole class.
7.) Provide opportunity for students to ask questions.
8.) Teacher monitors and provides specific corrective feedback & positive.
a. Circulate around the table and check on children’s responses.
b. Make sure that each child receives feedback on his/her decision.
c. Ask each child in the class to share his/her decisions at least once either with the entire class or individually with the teacher.
d. Provide corrective feedback to students as needed.
Purpose: to provide you 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 matched and unmatched groups; bins 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 so students can respond.
Suggestions:
Receptive/recognition level:
Student can correctly recognize groups show grouping by tens.
Expressive level:
Student can count given objects by grouping by tens.
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 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. (e.g. “Did you fill up all your ten frames? How many groups of ten do you have?”)
10.) Evaluate whether students are ready to move to the next level of understanding or have mastered the skill using the following guide:
Concrete Level: 100% accuracy (given 3-5 trials) over three consecutive days.
11.) Based on students’ performance, determine whether you need to alter or modify your instruction.
Flexible Math Interview
Purpose: to provide you with additional diagnostic information in order to check student understanding and plan and/or modify instruction accordingly.
Materials:
Groups of concrete objects
Ten frames
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 count a group of objects by grouping by tens. The teacher should note errors or misconceptions while the student is “teaching,” but 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 confers with students regarding specific errors or misconceptions afterwards.
Purpose: to provide periodic student practice activities & teacher directed review of this skill after students have mastered it.
1. Calendar Time
Materials:
Straws or other objects that can be bundled
Boxes or cans for 1’s, 10’s and 100’s
Description:
Count the number of days in school by grouping straws into bundles of 10 as appropriate, and counting by tens.
2. Center Time
Materials:
Laminated folder or paper with ten frames drawn on it and velcro on each square
Small, flat counting objects with velcro or counting buttons made from flannel
Tape player or language master (optional)
Description:
Student will choose a folder, take counting objects from envelope, and count them using ten frames. Student can tell the teacher or record his/her answer (e.g. “Folder number one: four tens and three ones. I have 43 buttons”) and the folder can be left for teacher to check.
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