Counting (Dots in Various Arrangements)
Kindergarten
Formative Asssment Lesson
Designed and revid by Kentucky Department of Education Mathematics Specialists
Field-tested by Kentucky Mathematics Leadership Network Teachers
Created for the sole purpo of assisting teachers as they develop student understanding of Kentucky’s Core Academic Standard through the u of highly effective teaching and learning.
Not intended for sale.
Counting (Dots in Various Arrangements) Kindergarten This Formative Asssment Lesson is designed to be part of an instructional unit. This task should be implemented approximately two-thirds of the way through the instructional unit. The results of this task should then be ud to inform the instruction that will take place for the remainder of your unit.
Mathematical goals
This lesson unit is intended to help you asss how well students are able to count objects up to 10 no matter how they are arranged and also how well they are able to reprent their counts with written numerals. It will help you to identify students who have the following difficulties:
∙Not being able to track where they start/stop counting
∙Arranging objects to be counted简单的美白方法
∙One-to-one correspondence
防疫制度Common Core State Standards
This lesson involves mathematical content in the standards from across the grade, with emphasis on:
Counting and Cardinality K.CC
∙Know number names and the count quence.
∙Count to tell the number of objects.
This lesson involves a range of Standards for Mathematical Practice, with emphasis on:
2. Reason abstractly and quantitatively.
7. Look at and make u of structure.
淮委Introduction
This lesson is structured in the following way:
∙Before the lesson, students work individually on an asssment task that is designed to reveal their current understandings and difficulties. You then review their work and create questions for students to answer in
order to improve their solutions.
∙Students work in small groups on collaborative discussion tasks, to match cards with dots in regular patterns, structured 10 frame patterns, unstructured arrangements, and numerals. As they do this, they interpret the
寄生虫影评
cards’ meanings and begin to link them together. Through out their work, students justify and explain their
decisions to their peers.
∙Students return to their original asssment tasks, and try to improve their own respons.
Materials required
Each individual student will need:
∙Two copies of the asssment task Counting Dots.
∙ A sheet of sticky dots or bingo daubers
Each small group of students will need the following resources:
∙Card ts: A, B, C, and D. All cards should be cut up before the lesson and it would be helpful if each t were a different color.
Time needed
Approximately 15 minutes before the lesson (for the individual asssment task), one 40 minute lesson, and 15 minutes for a follow-up lesson (for students to revisit individual asssment task). Timings given are only approximate. All students need not complete all ts of activity cards. Exact timings will depend on the needs of the class.
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Before the Lesson象山美食
Asssment task: Counting Dots (15-20 minutes)
Have students do this task individually in class a day or more before the formative asssment lesson. This will give you an opportunity to asss the work, and to find out the kinds of difficulties students have with it. You will be able to target your help more effectively in the follow-up lesson. Depending on your class you can have them complete the asssment task in whole group or small groups (they should still work individually).
Frame the Pre-Asssment
经济工作会议讲话Give each student a copy of the asssment task Counting Dots.
Today we are going to work on a task about counting. This task is to help me e ways that I can he
lp you if you are having any problems counting. If you are not sure about all of your answers, it is okay. We are going to do an activity that will help us get better at counting.
On the first page you are going to count the number of dots in each picture. Write the numeral that tells how many dots in the box beside the picture. On the next page, count out sticker dots that match the number in the box. Place them in the box beside of the number.
It is important that the students are allowed to answer the questions without your assistance, as far as possible.
Students should not worry too much if they cannot understand or do everything, becau in the next lesson they will engage in a similar task, which should help them. Explain to students that by the end of the next lesson, they should expect to answer questions such as the confidently. This is their goal.
Asssing students’ respons
Collect students’ respons to the task. Make some notes about what their work reveals about their current levels of understanding, and their different problem solving approaches. Partner/Group students with others who displayed similar errors/misconceptions on the pre-asssment task.描写向日葵的作文
We suggest that you do not score stude nt’s work. The rearch shows that this will be counterproductive, as it will encourage students to compare their scores, and will distract their attention from what they can do to improve their mathematics.
Instead, help students to make further progress by summarizing their difficulties as a ries of questions. Some questions on the following page may rve as examples. The questions have been drawn from commonly identified student misconceptions.
We suggest that you write a list of your own questi ons, bad on your students’ work, using, but not limited to, the ideas that follow. You may choo to write questions on each student’s work. If you do not have time to do this, lect a few questions that will be of help to the majority of students. The can be written on the board at the end of the lesson before the students are given the post asssment task.
The solution to all the difficulties is not to teach one particular way of counting-one to one matching-but to help students to find a variety of ways that work in different situations and make n to them.
Below is a list of common issues and questions/prompts that may be written on individual initial tasks
or during the collaborative activity to help students clarify and extend their thinking.
Suggested lesson outline
Collaborative Activity: matching Card Sets A, B, C, and D (30 min.)
Strategically group students bad on pre-asssment data in to groups of two or three. With larger groups, some students may not fully engage in the task. Group students with others who displayed similar errors/misconceptions on the pre-asssment task.
Give each group Card Sets A (numerals) and B (structured 10-frames).
Introduce the lesson carefully:
I want you to work as a team. Take turns placing a numeral card with a dot card that has the same number of
dots. Each time you do this, explain your thinking clearly to your partner. If your partner disagrees with your
match then challenge him or her to explain why. It is important that you both understand why each card is
matched with another one. You will also find some cards that d on’t have a match. It will be your job to u a blank card and create the match. There is a lot of work to do today and you may not all finish. The important thing is to learn something new, so take your time.
Your tasks during the small group work are to make a note of student approaches to the task, and to support student problem solving. As you monitor the work, listen to the discussion and help students to look for patterns and generalizations.
Make a note of student approaches to the task
You can then u this information to focus a whole-class discussion towards the end of the lesson. In particular, notice any common mistakes. For example, students may consistently loo count or forget where they started and re-count dots.
Support student problem solving
Try not to make suggestions that move students toward a particular approach to the task. Instead, ask questions to help students clarify their thinking. Encourage students to u each other as a resource for learning.
If one student has placed a particular card to make a match, challenge their partner to provide an explanation.
If you find students have difficulty articulating their decisions, then you may want to u the questions from the Common Issues table to support your questioning.
If the whole class is struggling on the same issue, then you may want to write a couple of questions on the board and organize a whole class discussion.
Placing Card Set C (regular patterns)
As students finish with matching card ts A and B and can explain their work, hand out card t C. The provide students with a different way of interpreting the numbers.
Do not collect card t B. An important part of this task is for students to make connections between different reprentations of numbers.
