## Math Lesson Plan: Dot Cards and Number Sense

This is a summary of the lesson, including core decisions related to lesson planning, my pedagogical focus, and the plan itself. It was revised based on feedback from my math methods professor, Classroom Mentor, and Penn Mentor.

Please click here to view the lesson plan in its entirety.

Please click here to view the lesson plan in its entirety.

## Core Decisions in Lesson Planning

__What:__My lesson is an expanded number talk designed to deepen students’ number sense and enhance their ability to use discourse. Mathematical content includes one-to-one correspondence and number composition. The dot cards we will use encourage students to subitize (chunk quantities into subgroups), which is a foundational for addition and subtraction as well as for understanding place value in our base-10 system. As students become proficient at chunking, they begin to understand “teen” numbers as "ten and some ones," which is a PA Math Standard for Kindergarten. A secondary goal of this lesson is numeral formations. If students cannot write numerals correctly, they will struggle to communicate quantities with precision and accuracy. Students need to be “fluent” in their written communication of mathematical ideas. This lesson builds on in-class work on representing quantities and explaining strategies. Students will explain their strategies for counting quantities and engage in discourse about counting and grouping strategies.

__How:__The dot cards for this lesson display quantities from 3-10 in various arrangements. First, students will identify the quantity on each card. Then, the students will write the numeral that represents the quantity on each card. Last, the students will see a numeral and make their own dot arrangements. At each stage, students will explain their counting strategies. I will use discourse to enhance student thinking by questioning and by revoicing students’ strategies. The tools we will use during this lesson are the dot cards, counting chips, and whiteboard kits. For the first and second activity, an important norm is that students use the appropriate "ready" signal (either thumbs up or writing). Throughout the lesson, I will cultivate the norm of discussing our solutions, valuing everyone’s solutions, and respecting our classmates.

__Why:__During math class, I observed that most students count by ones even when they are counting a large number of items. Through the dot card activities, I hope to help students begin to be able to group the dots and subitize, and then understand that if they see 3 and 2, that makes 5 – they don’t have to count by ones up to 5. Dot card activities are a common and effective tool for teaching number sense. I chose to have students write their answers on whiteboards to accomplish two things: students will come up with the answer on their own, without being influenced by their classmates, and students will improve their numeration skills, assigning numerals to quantities. Having students create their own dot arrays will push the students to think more deeply about number composition and grouping, because they can represent the quantity in whatever arrangement they choose. I decided to have the children use chips instead of draw their arrangements because I think it will be easier for them to manipulate physical objects.

__Pedagogical Focus:__My pedagogical focus as a teacher during this lesson is facilitating discussion around mathematical ideas by eliciting, clarifying, and following up on student explanations. Thinking about discourse in math is a fairly new concept for me as a teacher, but I know that discourse plays a key role in student learning and in building a classroom community. I want to improve both my own use of discourse and my strategies (talk moves) for leading my students in effective mathematical discourse that enhances their learning. Specific talk moves I will focus on in this lesson are revoicing, having students restate their classmates’ explanations, and having students apply a classmate’s reasoning to a problem.

## Lesson Plan

(Again, click here to view the entire lesson plan.)

K.CC.3 - Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a

count of no objects).

K.CC.4 - Understand the relationship between numbers and quantities; connect counting to cardinality.

a. When counting objects, say the number names in the standard order, pairing each object with one and only one

number name and each number name with one and only one object.

b. Understand that the last number name said tells the number of objects counted. The number of objects is the

same regardless of their arrangement or the order in which they were counted.

CC2.1.K.A.2 - Apply one-to-one correspondence to count the number of objects.

CC.2.1.K.B.1 - Use place value to compose and decompose numbers within 19.

Use appropriate tools strategically

Activity 1: Introducing Dot Cards (6 minutes)

Assessment will take place through observation. For the first objective, during activities 1 and 2, I will observe whether each student is able to identify the correct number of dots on each dot card. During activity 2, I will observe whether the students are writing the correct numeral. To assess the second objective, I will observe the students during activity 3 to determine if they can accurately represent quantities from 1-10. Assessment for the third objective will take place during all three activities as I listen to students explain how they counted the dots. As I observe the students during the lesson, I will also be filling out an assessment checklist (shown below).

Objectives:Objectives:

- SWBAT correctly identify the number of dots from 3-10 in various arrangements and write the corresponding numeral.
- SWBAT represent quantities 3-10.
- SWBAT articulate counting strategies.

__Standards:__*Common Core:*K.CC.3 - Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a

count of no objects).

K.CC.4 - Understand the relationship between numbers and quantities; connect counting to cardinality.

a. When counting objects, say the number names in the standard order, pairing each object with one and only one

number name and each number name with one and only one object.

b. Understand that the last number name said tells the number of objects counted. The number of objects is the

same regardless of their arrangement or the order in which they were counted.

*PA Math Standards:*

CC.2.1.K.A.1 - Know number names and write and recite the count sequence.CC2.1.K.A.2 - Apply one-to-one correspondence to count the number of objects.

CC.2.1.K.B.1 - Use place value to compose and decompose numbers within 19.

*Standards for Mathematical Practice:*

Reason abstractly and quantitativelyUse appropriate tools strategically

__Plan:__Activity 1: Introducing Dot Cards (6 minutes)

- Explain and model counting a dot card for students. Remind them to use "silent thumbs-up" as the answer signal.
- Display a dot card, wait for all thumbs to be up. Lead student discussion on the various strategies students used to count or group the dots. Repeat with two more dot cards.

- Explain that students will now write the answer instead of showing a thumbs up. Pass out whiteboard kits.
- Display a dot card, wait for all students two write a number. Lead student discussion on the various strategies students used to count or group the dots. Use talk moves to encourage students to restate each other’s strategies. Check that students have written the numerals correctly; if not, remind them to check the number poster.
- Repeat with three more dot cards. If students are only counting by ones, model chunking.

- Give each student a bag with 10 counting chips and a piece of construction paper. Explain that students will use chips to represent the numeral the teacher displays.
- Students make arrays to represent the number 4. Students count each other’s arrays and explain strategies.
- Repeat activity with three more numbers. If necessary, model “chunking” of dots for students.

__Assessment:__Assessment will take place through observation. For the first objective, during activities 1 and 2, I will observe whether each student is able to identify the correct number of dots on each dot card. During activity 2, I will observe whether the students are writing the correct numeral. To assess the second objective, I will observe the students during activity 3 to determine if they can accurately represent quantities from 1-10. Assessment for the third objective will take place during all three activities as I listen to students explain how they counted the dots. As I observe the students during the lesson, I will also be filling out an assessment checklist (shown below).

Click here to view the original lesson plan with my math methods professor's notes.