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Mathematics: a unit plan and Lesson plan
Candidate’s Name:Margaret Nelson *Student ID omitted for privacy
Subject: Mathematics Grade: 2 Lesson Topic: Understand <, >, and =
A unit plan
Major Content Area (eg: Adding fractions)
Understanding and building fluency with base-ten notation.
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Learning Goal for the Unit: (Briefly explain what students should attain at the end of the unit)
At the end of the unit, students should understand base-ten numbers, and be fluent in them.
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Standard To Be Addressed in Unit: (List specific Content Standards aligned to the learning goal)
Specific content standards to be addressed in this unit are:
CSS.MATH.CONTENT.2.NBT.A3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
CSS.MATH.CONTENT.2.NBT.A4: Compare two three-digit numbers based on meanings of the hundred
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Pre and Post Assessment for Unit (How will you determine students’ prior knowledge for this unit? How will you assess students’ mastery of intended outcomes?)
Students are expected to already have a prior knowledge of the numbers system and the place value of numbers. I think a great way to assess prior knowledge of place values is through informal assessment by asking students to explain the place values of a set of numbers.
For post assessment, students will be able to show fluency in base-ten numbers and place value by being able to demonstrate understanding of the <,=, and > symbols.
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Rationale for Lesson Sequence: Why are you sequencing the lessons in the following order?
These lessons are ordered so that students can first understand place value, build fluency, and then use that knowledge to manipulate number sentences with their number sense in order to begin algebraic thinking in terms of visualizing the = symbol as a balance point within an equation.
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Lesson
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Content Standard(s)
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Learning Outcomes
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Math Practice (MP) Standards for aligned to this lesson and WHY
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Instructional Strategies
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1
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CSS.MATH.CONTENT.2.NBT.A3
CSS.MATH.CONTENT.2.NBT.A4
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Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
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CSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
Solving several problems in class and independently provides knowledge experience that is reliable; meaning, it does not change with the environment.
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Utilizing direct instruction to scaffold solving problems, followed by group work and independent practices which also include handouts to provide multiple opportunities to persevere and solve problems.
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2
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CSS.MATH.CONTENT.2.NBT.A3
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Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using <, =, and > symbols to record the results of comparisons.
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CSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively.
Through a conceptual understanding of mathematics, students develop a personal relationship with mathematics knowledge and adopt a self-governed locus of control.
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Utilizing illustrations, models, and examples, students will approach solving problems through conceptual understanding and then encounter and adopt systems with numbers to represent the concepts they have learned.
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3
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CSS.MATH.CONTENT.2.NBT.A3
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Achieve enough proficiency in solving problems to be able to correct the work of other students.
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CSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.
This provides more opportunities for scaffolding, since students are participating in viewing demonstrated work from other students, who may be more proficient in the current task.
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Working in centers allows students to see and correct the work of other groups.
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4
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CSS.MATH.CONTENT.2.NBT.A3
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Translate word problems in to number problems which represent fluency and practice in base-ten numbers.
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CSS.MATH.PRACTICE.MP4: Model with mathematics.
Demonstrates conceptual understanding of mathematics knowledge.
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Solving word problems that require translating lifelike scenarios into numbers prepares this conceptual understanding.
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5
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CSS.MATH.CONTENT.2.NBT.A4
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Understanding the <, >, and = symbols.
See the = symbol as representative of two sides that are balanced.
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CSS.MATH.PRACTICE.MP7: Look for and make use of structure.
Understanding structure of <, >, and = problems can help students see the = as part of an equation where both sides are balanced. This paves the way for algebraic thinking.
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I will use the approach of “show, then tell,” utilizing a balance scale in order to introduce the concept of <, and >, with the scale itself representing the = symbol.
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Mathematics Lesson Plan Design Template
1. K12 Academic Content Standards: (List the state-adopted academic content standard(s) for students you will address in the lesson)
Content standard(s):
CSS.MATH.CONTENT.2.NBT.A3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
CSS.MATH.CONTENT.2.NBT.A4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using <, =, and > symbols to record the results of comparisons.
Mathematical Practice Standard(s):
CSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
CSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively.
CSS.MATH.PRACTICE.MP3: Collect viable arguments and critique the reasoning of others.
CSS.MATH.PRACTICE.MP4: Model with mathematics.
CSS.MATH.PRACTICE.MP7: Look for and make use of structure.
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2. Learning Objective(s): (What specifically do you expect students to know or be able to do as a result of the lesson?)
For prior knowledge, students should be proficient in these standards:
Understand place value in regards to the ones, tens, and hundredths place values.
Have a conceptual understanding of the <, =, and > symbols
Demonstrate knowledge of these symbols in group settings, and in independent work.
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Rationale:
This satisfies CSS.MATH.CONTENT.2.NBT.A3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
And
CSS.MATH.CONTENT.NBT.A4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using <, =, and > symbols to record the results of comparisons.
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3. Pre-assessment Activity: (How will the content of the lesson connect to the prior knowledge?)
For the Pre-assessment Activity, students will gather as a group to talk about large numbers. Volunteers will be asked to come up with numbers that have three digits, and these numbers will be written on the board.
The numbers will be written in a column, so that class can discuss as a group which digit is in the hundredths place, the tens, the ones, etc.
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Rationale:
This reviews what students know about place value, and also provides a reference point with which to scaffold learning by referring to throughout the lesson.
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4. Differentiation, Adaptation & Accommodation Strategies: (Based on the pre-assessments, modify Learning Activities based on learner characteristics to meet the needs of ELL & special needs students, highly achieving students, average achieving students, and low achieving students)
1. ELL:
This lesson is inclusive for students to develop understanding and use of language referring to “greater,” “least,” “less,” and “equals.” It is also appropriate to include words like “more” and “less.”
2. Students with Special Needs:
Students can be given more time to complete worksheets. Students with mobility issues can be included by being leaders when holding up number cards. Students with visual problems can utilize the song, as well as the projector. Students with problems such as EBD or numbers problems can have multiple opportunities to leave their seats
3. Proficient Students:
Students who complete handout with proficiency can move on to one or more “Mathigator” worksheets. Subsequent project pages could also contain addition or subtraction on both sides, so students would have to solve the problem and evaluate the results based on the symbols learned in this lesson.
4. General Education Students:
General Education students will work with direct instruction, multiple opportunities for group work, and individual practice.
5. Low Proficiency Students:
Low proficiency students may likely be struggling with the idea of an alligator being representative of a symbol. Low proficiency students may need more intervention during group work to discuss number sense and place values.
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Rationale:
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5. Resources: (Identify materials needed for this lesson accounting for varying degrees of skill level)
Number Cards (index cards with three-digit numbers written on them)
Jars of jellybeans, with different numbers of beans inside, and numbers written on the outside of the jar.
Projector (for displaying NUMBEROCK video)
Construction Paper
Markers
Alligator < and > illustrations (See sample illustration after the conclusion of this lesson plan)
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Rationale:
Materials used are meant to be meaningful in that they encourage and bolster the use of all five senses while learning in this lesson.
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6. Learning Activities - Explicit Teacher Instruction: (Explain, Model, Demonstrate, Check for Understanding)
Instructional plan in communicating the academic learning goal(s) to the students
1. I would first tell them that we will be learning about different symbols. These symbols are the >, <, and = symbols.
I would ask students what they know already about these symbols. I expect that some of them would know what the = symbol is, but perhaps might not be able to explain it in words.
I would introduce the idea that the >, and < symbols resemble the mouth of an alligator, and that is a way we can remember what they mean.
2. Say: “These symbols talk about numbers that are greater than others, less than others, or equal to each other.”
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Rationale:
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Instructional strategies
1. We will first watch the video “Greater Than Less Than Song for Kids” by NUMBEROCK (2017), and learn the song they sing.
2. Then I will present the jars of jellybeans. Comparing two jars at a time, I would ask students which jar of jellybeans a math alligator would eat. After each answer, I would draw the corresponding symbol on the board.
3. Then I would refer back to the list of numbers students came up with, which were listed on the whiteboard. Comparing two numbers at a time, I would ask students which numbers a math alligator would eat. I would begin using math language such as “greater,” “less than,” and “equal.”
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Rationale:
2. This video provides an introduction to the mnemonic device we will be utilizing throughout this lesson. It also encourages children to engage by learning and singing the song.
2. This helps understanding by showing as soon as possible the concept behind the values of numbers. This is scaffolded on the presentation provided by the video, which does not show objects in terms of quantity.
3. This scaffolds information in the same way we have just covered with the jellybeans. Since jellybeans would have likely gotten the attention of students, this is a great opportunity to then dive right into numbers.
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Student grouping
1. Large Groups: I would ask for two volunteers to hold number cards on opposite sides of the classroom. Each volunteer would hold up a card with a number on it, and students could use their arms to form < and > symbols, and “chomp” their way towards the bigger number. We would continue singing the song we learned while we “chomp” as a class.
2. Small Groups: I would then group students in smaller groups, likely at their group tables, or just in groups of 3-4 students. Their instructions would be to tell a story about a math alligator who saw two numbers, and what the numbers were.
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Rationale:
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Monitoring student learning
Students would present their story (3-4 sentences) to the class, singing the song from the video at each presentation.
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Rationale:
Students would demonstrate understanding by using appropriate language and terms, in words and numbers.
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7. Guided Practice: (Check for understanding and provide feedback and re-teaching)
The whole class would form a circle, and each student would receive a number card to hold.
Say: “We are now going to try to find the greatest number in the whole class.”
One student would begin by comparing his/her card to the student on the right.
Say: “Is the new card greater or less than the original student’s (use student’s name)?”
The student with the greater card moves through the circle to compare with the next student, and so on, until the greatest number is discovered.
If time allows, reverse the process to have students find the card with the smallest number. Continue to use math language such as “greater” and “least.”
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Rationale:
This provides multiple opportunities for practice, and since each student would get a turn to be the focus of attention, it also provides practice for an exercise with increased stakes. Feedback can come in the form of collaborative class correction and re-teaching through talking about the place values within each number.
CSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
CSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.
CSS.MATH.PRACTICE.MP7: Look for and make use of structure.
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8. Independent Practice: (Provide practice that supports the learning outcome. Note: Independent activities are assigned assuming that students understand the concept well enough to work on their own.)
Hand out worksheet. Instruct students to spend class time on practicing the <, >, and = symbols with numbers. If possible, students should not need to rely on the alligator mnemonic, so use only the real names of the symbols.
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Rationale:
Students independently persevere to solve problems. Independent practice also establishes and encourages a personal locus of control over learning this and other lessons.
CSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively
CSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.
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9. Post Assessment Activities: (Describe how you will assess students’ learning. Describe differentiating assessment strategies you will use for ELL, special needs students, highly achieving students and low achieving students.)
Students will complete a “Mathigator” project. This is a class craft, beginning with a large piece of construction paper. Students will write a three-digit number on either side of the paper. Students can color and cut out alligator shapes, pointing the mouth of the gator to either side, depending on which is the greater number. On the bottom of the paper, Students can write what they are depicting using words and numbers. For example, a student who has chosen the numbers 123 and 146 would have the alligator showing the number 146 as greater. Below, they would write in symbols: “123 < 146.” Below that, they would write in words: “123 is less than 146.”
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Rationale:
This approach engages students by encouraging creativity. Students also have an opportunity to work individually to write the problems conceptually, using numbers, and using words. This ties into the things they have practiced as a group and in small groups during the course of this lesson.
CSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively.
CSS.MATH.PRACTICE.MP4: Model with mathematics.
CSS.MATH.PRACTICE.MP5: Use appropriate tools strategically.
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10. Closure: (Describe how students will reflect on what they have learned.)
The lesson will close with an additional song, sung together as a class. Students can submit their completed “Mathigator” project to be displayed in the classroom.
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Rationale:
Displaying student work provides more opportunities for students to see and consider the lessons they’ve learned throughout the days and weeks to come.
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Sources:
Common Core Standards. (2019). Retrieved May 4, 2019 from:
http://www.corestandards.org/Math/Content/2/NBT/
http://www.corestandards.org/Math/Content/2/NBT/
Common Core Standards. (2019). Standards for Mathematical Practice. Retrieved May 4, 2019
from: http://www.corestandards.org/Math/Practice/
from: http://www.corestandards.org/Math/Practice/
NUMBEROCK. (2017). “Greater Than Less Than Song for Kids.” Retrieved from: https://
numberock.com/lessons/less-than-greater-than/
numberock.com/lessons/less-than-greater-than/
Wadsworth, B., & Wadsworth, B. (1984). Piaget’s theory of cognitive and affective
development (3rd ed.). New York: Longman.
development (3rd ed.). New York: Longman.
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