How to Write a Mathematics Lesson 1. Always think about “what is it that I want the students to learn?” a. These should be your lesson objectives b. AND they should reflect what is on your assessment à You can create your assessment first so that you know exactly at what “end” you want to be, what you value, and what you ultimately want the students to know c. KUD’s: What you want your students to Know, Understand, & Do 2. Then try to think of why this is important a. Is it a foundational idea in which other concepts will build? b. Does it have great historical or practical importance? c. Where is it used in the real world or how will it help the students? 3. This “why” should lead you to how to formulate your lesson a. Have this be the starting off point to motivate the students to learn b. This should be a theme throughout your lesson 4. ALWAYS start with something concrete that the students can relate to and grab hold of – this is your opportunity to create a “problem” so your students can become better “problem solvers” a. This is also your opportunity to spark curiosity and instill motivation: show the power and importance of math b. Hopefully this will avoid the “why do we have to know this anyway,” “what is the point of this,” and the “why should we care about this” 5. Once you have their attention and motivation use it to empower them and teach them math! a. Think about all of the ways you can engage the students: does this topic lend itself to group work, pairs, or whole class instruction? b. Can you create enough scaffolding so that the students can be the center of the lesson (you do the least amount of talking as possible)? ALWAYS think to yourself – “how can my students understand this topic without me telling it to them?” c. Always want the students to be doing more “work” than you in the classroom (outside of the classroom is a different story) 6. After you have created positive-­‐minded, motivated, and enthusiastic students you can move towards the abstract and practice “math problems” Figure out the importance of HW – why should they do it: practice? Extension? You as the teacher need to determine the value you place on HW. Just don’t give them HW for the sake of giving HW, make it meaningful! If you are going to assign it, and you expect your students to do it, then you better be prepared to spend adequate time on it. If you do not have adequate time, make it optional – say these are practice problems that would behoove you to do, especially if you need the practice. For a student looking in the math textbook, all of the problems look the same, so lead them in right direction of where you want them to focus their attention and energy. EDU 556 Mathematics Lesson Plan Format Develop a problem-­‐based lesson plan that engages the students in the Standards for Mathematical Practice and promotes the learning of the identified objective. Title: [Insert text here] Grade Level [Insert text here] 1. Lesson Overview [Insert text here] Summarize the lesson content, rationale, and purpose Sentence 1: Lesson overview – what are you (goals of the lesson) in 3-­‐4 sentences. teaching & to whom? Sentence 2: why are you teaching it in this way? How in this lesson might you . . . Why did you choose the activities you did? • Engage students in productive struggle?
Sentence 3: What goal(s) do you hope to meet by • Get students to think and make connections?
the end of this lesson? •
Provide support for each student?
2. Learning Objectives [Insert text here] • List here in bullet points 3a. Common Core Content Standards [Insert text here] • One primary and (potentially) secondary standard(s) [Insert text here] • List the practices your lesson addresses Identify the measureable behaviors students should demonstrate. 3b. Common Core Standards for Mathematical Practice 4. Materials and Resources Identify materials and resources essential for successful completion of the lesson tasks or activities. [Insert text here] • List all mathematics manipulatives, tools, software, special paper (graph paper, card stock, etc.) and/or tools 5. Lesson Development (include time designations for each component) Outline the instructional strategies you will use to incorporate the materials and activities you have planned to obtain your objectives. Basically, what are you and the students going to be doing during class time? a. Engagement/Motivation (beginning): Describe the initial task or activity to engage and motivate students, activate relevant prior knowledge, and introduce the learning objectives. Activate prior knowledge & provide background information: •
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Determine how you will introduce the task/problem scenario (what problem(s) will the students have to solve?) – will you show a video, read a story, or something else? Consider warm-­‐ups that orient students’ thinking Build background; link to prior learning and to familiar concepts Incorporate review of key vocabulary Set task in written and oral form Make sure students understand the task Provide visual and real objects Be sure to set the stage for the day’s activities [Insert text here] • This should be short bullet points. • Consider the bullets list in box to the left; you should address at least four of these points here by providing the answer to “why is this important?” b. Instructional Procedures (during): Consider the following components as appropriate for this lesson: o Instructional model(s) o Groupings o Interactive Techniques/Tasks/Investigations o Questions o Explanations o Modeling/Demonstration o Practice (Guided, Collaborative, Independent) o Ongoing Formative Assessment Strategies and activities used to support the standards: •
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Anticipate students thinking Think about ways you will assist students Consider extensions or challenges Use demonstrations, modeling, etc. Maximize language. Ask students to explain and defend Encourage students to draw and/or model their thinking Use multiple representations of the content and encourage students to use many different representations as well What are your hinge questions that will determine where you take the class next? c. Closure (End): •
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How will students report their findings? Determine how you will format the discussion of the task What questions will you ask? What HW or follow up activities are needed? d. Debriefing and Next Steps Revisit the objectives and explain how will you will summarize the lesson and connect new knowledge to existing knowledge and future knowledge. Indicate plans for student self-­‐evaluation. [Insert text here] • These should be short bullet points that walk you through what you & your students will DO during this lesson • Try to anticipate at least two things students may do, ask, or say then think of how you might respond to these things. You can anticipate students use correct or incorrect strategies • Indicate any scaffolds you may have to use with students. • Include ALL discussion questions (questions you will pose to the class), example problems, or anything else that is essential to the lesson [Insert text here] • Report how students will share strategies and/or solutions • Write two questions that you would pose to students to ensure that they understand the primary objective. [Insert text here] • Pose a problem, strategy, or question that could tie to future knowledge • How will students know if they were successful in this lesson? 6. Differentiation Describe plans to differentiate content, processes, context, and/or products. Identify accommodations, extensions, and/or enhancements to meet individual needs, including those of English language learners, special education students, and learners with gifts/talents. For example, strategies for English-language learners
[Insert text here] • Include specific plans for individual students as necessary – this can be creating specific groups or partners for an activity, providing different representations, or having students report findings/understandings in different ways such as attending to key vocabulary, using visuals and
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7. Assessment/Evidence of Success: Describe how [Insert text here] you will measure student performance, understanding, • List at least two ways you will assess students’ and achievement. learning. • What evidence will be collected (consider • How will you know what your students informal and formal evidence)? understood? • How will the evidence be evaluated? • Discuss whether evidence will be evaluated; if • How will you know who understands what? so, how? EXAMPLE LESSON PLAN: Centipede’s 100 Shoes – Repeated Addition Lesson Plan Grade Level 2 1. Lesson While reading Centipede’s 100 Shoes students will find the total number of shoes the Overview centipede has at different points in the story using strategies of repeated addition. Students can work together in pairs to draw pictures corresponding to the story (or use other strategies) and then create the repeated addition equations to match each picture. The goal/purpose of the lesson is for students to use, understand when and why to use, and practice repeated addition. • Use repeated addition to find the total number of objects 2. Learning Objectives 3a. Common 2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays Core Content with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of Standards equal addends. 3b. Common • MP1. Make sense of problems and preserve in solving them Core • MP2. Reason abstractly and quantitatively Standards for • MP3. Construct viable arguments and critique the reasoning of others Mathematical • MP4. Model with mathematics Practice • MP8. Look for and express regularity in repeated reasoning 4. Materials • Centipede’s 100 Shoes by Tony Ross and Resources • Chart paper • Markers & pencils • List of animals/insects in the book • Pictures of animals/insects in book for students to glue onto papers • Glue • Unifix cubes, toothpicks, chips, or other objects students can use to model legs/shoes 5. Lesson Development (include time designations for each component) a. About 10-­‐15 minutes: Engagement/ • Students pick up warm up worksheet as them come into class Motivation • Question: “What is the total number of shoes in our classroom?” (beginning): • Tell students they can solve in any way – words, pictures, manipulatives, equations, etc. • Answer any clarifying questions as needed • Put directions on the front board: “Take warm up worksheet from front and solve the problem in any way. When you are done, find a neighbor to discuss your solutions. How do they compare? Did you get the same answer? Explain how you got your answer.” • Circulate around the room to check-­‐in on students – see what they are doing and listen to their conversations About 5 minutes: • When most students are done sharing strategies with a neighbor or are in the process of sharing the strategy (have already completed the task), have a few volunteers share their strategies (if found different solution strategies while walking around, can ask those specific students) • If repeated addition does not come up, show students this strategy as if I was a student sharing my solution strategy • Have students evaluate this strategy (as they evaluated each of their classmates’ strategies presented) and start to see its efficiency b. 5 minutes: Instructional • Introduce story: “Today we are going to read Centipede’s 100 Shoes. How many feet do Procedures you think the centipede has?” (allow students to share responses) (during): • “Actually, according to the story, a centipede only has 42 legs. How many legs would be on each side of his body? How do you know?” (again allow students to share responses) • “This centipede bought some shoes, but decides he does not want to wear them and gives them all away. We are going to try to find out how many shoes the centipede has left to give out and who he could give them to.” 5 minutes: • Read story, stopping at sticky note (p.22) 5 minutes: • Give directions for activity: “Your job is to figure out how many shoes the centipede has already given away, how many he has left to give, and who the leftover shoes could be given to. You will work with a partner and show your thinking on the chart paper. You can show your thinking in any way, but you want to be efficient and accurate in your work. What could be the best way to show your work?” Have students fold paper into sixths and glue an insect picture at the top of each section to designate it. 15 minutes: • Student work time – circulate to groups and observe thinking: o Which students are able to articulate thinking? If a student is not able to articulate thinking, ask questions like “what did you do here?” in succession (at each step – c. Closure (End): d. Debriefing and Next Steps point to the steps on the student’s paper) until he/she has given complete argument o Who is able to show repeated addition for each of the insects to quickly determine the number of shoes given away? o Anticipated student responses/actions: § Correctly use the manipulatives to model the problems, then draw the corresponding pictures and equations on their chart paper with their partner § Get stuck – “I don’t know how/where to start” (see scaffolds for strategies to help) • Hinge question: How many shoes for the 5 spiders (8 legs each)? – allow students some time to work through (possibly struggle through) the grasshopper (6 legs each), two woodlice (14 legs each), and four beetles (6 legs each), but if student(s) still struggling by the time they are on the 4th insect (or do not get to the fourth insect within a reasonable amount of time (~8 minutes)), I will intervene as described below. • Scaffolds: Guide thinking for struggling students (students that are “stuck”) with questions such as: o How did you solve the warm-­‐up activity? How can you do the same thing here? o How can you write this as an addition equation? Help the students draw pictures or use the manipulatives to model (pretend the unifix cubes are shoes) the situations. Have students count out each of the cubes, then put them in groups, and write as an addition problem. After they add the numbers together, they will see that the number they got from counting all of the cubes was the same as the number they got from adding. 10 minutes • Bring pairs back together and have them share their posters. Discuss the idea of repeated addition: o How is repeated addition faster than just counting all of the shoes? o Why do we use repeated addition? o How many shoes were left? (2) o To whom could the centipede give those shoes? • Show the last page of the book so students can see that there were two shoes left and given to the two worms. 10 minutes • Ask the students: “Why do we use repeated addition? How is it faster? What does it allow us to do?” Solicit answers from about 2-­‐4 students. • For an exit task, students will answer: If there are 5 dogs at the dog park, what is the total number of legs? Use repeated addition to show your thinking & write down your equation. Is there another way we can model this situation with mathematics? If so, write down both equations.” This tasks hints that there is another way to do this task – maybe students will link it to multiplication. Arrange dogs on SMARTboard in an array 6. •
Differentiation For students who struggle, model another example for them and walk them through the next insect. Incorporate other insects or animals that students are familiar with and ask them to determine the number of shoes a specified number of that insect/animal would need (i.e. how many shoes would 1, 2, or 3 dogs or ants need?) •
7. Assessment/ Evidence of Success: For students that need an extension, ask them to write the matching multiplication sentence under their repeated addition sentence. If needed, provide more difficult situations for repeated addition like finding other combinations of animals/insects that could take all of the centipede’s shoes. Student work on posters will be evaluated informally. This will show who understands the concepts as we work through the 4 insects. If students get stuck, I will be circulating around to help them (as described above) and looking for: o Do the repeated addition strategies match the animal? o Did students correctly add to find how many shoes? o Were they able to find out how many were left? • Student sharing of strategies will be evaluated informally: o Were students able to explain what they did? Did it make sense? o Were students able to explain why repeated addition is useful? •