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Planning Step 1: Lesson Curriculum: What are the Learning Goals for this lesson?

Lesson Standards

Always include a writing standard.

4.MD.A.3 (partial standard) – Apply the area formula for rectangles in real-world and mathematical problems.
MP3 – Construct viable arguments and critique the reasoning of others.
W.4.1 – Write opinion pieces on topics or texts, supporting a point of view with reasons and information.

Students Will Be Able To… (Do)

  • Skills from standards including thinking (cognitive verbs).
  • This is not activities.
  • One or more goals should be Higher Order Thinking (Levels of Learning 3 or 4), and/or Reading Comprehension.
  • Sequence these goals in the order in which they should be learned.

1. Evaluate given solutions for errors
2. Construct arguments supported by reasons and facts

Students Will Know

Knowledge from standards such as vocabulary, facts, formulas.

Error points for computing area
Evaluate

Lesson Essential Question

  • A question that communicates the Learning Goals.
  • Reflect the Higher Order Thinking and/or Reading Comprehension Learning Goal(s).

How do I use error analysis to help me solve and evaluate solutions to area problems?

Planning Step 3: Lesson Instruction: How will students learn?

Activating Strategy

  • Plan this after you plan your Learning Activities. How will you introduce the Lesson Essential Question?
  • How will you draw attention to important vocabulary in the Lesson Essential Question?
  • How will you build/link background knowledge?
  • What prerequisite content might students need to know before the lesson?
  • >Which key vocabulary from the Learning Goals needs to be explicitly taught?
  • Are there other vocabulary words that you think need to be taught?
  • Which vocabulary strategy will you use?
  • Previewing:
    • Advance Organizer
    • Prerequisite Content
    • Vocabulary

“What’s Wrong with this Picture” activity in which students work with a partner to identify all the things that are wrong in the picture. Introduce the Lesson Essential Question by cloud bubbling the words “error analysis” and “evaluate.” Review error analysis as looking for errors and figuring out what went wrong so the errors can be fixed. Explain to students that evaluate means to judge the quality of something. In this lesson, we will be judging the quality of the thinking and the process of solving math problems involving area. Since we have already learned how to find the area of a shape, now we are going to look at real-world problems involving area, and find errors in the thinking or solving of the problems.
Key Vocabulary (for explicit instruction):
Evaluate

Vocabulary Strategy:
Students complete a Word Map for “Evaluate”

Previewing (what, who, when):
Whole Group: Provide the menu for an upcoming week in the school cafeteria. Use a checklist to help you decide on one day during the week you would rather bring your lunch from home. Form groups of according to the days of the week. As a weekday team, create a visual that shows why you would not eat school lunch that day. Each team uses the visual to evaluate why that day was not a good day to eat the school lunch.

Scaffolding (what, who, when):
Struggling Students: Provide partially completed Word Map.

Graphic Organizer

  • How will students store and organize information as they learn during this lesson?
  • Base the organizer on the Higher Order Thinking or Reading Comprehension in the Will Be Able To… (Do) Learning Goals.
  • Determine how the organizer will be previewed for struggling students.
  • Determine how the organizer will be scaffolded for struggling students.

Error Analysis Organizer

Previewing (what, who, when):
Struggling Students: Using a simple example, demonstrate how to use the steps of error analysis. Introduce the Anchor Chart and have students annotate the steps on the graphic organizer.

Scaffolding (what, who, when):

Learning Activity 1

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

  • Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
  • Content students need to learn
  • Chunk activity:
    • Several opportunities for thinking, talking, writing to learn
    • Distributed summarizing and/or practice
    • Questions to ask
    • Higher Order Thinking and/or Reading Comprehension Questions to ask
  • Active engagement:
    • Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
    • Variety
    • Movement
  • Previewing prerequisite knowledge/skills
  • Scaffolding content and process

Present the following word problem to students: Jake built a backyard pen for his new pet pig. The length of the pen is 12 feet, and the width was half that. What is the area of the pen? Lisa says 6 sq ft, Tom says 72 sq ft, and John says 84 sq ft. Who is correct? How do you know? What errors did each of the other two make? Do a Think Aloud to work through the problem, circling important information and showing work with the area formula.

Numbered Heads: 1’s tell 2’s how to solve for area; 2’s tell 1’s a mistake to avoid when solving for area. In Collaborative Pairs, students will solve two similar problems on mini whiteboards, and teacher will monitor for accuracy.
Collaborative Pairs partners will then complete two problems using Pairs Checking, with one check-in.

Previewing (what, who, when):

Scaffolding (what, who, when):

Assessment Prompt for Learning Activity 1

  • Formative assessment of the Learning Goal(s).
  • Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
  • Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

Write a Note to an Absent Student describing how to evaluate solutions to area problems for errors.

Learning Activity 2

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

  • Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
  • Content students need to learn
  • Chunk activity:
    • Several opportunities for thinking, talking, writing to learn
    • Distributed summarizing and/or practice
    • Questions to ask
    • Higher Order Thinking and/or Reading Comprehension Questions to ask
  • Active engagement:
    • Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
    • Variety
    • Movement
  • Previewing prerequisite knowledge/skills
  • Scaffolding content and process

Using a Think Aloud and the Error Analysis Organizer, model for students how to analyze real-world problems involving solving for area. These problems will have two possible solutions. Model for students how to consider both solutions, then work through the entire problem to solve for area and determine which solution is correct. Also, provide a rationale for why the incorrect solution is indeed incorrect. Use the Error Analysis Organizer to document the given information, possible errors, considered solution, and new information for each problem. Emphasize that the organizer allows students to see the facts and reasons that support the correct solution. Students then use the organizer as they are guided through another problem with two possible solutions. Students then work in Collaborative Pairs to solve four problems with two possible solutions, using the Error Analysis Organizer, and Pairs Checking on problems 2 and 4.

Previewing (what, who, when):

Scaffolding (what, who, when):
Struggling Students: Provide examples of facts and reasons on a partially completed graphic organizer

Assessment Prompt for Learning Activity 2

  • Formative assessment of the Learning Goal(s).
  • Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
  • Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

Choose one of the problems that had errors. Write a note to the student who solved the problem explaining and supporting why the solution is incorrect and how to avoid the error in the future.

Planning Step 2: Lesson Assessment: How will students demonstrate understanding of the Learning Goals for this lesson?

Assignment

  • Plan this before planning Lesson Instruction.
  • How will students demonstrate their knowledge of the Will Know Learning Goals and the skills in the Will Be Able To… (Do) Learning Goals (especially the Higher Order Thinking and/or Reading Comprehension)?
  • How will the Assignment be differentiated for support and challenge?
  • Which students receive differentiation?
  • For students who struggle with the Assignment, how will you remediate this lesson?

Emma’s big sister is moving away to go to college, and has left her the tree house fort in the back yard. It’s all hers now! The problem is that it’s painted bright yellow, and Emma can’t stand it any longer. It must be painted blue! Emma measures the inside of the tree house, and finds that the two longer sides were 12 feet long and 8 feet high, and the ends were 8 feet long and 8 feet high. The roof isn’t going to be painted. Because the tree house is bright yellow, it will require two coats of paint. Emma’s mom takes her to the store, and she is ready to buy paint. “This paint can says it will cover 350 square feet. The longer sides of the tree house are 12×8, which is 92 square feet, and there are two of them, so that makes 184 square feet. The ends are 8×8, so that’s 64 square feet, and there are two, so that makes 112 square feet. Add 184 square feet and 112 square feet, and that equals 296 square feet. I need two coats, so that means 592 square feet. I’ll buy two cans of paint.” Emma’s mom reminds her that she hasn’t considered the floor yet, and might need a third can of paint to cover it. Emma asks her mom to drive her back home so that she can measure the floor to see if she really needs to spend the money on a third can of paint. Emma’s mom says she doesn’t have to drive home, and should buy three cans of paint. Who is correct? How do you know? Use the Error Analysis Organizer to document your findings, and write an explanation in paragraph form.

Differentiated Assignment for Struggling Students:
Provide a visual of the treehouse with the measurements.

More Challenge: Students create their own examples of real world or mathematical problems that are solved by applying the formula for determining the area of rectangles. Students then rewrite the problem so is has an error. Partners exchange problems and determine where the error is located.

Remediation: Use an Anchor Chart and manipulatives to help students apply the formula for finding the area of rectangles in both real world and mathematical problems.

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