Quiz + Area Models & Expressions

Students enter silently. Quizzes are on their desks and they are to begin as soon as possible. They are allowed to spread out and sit at empty tables and are given the option to use cardboard dividers and noise canceling head phones. Instructions on the board notify students that they will only have 30 minutes to complete this quiz (a timer will be displayed) and that there are available optional “bonus” questions in the front of the room if they finish early. Incorrectly answered problems in the bonus section will not be held against them. At the end of the quiz, all students will be asked to turn in their quizzes, bonus questions, and the Task + Notes will be distributed.

My aim on this quiz is to assess the following skills and major understandings:

• Questions 1 – 5: students must use properties of equality to identify solution steps.
  • Vocabulary to be assessed: equation, reciprocal, LCD, coefficient
  • Students must translate simple expressions. This will ensure ability to move forward with the translation of multistep equations in the form px + q, according to upcoming standard 7.EE.B.4a
  • Questions 6 – 8: students must show that they are able to solve multi-step equations, including those using rational numbers and quotients of quantities (i.e. problem #8 where students multiply by the denominator to simplify).
  • Questions 9 – 10: students must show that they can use strategies taught this week (i.e. verbal models) to translate and solve one-step equations. The data for these two questions will help me determine how to move forward with standard 7.EE.4a.
  • Question 11: We have been practicing problems like this throughout the week as some students continue to struggle with the distribution of negatives and the following combination of integer and algebraic terms; this question will assess student progress toward mastery 

Once quizzes are collected I distribute “Task + Notes” sheets. I remind students to copy anything I write on the board onto their paper. I ask for a reader for the first problem. This problem asks us to identify the picture which will NOT result in the expression 4x + 4. I ask students to notice the writing inside each figure. Then I ask how they think I should proceed. I pick several different students to explain the procedure and restrain from giving any steps myself. I ask students to evaluate each other’s thoughts (i.e “What do you think?”, “does that make sense to you?”, “do you agree with that step?”)(MP3). It is important to know students well enough at this point to predict which students will push others’ thinking with questions and thoughts. Students who tend to shy away from participation can be called upon to summarize others’ thinking in their own words. For example, I may call on a student with innate higher order thinking skills to share ideas for the first few steps to be taken to solve, and on a student who struggles with higher order thinking skills to summarize what those steps should be. Specifically, I am looking for the following:

• A student to restate the question in their own words, for example “we need to find the figure whose expression does not equal 4x + 4”
• Another student who can identify finding the areas of the first two shapes and the perimeters of the last two shapes
• A student who can apply the distributive property to the area formulas of the first two shapes (MP2)
  • Questions to push thinking: for the first rectangle, if A = bh, why can’t we use the expression 2x + 4 * 2? Why do we need the parentheses (2x + 4)*2?
    • Answer: the parentheses include 2x + 4 as the entire length of the base. Without the parentheses we are only multiplying 4 by 2.
    • Students who can find more than one way to solve. For example, one student may choose to find the perimeter of the fourth figure, the square, by using the formula P = 4x = 4(x+1), while another student may choose to write an addition sentence to combine the lengths P = (x+1) + (x+1) + (x+1) + (x+1)

The resource sheet attached shows how I guided students to set up their paper for the first 5 minutes of this section. Once the paper is set up as I have shown, I ask students to raise their hand if they would like to show how to calculate the areas and/or perimeters a different way than I have instructed. These students will be asked to put their work in the board. I will then give all students 6-7 minutes to complete this problem including writing an explanation of the right answer. 

At the end of the previous section I will ask all students to return to their seats. We will review the answers displayed for #2 and the student who copied his work for #3 will explain. If he did not finish, we will guide the rest of the class to the answer. This video models this last piece.

Two homework assignments will be distributed at the end of class. One will review area models and the other includes 37 questions to study for the upcoming Unit 3 Test. Students are instructed to select 5 of the most challenging questions on that sheet and use the rest for study material. Answers are posted on our class website.