Quiz + Bar Models and Translating Equations
Lesson 10 of 20
Objective: Quiz + SWBAT solve word problems by writing and solving equations.
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). At the end of the quiz, all students will be asked to turn in their quizzes, and the Class Work will be distributed.
The first part of the quiz will assess student knowledge of vocabulary terms this week: factors/multiples, prime/composite numbers, prime factorization, twin primes, and binomials. There are two purposes for beginning the quiz this way – as a warm up for students to complete the word problems that follow and to assess student knowledge in order to target remediation groups.
The next part will assess student application of terms and skills to show the prime factorization and use it to identify the GCF of 2 or three numbers. I include a problem that asks for the prime factorization of a negative, anticipating that this may be a difficult problem for many of my students. I base this on my experience with the lesson three days ago. Many of my students struggled to understand why I would factor out a negative 1 first. The video below details how this question (#10) should be answered and why we factor out a negative 1.
The last question in this section is very complex and perhaps the most representative of the types of questions students will see in their Unit Tests. While prime factorization does not appear to be listed in the 7th grade common core standards, I teach it and use it in my assessments to expose students to complex word problems where it is imperative to understand the underlying concepts of the skill and apply them to answering different questions. In #12 for example, asking for the “greatest number of gift boxes” is the same as asking for the GCF, but students have to connect those dots on their own. Asking for the number of cinnamon, gingerbread, and chocolate chip cookies means students will need to be able to identify the operation as division and divide each of the total numbers by the GCF.
The last section will assess the factoring within binomials, a skill that HAS come up in several of our practice assessments as well as this sample question posted on our state site.
After students have turned in their quizzes they will receive their class work. They are all advised that any class work not completed during class will be taken home for homework. They must first fill out the heading at the top of their paper and copy the aim off the whiteboard.
I begin by asking one student to read the first question. Then I explain that we will be using bar models to help us write equations. This video demonstrates how I model drawing the bar for this question:
After showing students how to draw the bar model using the information in the problem, I ask:
Raise your hand and tell me if you can figure out a how to use this bar model to write an equation that will help you solve for the price of each notebook.
The bar model can also help review solutions to equations. If I “erase” or take away the $2 from the bar model this is the same as subtracting 2 from both sides. The total changes. If there are 6 boxes left, each representing the same value, and the total of these boxes is $24, then “how can we figure out what each box represents?” and “this is the same as doing what to both sides of the equation”.
After reviewing the first question, students are asked to work in pairs. Students who are still struggling will be working with me, at the chalk board. Each student will take a term putting work up on the board as I guide them with questions:
- What should we draw first?
- What part do we know?
- What don’t we know?
- How do we represent that? (If a student gets stuck: Who wants to take over?)
- What equation can we write to represent this bar model?
- How do we solve?
- How does the solution to the equation relate to the bar mode? Or Show me this step in the solution o on the bar model.
During this time I may also leave students to work on the board so that I may go check on students working in pairs. Any pair which is not making progress in their solutions and is off task will be given a warning and then moved a different part of the room to work silently. Good progress means I need to see students completing an average of 1 problem every 3 minutes.
Once there are 5 minutes left in class I should have some work on the board completed by students who were working with me. All will be asked to return to their seat to ask questions or copy any work they may need off the board. All will be reminded that the rest of this sheet will be due the following Monday for homework.