Word Problem Applications A

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SWBAT apply addition and subtractions rules of rational numbers to solve word problems by working in groups.

Big Idea

Students complete fluency tests and work in groups to solve word problems through addition and subtraction of rational numbers.

Do Now + Quiz Review + HW Check

18 minutes

As per routine, my students enter silently and they find a Do Now on their desk. It instructs students to have their pencils ready for a speed test. This assessment will include 15 questions to be completed in 3 minutes. There are 3 sections:

  1. Rational numbers written as fractions (quotient of two integers, i.e. -4 = –4/1 or –(4/1))
  2. Writing fractions as decimals (i.e. 1/5=0.2)
  3. Writing decimals as fractions and mixed numbers(i.e. 0.54 = 54/100 = 27/50)

After three minutes of pencil and paper work, students will have one minute to enter all of their answers using their clickers. This personal response system (PRS) technology makes it easy to share results instantly. It also saves me time hand scoring each sheet.

I love using the PRS results to launch instant celebration of good work.I use a bar graph of different class’ scores to inspire some competition amongst the 3 classes I teach. For Grade 7 students, this is good motivation. After today's celebrations of scores, students transition to homework check while I distribute last week's quizzes. 

As I hand out the graded Quizzes, I allow students to ask clarifying questions about what they answered correctly or incorrectly as well as answering any questions about partial credit awarded during the quiz.

While I am distributing quizzes, my students are checking homework answers (see Day 27 - PPT - add.sub fractions word prb apps for the answers). I am planning to work with students to promote the idea of drawing models when solving problems. For my students, one model that I want them to be proficient with is the number line (see CCSS 7.NS.1). 

The first few problems on the assignment included number lines that students must use to show their answers. Problems #4 and #5, however, did not include number lines. All students will be expected to draw a number line if not previously done to show the correct answer. Drawing the number line models for these problems enables students to identify and study the relationships between different rational numbers on the number line (MP5).


Intro to Lesson + Class Notes

10 minutes

I provide Cornell Notes for today’s lesson. I expect my students to fill in the blanks for the rules of adding and subtracting rational numbers. (The red font included in the word document is meant to be written on the board and copied by students.) Though this is a more passive form of note taking, I want students to have tool to refer back to so that they can focus on strategies in the problem solving aspect of the lesson. 

After reviewing the definitions together, students must work with a neighbor to complete the problems at the bottom and on the back of the notes. We will review the answers together in the last ten minutes of this section. As I am walking around listening to students' conversations about the work, I am also looking to spend some additional time with struggling students, referring back to number line models and red/blue chip models used at the beginning of the year. Students better understand abstract concepts through many examples. 

The most important point I want students to get during the notes is that they have many visual and numeric strategies at their disposal when it comes to solving these problems. They should be used when they feel stuck or to check their work. 

Guided and Independent Practice

18 minutes

The set of addition/subtraction problems at the bottom of the first page of Day 27 - Cornell Notes will be completed as a class. There is a group of 3 integer problems for each rule/situation on the front of the class notes (arranged in rows). I model the first problem in each set, then ask students to work in pairs on the second problem (then check we the answer together), and finally to complete the last problem in each row independently (and check together). As students are reviewing solutions together they are asked to defend their answers using one of the visual models and are thus also using MP3 to defend their arguments.

After practicing with integers, students are instructed to apply the rules to the rational number operations on the back of Day 27 - Cornell Notes. During this time, work is independent and silent. Students may raise their hand to ask for help. The guidance I provide is in the form of asking students to point to the rule on their notes they need to use to solve each problem. This way, students are practicing the the use of notes to find answers. If a student finishes early, they are given the homework to begin during class. 



6 minutes

At the end of today's lesson, I give students a 1/4th (of 8.5 x 11 in) sheet of scrap paper. I ask students to write their name and then complete the following two problems. 

1) 3.6 + (-19.08)

2) -1/6 - 2/3 

I make sure to remind them to show their work so that I can understand their strategy.