Expressions and Word Problems
Lesson 16 of 19
Objective: SWBAT write and evaluate expressions to solve multi-step word problems.
Do Now - Sprint
Students enter silently and find another “sprint” on their desks. This assessment includes 25 questions to be completed in 1.5 minutes. The first 10 questions are fraction/decimal conversions and the remaining 15 questions are multiplication facts using positive and negative integers. Students who raise their hand to indicate they’re finished will have their paper collected for scoring. Students who answer all problems correctly earn three achievement points.
Next, students receive graded quizzes from last week and I take questions about the answers and the work for three minutes. Whenever appropriate, students are encouraged to use expressions to show work (side by side) and to simplify step by step by working from left to right. For example, many students missed question #3 which states “Gustavo has $625 in his checking account. He writes two checks for $23 each and then makes one deposit of $146. What is Gustavo’s final checking account balance”? Students will be asked to copy the expression, 625-23-23+146, and solve from left to right step by step so that the work looks like the example below:
625 – 23 – 23 + 146
= 602 – 23 + 146
= 579 + 146
Many students are only using arithmetic (up and down work) to solve these problems, and are therefore dropping numbers and signs. Another issue may be the understanding the definition of the word “deposit” and the idea that when checks are written they are taken out, or subtracted from, an account. We review these concepts as well.
Lastly, students are reminded that their Unit 2 test will take place at the end of the week and they are given an updated schedule of upcoming assessments (syllabus).
The answers to the homework over the weekend were provided on our class website. Students are given the opportunity to ask about specific steps in the answers for 4-5 minutes. I emphasize the use of expressions (side by side work as shown above) for each problem. This helps introduce the lesson and make a smooth transition.
Intro to Lesson
I project three examples of work from students’ quizzes on the board. Each example shows a student’s solution to #7:
Julissa set a goal of running a total of 32 miles this week. She ran 4½ miles each morning, Monday through Friday. How many miles does she need to run this weekend in order to reach her goal for the week?
We review each example and I ask students to evaluate the ways in which students showed their work. Most students who answered this question correctly used expressions to show their work. All students are asked to copy the expressions needed to correctly solve these problems and work step by step with partners to evaluate the expression:
32 – 5(4½)
We review the solution and transition to the task.
Students work with partner pairs, independently, or with me at the front of the room to complete the task. The work is displayed on the SMARTboard for all students to check. Students who choose to work in a small group with me will try every other problem independently while I walk around the room to ensure students are showing work neatly, with the use of expressions (student sample included).
The expectations are set before students get to work. After 5 minutes of the task, I will do a quick walk around to ensure students have completed at least one problem. After 10 minutes, I should be able to find some correct work/answers for students to put on the board. Each time that I walk around the room to check on independent workers, my struggling students are getting an opportunity to practice independently. They are expected to have some work on their paper and be close to, if not have already, solved the problem I gave them to work on independently. Once they have consistently completed problems correctly and independently by showing complete steps in the work, I can allow them to work with other groups. This can motivate students to prove that they understand the work because they want the freedom to select a friend to work with. I expect them to work and improve before I can trust them to choose independently.
Students are asked to complete the exit ticket at the end of their class work and place it in a basket before they leave the room.
The problem included in the exit ticket is about taking money in and out of the bank. I am looking to assess first, and most basic, whether students can read and understand which situations require subtracting the amount and which require asking the amount of money. The work shown by students will ultimately tell me if they bought into, or simply did not understand, writing numeric expressions to solve multi-step problems. If a student shows his work without using a singular numeric expression, my written feedback will read, "write ONE numeric expression that summarizes everything that happened in the word problem". Students who are able to "understand the relationships between problem scenarios and mathematical representation" are also practicing MP2.