Topic or Unit of Study: Solving multi-step math problems
It is a third grade classroom of 20 students (8 girls and 12 boys) seated in 5 groups of 4. Most of the students are of Hispanic ethnicity, and the teacher can speak Spanish fluently and uses this skill when deemed necessary. Some students are also Caucasian, and there are a couple of African American and Asian students as well.
STANDARDS AND OBJECTIVES
Your State Core Curriculum/Student Achievement Standard(s):
1.3.8: Students will generate and solve two-step addition and subtraction problems and one-step multiplication problems based on practical situations. Model addition, subtraction, multiplication, and division in a variety of ways. Use mathematical vocabulary and symbols to describe multiplication and division.
Students will learn how to solve multi-step math problems.
By the end of the lesson, students will complete a short test composed of 5 multi-step math problems, similar to the ones studied in class, and receive a score of at least 80%.
MATERIALS AND RESOURCES
post-test worksheet with math problems
Department of Education. (n.d.). Assessments and Standards. State of Nevada
Department of Education. Retrieved October 7, 2013,
INSTRUCTIONAL PLAN (60 min)
Sequence of Instructional Procedures/Activities/Events (provide description and indicate approximate time for each):
1. Identification of Student Prerequisite Skills Needed for Lesson: Students will know how to perform basic mathematical operations (addition and subtraction) and will be able to know from “clue words” in the problem what operations to perform (i.e. “more than” = subtraction)
2. Presentation of New Information or Modeling (15 min):
The teacher will begin by telling the students that first it is his/her turn to solve the problem, and the students simply have to observe. The teacher will put up an example of a multi-step problem on the overhead projector and solve it step-by-step, explaining each part of the problem and explaining how to find the solution.
An example of the problem could be:
Mary received a box of 36 chocolates as a present. 10 were white chocolate, 12 were milk chocolate and the rest were dark chocolate. Mary ate 5 dark chocolates. How many dark chocolates were left?
The teacher will begin solving the problem above by first “illustrating” it using counters. 36 counters = 36 chocolates. The teacher will then separate 10 counters from the general pile and explain that these are white chocolate, then do the same for the milk chocolate. The teacher will explain that the ones left after taking away the white and milk chocolate are the dark chocolate and will count how many counters are left. Next, the teacher will take 5 “dark chocolate” counters away, since Mary ate 5, and again count how many are left, explaining that this is the answer to the problem.
After illustrating with counters, the teacher will demonstrate how everything done with counters can be shown in an equation (since the quantities in math problems are not always so small that they can be drawn individually). The teacher will repeat what she did with the counters – write 36, then subtract the white and milk chocolate (36-10-12), and subtract 5 dark chocolates (36-10-12-5).
3. Guided Practice (15 min):
The teacher will ask whether the students have any questions regarding the previous problem. Then, the teacher will place another multi-step problem on the projector and ask the students to solve it as a class.
The problem could be:
John borrowed a 43-page book from the library. On the first day, he read 14 pages. The second day, he read only 7 pages. On the last day, the book’s ending was so interesting that John finished the entire book. How many pages did John read on the last day?
The teacher will prompt the students with questions. For example, if the students do not know where to begin, the teacher may ask: “What do we do first? We have to underline all the important information in the problem that we need to solve it” – the students will then point out all of the important information for the teacher to underline (i.e. “43-page book”, “first day – 14 pages”, etc.) As with the problem modeled by the teacher, the students will first decide how to demonstrate the problem using counters.
As the teacher places and counts the counters on the overhead projector, students can use their own counters to try and solve the problem on their desks. Afterwards, the teacher will help the students make an equation for the problem based on the actions they performed with the counters.
4. Independent Student Practice (10 min):
The teacher will place 3 problems on the overhead projector that are similar to the ones solved before. The students will work in groups of 4 to solve the problems together. They will use pencils, paper, and counters for the task. As the students work, the teacher will circulate around the classroom to help out if a group is completely “stuck” and to observe what the students are doing well and where they are struggling. Once each group has a solution, the class will discuss what each group came up with and how the answer was found.
5. Culminating or Closing Procedure/Activity/Event (20 min): Students will be given a worksheet with 5 multi-step math problems similar to the ones discussed in class. They will complete the worksheet and turn it in to the teacher for grading.
Pedagogical Strategy (or Strategies):
direct instruction: The teacher models how to solve a multi-step problem at the beginning of the lesson. cooperative learning groups: Students work in groups during independent practice to solve the problems. independent practice: Students complete the final assessment worksheet on their own using the knowledge they gained from the lesson.
dyslexia – When the students are working in groups, the students with dyslexia can have other group members read the problem to them. During independent practice, the teacher can read the problems aloud for the entire class. gifted – The teacher can bring a few worksheets with more examples of multi-step problems and give them out to students for practice if the students finish the given assignment much earlier than the rest of the class.
formal post-assessment – At the end of the lesson, students will solve 5 multi-step math problems written on a worksheet. informal assessment – Based on the answers of each group during independent practice, the teacher can judge how well students had understood the concept of solving multi-step problems. By walking around the classroom while the groups are working, the teacher can also determine the specific areas that need more explaining or clarification.