Thursday, July 30, 2015

Lesson Plan: Problem Solving: Multi-Step Problems

This lesson utilizes enVision Math, but ideas can be adapted for other texts.  Many of the hyperlinks will direct you to a place to download the resources used throughout this lesson. (Note: You must have ActivInspire downloaded to view the Promethean Board slides)

Subject: Math
Grade: 5th

Source: enVision Math 2.8

Integration of Learning Outcomes

  • Students will be able to use multi-steps to solve a variety of problems by making sense of problems and persevering in solving them, reasoning abstractly and quantitatively, attending to precision, looking for and making use of structure, and looking for and expressing regularity in repeated reasoning.
  • Students will be able to add and subtract decimals by solving word problems.
  • 5.NBT.7: Add and subtract decimals to hundredths; relate the strategy to a written method and explain the reasoning used.
Anticipatory Set

· “Multi-step problems can be challenging. It is important to figure out what you know and what you need to know and to plan the steps necessary to solve the problem. Suppose you are given this problem:”
o   Julia wants to buy three pens at $1.99 each and two notebooks at $2.50 each. What is the total cost?
o   Students will list what they know, what they need to know, and the steps to solving the problem before solving the problem.
o   Drag the parts of the question into the appropriate column on the Promethean Board.
o   Students will write out the steps to solving the problem
§  Find the cost of three pens at $1.99 each. ($5.97)
§  Find the cost of two notebooks at $2.50 each. ($5.00)
§  Find the total cost. ($10.97)
o   Students will solve problem on their whiteboards.


Explain that a real math problem came up in real life and the teacher needs help from the students to solve the problem. Show the screenshot of the ticket order. Ask students “What does this information tell us?” Have them analyze the text graphic to a partner. Have students share their answers.

Propose problem: Miss Orr is going to buy 3 Flyers Tickets at $22.34 each. She paid $70.00. How much change will she receive in return. 
  • Break problem into important information through annotating. Mention that there is a “hidden question” that we need to answer.
  • Ask, “What information do we know?” “What question is being asked?” “What do we need to find out before we can answer the question?” “Why do we have to follow those steps?” “What is the hidden question?” Students will discuss most questions in their small groups.
  • Students will solve the problem with a partner on their whiteboards (Answer: $2.98) 
Propose next question: Jack bought a t-shirt on sale for $5 off. It originally cost $14.50. He also bought a cap for $7.95. How much did he spend in all?
  • Work with partner to identify the part of the problem that must be answered first. Have students identify the hidden question.
  • Students will solve problems on whiteboard.
Students will receive a “puzzle piece.”  Each puzzle piece has three parts that go with it to make a puzzle. One piece has the word problem. The second puzzle piece has the first step. The third puzzle piece has the second step.  Students must walk around the room to find their matches.  Students must then solve the problem.

Complete problem #1 on page 51 together as a class. Students will solve #4 and #5 independently.  Once students have their answers checked by a teacher, they may work on a station from the previous lessons (grocery list, menu, Halloween worksheet, etc.)

  • Students are given opportunities to move around the room during puzzle exercise.
  • Students are able to work with partners who can assist them. They can also build ideas off their groups.
  • Problems posted on board will act as visual for visual learners.
  • Breaking down and annotating problem will help those who need help with reading.
  • Hockey ticket word problem will spark interest.


State that students have learned how to solve multi-step problems.  Have students put their heads down.  Have them raise their hand if they understand the material. Then, have them raise their hands if they are still unsure.

Formative/Summative Assessment
  • Closure provides formative assessment to see what students know/how they feel about material.
  • Students will be assessed summatively at the end of the unit via test.
  • Teacher will walk around and observe throughout the lesson.
  • Promethean Board
  • enVisions Math textbook
  • Active Inspire (2.8 Multi-Step Problem Solving)
  • Whiteboards and markers
  • Pre-made puzzle piece cards
  • Promethean Board
Reflection on Planning

I think students will be interested by the Flyers problem.  I try to put as many real life examples into word problems as possible.  I also try to use topics that will interest students.  Word problems tend to scare students away, so I think making the word problems more appealing will keep their interest.  They’ll want to solve them instead of shying away from them.

I do think this will be difficult for students.  They have to realize that there is more than one step to solving the problem. I don’t think all the students will originally pick up that there’s more than one step needed.

Reflection on Instruction

Students had a simple time solving the problem.  However, they had trouble identifying the hidden questions.  For example, they knew they had to add two numbers together, than subtract from another number.  However, they were unsure of what those two numbers added together represented.  For example, they could not comprehend that $14.50 – $5.00 represented the new price of the shirt.  They also couldn’t realize that the hidden question would be “What is the new price of the shirt?”  They were able to solve the problems, but they could not comprehend what the information meant.

The Flyers problem really did engage them though. They wanted to know if I really bought the tickets.  They were quick to notice the informational text and the information it provided.  I expanded on the problem and said, “If I need $5.00 for lunch the next day, would I be able to buy the tickets?”  The students were quickly to respond “no” knowing that my change would be less than $5.00.

Students really like the puzzle activity.  I had them solve the problems on their whiteboards before finding their matches.  This helped them find their partner quicker.  One student said to me “This was a fun activity.”

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