##
* *Reflection: Perseverance
Review 6.EE.1, 6.EE.2, 6.EE.3, and 6.EE.4 - Section 2: Problem Solving Review

The triangle problem was difficult for most of the students. I started by giving them 10 minutes of struggle time (working independently with no help from the teacher or other students). Struggle time gives them an opportunity to implement SMP1 by looking for a starting point within the problem. Before struggle time starts, I read the problem to the students. Then I instruct them to rely upon their tool box to help them find a way to start the problem. Their tool box is everything we have learned thus far. Once struggle time begins, the class is silently working and I make myself unavailable to them. After 10 minutes I say, "let's see if 2 heads are better than 1". Now they get to work with a partner. I allow partner work to go on as long as I hear mathematical talk happening. Once I either hear nothing or conversation about something other than math, I regroup them to talk with other students in the class. This time I made them get in groups of 3. By doing this, students are hearing and seeing what other students are doing to attack this complex task. When they are done talking, I have them say thank you and go back to their seats. Then we discuss this as a whole group.

Some common problems with the triangle task: students wanted to see the pattern as +3, +5, +7... So, I asked "what if I asked you to find the 100th pattern?" They realized that their pattern would make it difficult to find. I would encourage them to find a faster way. They also wanted to draw out each pattern. Again, I would encourage them to look for a mathematical pattern to speed up the process.

Digging for dinosaurs

I used the same process as with the triangle problem. We didn't finish all of these in one day, so I will continue this problem first thing tomorrow before the exam.

As students started working on this problem, they were quick to make a judgment call on which plan they felt was the best without doing the math. They also forgot about the fact that they wanted to visit the museum 8 times each month over the 3 months of summer. Students made tables to help organize their information. One student even said that his mom was having this dilemma while trying to choose a fitness plan at one of the local clubs (great connection). We also talked about cell phone plans.

*Perseverance: Ways to persevere through complex tasks*

# Review 6.EE.1, 6.EE.2, 6.EE.3, and 6.EE.4

Lesson 12 of 14

## Objective: SWBAT write and evaluate expressions while reviewing for a test.

*90 minutes*

#### DO NOW

*20 min*

The do now is a problem that has the students determining values that grow in a square area relationship and then explaining how to find these values and extending the pattern. I liked this problem because the students will get to implement **SMP 3** by critiquing other’s work. It also supporst **SMP 4 **because the students will be modeling their solution with an expression.

In this problem, students will be looking at the triangles and making a generalization about the pattern. **(SMP 7 and 8)** They can make a table to help support their answer. Students should conclude that if you square the pattern number it will result in the amount of triangles in the pattern. The expression could look something like this T = p².

Tools: Triangles Activity (Noyce foundation, 2007)

#### Resources

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#### Problem Solving Review

*60 min*

The students will be working on 2 problem solving questions. The answers to these questions are not within reach. They will need to make sense of the problem (SMP 1) to understand what they are being asked to do . Students should work independently on each problem. I’m going to use 30 minutes for each problem. 15 minutes should be used for independent work and the other 15 minutes, students should share strategies with their table mates. After each problem, do a whole class discussion on solutions and strategies.

Problem 1

Digging Dinosaurs

The students will be looking at writing different expressions by determining the best rate plan to visit a museum when given a number of rate plans which have changed in both cost and time. The students will need to decide which is the plan that will save them the most money and consider whether another plan may be better depending on different criteria.

This problem supports 6.EE.2b where students identify parts of an expression using mathematical terms and 6.EE.2 evaluating expressions.

I chose this problem because this directly correlates with our unit of study. The problem is just beyond reach where an answer is not readily available. This problem supports **SMP 2** because the students need to find the important information to decide what the numbers are telling them. Additionally, it supports **SMP 4** because the students will be writing out the expressions to help them find a solution.

I love this problem because there are a lot of ways to solve and a lot of assumptions to be made. Let students play around with the numbers. It will be interesting to see their take on what they best value would be. The only parameters that are set by the problem is that it is for 2 people and they want to visit the museum 8 times over a 3 month period.

Problem 2: Boxes

Students will be looking at equivalent expressions in this activity. They have to determine which box is the heaviest by looking at scales. Some students may not have any background knowledge on how these scales work so it might be a good idea to explain what the scales are used for and how they measure items.

This problem supports 6.EE.4 identifying when 2 expressions are the same no matter what the value of the variable. It also supports **SMP 3** as students will need to justify their answers and **SMP 7** as students will be explain why it happens this way.

As students work through the problem, they should reason that box 4,5, or 6 is the heaviest box. As they move through more of the scales, students should see that box 6 is the heaviest and be able to explain that 4 and 5 weigh the same, therefore 6 is the heaviest.

Tool: Digging Dinosaurs (Noyce Foundation, 2007) and Boxes (Noyce Foundation, 2012)

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#### Closure + Homework

*10 min*

The students will get their study guide to continue to prepare for tomorrow’s assessment. Hand out the study guide and allow students time to look over each problem. Ask students if there is anything on the study guide that they feel may give them difficulty? Give guidance to students as to where they can look for help or what notes section they should use to help them study. If time permits, let students get started on their study guide. Students should be well prepared for this assessment. They have taken notes in prior lessons and used problem solving strategies today to help them prepare. We will go over the study guide prior to the assessment.

Tools: Study guide expressions.

#### Resources

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- LESSON 1: Exploring Exponents
- LESSON 2: Learning About the Orders of Operations
- LESSON 3: Orders of Operations - Stations
- LESSON 4: What is Algebra?
- LESSON 5: Evaluating Expressions and Not the Emotional Kind!
- LESSON 6: Writing Expressions the Right Way!
- LESSON 7: Working with the Properties!
- LESSON 8: Area and Expressions
- LESSON 9: Exploring the Distributive Property
- LESSON 10: Are We Alike?
- LESSON 11: Expressions in the Real World
- LESSON 12: Review 6.EE.1, 6.EE.2, 6.EE.3, and 6.EE.4
- LESSON 13: Assessment Day!
- LESSON 14: Deepening our understanding